Symposium MQ01 : Coherent and Correlated Magnetic Materials for Hybrid Quantum Interfaces

Rare earth ions in oxide materials have been extensively studied due to narrow transitions with long coherence times and high quantum efficiency between electronic levels of partially filled f-shells. This results in the fabrication of optical amplifiers with high quantum efficiency and optimal wavelength in telecommunication applications, high power solid-state lasers, and usage in optical storage, data, and quantum information processing [1]. Furthermore, yttrium oxide (Y₂O₃) as one of these oxide materials with a high dielectric constant has gained attraction for being an alternative for replacing silicon dioxide in metal-oxide-semiconductor devices [2].

Here we study electronic, structural, and spin properties of trivalent rare-earth element erbium (Er³⁺) impurities in the cubic bulk Y₂O₃ with a wide band gap of 5.8 eV. The primitive cell of the yttria has 40 atoms, however, a conventional bixbyite supercell with 80 atoms is used for impurity calculations. As one of the most promising dopants, Er³⁺ substitutes an yttrium atom at two symmetrically inequivalent and octahedrally coordinated cation sites (C₂ and C_3i) with an equal probability. First, we compute structural parameters such as lattice constant and elastic properties within the density functional theory using a Monkhorst-Pack k-point grid of 2x2x2 for Brillouin zone integration, the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof exchange-correlation potential and the pseudopotential method in a plane wave basis. We also calculate the electronic band structure and the density of states of the bulk and doped yttria. The results of the electronic and structural calculations are in a good agreement with experimental measurements. Then we proceed to calculate the formation energies of Er³⁺ impurities as point defects at two different sites using the defect formation energy formula [3]. We also investigate the formation energies of different charged states as a function of the Fermi level.

We also calculate individual defect properties such as level splittings and g-tensors using an effective crystal field Hamiltonian with Wybourne normalization and treat the Zeeman and hyperfine interactions as a perturbation. Group theoretical studies [4] show that the low crystal symmetry of Er³⁺ sites requires only a small number of crystal-field parameters to model energy levels of the dopants sufficiently. We show that g-tensor of the ground state that is calculated from this Hamiltonian is highly anisotropic with a large component along one direction. Presence of an abundant isotope of the ¹⁶⁷Er with a non-zero nuclear spin and anisotropic g-tensor suggest that an experimental control of the spin dynamics of this system is possible through the Zeeman and hyperfine interaction.

We acknowledge funding from the Center for Emergent Materials, an NSF MRSEC under Award No. DMR-1420451 and by NSF EAGER Award No. 1843044.

[1] Spectroscopic Properties of Rare Earths in Optical Materials, ed. by G. Liu and B. Jacquier, Springer Press (2005)
[2] R. McKee, F. Walker, and M. Chisholm, MRS Proceedings, 567, 415 (1999)
[3] S. B. Zhang and J. E. Northrup, Phys. Rev. Lett. 67, 2339 (1991)
[4] M. Dammak, R. Maalej, M. Kamoun, and J.L. Deschanvres, physica status solidi (b), 239(1), 193-202 (2003)

The localized electron spin of a single impurity in a semiconductor is a promising system to realize quantum information schemes [1]. Coherent control of this spin depends on understanding the structure of the magnetic moment that couples the system with external fields. In this work we investigate the orbital contribution to the magnetic moment originated from the spin-orbit induced circulating current associated with the ground state of a single magnetic impurity in zincblende III-V semiconductor. This circulating current is dissipationless and represents an electron moving in a closed trajectory [2]. The orbital moment associated with the circulating current could be directly measured by the dc-magnetic field it produces through nanoscale magnetometry techniques provided by NV-centers in diamond [3].

In this project we developed a formalism employing Green's functions obtained by the Koster-Slater technique [4] with a sp³d⁵s^* empirical tight-binding Hamiltonian [5,6] to describe the host material. We calculated the circulating current and orbital moments of a single Mn dopant in GaAs. The spin-correlated orbital moments originates from the hybridization between the Mn(d⁵) spin-polarized electrons and the As dangling bonds leading to t₂-symmetric triplet acceptor states in the band-gap above the valence band edge.

