Symposium MQ03 : Predictive Synthesis and Advanced Characterization of Emerging Quantum Materials

Suitably structured HgTe is a topological insulator in both 2- (a quantum well wider than some 6.3 nm) and 3 (an epilayer grown under tensile strain) dimensions. The material has favorable properties for quantum transport studies, i.e. a good mobility and a complete absence of bulk carriers, which allowed us to demonstrate variety of novel transport effects.
A novel development is the use of wet etching technogies to fabricate HgTe based nanostructures. This approach allows a much higher transport quality in nanodevices. We have fabricated quantum point contacts, which show remarkable spin selective transport behavior. Additionally, we have developed a gate-training technique, which pushes the scattering length for the quantum spin Hall effect well above 100 mum. A further recent development is the realization that van Hove singularities in the valence band may give rise to remarkable transport effect, such as e.g. the realization of a n=-1 quantum Hall plateau at fields as low as 20 mT.
Another regime we can study is topological superconductivity, which can be achieved by inducing superconductivity in the topological surface states of these materials. Special emphasis will be given to recent results on the ac Josephson effect. We will present data on Shapiro step behavior that is a very strong indication for the presence of a gapless Andreev mode in our Josephson junctions, both in 2- and in 3-dimensional structure. An additional and very direct evidence for the presence of a zero mode is our observation of Josephson radiation at an energy equal to half the superconducting gap.
Controlling the strain of the HgTe layers strain opens up yet another line a research. We have recently optimized MBE growth of so-called virtual substrates ((Cd,Zn)Te superlattices as a buffer on a GaAs substrate), that allow us to vary the strain from 0.4% tensile to 1.5% compressive. While tensile strain turns 3-dimensional HgTe into a narrow gap insulator, compressive strain turns the material into a topological (Weyl) semimetal, exhibiting clear signs of the Adler-Bell-Jackiw anomaly in its magnetoresistance. In quantum wells, compressive strain allows inverted energy gaps up to 60 meV.

The quantum anomalous Hall (QAH) effect is a quantum Hall effect induced by spontaneous magnetization, and occurs in two-dimensional insulators with topologically nontrivial electronic band structure which is characterized by a non-zero Chern number. It was first experimentally observed in the thin films of magnetically doped (Bi,Sb)₂Te₃ topological insulators (TIs) in 2013, more than thirty years after the discovery of the first quantum Hall effect by Klaus von Klitzing. In this talk, I will report on some recent experimental progresses in this direction. By co-doping of Cr and V into (Bi,Sb)₂Te₃ TI films and developing intrinsic magnetic topological insulator, we are able to significantly increase the observation temperature of QAH effect. More interestingly, we can construct other topological states of matter such as axion insulator, quantum spin Hall insulator and QAH insulator of high Chern number by growing QAH insulator-based heterostructures.

Thin film synthesis of the emergent quantum materials is a prerequisite technique to observe novel topological phases such as quantum Hall [1] or quantum anomalous Hall (QAH) state [2-5] and exotic proximity effects at hetero-junction with magnets and superconductors [6]. The QAH phase accompanying a dissipation-less chiral edge channel has been achieved in one example of three-dimensional topological insulator (3D-TI), (Bi,Sb)₂Te₃ with a magnetic dopant Cr or V, which fulfills two requirements: (i) inducing an exchange gap by magnetic impurity doping and (ii) tuning Fermi level (E_F) into the gap by electrostatic gating in a thin film form [2]. A representative 3D-TI Bi₂Se₃ is another candidate platform to study such an exotic topological phase because of an inherently large bulk insulating gap [7]. However, by comparing with a well-investigated (Bi,Sb)₂Te₃ 3D-TI compound, there has been little progress on E_F tuning technique in (Bi_1-xSb_x)₂Se₃ probably owing to a low solubility limit of Sb below x ~ 0.5 [8], making it difficult to study the Dirac feature of this system by electrical transport measurements. To date, we have developed a buffer layer technique to stabilize rich Sb-doped (Bi_1-xSb_x)₂Se₃ in molecular beam epitaxy. With precise tuning of Bi/Sb composition ratio and thickness in a field-effect transistor (FET), we materialized the E_F tuning across the charge neutral point (CNP) [9,10].
In this study, based on these established E_F tuning techniques, we investigate magneto-transport properties of Fe-doped (Bi_1-xSb_x)₂Se₃ heterostructures. The Fe-doped sample with E_F tuned around CNP behaves like an insulator at zero magnetic field. By sweeping a perpendicular magnetic field, topological phase transition emerges from Anderson insulator to QAH state [11]. A clear insulator-to-metal transition was observed in magnetoresistance with a large Hall resistance by application of a high magnetic field up to 24 T. Furthermore, a (Bi_1-xSb_x)₂Se₃-based FET exhibits the large Hall resistance approaching the quantized value (h/e²) at around 14 T. With these set of the data, we concluded that a magnetic-field-induced QAH state was verified in Fe-doped (Bi_1-xSb_x)₂Se₃ thin films. Combining well-regulated growth technique for precise tuning of E_F and high-field transport measurements sheds light on the hidden topological phases in a wide variety of emerging quantum materials.
[1] R. Yoshimi et al., Nat. Commun. 6, 6627 (2015). [2] R. Yu et al., Science 329, 61 (2010). [3] C. Z. Chang et al., Science 340, 167 (2013). [4] J. G. Checkelsky et al., Nat. Phys. 10, 731 (2014). [5] C. Z. Chang et al., Nat. Mater. 14, 473 (2015). [6] X. L. Qi and S. C. Zhang, Rev. Mod. Phys. 83, 1057 (2011). [7] H. Zhang et al., Nat. Phys. 5, 438 (2009). [8] Y. Liu et al., Jpn. J. Appl. Phys. 56, 070311 (2017). [9] Y. Satake, J. Shiogai et al., J. Phys. Conden. Matter 30, 085501 (2018). [10] Y. Satake, J. Shiogai et al., Phys. Rev. B 98, 125415 (2018). [11] Y. Satake, J. Shoigai et al., submitted.

The rare-earth based ternary compounds RAlGe (R=La, Ce, Pr) are Weyl semimetals, in which LaAlGe exhibits type II Weyl semimetal behavior with space-inversion symmetry breaking. In this article, we report the growth, characterization, and transport measurements of LaAlGe thin films grown by molecular beam epitaxy. Extensive analysis of the longitudinal resistivity shows that the system displays semimetalic behavior. An upturn at a temperature below 35 K is observed in the resistivity curve due to weak localization. Observed resistivity behavior and a leap in activation energy gap from 1.67 meV to 103 meV suggest a near room temperature semimetal-to-semiconductor transition. We also observed a positive longitudinal magnetoresistance at and below 30 K and an ordinary Hall effect with nearly temperature independent Hall coefficient between 10 and 200 K. Furthermore, electrons are the majority of the charge carriers in our thin film samples.

Mott insulating behavior is induced by strong electron correlation and can lead to exotic states of matter such as unconventional superconductivity and quantum spin liquids. Recent advances in van der Waals material synthesis enable the exploration of novel Mott systems in the two-dimensional (2D) limit. Here we report characterization of the local electronic properties of the single-layer Mott insulator 1T-TaSe₂ via spatial- and momentum-resolved spectroscopy involving scanning tunneling microscopy (STM) and angle-resolved photoemission. Our combined experimental and theoretical study indicates that electron correlation induces a robust Mott insulator state in single-layer 1T-TaSe₂ that is accompanied by novel real-space orbital texture. By placing single-layer 1T-TaSe₂ onto a metal, we observe a strong Kondo resonance peak at the Fermi level, verifying the existence of local moments in this 2D Mott insulator. Finally, STM dI/dV imaging at the Hubbard band edges reveals a new incommensurate superstructure with a wavevector close to 2k_F of a half-filled spinon band, indicating a possible formation of a spinon-related density wave.

Quantum materials are rapidly advancing but still present great challenges. Topological quantum materials in particular are receiving great attention as they provide potentially robust routes to quantum information processing that are protected against decoherence processes. Among key challenges are the prediction and realization of magnetic materials in the form of magnetic Weyl semimetals and quantum spin liquids as ways of realizing exotic quasiparticles such as Majorana fermions that can be used for application. These materials present new experimental challenges in terms of identifying their quasiparticles and demonstrating quantum coherence in their ground states states. Here I will show how we are using the integrated application of machine learning along with experiment and synthesis to advance the discovery and understanding of these materials.

We make detailed polarized micro-Raman spectroscopy measurements of single nanoflake of the layered ternary compound NbIrTe₄. Thin 10 to 100 nm thick layers were exfoliated from single crystals and dispersed onto a silicon substrate. The a and b crystalline axes lay in the plane of the nanoflake with the c-axis perpendicular to the layer. Micro-Raman spectra were taken in the backscattered geometry using both 633 nm and 514 nm laser light with the incoming and outgoing light parallel to the c-axis with the scattered light polarization selected to be both parallel and perpendicular to the incoming laser polarization. Our results indicate strongly anisotropic Raman peaks which are consistent with the broken inversion symmetry of the crystal, which is an essential enabling condition for a Weyl semimetal. The large orthorhombic unit cell of this material has 24 atoms and belongs to the space group Pmn2₁ (point group c_2v) which predicts 69 active Raman modes with A_1,2 and B_1,2 irreducible representations. Since our excitation is parallel to the c-axis we can only detect the A_1,2 modes. Density Functional Theory (DFT) calculations for the A_1,2 modes show close correspondence with both the frequency and symmetries of the modes detected in our measurement. The normal mode vibrations for each mode are also determined. All A₁ modes have vibrations in the bc-plane of the crystal structure, so they include out-of-plane vibrations, while the A₂ modes show atoms which vibrate only along the a-axis of the lattice structure, with in-plane vibrations. Fits to the rotational symmetry of each mode allow us to extract the relative electron-phonon constants for each mode. Some evidence is seen that the electron-phonon interaction is modified for the different energy excitation conditions.

We acknowledge the financial support of the NSF through grants DMR 1507844, DMR 1531373, DMR 1505549 and ECCS 1509706.

Weyl semimetals have recently attracted intense research interest for exhibiting chiral Weyl nodes which are displaced in momentum space because of band crossings. When photoexcited with circularly polarized light transport measurements have been shown to be consistent with a chiral anomaly where the number of particles with a given chirality are not conserved. Though such photogalvanic measurements have confirmed the presence of chiral nodes in Weyl semimetals, little is presently understood about the dynamic behavior of the chiral particles. We exfoliate single thin flakes from a bulk crystal of NbIrTe₄ which is a ternary variant of WTe₂ with broken inversion symmetry. DFT calculations have shown that there are 16 Weyl nodes in the Brillouin zone, eight lying in the kz = 0 plane and eight lying in the kz = ±0.2 plane. We excite the flake with laser pulses incident along the c crystal axis, which is normal to plane of the flake defined by the a and b axes. The thin flake is excited by a near-infrared (NIR) 1.5 eV 140 fs pump laser pulse, and probed by a delayed circularly polarized mid-infrared (MIR) pulse with an energy which can be tuned from 0.3 to 1.2 eV. We show that the transient reflectivity response of the NbIrTe₄ exhibits distinct dynamics depending on the circular polarization of the MIR probe pulse. The peak response at zero time has opposite phase for probe pulses of opposite handedness. This initial strong polarized response decays rapidly within 1 ps, but the weaker remaining signal decays slowly within 500 to 1000 ps before reaching equilibrium. The dynamics of the polarized transient reflectivity do not respond to the circular polarization of the NIR pump pulse. We suggest that the distribution of the chiral particles is perturbed by the modulation of the Fermi level caused by the strong NIR pump pulse.

We acknowledge the financial support of the NSF through grants DMR 1507844, DMR 1531373, and ECCS 1509706. S.D.W. acknowledges the support of NSF DMR 1505549.

We investigate the optically driven transport properties of NbIrTe₄, which is a candidate type II Weyl semimetal which lacks spatial inversion symmetry. DFT calculations show that this ternary analog to WTe₂ exhibits 16 Weyl nodes, eight in the k_z = 0 plane and eight in the k_z = ± 0.2 plane. A 100 nm flake of this material was exfoliated from a bulk crystal and dispersed on a Si++/SiO₂ substrate. 300 nm thick Ti/Al metal pads were deposited on two sides of the nanoflake by photolithography, metal deposition and liftoff. The device was mounted on a gold chip carrier, and after wire bonding, it was placed on the cold finger of an optical cryostat. A tunable polarized infrared laser was used to excite the device parallel to the c-axis normal to the flake. The I-V measurement shows that the resistivity of the device is about 2 mm.W at 300K and 0.2 mm.W at 10K. The photocurrent measurement with light linearly polarized along the “a” and “b” crystal directions shows photoresponse with different magnitudes in these two directions. Using a quarter wave plate for excitation between 1000 and 3000 nm (0.4 to 1.2 eV), the photoresponse was measured for a full rotation, with different amplitudes seen for right hand and left hand circular polarizations, revealing the circular photogalvanic effect which is consistent with the chiral nature of the Weyl nodes in this material.

We acknowledge the financial support of NSF through grants DMR 1507844, DMR 1531373, DMR 1505549 and ECCS 1509706.

Weyl semimetals are a class of recently realized topological semimetals characterized by
three-dimensional linear dispersions known as Weyl nodes. A key feature of these materials is the
low energy excitations in the vicinity of the Weyl nodes possess a chirality – their spins and
momentum are locked either parallel or anti-parallel to one another. As such, considerable
research attention has been focused on investigating these novel electronic properties. Despite
this, little effort has been directed towards an understanding of their vibrational properties or the
coupling between the two systems. In this talk we present experimental and computational
results which reveal the interplay between the vibrational and electronic systems for the
prototypical type-I Weyl semimetals NbAs and TaAs. In temperature dependent Raman
measurements of phonon linewidths we observe an unusual dominance of electron-phonon based
scattering of optical phonons into electron-hole pairs. Computational calculations of the mode
resolved electron-phonon coupling strength not only confirm the presence of this scattering
channel, but reveal other phonon mediated scattering channels which connect the disparate Fermi
surfaces in the vicinity of the Weyl nodes.

The three-dimensional Dirac semimetal Cd₃As₂ has exhibited a number of interesting properties, including linear dispersion in the bulk electronic structure, Fermi arc surface states and giant magnetoresistance [1-3]. Many of these discoveries were made in bulk single crystal material due to the relative ease of synthesis. Epitaxial thin films have also been instrumental in detecting the quantum Hall effect and studying the influence of confinement on its properties [4]. Future investigation of Cd₃As₂ properties and devices will increasingly benefit from synthesis in thin film form and will critically depend on our ability to control defects, dopants, surfaces and interfaces during the growth process.

Here, we present a framework for imparting control during the growth of high quality Cd₃As₂ epilayers by molecular beam epitaxy. Our approach consists of three tactics to improve the electron mobility. The use of lattice-engineered II-VI Cd_1-xZn_xTe buffer layers grown on GaAs substrates with a small degree of miscut reduces extended twin and dislocation defects. Growth from elemental Cd and As₄ sources rather than a Cd₃As₂ compound source allows for careful control of the chemical potential during growth and the resulting point defect populations. Illumination of the growth surfaces of both the II-VI buffer layer and Cd₃As₂ epilayer with a broadband source is further found to improve surface smoothness. Together, these methods have produced electron mobilities as high as 18,000 cm²/Vs in bulk epilayers even though growth is carried out at substrate temperatures no higher than 120 C. We will discuss the underlying mechanisms as well as prospects for using them to probe various aspects of defect physics in Cd₃As₂.

[1] M. Neupane, et al., Nat. Commun., 5, 3786 (2014)
[2] P.J. Moll, et al., Nature, 535, 266 (2016)
[3] T. Liang, et al., Nat. Mater., 14, 280 (2015)
[4] T. Schumann, et al., Phys. Rev. Lett., 120, 016801 (2018)

A detailed understanding of lattice vibrations is needed to build microscopic theories of transport and thermodynamics in emerging quantum materials. The interplay between phonons and other degrees-of-freedom of charge and spin has long been known to be critical in ferroelectrics/multiferroics, metal insulator transitions, as well as some aspects of superconductivity, including at high pressures or in nematic phases. Large deviations from harmonic potential energy surfaces, as in the Landau double-well picture, also give rise to interesting anharmonic phonon properties characterized by extensive interactions between phonon quasiparticles and pronounced renormalization effects, which can be tuned to zero temperature at ferroelectric quantum critical points. Further, phonons directly modulate the potential seen by electrons and offer a means to control the electronic structure and its topology, either thermally or via coherent excitations. I will highlight recent developments and achievements in studies of phonons in emergent quantum materials. In particular, I will discuss scattering techniques such as inelastic neutron / x-ray scattering, which can map phonon dispersions and linewidths throughout the Brillouin zone, and time-domain spectroscopies that can probe coupling mechanisms and far-from-equilibrium regimes. In addition, first-principles simulations of phonons can often be directly compared to these experiments and provide further insights into phonon couplings to charge, spin and orbital degrees of freedom.

Determining the broken symmetries at a thermodynamic phase transition is an essential tool for understanding, or at least constraining, the microscopic mechanisms that lead to novel ground states in quantum materials. Resonant Ultrasound Spectroscopy (RUS) is a characterization technique that measures the spectrum of mechanical resonances of a solid, which allows the determination of its elastic tensor, a thermodynamic quantity that contains symmetry specific information of the ground state. Tracking the evolution of the elastic tensor through a phase transition allows determining which symmetries are broken in the transition, and to propose better suited order parameters.

In this talk I will present RUS measurements of unconventional superconductors and charge density wave compounds. I will focus on the La_2-xSr_xCuO₄ cuprate superconductor, for which we observe a strong softening of the C₆₆ elastic shear moduli, associated with the B_2g symmetry channel, as temperature is decreased and an orthorhombic to tetragonal structural phase transition is approached. The temperature dependence of this softening is consistent with a Curie-like temperature dependence. This softening persists even for Sr compositions for which the tetragonal to orthorhombic structural transition is not seen. The B_2g softening is truncated by the opening of the superconducting gap, evidenced by the stiffening of C₆₆ below T_c. These observations suggest an electronic nematic origin for this softening, similar to what has been observed in Ba-pnictide superconductors.