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[3] Casola, F. and van der Sar, T. and Yacoby, A., Nature Reviews Materials, 3(1), 17088 (2018).
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* This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 721394

The neutral divacancy (VV0) in silicon carbide (SiC) exhibits robust spin coherence and a high-quality near-infrared spin-photon interface in a material compatible with mature fabrication techniques. Here, we make use of this scalable semiconductor host and design electronic devices to manipulate embedded isolated quantum systems. Specifically, we create and isolate single VV0 defects in a commercial p-i-n diode [1]. This simple integration enables engineering of the defect’s charge environment and drastically reduces electric field noise. Surprisingly, the use of electrical gating results in mitigating spectral diffusion and achieving near-lifetime limited optical lines. Furthermore, by exploiting field confinement of the junction, we show that the optical transitions can be gate-tuned by nearly a terahertz. This geometry also provides a method for using electric fields combined with optical excitation to enable deterministic charge state control.
Applying gigahertz ac electric fields to SiC devices produces coherent interference in the form of Landau-Zener-Stückelberg fringes, arising from interactions between microwave and optical photons [2], even in the absence of a microwave resonator. We demonstrate lifetime-limited optical coherence and clock-like spin transitions that result in increased robustness against magnetic noise. Electrical driving of optical transitions offers advantages over spin-based coupling and points towards new types of hybrid quantum systems. These results reveal new opportunities for electrical manipulation of spin-based quantum systems in scalable SiC electronic devices.
This work was done in collaboration with S. L. Bayliss, A. L. Crook, P. J. Mintun, S. J. Whiteley, G. Wolfowicz, H. Abe, A. Gali, V. Ivady, T. Ohshima, G. Thiering, P. Udvarhelyi.
[1] C. P. Anderson*, A. Bourassa*, K. C. Miao, G. Wolfowicz, P. J. Mintun, A. L. Crook, H. Abe, J. U. Hassan, N. T. Son, T. Oshima, D. D. Awschalom, “Electrical and optical control of single spins integrated in scalable semiconductor devices,” arXiv: 1906.08328
[2] K. C. Miao, A. Bourassa, C. P. Anderson, S. J. Whiteley, A. L. Crook, S. L. Bayliss, G. Wolfowicz, G. Thiering, P. Udvarhelyi, V. Ivady, H. Abe, T. Ohshima, A. Gali, D. D. Awschalom, “Electrically driven optical interferometry with spins in silicon carbide,” arXiv: 1905.12780

Inversion-symmetric quantum emitters in diamond, such as the silicon-vacancy, germanium-vacancy, and the recently-discovered tin-vacancy complexes, are promising candidates for quantum networking as their optical coherence is protected from electric field noise. Emitters containing a heavier element, such as Sn or Pb, are of particular interest as their large spin-orbit coupling reduces phonon scattering at easily achievable (non-³He dilution) temperatures, offering the possibility of long spin coherence – a key requirement for scalable quantum networks. Here we report on the development of coherent spin-photon interfaces based on Sn-vacancy emitters, including optical and spin coherence measurements and integration into nanophotonic devices. The narrow optical linewidths and long spin coherence times observed, combined with robustness to fabrication-induced damage, place the SnV among the best-known solid-state spin-photon interfaces.

Color centers have emerged as leading solid-state “artificial atoms” for a range of technologies from quantum sensing to quantum networks. Concerted research efforts are now underway to identify new color centers that combine the favorable spin properties of the nitrogen vacancy (NV−) with the spectral stability of the silicon vacancy (SiV−) centers of diamond. Using a first principles approach, we investigate quantum defects in both 3D (diamond) and 2D (hexagonal boron nitride) hosts with the aim of unlocking and understanding the optical and spin physics. In diamond, we will discuss insights into Jahn-Teller interactions, including the product and dynamic Jahn-Teller distortions related to both group III and group IV color centers. Further, we show the instabilities and charge-states associated with each of these group III/IV defects and the implications in quantum information science related to both spin and spectral stability. In hBN, we discuss the origin of defect emission, in particular the importance of the level of theory invoked to describe charge states and defect-defect interactions.

Quantum emitters in the solid state with addressable spin registers are promising platforms for quantum communication, yet few emit in the narrow telecom band necessary for low-loss fiber networks. This scarcity is compounded by the low brightness and hard-to-engineer host materials of erbium ions, the prototypical telecom emitter, motivating the search for alternative systems.

Here we create and isolate single vanadium dopants in silicon carbide (SiC) with emission in the O-band (1278-1388 nm) and with brightness allowing cavity-free detection, in a commercial, wafer scale and CMOS-compatible material [1]. We demonstrate that their emission is stable and relatively narrow even near surfaces, showing strong promise for integration with nanoscale devices.

In ensembles, we characterize the complex physics provided by the d¹ orbital of these transition metals, including a systematic study of the five different sites available in the 4H and 6H polytypes of SiC. The optical transitions are observed to be sensitive to mass shifts from the distribution of nearest neighbor silicon and carbon isotopes, potentially enabling optically-resolved nuclear spin registers.

Optically detected magnetic resonance of ground state and excited spin transitions reveal a variety of hyperfine interactions with the vanadium nuclear spin and their related clock transitions for use as quantum memories. Finally, we demonstrate coherent quantum control of the spin state at 3.3 K, limited by thermal relaxation effects. These results provide a path for telecom emitters in the solid-state for quantum applications.

[1] G. Wolfowicz, C. P. Anderson, B. Diler, O. G. Poluektov, F. J. Heremans and D. D. Awschalom, Vanadium spin qubits as telecom quantum emitters in silicon carbide, arXiv:1908.09817 (2019)

The effect of structural chirality-induced spin selectivity (CISS) has been observed in a host of nanostructures involving chiral molecule monolayers on noble metals.¹ Realizing CISS on semiconductors could open new pathways of spin injection and detection on semiconductors without using any magnetic materials. However, there has been no report of such experiments on planar semiconductor surfaces. Here, we report on the self-assembly of thiolated dsDNA and polyalanine monolayers on GaAs and its magnetic variant, (Ga,Mn)As, which is used as a spin analyzer to ascertain CISS through the chiral molecules. The monolayer assemblies on GaAs are studied by AFM and ellipsometry and compared with those on Au. On Au, "blocking" by hydrophobic alkanethiol self-assembled monolayers is necessary to achieve assembly of dsDNA oriented away from the substrate. The assembly on GaAs is made possible by an ammonium sulfide treatment for oxide removal and surface passivation,² on which the polyalanines form oriented SAM without any "blocking".
We further study the spin-selective electron transport across vertical junctions of (Ga,Mn)As/polyalanine/Au. The bottom (Ga,Mn)As electrode is epitaxially strained, resulting in perpendicular magnetic anisotropy. The micrometer scale junctions are formed in openings in a hardened PMMA layer on the (Ga,Mn)As defined by electron beam lithography. The native oxide on the exposed (Ga,Mn)As is removed by ion milling, followed immediately by polyalanine monolayer self-assembly in a solution. The top Cr/Au electrodes are thermally evaporated under liquid nitrogen cooling. The CISS effect is evidenced by measuring the magnetoresistance of the junctions: Sweeping the perpendicular magnetic field at low temperatures, sharp changes in the junction resistance are observed at the coercive fields of the (Ga,Mn)As, indicating spin filtering of electrons from the Au electrode by the polyalanine monolayer. The spin polarization of the electrons from GaAs filtered by polyalanines may be determined quantitatively by spin-resolved superconducting tunneling with a thin Al counter-electrode.

[1] R. Naaman and D. H. Waldeck, Annu. Rev. Phys. Chem. 66, 263 (2015).
[2] T. Liu, et. al, ACS Appl. Mater. Interfaces 9, 43363 (2017).

A detailed understanding of two-level quantum systems in complex environments is necessary for the development of quantum information and sensing applications [1,2]. Individual or small clusters of dopants with remarkably long coherence times are addressable via scanning tunneling microscopy (STM) and the exchange interaction between dopants can be measured [3-6]. Through the use of localized magnetic contacts, for instance a spin-polarized STM, the correlations between the dopant spin state and the magnetization of the tip yields insight into the coherent dynamics at the addressed site. We propose a method to dynamically probe the spin-dependent properties of a spin-1/2 dopant exchange coupled to a charge-stable spin-1/2 state in the presence of a milliTesla dc transverse magnetic field embedded in a weakly conducting host. Calculations of the magnetoresistance through the mediating dopant rely on a stochastic Liouville approach where the density matrix of the two-dopant system is tracked and a steady state solution is found. The MR in these systems provides signatures of the exchange interaction, hyperfine coupling, spin decoherence, and g-factor. An extension of the spin-1/2 case to a system with spin-1 is applicable to systems like the divacancy defect in silicon carbide.
We acknowledge support from DOE BES through Grant No. DE-SC0016447.