Properties relevant to quantum materials are characterized by the material’s ground states and excitations. Complementary to electrical and optical measurements, heat capacity measurements performed on quantum materials can reveal information about the material’s density of states. Many emergent materials that are synthesized in the laboratory exist at nanometer length scales, and performing heat capacity measurements on these materials in the monolayer limit presents a formidable challenge. Typical commercial calorimeters require bulk samples and operate between 300K to 2K. Microfabricated calorimeters, compared to commercial systems, possess a significantly smaller thermal mass, and because of this drastically reduced size, they inherently have greater sensitivity to thermal signals. Here we present a method of performing ultrasensitive calorimetry on nanoscale quantum materials. Our microfabricated calorimeter possesses an intrinsic heat capacity that is 1000 times lower than state-of-the-art thin-film calorimeters and has been designed to operate over a wide temperature range, permitting measurements of low-energy excitations that occur at sub-Kelvin temperatures. Our calorimeter design also facilitates transmission electron microscopy measurements, allowing structure-property correlations on the same material of interest. In this presentation, I will explain the design and operation of this ultrasensitive calorimeter, present heat capacity measurements, and discuss various nanoscale material loading techniques, including the opportunities and the challenges inherent to these measurements.

Ternary III-As nanowire (NW) heterostructures provide a path to quantum confined structures of zero, one, and two dimensions integrated on Si, making them candidates for quantum-enabled applications including single photon emission and manipulation of Majorana Fermions [1,2]. Tomographic imaging of nanoscale composition is necessary to determine the confinement potentials of charge carriers and to understand and optimize growth. Furthermore, correlated analysis of nanoscale properties is needed to develop quantitative understanding of the influence that composition, strain, phase, and defect structure has on band structure. We have used a novel combination of characterization methods to correlate the 3-D structure of (In,Ga)As quantum wells (QWs) on GaAs NWs with their spatially varying optical properties at the nanoscale. While these classes of heterostructures are being developed both as quantum wires and emitter structures, we focus here on emission due to the significant interest in efficient compact and near-IR lasers for on-chip optical interconnects. Towards that end, spatially resolved cathodoluminescence (CL) was used to investigate the emission of InGaAs QWs grown on GaAs NWs that switched from the zincblende (ZB) to wurtzite (WZ) phase along their length, leading to brighter and blue-shifted emission in the WZ region. Electron backscatter diffraction and nano-probe based x-ray diffraction (nanoXRD), directly correlated with CL, established this correlation. Synchrotron-based nanoXRD was also used to probe position-dependent strain along multiple crystallographic directions with 25-50 nm spatial resolution. Atom probe tomography (APT) was then used in direct correlation with CL to image the composition and morphology of the embedded (In,Ga)As QWs. APT revealed that the In mole fraction is significantly reduced in WZ compared to ZB QWs, while the QW thickness is unchanged. Correlated measurements of composition, morphology, strain, and structure were combined as input for band structure calculations, leading to a predicted emission shift of 95 meV between the WZ and ZB region that is in reasonable agreement with the CL results (70-80 meV shift). This correlative analysis, using an array of advanced characterization tools, ultimately enabled deconvolution of complex spatial variations in electronic structure in a way not previously possible, and can be extended to a range of buried quantum heterostructures. To explore the limits of the methodology, we will also discuss the application of coherent x-ray diffraction imaging to non-destructively image strain in embedded radial QWs as small as 8 nm in diameter.
1. Friedl, M., …, Lauhon, L.J., Zumbühl, D.M., & Fontcuberta i Morral, A. "Template-assisted scalable nanowire networks." Nano Letters 18.4 (2018): 2666-2671.
2. Lähnemann, J., Hill, M.O., …, Lauhon, L.J., & Geelhaar, L. "Correlated nanoscale analysis of the emission from wurtzite versus zincblende (In, Ga) As/GaAs nanowire core-shell quantum wells." Nano Letters 19 (2019) ASAP. DOI: 10.1021/acs.nanolett.9b01241

Twisted bilayer graphene with a twist angle close to 1° features isolated flat electronic bands that form a strongly correlated electronic system. Here we investigate properties of this system by probing local tunneling density of states using scanning tunneling microscopy and spectroscopy. We show that the flat bands get highly deformed when they are aligned with the Fermi level using electrostatic gating. At half filling of the bands, we observe the development of gaps originating from correlated insulating states. Near charge neutrality, we find a previously unidentified correlated regime featuring a substantially enhanced flat band splitting that we describe within a microscopic model predicting a strong tendency towards nematic ordering. Our results provide basis for microscopic understanding of correlated quantum phases in small angle twisted bilayer graphene.

The energy positions of the valence and conduction electronic states with respect to the vacuum level are essential parameters to evaluate how the band gaps of semiconductors or Fermi-levels of metals would line up with respect to each other. Defined as an energy separation between the vacuum level and the highest occupied electronic states, the ionization energy is of particular importance for atomically-thin transition metal dichalcogenides (TMD) to predict the performance of their heterostructures as well as their interfaces with metal contacts. Ionization energies have been investigated based on theoretical calculations, but to the best of our knowledge, no systematic experimental confirmation is reported for the wide range of TMDs and other emerging quantum materials, despite their importance.
Here we present a new approach to study the electronic properties of prototypical TMDs, MoS₂, WS₂, and MoSe₂ monolayer and multilayer flakes, supported on thick silicon oxide (SiO₂) film, using a photoemission electron microscopy combined with a deep ultraviolet (DUV) illumination. We determine the band alignments of monolayer to multilayer junctions in these four materials, and show that the ionization energy decreases from MoS₂, WS₂, to MoSe₂ as predicted by density functional calculations. We further extend this experimental approach to quantify Schottky barriers at the TMDs-metal contacts. This work reveals a new metrology approach to conduct systematic studies of electronic properties of TMDs.
The PEEM work was performed at the Center for Integrated Nanotechnologies, an Office of Science User Facility (DE-AC04-94AL85000). T. O. is supported by the CINT user program and Sandia LDRD. The work performed by M. B. is supported by the CINT postdoc program. K. K. was supported by the Army Research Office MURI grant W911NF-11-1-0362. A. D. M. is supported by LANL LDRD program. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. The views expressed in the article do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

Motivating experimental and theoretical physics is a desire for grand unification and practical solutions to real world problems. The highest resolution visualization of nanomaterials comes from the scanning tunneling electron microscope (STM). It probes quantum states through a conducting stylus. Further investigation into the collapse of the wavefunction necessitates the creation of a new particle that solves a problem in Yang-Mills symplectic rotations. From Clebsch-Gordon coefficients and the resultant Green’s functions fields, a single source particle is uncovered, the observe-on. This unification means that the neutrino does not exist. Regge theory and angular momentum at the quantum scale imply funny SU(2) particle states that carry the Fermi-Curie deconvolution. When applying this rotational correction to galactic cores, the perturbation to the mass density length contraction generates a pseudo-energy and pseudo-central force from a frame dragging effect. This is dark matter. This work is a theoretical exploration into ideas central to hyperspace Aharonov-Bohm dimensions, dark matter, Yang-Mills theory, quantum STM experiments, fusion, and the connections that make emergent properties like the scientific endeavor a conscious entity. New s-matrix theory and string geodesic landscapes discard quantum loop theories. Really, though, this is an experimental thrust into tunneling and how quantum probes unify with relativity to allow scientists to predict the properties of particles and surfaces with unique electronic and nuclear states beyond the standard model.

The enigma of the emergent ferromagnetic state in tensile-strained LaCoO₃ thin films remains to be explored because of the lack of a well agreed explanation. The direct magnetic imaging technique using a low-temperature magnetic force microscope (MFM) is critical to reveal new aspects of the ferromagnetism by investigating the lateral magnetic phase distribution. Here we show the experimental demonstration of the rare halved occupation of the ferromagnetic state in tensile-strained LaCoO₃ thin films on SrTiO₃ substrates using the MFM. The films have uniformly strained lattice structure and minimal oxygen vacancies beyond the measurement limit. It is found that percolated ferromagnetic regions with typical sizes between 100 nm and 200 nm occupy about 50% of the entire film, even down to the lowest achievable temperature of 4.5 K and up to the largest magnetic field of 13.4 T. Preformed ferromagnetic droplets were still observed when the temperature is 20 K above the Curie temperature indicating the existence of possible Griffiths phase. Our study demonstrated a sub-micron level phase separation in high quality LaCoO₃ thin films, which has substantial implications in revealing the intrinsic nature of the emergent ferromagnetism.

[1] D. Meng, H. Guo, Z. Cui, et al. P. Natl. Acad. Sci. USA 115, 2873 (2018).
[2] Q. Feng, D. Meng, H. Zhou, et al. arXiv:1906.03825 (2019)

Whether it originates in crystallinity, magnetism, or electronic structure, interfacial symmetry breaking represents one of the most powerful tools for the realization of new quantum materials with advanced functionality. Mismatches in band topology and time reversal symmetry across interfaces have been harnessed to open gaps in the surface states of topological insulators or to induce topological transitions. Heterostructures interfacing superconductors with a quantum anomalous hall insulator (QAHI) have been reported to exhibit signatures of Majorana fermions, while two-dimensional systems with strong spin-orbit interactions have long been suspected of harboring skyrmions at interfaces with perpendicular magnetic materials. In all of these cases, our understanding of the underlying physics has hinged critically on the ability to precisely understand and isolate the properties of the interface from the bulk of the system. By decomposing the magnetic and electronic properties on a layer-by-layer and element-resolved basis, new quantum material systems may be robustly understood and designed. In this talk, I will discuss our recent progress in combining depth-resolved information from polarized neutron reflectometry with element-specific information from soft X-ray spectroscopy to design and control magnetic interfaces in topologically nontrivial systems such as (Bi,Sb)₂Te₃/antiferromagnet and Bi₂Se₃/oxide heterostructures. I will focus in particular on the new capabilities enabled by CANDOR, the new polychromatic neutron reflectometer at the NIST Center for Neutron Research. A highly intensity-limited technique, the application of neutron reflectometry has been critically hampered by the long measurement times necessary to probe the trace magnetic signal in systems such as superconductors and QAHIs. By implementing a polychromatic beam with multiplexed energy analyzing detectors, CANDOR allows for multiple orders of magnitude intensity gains, allowing even more sensitive measurements to be performed in hours instead of days.

More and more frequently, the interfaces between electronic thin films are playing critical roles in the operations and functions of our electronic devices. As we move towards new computing paradigms, it’s the interfaces of quantum materials with strongly coupled degrees of freedom and complex phase behavior that show the greatest potential to revolutionize the ways we store, process, and transfer information. Yet, the same coupled degrees of freedom that give quantum materials their unique and desirable properties place stringent requirements on the local structure and composition at the interfaces, where the presence of unintended defects can diminish spin polarized currents and destroy coherent quantum states. However, characterizing the physics at these interfaces, which are often buried deep below the sample surface, remains difficult. Addressing this challenge requires a technique capable of measuring the local electronic structure with high-resolution depth dependence.

In this talk, we show how linearly polarized resonant X-ray reflectometry (RXR) can be used to visualize charge transfer in complex oxide superlattices with atomic layer resolution. From our RXR measurements, we extract valence depth profiles of SmTiO₃(SmTO)/SrTiO₃ (STO) heterostructures with STO quantum wells varying in thickness from five SrO planes to a single SrO plane. At the polar-nonpolar SmTO/STO interface, an electrostatic discontinuity leads to approximately half an electron per areal unit cell transferred from the interfacial SmO layer into the neighboring STO quantum well. We observe this charge transfer as a suppression of the t_2g absorption peaks that minimizes contrast with the neighboring SmTO layers at those energies and leads to a pronounced absence of superlattice peaks in the reflectivity data. Our results demonstrate the sensitivity of RXR to electronic reconstruction in the monolayer limit and establish RXR as a powerful means of characterizing charge transfer at the buried interfaces of quantum materials.

Epitaxial thin films, especially the oxide thin films, have been studied extensively due to their emerging properties and potentials in various applications, such as energy storage and data storage. Many factors, such as the chemical state, the strain state, and presence of the external field, can affects the thin film structure, which in turn influences the properties. While the unit cell level atomic structures of such thin film materials are fairly well known/defined, the recent interests are steered towards how the unit cells and nano-sized domains are organized into the macroscopic functional materials. This so-called meso-scale structure turns out to be not that simple due to the spatial inhomogeneity in the thin film as it minimizes the total energy in response to the internal and external stimulant. Availability of spatial-resolved and/or time-resolved structures of such systems would be critical to a better understanding and eventually designing function-oriented new materials. A diffraction based, full field X-ray microscopy method, the X-ray reflection interface microscopy (XRIM), has been adopted to study the surfaces, buried interfaces, and thin film material systems at meso-scale, with sub-nanometer`+ sensitivity in the surface normal direction and <80 nm lateral resolution.

With the penetrating power of hard X-rays, XRIM can emphasize the features at different depth from the top surface by choosing proper scattering conditions, making it an excellent candidate to study the films in-operando in real time. Combined with the reciprocal space mapping (RSM), the spatially resolved structure evolution can be identified. A few examples will be discussed to demonstrate the capability of XRIM method and its potential applications in a broader field.

Modern materials science often concerns not isolated, bulk materials, but materials as part of larger, complex thinfilm-based heterostructures. The final behaviour of such systems is in many cases dominated by the interfaces between materials and cannot usually be inferred from the bulk characteristics of the individual components.

One of the main challenges complicating a full understanding of such complex systems is the availability of direct characterisation methods for buried layers and in particular the interfaces between them. We greatly lack direct probes for chemical states and electronic structure at interfaces, which present a special challenge for physical characterisation techniques due to their spatial confinement, the fact that by their nature interfaces are buried beneath a variety of overlayers, and the starkly different behaviour of chemical species at interfaces compared to surfaces and the bulk. Advanced X-ray spectroscopy methods can tackle some of these issues, and X-ray Photoelectron Spectroscopy (XPS) in particular can deliver great insight as it combines both qualitative and quantitative information on elemental distributions, chemical environments, and valence states.

Here, we present a systematic study using angle-resolved hard X-ray photoelectron spectroscopy (AR-HAXPES) to study buried layers and interfaces. Hard X-rays provide increased depth information and using an angle-resolved approach, highly depth-resolved information monitoring elemental and electronic structure changes across thin films stacks and interfaces is possible. Well defined 4H-SiC/SiO₂ heterostructures are used as a test system representing a complex, defect rich system, in which knowledge of the precise nature of defects is limited. The samples were treated in a variety of nitrogen-containing atmospheres (N₂, NO, NH₃ and NO+NH₃) after the initial fabrication procedure, which leads to different distributions and chemical states of nitrogen across the heterostructures, which can compensate defects in particular at the interface. SiC is a wide band gap semiconductor, that is widely used for power electronic applications and therefore of great interest in itself.

Clear differences are observed in HAXPES spectra after high temperature treatments and across the heterostructures. Angle-resolved Si 2s and 1s, C 1s, O 1s, and N 1s core level spectra are analysed to give a complete picture of chemical environments present in the oxide and carbide layers and particularly at and around the interface. In addition, valence band spectra are used to provide an insight into changes in the electronic structure of the materials. Ultimately, we show that AR-HAXPES can be applied to the investigation of buried features and interfaces and related phenomena.

Perovskite transition metal oxides exhibit various novel properties due to the interactions of strongly correlated electrons. These interactions are well known in the 3d transition metal oxides, such as LaCoO₃, where multiple spin states can be observed. Electronic correlations are expected to change as the transition metal is changed from Co to Rh in the same column of the periodic table. To explore these changes, we grow high quality La_1-xSr_xRhO₃ thin films with Sr concentrations as high as 50% on both LaAlO₃ and SrTiO₃ substrates by molecular beam epitaxy. Systematic changes in both structure and electronic transport have been observed that can be directly tied to the doping concentration and electronic correlations.

This work is supported by a grant from the Department of Energy, Basic Energy Sciences under grant number DE-SC0019211.

Complex-oxide heterostructures have garnered much attention as a path to couple the rich variety of properties of these materials, but also for the many routes they offer for the stabilization of novel behaviors. Understanding the electronic and structural reconstructions occurring at interfaces is therefore key for the success of interface engineering. In the last years, control of the structural couplings of the oxygen sublattices during epitaxy synthesis is arising as a very powerful route to manipulate the states of matter in complex oxides. Whereas this strategy is starting to settle as one of the main mechanisms governing interfacial couplings in oxide heterostructures, we show here a system where, despite first glance prognosis, the dominant coupling is instead electronic in nature. The chosen heterostructures are high quality epitaxial NdNiO₃/SmNiO₃ superlattices and the occurring of the metal-insulating transition (single or double depending on the layer period) is the interesting functionality investigated. I will also focus on the family of double-perovskite compounds A₂NiMnO₆ (A being a rare earth cation), which is characterized by an insulating ferromagnetic behavior, with the end member La₂NiMnO₆ displaying a Curie temperature approaching room temperature (≈ 280K). The magnetism of these double-perovskite thin films will be investigated down to few unit cells. All thin films and superlattices are grown by off-axis magnetron sputtering.

The electronic structure and electromagnetic properties of perovskite nickelate quantum materials are highly sensitive to orbital occupancy and strain. In this work, we will discuss how oxygen vacancies can be injected into perovskite nickelates such as NdNiO₃ in a reversible and controlled manner and can cause massive electronic phase changes by which the charge carriers are localized within unit cell dimensions. The distribution of oxygen vacancies can further be controlled spatially by bias voltage in a solid-state device creating functionally graded quantum systems. We will present experimental results combining variable temperature electronic transport and X-ray spectroscopic data to illustrate how the Ni-site orbital filling influences multiple order parameters such as electronic band gap, optical gap and spin ordering. These studies suggest the potential of nickelates as model systems for fundamental understanding of strong electron interactions by controlling concentration of oxygen vacancies and further their potential use in electronic switches.

The tunable resistivity of materials undergoing metal-insulator transitions (MIT) holds great promise for resistive switching applications, such as adaptable electronics and cognitive computing. Among the materials with MIT, rare-earth nickelates (RENiO₃ with RE denoting a trivalent rare earth element) present a very interesting case because their MIT can be controlled by using different RE elements or by epitaxial strain [1-3]. Moreover, it has been reported that eliminating the MIT in nickelates by orbital engineering would give rise to a superconducting state, which could be more robust than that of the cuprates [4]. Thus, it becomes important to have an accurate picture of the relevant electron interactions in the intermediate temperature regimes, just before the MIT takes place. However, despite the vast amount of recent works, transport in nickelates is not yet fully understood.
Based on different scaling exponents of the resistivity as a function of temperature reported in this material, various hypotheses, such as bad metal, Fermi-liquid (FL), non-fermi liquid (NFL), or even the crossover between FL and NFL, had been proposed to describe the intriguing behavior of nickelates. However, the issue of matching these different hypotheses in one material rises the question on how to interpret the experimentally obtained apparent exponents.
Here, by investigating a series of NNO films grown on different substrates, we reveal an evolution of the resistivity-temperature apparent power law exponent of the metallic phase as a function of epitaxial strain and the associated induced disorder. Our experimental results support recent theoretical predictions by Patel et al. [5], which propose that the combined effect of electron interactions and disorder can give rise to a continuous variation of the exponents. These results demonstrate that the assessment of FL or NFL behavior based on the measurement of exponent of the power law temperature dependence of resistivity should be preceded by a detail analysis of the disorder.