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A broad range of quantum-coherent spin centers have been identified in optically-accessible materials, especially including nitrogen-vacancy, silicon-vacancy, and germanium-vacancy centers in diamond, divacancies and transition-metal dopants in several polytypes of silicon carbide, and even spin centers in two-dimensional materials such as hexagonal boron nitride. Some of these materials, however, allow good electrical transport (such as silicon carbide), and other spin centers have been found in materials that cannot be easily probed optically. Some of these, such as dopants in silicon, have been probed using electron spin resonance techniques that require an rf field. Recently, however, it has become clear that dc techniques can electrically manipulate and measure the spin orientations of spin centers through the establishment and release of electrical transport bottlenecks. The key requirements of these approaches are a spin-polarized electrical contact and a small transverse magnetic field, however no ac field of any type is required. Some examples of the potential for this approach will be described, including the proposal to measure, at room temperature, the micro-eV-scale exchange and hyperfine fields between spins in a semiconductor using dc magnetoresistance, and the room-temperature observation of hyperfine interactions in a trap at the Si-SiOx interface in a MOSFET.

Aspects of this work were supported by DOE DE-SC0016447 and HDTRA1-18-1-0012.

Electron paramagnetic resonance (EPR) techniques offer unrivaled analytical power in the identification of the physical and chemical nature of point defects in semiconductors and insulators. However, the sensitivity of conventional EPR is about 10 billion defects. This number greatly exceeds the number of performance-limiting defects in technologically relevant solid-state devices. Electrically detected magnetic resonance (EDMR) is at least 7 orders of magnitude more sensitive than its parent technique, EPR [1,2]. This enormous enhancement in sensitivity makes EDMR a powerful tool in the investigation of point defects in nano-scale electronic device. This sensitivity also makes EDMR potentially useful in various spintronic applications. Although EDMR is a powerful tool, its analytical power could be greatly enhanced with the addition of a nuclear magnetic resonance (NMR) component. The conventional double resonance technique known as electron nuclear double resonance (ENDOR) combines EPR and NMR and has the analytical power to provide detailed atomic scale information about paramagnetic defects in semiconductors and insulators [3]. The absolute sensitivity of conventional ENDOR is grossly inferior that of classical EPR, making the technique essentially impossible for studies of nano-scale electronic devices. This also makes the exploitation of long nuclear spin decoherence times quite difficult via classical ENDOR. We show that, by utilizing EDMR detection, ENDOR sensitivity may be enhanced by many orders of magnitude, opening possibilities for electrically detected ENDOR (EDENDOR) to contribute substantially to solid-state device physics, possibly including some spintronic applications. We have developed a sensitive EDENDOR spectrometer and demonstrate that it can provide reasonably high signal to noise spectra involving ¹⁴N nuclear spins interacting with deep level defects in the base-emitter junction of a fully processed 4H-SIC bipolar junction transistor at room temperature. The EDENDOR spectrometer utilizes a single loop non-resonant antenna that is placed within a TE₁₀₂ microwave cavity adjacent to the transistor to generate the NMR oscillating magnetic field. A frequency sweep is supplied to the NMR coil loop via an arbitrary waveform generator (AWG). To maintain constant power to the loop, a proportional-integral-derivative (PID) controller has been used to feedback a real time measurement of the power through the loop and adjust the output. This suppresses the non-resonant background which could otherwise obscure the EDENDOR response. To the best of our knowledge this is the first time ENDOR measurements have ever been made within a fully processed transistor.

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Silicon Carbide (SiC) has recently established itself as a viable host for defect-based spin qubits, providing a diamond-like host for spins with silicon-like fabrication and doping control. In particular, neutral divacancies (VV⁰) in SiC have shown exceptional spin coherence and a viable telecom spin-photon interface for entanglement schemes. Here, we isolate for the first time single VV⁰ in functioning, doped, commercial semiconductor p-i-n devices and use the diode to control and tune these defects. In this talk, we focus in particular on the control of the charge state of the single spins in the device.

Controlling charge dynamics has allowed for key demonstrations in quantum sensing and communications. Additionally, the charge states of single spins can be utilized in spin-to-charge conversion, enabling single-shot optical readout and even electrical readout of single spins. However, the understanding and control of charge for single spins in SiC remains unexplored.