[1] Catalan, G. Phase Transitions 81.7-8 (2008): 729-749.
[2] Catalano, S., et al. Reports on Progress in Physics 81.4 (2018): 046501.
[3] Middey, S., et al. Annual Review of Materials Research 46 (2016): 305-334.
[4] Hansmann, P., et al. Physical Review Letters 103.1 (2009): 016401.
[5] Patel, N.D., et al. Physical Review Letters 119.8 (2017): 086601.

Among various efforts to integrate quantum technology-associated complex oxides materials (e.g. nonlinear and strongly correlated oxides) on electronic substrates, thin film epitaxy has been regarded as one promising solution due to its feasibility for mass production, controllability over film dimension and high-density device integrability. However, most epitaxial oxides grown on Si are populated with defects such as grain boundaries and dislocations. The fundamental challenge lies in the fact that Si and most oxides have large lattice mismatch, which brings significant strain energy when film is below critical thickness but leads to populated misfit dislocations and threading dislocations when film is above its critical thickness. In this talk, to tackle these issues, I will show how we design and develop unconventional epitaxy approaches featured by weakly-coupled film-substrate interface. The model materials in this talk include correlated oxides and nonlinear electro-optic oxides. I will also show how the weakly-coupled complex oxides behave differently from films produced by conventional epitaxy under external stimuli.

Disorder is an important aspect of correlated quantum systems. As examples, it can be used to manipulate superconductivity, stabilize quantum spin liquid states, and enable scaling of non-fermi liquid responses. While synthesis of new quantum materials is generally focused on creating perfect crystals comprised of only a few elemental building blocks, we will present our recent efforts to create high quality crystals with a high degree of configurational elemental disorder on sublattice sites. The intent is to gain knowledge of how maximizing local microstates might enable the emergence of new and unexpected macrostates. Complex crystal structures comprising two or more sublattices, such as those in the perovskite family, are particularly promising. This is due to the nearest neighbor cations on one configurationally disordered sublattice being tied together by an intermediate common and uniform anion sublattice.
As an example, we present our recent stabilization of single crystal epitaxial films of the ABO₃ perovskite La(Cr_0.2Mn_0.2Fe_0.2Co_0.2Ni_0.2)O₃. XRD and STEM-EELS studies confirm crystallinity, epitaxy, and full site mixing of the 5 B-site elements (no single element clustering). Experimental results from neutron studies, XMCD, and SQUID magnetometry demonstrate unexpected long-range magnetic ordering which is highly tunable through lattice symmetry modification.

Semiconductor nanowires have seen great success for the last two decades and have opened the doors to a multitude of device applications [1]. However, emerging quantum devices often require more elaborate geometries that go beyond single one-dimensional wires. Selective-area-epitaxy (SAE) can overcome this limitation because it offers an approach to growing nearly arbitrary shapes, as demonstrated recently [2-4]. Most SAE-grown nanostructures are bound to their growth substrate which, while attractive for large scale processing, makes few-sample fabrication costly and challenging. We report on growth and electrical characterization of free standing InAs nanofins grown by selective-area-epitaxy [5]. Their rectangular footprint can be deliberately tuned to give structures ranging from 1D nanorods to thin 2D nanosheets with good height control. The high aspect ratio allows us to mechanically transfer them to device substrates where they lie flat and can be fabricated into devices with multiple contacts, top- and back-gates. Our devices show excellent prospects for fabrication into more sophisticated devices, e.g., by adding functional elements like superconducting contacts or by top-down patterning them into desired shapes after growth.
InAs nanofin growth proceeded via metal-organic vapor phase epitaxy (MOVPE) on an InP (111B) substrate covered with a SiO_X mask. During growth, nucleation occurs in lithographically pre-patterned rectangular openings in the SiO_X. As with SAE growth of nanowires, the crystal retains the shape given by the rectangular openings if their long axis is aligned correctly relative to underlying crystallographic axes. Rectangular nanofins with typical width 1-4 μm, height ~ 4 μm and thickness < 85 nm were grown.
After mechanical transfer to a prepatterned substrate these nanofins were fabricated into field-effect transistor devices with multiple ohmic contacts, a global back-gate and local top-gates. Low-temperature (T = 300 mK) electrical characterisation shows reliable contact performance with resistances below 10 kΩ. Hall measurements give electron densities of 1.5 – 7x10¹⁷/cm³ with good density control via the back-gate. We obtain field-effect mobilities of up 4400 cm²/Vs, systematically higher than transport mobilities extracted from Hall effect data, yet similar to what is found in InAs nanowires [6]. Reproducible quantum interference is visible in the magnetoconductance at large and small magnetic field scales. A robust weak anti-localisation (WAL) peak is visible around B = 0 T, which evolves with back-gate voltage. Fitting to this peak gives phase-coherence lengths L_Φ = 200-600 nm and spin-relaxation lengths L_SO = 150-350 nm. We see no signs of quantum-Hall effect in our accessible field range (B ≤ 2 T).

[1] Dasgupta, N. P. et al. 25th anniversary article: Semiconductor nanowires - Synthesis, characterization, and applications. Adv. Mater. 26, 2137–2183 (2014).

[2] Conesa-Boj, S. et al. Vertical ‘III-V’ V-shaped nanomembranes epitaxially grown on a patterned Si[001] substrate and their enhanced light scattering. ACS Nano 6, 10982–10991 (2012).

[3] Krizek, F. et al. Field effect enhancement in buffered quantum nanowire networks. Phys. Rev. Mater. 2, 1–8 (2018).

[4] Aseev, P. et al. Selectivity Map for Molecular Beam Epitaxy of Advanced III-V Quantum Nanowire Networks. Nano Lett. 19, 218–227 (2019).

[5] Seidl et al. Regaining a dimension: Mechanically-transferrable 2D InAs Nanofins Grown by Selective-Area-Epitaxy, Submitted to Nano Letters (currently under Review).

[6] Blömers, C. et al. Hall effect measurements on InAs nanowires. Appl. Phys. Lett. 101, 152106 (2012).

In multiferroics having two or more ferroic orders simultaneously, multiple order parameters coexist in a system, sometimes couple with each other, and exhibit nontrivial crossed phenomena such as magnetoelectric effect. To date, various mechanisms have been proposed for the origin of multiferroicity. For example, in multiferroics which exhibit a certain conical spiral spin order, both ferromagnetic and ferroelectric order parameters can develop due to the magnetic order and their domains can be coupled with each other. In this presentation, we show selective observations, control, and understanding of coupled order parameters and domains which coexist in magnetoelectric multiferroics breaking both space inversion and time reversal symmetries. Examples of such multiferroic oxides are hexaferrites (e.g., Ba_1.3Sr_0.7CoZnFe₁₁AlO₂₂) showing the so-called alternating longitudinal conical structure and olivine-type manganese germanate Mn₂GeO₄ showing canted antiferromagnetic conical spin chains. For the observations, we adopted single-crystal measurements of scanning resonant x-ray microdiffraction for the hexaferrites or (un)polarized neutron scattering for the manganese germanate. These techniques clarify multiple magnetic order parameters and domain structures and their manipulations by external stimuli such as magnetic and electric fields in these peculiar multiferroics. This work has been done in collaboration with H. Ueda, R. Misawa, J. K. H. Fischer, K. Kimura, Y. Tanaka, Y. Wakabayashi, T. Honda, J. S. White, M. Kenzelmann, and A. B. Harris.

Dielectric capacitors hold a tremendous advantage for energy storage due to their fast charge/discharge times and stability in comparison to batteries and supercapacitors. A key limitation to today's dielectric capacitors, however, is the low storage capacity of conventional dielectric materials. To mitigate this issue, antiferroelectric materials have been proposed, but relatively few families of antiferroelectric materials have been identified to date. Here, we propose a new design strategy for the construction of lead-free antiferroelectric materials using interfacial electrostatic engineering. We begin with a ferroelectric material with one of the highest known bulk polarizations, BiFeO3. We show that by confining atomically-precise thin layers of BiFeO3 in a dielectric matrix that we can induce a metastable antiferroelectric structure. Application of an electric field reversibly switches between this new phase and a ferroelectric state, in addition, tuning of the dielectric layer causes coexistence of the ferroelectric and antiferroelectric states. Precise engineering of the structure generates an antiferroelectric phase with energy storage comparable to that of the best lead-based materials. The use of electrostatic confinement provides a new pathway for the design of engineered antiferroelectric materials with large and potentially coupled responses.

Reversibly controlling topological orders is fundamentally important but challenging. Strongly correlated oxides with coexistence and competition of multiple d electron order parameters may provide a platform for robust and controllable topological phases. Here, high-spin state and topological Hall effect are achieved in ultrathin SrRuO3thin filmson SrTiO3substrates. Oxygen vacanciestransferred from SrTiO3tothe ultrathinSrRuO3reconstructs Ru-4d electronic structure and orbital occupancy, leading to an enhancement of magnetic moment and a ~370 meV energy gap opening. Therefore, symmetry broken and Dzyaloshinskii–Moriya interaction in this ultrathin oxide structuregive rise to a topological order in spin state, where the topological Hall effect can be reversibly switched by an electric-field-rectifying oxygen ionic diode.