In this work, integration of single spins into the p-i-n device enables a demonstration of deterministic charge state control of single VV⁰ spin defects, and a careful study the defect’s photo-dynamics. These results allow for the stabilization of the desired charge state of the defect and reduce ionization and spectral hopping of the orbital structure. Furthermore, integration into the device allows for electrically gating of the single photon emission, and control of formation of these defects using fermi-level engineering.

Leveraging of the mature SiC semiconductor device technology creates exciting opportunities for electrical control, manipulation and readout of both the spin and charge degrees of freedom in these quantum emitters.

Related publication:
C. P. Anderson*, A. Bourassa*, K. C. Miao, G. Wolfowicz, P. J. Mintun, A. L. Crook, H. Abe,
J. U. Hassan, N. T. Son, T. Oshima, D. D. Awschalom, “Electrical and optical control of single
spins integrated in scalable semiconductor devices”, arXiv: 1906.08328

Quantum bits based on soli-state spins are promising and potentially scalable systems for the implementation of quantum technologies ranging from quantum information processing to quantum-enhanced sensing and metrology. Ideally, they combine individually addressable spins with very long coherence times, optical emission spectra with narrow homogeneous and inhomogeneous broadenings and bright single-photon emission. In this respect, impurity-vacancy color centers in diamond based on group-IV elements (SiV, GeV, SnV, PbV) have emerged as interesting systems promising to combine all desired favorable properties.

Both the SiV and the GeV center feature superior spectral properties, i.e. at liquid helium temperatures (4K), they exhibit a narrow zero phonon line (ZPL) with a four-line fine structure and close to lifetime-limited linewidths [1,2]. Furthermore, both allow for fast all-optical addressing and control of their spin states [3,4]. However, at temperatures around 4K both color centers exhibit spin coherence times (T₂^*) of only a few ten nanoseconds due to phonon-induced decoherence processes [3,4] and the SiV reaches millisecond spin coherence times only at millikelvin temperatures and in pure samples [3,5]. A potential resort are vacancy defects with a heavier group-IV impurity atom, such as SnV and PbV centers, featuring a larger ground state splitting and thus less susceptibility to phonon-induced decoherence.

Here, we report on spectroscopy of SnV centers [6,7,8] where we find two charge states, i.e. SnV(-) and SnV(0), which both show promising optical properties. The SnV(-) features a ground and excited state splitting considerably larger (850 GHz and 3000 GHz, respectively) as compared to the SiV center, potentially enabling long spin coherence times even at liquid He temperatures. This defect is a bright single photon emitter, showing a narrow inhomogeneous distribution of zero phonon lines in a high-temperature annealed sample [6] and truly lifetime-limited transition linewidths down to 20 MHz. Furthermore, we determine the charge transition from the negative to the neutral charge state as a function of the excitation wavelength and find it to coincide well with theoretical predictions [9]. For the SnV(0) center we find emission lines that again agree well with theoretical calculations [10]. The neutral charge state is particularly interesting due to its potentially long electron spin coherence times.

[1] L. J. Rogers et al., Nat. Commun. 5, 4739 (2014).
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[7] S. D. Tchernij et al., ACS Photonics 4, 2580 (2017).
[8] M.E. Trusheim et al., arXiv:1811.07777
[9] G. Thiering et al., Phys. Rev. X 8, 021063 (2018).
[10] G. Thiering et al., NPJ CompMat.5, 18 (2019).

The unique properties of the negatively charged nitrogen vacancy color center (NV^-) in single crystalline diamond have been explored for developing new types of devices for photonics and scanning probe magnetometers with high sensitivity and spatial resolution over more than a decade. This growing field is in need of thin, free-standing ultra-clean diamond devices with complex geometries. The fabrication of such structures in large numbers will be the topic of this presentation.
Free-standing diamond devices as photonic crystals or NV-scanning-probe heads¹ are typically manufactured from diamond membranes of below 30µm thickness. The latter are expensive and available only in small numbers which makes a scaling of the production very challenging. In addition to this, the homogeneity in thickness below micron level is crucial for many applications and remains practically unachievable via polishing on large surfaces.

An alternative method based on so-called faraday-cage-angled-etch (FCAE) pioneered at the group of prof. Loncar at Harvard university² is based on the capability to create free-standing diamond devices via dry chemical underetching. We have employed FCAE to create mechanical and optical components and will report on the characteristics of the devices investigated via SEM as well as optical and mechanical metrology.