Correlated compounds serve as model systems to study interactions among lattice, spin, charge and orbital degree of freedom. Understanding the correlation and phase transition mechanisms in these compounds is paramount for the innovation of next-generation ultrafast and high-efficiency electronic/photonic devices. However, the number of discovered correlated oxides by now is still quite limited. Here we apply hydrogenation to create a new phase of correlated material HCsBiNb₂O₇ (HCBNO). We first synthesize CsBiNb₂O₇ (CBNO), a layered in-plane ferroelectric perovskite, by molten salt method and then dope it via hydrogenation in 5% H₂ of Ar/H₂ gas. This doping process is reversible and can induce pronounced changes in its optical properties, accompanying with electronic modulations. To achieve sufficient hydrogenation of the CBNO, atomically dispersed Pt catalyst was used to promote hydrogen spillover under a temperature of 475 °C. Raman and XRD characterization indicate the hydrogen is reversibly absorbed into, and released from CBNO without destroying its lattice structure. Ultraviolet-visible spectrum shows a significant increase (~ 3 times) in absorption after hydrogenation and transport measurement shows a nearly 10 times increase in electric conductivity, comparing to the pure CBNO at room temperature. Resistance-temperature measurement and ultraviolet photoelectron spectrum further confirm the transition of electronic orbital configurations. Our finding suggests the possibility of reversible modulation in CBNO via hydrogenation and may give some enlightenment in exploring novel electronic and photonic devices with complex correlated oxides.

Spintronics basedonantiferromagnetic (AF) materials are attractive for energy efficient device technology, offering robustness against magnetic perturbations and ultra-high frequency spin dynamics allowing for THz device technology. Currently, there is focus on developing methodologies to tailor the AF spin texture. Transition metal oxide-based systems are in this regard promising candidates, and here, we present how anisotropic strain engineering permits tailoring of the AF Neel vector in epitaxial single crystalline LaFeO₃ thin films synthesized by pulsed laser deposition. LaFeO₃ is a prototypical G-type antiferromagnet with high Néel temperature. To impose anisotropic strain, we rely on the (111) pseudocubic facet of orthorhombic scandate- and gallate-based oxide substrates. X-ray studies confirm a lowering of LaFeO₃ symmetry, from orthorhombic in bulk to monoclinic or triclinic, depending on the choice of substrate and the magnitude of anisotropic strain, in thin films. This is in accordance with DFT calculations. Epitaxial engineering allows us to efficiently tune the magnetic anisotropy from bi-axial in bulk to uniaxial in our thin films, as inferred from soft x-ray spectroscopy. By increasing the LaFeO₃ thickness transition of the uniaxial spin direction takes place, a change from an out-of-plane to an in-plane AF spin axis above 16 d₁₁₁-layers.We will discuss the possibilities that anisotropic strain engineering offers to tune the interface AF spin texture between LaFeO₃ and a ferromagnet in a deterministic fashion, as confirmed by soft x-ray spectroscopy and spin-polarized neutron reflectivity. Furthermore, we will present non-local spin transport studies to exemplify that the uniaxial Néel vector control allows engineering of anisotropic spin transport. The experimental data will be correlated to spin transport theory.

Understanding the dynamics and energetics of the antiferromagnetic (AF) domains is of general and timely interest for the application of these magnetic materials in spin-based electronics for computing and communications. A fundamental requirement to understand and control AF domains involves the ability to image them. X-ray photon correlation spectroscopy (XPCS) measurements via coherent x-ray scattering can be employed to image the AF order parameter in thin films and to access the information about their dynamics. Recent studies on NdNiO₃ (NNO) have shown that its electronic and magnetic phase transitions can be tuned by confining the nickelate layers to reduced dimensions in heterostructures. We study the AF ground state for atomically layered (NdNiO₃)_m/(NdAlO₃)₄ heterostructures to demonstrate that dimensional confinement enhances the phase fluctuations at AF domain boundaries. We analyze the speckle patterns arising from coherent x-ray scattering to access the information on long- and short- ranged correlations for varying thickness of nickelate layers, m. We find that the dynamics of the AF domain boundaries are dramatically enhanced as the reduced dimensionality of the NNO layers approach the 2D limit. Our study demonstrates a path to characterize dimensional effects on long-range order and the ability to control AF domain configurations in oxide heterostructures.

We have carried out neutron diffraction and small angle neutron scattering measurements on a high quality single crystal of the cubic lacunar spinel GaV₄S₈ multiferroic as a function of magnetic field and temperature. The system undergoes a structural transition at 44 K to a non-centrosymmetric rhombohedral symmetry and becomes ferroelectric. The system then orders magnetically below ~13 K into an incommensurate cycloidal phase. Further reduction of temperature transforms the system below 7 K into a ferromagnetic ground state. The ferromagnetic order parameter appears to be continuous with an ordered moment of 0.9 μ_B at the lowest temperature. Measurements of the magnetic intensities using both polarized neutron diffraction measurements and unpolarized field-induced moment measurements in the temperature range between the magnetic and ferroelectric transitions demonstrate that the single electron spin is distributed across all four V ions of the V₄ molecular unit, and does not just reside on the single apical V ion. This is in reasonable agreement with DFT calculations which show a moment on all four V but with an enhanced occupancy on the apical V in the ferroelectric phase. In the vicinity and below the transition to long range magnetic order there is a clear coupling of the ferroelectric and magnetic order parameters, necessitating polarized neutron measurements to determine the magnetic form factor. Field-dependent SANS data exhibit the cycloidal and skyrmion phases, which have been investigated in detail as a function of temperature and applied magnetic field. The intensities depend strongly on both temperature and field, while the incommensurate wave vector is strongly temperature dependent but exhibits a very weak field dependence. Finally, the skyrmion dynamics have been investigated at long time scales using the neutron time-tagging technique with a periodic perturbative magnetic field complementing the steady-state applied field. Varying the amplitude and frequency of the perturbation has been used to reveal important details of the time dependence of the Néel-type skyrmions as well as other aspects of the magnetic order.

Recent observations of long-ranged magnetic ordering in van der Waals bonded, layered magnetic materials down to the single layer limit has led to a plethora of research dedicated to the study of two-dimensional (2D) magnets, with plenty of opportunities to investigate fundamental physics and potential quantum applications. With these materials, the properties are typically strongly correlated to the number of layers, with new physics occurring in the few-layer (~few nm) regime. In this sense, common techniques used to measure magnetic behavior such as neutron scattering and SQUID are at a disadvantage due to sample size requirements. On the other hand, Raman spectroscopy, which has diffraction-limited spatial resolution, is a powerful, non-destructive optical method to probe magnetism in 2D layered materials through inelastic scattering. An amazing amount of information is quantified from the Raman spectra such as layer thickness, disorder, edge and grain boundaries, strain, etc. Raman also efficiently probes the evolution of the spin-phonon interactions and magnetic excitations, such as magnons, as a function of temperature, laser energy, polarization, and magnetic field. I will discuss how we used our unique magneto-Raman capabilities to study the magnetic properties of the metal phosphorus trisulfide family (MPS₃, where M = Fe, Mn, and Ni) which are layered antiferromagnetic semiconductors. While the three materials have the same crystal structure, their varying spin structures result in distinct behavior as a function of temperature and magnetic field, which will be presented herein. In FePS₃, we investigated spin-phonon coupling as well as the emergence of new modes in the magnetically ordered state that were not present in MnPS₃. Through magneto-Raman spectroscopy, we will show that one of these modes is actually a Raman-active magnon, where the symmetry behavior of the magnon can be explained using the magnetic point group of FePS₃.

Since the discovery of high-T_c superconductivity in (La,Ba)₂CuO₄, superconductivity in nickel oxide compounds has been a target of interest for many years. We report the observation of superconductivity in an infinite-layer nickelate that is isostructural to the infinite-layer cuprates [1]. Using soft chemistry topotactic reduction, single crystal infinite-layer nickelate thin films are synthesized by reducing the perovskite precursor phase. Experiments on these films indicate a T_c of ~ 9-15 K. This compound can be considered one member of a series of reduced layered nickelate crystal structures, suggesting the possibility of a family of nickelate superconductors. In this talk, I will describe the film synthesis, discuss the superconductivity measurements, and present the latest developments in this emerging field.

[1] D. Li, K. Lee, B. Y. Wang, M. Osada, S. Crossley, H. R. Lee, Y. Cui, Y. Hikita, and H. Y. Hwang, Nature 572, 624-627 (2019).

Incommensurate charge order (CO) has been identified as the leading competitor of high-temperature superconductivity in all major families of layered copper oxides, but the perplexing variety of CO states in different cuprates has confounded investigations of its impact on the transport and thermodynamic properties. The three-dimensional (3D) CO observed in YBa₂Cu₃O_6+x (YBCO) in high magnetic fields is of particular interest, because quantum transport measurements have revealed detailed information about the corresponding Fermi surface.
Here, we report a high-resolution inelastic hard x-ray scattering study of the high-temperature superconductor YBa₂Cu₃O_6.67 under uniaxial stress and show that a 3D long-range-ordered charge density wave (CDW) state akin to that observed in field along the b-axis can be induced by pressure applied along the a-axis, in the absence of magnetic fields and after enhancing the planar 2D CDW [1]. The amplitude of the 3D CDW is strongly suppressed below the superconducting transition temperature, indicating strong thermodynamic competition with superconductivity. We also show that a strong softening of an optical phonon mode is associated with the transition.
We also used resonant soft X-ray scattering (RXS) at the Cu L₃ edge to investigate the planar symmetry of the strain-induced enhancement of the 2D CDW as well as the energy- and temperature-dependence of the 3D CDW scattering peak in single crystals of YBCO [2] and we compare the results with RXS data on the 3D charge order discovered in YBCO films grown epitaxially on SrTiO3 (STO) [3].
The findings offer fresh perspectives for experiments elucidating the influence of 3D CDW on the electronic properties of cuprates without the need to apply high magnetic fields.

References
[1] H.-H. Kim, S. M. Souliou, et al., "Uniaxial pressure control of competing orders in a high-temperature superconductor", Science 362, 1040 (2018)
[2] H.-H. Kim, M. Minola, et al. in preparation
[3] M Bluschke et al., "Stabilization of three-dimensional charge order in YBa₂Cu₃O_6+x via epitaxial growth" Nature Communications 9, 2978 (2018)

Charge order has now been observed in several cuprate high-temperature superconductors. We report a resonant inelastic x-ray scattering experiment on the electron-doped cuprate NCCO that demonstrates the existence of dynamic correlations at the charge-order wave vector. Upon cooling we observe a softening in the electronic response, which has been predicted to occur for a d-wave charge order in electron-doped cuprates. At low temperatures, the energy range of these excitations coincides with that of the dispersive magnetic modes known as paramagnons. Furthermore, measurements where the polarization of the scattered photon is resolved indicate that the dynamic response at the charge-order wave vector primarily involves spin-flip excitations. Overall, our findings indicate a coupling between dynamic magnetic and charge-order correlations in the cuprates.

The capability of controlling superconductivity by light is highly desirable for active quantum device applications. Since superconductors rarely exhibit strong photoresponses, and optically sensitive materials are often not superconducting, the efficient coupling of these two characters in a single material can be very challenging. Here we show that, in FeSe/SrTiO₃ heterostructures, the superconducting transition temperature in FeSe monolayer can be effectively raised by the interband photoexcitations in the SrTiO₃ substrate. Attributed to a light induced metastable polar distortion uniquely enabled by the FeSe/SrTiO₃ interface, this effect only requires a less than 50 µW cm^-2 continuous-wave light field. The fast optical generation of superconducting zero resistance state is non-volatile but can be rapidly reversed by applying voltage pulses to the back of SrTiO₃ substrate. The capability of switching FeSe repeatedly and reliably between normal and superconducting states demonstrate the great potential of making energy-efficient quantum optoelectronics at designed correlated interfaces.

High temperature Fe-based superconductors have recently drawn a strong attention due to their superconducting capability even in the presence of magnetic Fe, which has been regarded as a harmful element for superconductivity. Particularly, ThCr₂Si₂-structured Fe-based superconductors have been extensively studied due to their strong pressure sensitivity of structure and electronic/magnetic properties. Under hydrostatic pressure, they undergo the collapsed tetragonal (cT) phase transition through the formation of Si-Si type bonds. During this process, a magnetic state changes and superconductivity often disappears. Therefore, it is interesting to understand how mechanical deformation influences electronic structure, magnetism, and superconductivity.
For the last decade, nanomechanics community has reported numerous papers regarding the size-dependent strengthening and toughening at the nanometer scale; as the sample dimension decreases, a material can withstand the larger elastic deformation under uniaxial mechanical loading. For instance, silicon nanowire can be uniaxially stretched up to a strain above 15% before failure. This giant elastic deformability at the nano-scale can certainly open a new opportunity of “Strain-Engineering of Superconductors”. In this presentation, we will introduce our custom-built in-situ cryogenic micromechanical testing system that allows us to characterize mechanical behaviors of micron-sized iron-based high temperature superconductor under uniaxial mechanical loading. Micropillars of various ThCr₂Si₂-type iron-based superconductors were fabricated using focused ion beam milling, and uniaxial mechanical tests were performed along a [0 0 1] direction. Contrast to the conventional belief of easy brittle fracture under uniaxial loading, our results show the giant elastic strain over 10%, which is high enough to see the cT phase transition. This large elastic deformation is reversible, implying that it is possible to induce the forward and backward transitions continuously under the application of cyclic force. Thus, the giant elastic deformability at the nano-scale is still hold for iron-based superconductors. Compared to hydrostatic pressure, uniaxial mechanical loading has a great advantage to apply a mechanical force along a chosen crystallographic orientation. In addition, our on-going development of liquid helium cooling capability will allow us to explore the effects of uniaxial deformation on superconductivity. We will share some of our preliminary results of in-situ cryogenic mechanical testing on high temperature superconductor, CaKFe₄As₄ at T=40~298 K. We strongly believe that the combination of nanomechanics and superconductivity will create a unique opportunity to explore the effects of unconventionally large elastic strain on the critical temperature of superconductivity, magnetism, and electronic structures of superconductors.

An unusual form of two-dimensional (2D) superconductivity has been observed in bulk crystals of La_2-xBa_xCuO₄ (LBCO) with x ~ 1/8. To explain the apparent frustration of interlayer Josephson coupling, the occurrence of pair-density-wave superconductivity has been proposed [1], which is compatible with the known existence of spin and charge stripe orders. To test this possibility further, we recently performed transport measurements in a c-axis magnetic field of up to 35 T. At a temperature of less than 1 K, evidence was found for a progression, with increasing field, from 3D order to reentrant 2D superconductivity to an unusual metallic state with very large resistance per plane but negligible Hall effect. To see whether such behavior is unique to LBCO, crystals of La_2-xCa_1+xCu₂O₆ have been grown. Annealing in high-pressure oxygen results in dilute intergrowths of La₂CuO₄ and La₈Cu₈O₂₀; however, the apparent Ca-enrichment of the main phase results in a superconducting transition temperature T_c as high as 55 K [3]. Transport measurements demonstrate a decoupling of the superconducting bilayers in modest magnetic field [4]. Time-of-flight neutron scattering measurements reveal low-energy spin fluctuations that do not develop a gap below T_c [5]. This behavior is similar to that in LBCO, suggesting the importance of intertwined order.

Work at Brookhaven is supported by the Office of Basic Energy Sciences, Materials Sciences and Engineering Division, U.S. Department of Energy, through Contract No. DE-SC0012704.

1. D. F. Agterberg et al., arXiv:1904.09687.
2. Y. Li et al., arXiv:1810.10646.
3. J. A. Schneeloch et al., Phys. Rev. Materials 1, 074801 (2017).
4. R. Zhong et al., Phys. Rev. B 97, 134520 (2018).
5. J. A. Schneeloch et al., Phys. Rev. B 99, 174515 (2019).

This work is about the growth of high quality single crystals by the CVD method of dicalcogens that crystallize in the CdI2 prototype. Preliminary results shown in this plan strongly suggest that it is possible to grow high quality single crystals by this method represented by a member of the family which is Ni_0.02ZrTe₂. Band structure calculations, as well as some results reported in the literature, show that this type of prototype presents a non-trivial topology and, in this sense, the superconductivity that coming from this prototype can be a clear example of non-artificial topological superconductors. In addition to these aspects relevant to Condensed Matter Physics, the following plan intends to complement the formation of this candidate, in this effervescent area of the new Condensed Matter Physics

The properties of materials are determined by their dimensionality but also by the interatomic chemical bonding. It is then of interest to combine effort to control both aspects: chemical and dimensional. The low dimensional transition metal oxides showing 2D magnetic sheets, are of great interest due to their strong magnetic and electronic anisotropies which usually lead to complex phenomena (as spin density waves, superconducting, or step magnetization reversibility to name a few). In addition to the fundamental interest, spintronic applications are also of great interest: 2D spin-valve compounds, or magnetic tunnel junction are currently heavily exploited for magnetic random access memory (MRAM) memories. The latter two-dimensional structure compounds consist mainly of alternately ferromagnetic and non-magnetic layers that are generally obtained by the thin-film deposition technique. It is of interest to obtain new solid 2D materials with an angstrom-scale alternation of magnetic / non-magnetic layers inherent to their atomic structure, through which analysing the spin-dependent transport. On the other hand, this would avoid the current synthesis by thin film deposition more complicated to implement.
The use of voluminous polyanions can leads to original 2D atomic structures - This has been amply demonstrated in cuprates superconductors (Sr2CuO2(CO3), La1.85Sr0.15Cu1-x(SO4)xO4)). Paradoxically, few studies have been conducted in mixed polyanion iron oxide systems. We can nevertheless quote the oxyphosphate compound SrFe3(PO4)O or the oxycarbonate Sr4Fe2O6(CO3), described by Yamaura and Bréard. The latter is an intergrowth between SrFeO3 perovskite layers and "rock-salt" SrO layers where FeO6 octahedra of the middle perovskite layer has been replaced by carbonate groups showing the possibility to create intergrowths between carbonates and a transition metal which is not a Jahn-Teller element. This substitution strategy has been recently extended to sulfate anions which are also divalent but even larger than carbonates and more electronegative than oxygen and carbonates; They have also a radically different geometry. All these differences lead to different magneto electric behaviors that will be highlighted in the presentation.

Notwithstanding decades of work, the realization of a fundamental understanding of amorphous structures and their transport properties has remained a great challenge. In this research, we approach a description of amorphous structures by considering thermodynamic descriptions of the solidification of undercooled fluids upon the adoption of a quaternion orientational order parameter. Unlike the first-order transition of a liquid into a crystal, the glass transition is an entirely different phenomenon. In particular, as the temperature of an undercooled liquid decreases the difference in entropy between the liquid and solid phase decreases. At a certain point, known as the Kauzmann point that may be achieved in the limit of an infinitely slow cooling rate, the entropies of the liquid and crystal phase are equal. At the Kauzmann point, which occurs at a finite Kauzmann temperature, the liquid adopts a unique state of lowest energy such that its entropy approaches zero as temperature approaches zero. Herein, the "ideal glass transition" that occurs at the Kauzmann point is identified as a first order quantum phase transition between crystalline and non-crystalline solid states that are characterized by a four-dimensional quaternion orientational order parameter. In particular, there is a discrete change in the topology of the orientational order parameter manifold of the solid state at this critical point from a three-dimensional torus ($T^3$) to a three-dimensional sphere ($S^3$). Similarities between the finite temperature first-order crystal-to-glass transition and the superfluid-to-Mott insulator quantum phase transition are identified herein.

Pyrochlore iridates have been predicted to exhibit many fascinating topologically non-trivial states due to strong spin-orbit coupling (SOC) and electron correlations [1]. Importantly, they have the all-in-all-out (AIAO) antiferromagnetic ordering that breaks time reversal symmetry (TRS). With broken TRS, it was predicted that a magnetic Weyl semimetal (WSM) phase could emerge in pyrochlore iridates. In addition, theoretical studies revealed the emergence of a new topological phase of which are hidden in the bulk and manifest only in thin films [3-5]. In spite of these exotic phenomena, most of the works were focused on the bulk single crystals or ex-situ grown relaxed films. The multi-phase boundary of iridium presents an extreme difficulty in the in-situ epitaxial growth of such thin film samples.
Here, we report a high quality Nd₂Ir₂O₇ thin film grown on Yttrium stabilized ZrO₂ (YSZ) substrates by pulsed laser deposition, using a special in-situ growth technique called “repeated rapid pulse annealing epitaxy”. A large anomalous Hall effect (AHE) signal was observed in Nd₂Ir₂O₇ thin film where the size is ~ 10⁶ times larger than that of Nd₂Ir₂O₇ bulk. The tight binding calculation provided that strain effect can produce large Berry curvatures in the system and responsible to give large anomalous Hall effect. Moreover, we have observed chiral anomaly from the transport measurement which considered to be related to its possible magnetic WSM states. Our finding highlights that strain effect in pyrochlore iridates can be the way to engineer Berry curvature. Moreover, it may open a door to investigate the Berry curvature engineered correlated topological states in the oxides.
References:
[1] X. Wan et al., Phys. Rev. B. (2011).
[2] William Witczak-Krempa et al., Annu. Rev. Condens. Matter Phys. (2014).
[3] B.-J. Yang et al., Phys. Rev. Lett. (2014).
[4] K. Hwang and Y. B. Kim, Scientific Reports (2016)
[5] P. Laurell and G. A. Fiete, Phys. Rev. Lett. (2018).

Realization of new states of quantum matter is persistently desired in condensed matter physics and material science engineering. Some outstanding example systems include high transition temperature superconductors (high Tc SC), topological insulators (TI), quantum spin liquids (QSL), etc… A recently reported spin trimer chain compound Ba4Ir3O10, which crystallizes in a different lattice than conventional geometrically frustrated motifs such as in pyrochrole and Kagome lattice, might offer a new platform for engineering unusual quantum spin liquid states. The similar chain compound BaIrO3, however, exhibits magnetic order at much elevated temperature 183 K, concomitant with the onset of charge density order. Here we report the powder and single crystal growth of a plethora of Barium Iridium Oxides with contrasting unconventional magnetic ground states which share a great deal of structural similarities. Our current explorations indicate a potential playground for emerging quantum materials in Barium Iridates.

Fabricating atomic scale structures remains as an ultimate goal of nanotechnology. Scanning Probe Microscopes and molecular self-assembly have demonstrated important successes towards achieving this goal. In this presentation, I discuss research activity towards the use of the atomically focused beam of a scanning transmission electron microscope (STEM) to control and direct matter on the atomic scale. Traditionally, STEM’s are perceived only as imaging tools and the material modifications induced by their highly energetic (on the order of 100 kV) and highly focused (sub-angstrom) beams considered as undesirable beam damage. However, if these material changes can be directed through precise control over beam trajectory, the use of active feed-back, and control over temperature and environment, it is possible to use the STEM as a platform for not just imaging, but manufacturing at the atomic scale. We have demonstrated single defect formation, controlled individual dopant placement and migration, and drilling and milling in single layer 2D materials with the goal of building materials and devices for quantum application. I will introduce several examples of beam-induced fabrication on the atomic level, and demonstrate how beam control, rapid image analytics based on traditional and artificial intelligence techniques, better insight through modelling, and image- and spectroscopy-based feedback allows for controlling matter on atomic level and investigating emergent properties.

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Division of Materials Science and Engineering, Basic Energy Sciences and was performed at the Oak Ridge National Laboratory’s Center for Nanophase Materials Sciences (CNMS), a U.S. Department of Energy, Office of Science User Facility.

Just when we thought the spin-orbit interaction in solids was finally explained, a plethora of new discoveries have appeared, challenging our understanding and imagination of what the implications and manifestation of this relativistic effect might be. Today the field of spin-orbit coupling is a vibrant one, ranging from the construction of revolutionary experimental tools for imaging spins of electrons in both momentum, energy and time domain, to the development of new theories and models aimed at predicting and explaining unexpected behaviors. In this talk I will present an overview on the state of the art experimental techniques to study such interaction in condensed matter physics, and I will discuss a couple of examples of how such interaction evolves from 2D transition metal dichalcogenides, to topological insulators and finally unconventional superconductors where such interaction gets coupled with strong correlation leading to novel behavior.

Magnetism, when combined with an unconventional electronic band structure, can give rise to forefront electronic properties such as the quantum anomalous Hall effect, axion electrodynamics and Majorana fermions. Here we report the characterization of high-quality crystals of EuSn₂P₂, a new quantum material specifically designed to engender unconventional electronic states plus magnetism. EuSn₂P₂ has a layered, Bi₂Te₃-type structure. Ferromagnetic interactions dominate the Curie-Weiss susceptibility, but a transition to antiferromagnetic ordering occurs near 30 K. Neutron diffraction reveals that this is due to two-dimensional ferromagnetic spin alignment within individual Eu layers and antiferromagnetic alignment between layers - this magnetic state surrounds the Sn-P layers at low temperatures. The bulk electrical resistivity is sensitive to the magnetism. Electronic structure calculations reveal that EuSn₂P₂ might be a strong topological insulator, which can be a new magnetic topological quantum material (MTQM) candidate. The calculations show that surface states should be present, and they are indeed observed by ARPES measurements.

Pb_1-xSn_xSe (x<0.4) is a narrow gap semiconductor and it can have topological phase transition to topological crystalline insulator (TCI) when the concentration of Sn increases. Its electronic properties are sensitive to electric and magnetic fields. It is thus worth considering in the fabrication of electronic devices. Here we investigated the MBE growth of Pb_1-xSn_xSe (x~0.2-0.3) doped with Bi and characterized the sample using X-ray diffraction (XRD), and magneto-transport measurement. We showed that doping Bismuth into the sample can significantly lower the carrier density, even change its type from p=2.9×10¹⁸ cm^-3 to n=1.1×10¹⁹ cm^-3. We studied how quantum coherent transport depends on this tuning process. This tunability can be useful in the fabrication of quantum devices.

Recently, about 25% of all known uncorrelated compounds have been predicted to host topological properties. According to these theoretical predictions, Ca2Pt2Ga is a filling-enforced topological semimetal candidate. Here we present a route for the synthesis of Ca2Pt2Ga single crystals, which are characterized by single crystal x-ray diffraction, energy dispersive spectroscopy, magnetic susceptibility, electrical resistivity, Hall effect and heat capacity at low temperatures. We will compare our experimental data with theoretical expectations.

Thin film β-tungsten (β-W) is attracting extensive attention due to its giant spin Hall effect and promising application in spintronics as memory devices. Large spin currents have been used to set the magnetization of adjacent magnetic layers using the spin torque effect [1], and utilization of the large spin-Hall angle of β-W (0.3) [2] appears promising. However, the reason for the large magnitude of the spin Hall angle in β-W is presently not known. Clarifying whether the giant spin Hall effect arises from extrinsic or intrinsic properties is the first step towards engineering β-W based spin torque devices. Extrinsic effects arise from spin-dependent scattering with impurities or band structure peculiarities. To date, no work has experimentally examined the electronic density of states in pure β-W thin films. In this work, we present high-resolution valence band spectra near the Fermi level of pure β-W thin films measured by photoelectron spectroscopy using synchrotron radiation. Only fine difference in the double peak structure between -2 and -4 eV is observed between β-W and α-W. Such effects are qualitatively reproduced in calculations. However, the experimental spectra are complicated by the presence of oxygen surface contamination, and its presence is never reduced completely even after successive in-vacuo sputtering. Large spin Hall angles reported in other thin film materials generally arise due to spin-orbit interaction of impurities [3], or resonant/surface skew scattering effects with impurity sites [4]. Our results indicate that the role of oxygen impurities on β-W surfaces should be clarified in the reported large spin Hall angles of β-W layered systems. The mechanical and structural properties of thin films were characterized using a combination of novel picosecond ultrasonic measurements and standard X-ray diffraction. The calculated elastic constants using density functional theory agreed within 10% of the experimental values for both β-W and α-W.

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