References
[1] C.J. Widmann, et al., Diam. Relat. Mater., 54(2015), pp. 2-8
[2] Burek, Michael J.; Leon, Nathalie P. de; Shields, Brendan J.; Hausmann, Birgit J. M.; Chu, Yiwen; Quan, Qimin et al. (2012), Nano letters 12 (12), S. 6084–6089.

Magnetic microparticles are used in a variety of research applications including cell sorting¹, targeted drug delivery² and optical force traction microscopy³. The magnetic properties of such particles can be customized for specific applications with the uniformity of individual magnetic microparticles having a significant bearing on their function. Prior to the study discussed here, most magnetic characterization techniques have quantified the magnetic properties from large bead ensembles⁴. As such, there is a significant demand for magnetic imaging techniques to evaluate and visualize the magnetic fields from single beads. New insights into the magnetic uniformity, anisotropy, and alignment of magnetic domains can be found through measurements of the magnetic properties of single beads.
Here, magnetic microscopy based on the nitrogen-vacancy centre in diamond is applied to image and characterize individual magnetic beads with varying magnetic and structural properties: ferromagnetic and superparamagnetic/paramagnetic, shell (coated with magnetic material), and solid (magnetic material dispersed in matrix). The magnetic microscopy described here probes both the fluctuating moments of the beads studied as well as their static magnetic moments. The single-bead magnetic images identify irregularities in the magnetic profiles from individual bead populations. Magnetic simulations account for the varying magnetic profiles and allow to infer the magnetization of individual beads⁵. Additionally, this work shows that the imaging technique can be adapted to achieve illumination-free tracking of magnetic beads, opening the possibility of tracking cell movements and mechanics in photosensitive contexts.

1. Reverte, L., Garibo, D., Flores, C. & Caixach, J. Magnetic Particle-Based Enzyme Assays and Immunoassays for Microcystins: From Colorimetric to Electrochemical Detection. (2013). doi:10.1021/es304234n
2. Veiseh, O., Gunn, J. W. & Zhang, M. Design and fabrication of magnetic nanoparticles for targeted drug delivery and imaging *. Adv. Drug Deliv. Rev. 62, 284–304 (2010).
3. Yoshie, H. et al. Article Traction Force Screening Enabled by Compliant PDMS Elastomers. Biophysj 114, 2194–2199 (2018).
4. Science, S. High temperature superconductor dc SQUID micro-susceptometer for. (2004). doi:10.1088/0953-2048/17/5/046
5. Tetienne, J. et al. Proximity-Induced Artefacts in Magnetic Imaging with Nitrogen-Vacancy Ensembles in Diamond. 13–16 doi:10.3390/s18041290

The recent discovery of long-range magnetic order in atomically thin ``van der Waals’’ (vdW) crystals has attracted significant attention due to their fundamental and technological interest, including predictions of exotic magnetic phases and unique opportunities to control magnetism at the atomic scale. I will present recent experiments, where we employ a single-spin-based quantum sensing technology for quantitative, nanoscale probing of atomically thin vdW magnets. Specifically, I will describe experiments, where we employ a diamondbased, scanning probe quantum sensor to address magnetism in the prototypical vdW magnet CrI3, down to the level of atomic monolayers. Our approach enabled nanoscale imaging of magnetic domains, quantitative determination of CrI3‘s layerdependent magnetization, and revealed a delicate interplay between magnetic and crystalline order in CrI3. Next to addressing fundamental open questions in the nanomagnetism of atomically
thin CrI3, our results yield attractive perspectives for future probing of dynamical properties of two-dimensional spin systems using single spin quantum sensors. Amongst other things, these could yield experimental evidence for the still elusive quantum spin liquid, which is believed to occur in monolayers of certain vdW compounds.

Antiferromagnetic materials are promising candidates for new memory devices with fast electrical writing and readout capabilities. Imaging the magnetic state of antiferromagnets on the sub-micrometer scale, however, is challenging because these materials do not exhibit a macroscopic magnetization.

In this talk, we will discuss the application of scanning diamond magentometry for investigating the microscopic domain structure of in-plane layered antiferromagnets, like tetragonal CuMnAs. After introducing the basics of the technique, we will discuss models and concepts for analyzing the magnetic stray field emanating from the antiferromagnetic domains. We will further show that current pulses lead to changes in the domain pattern and analyze these changes as a function of the current amplitude and direction.

The negative nitrogen-vacancy (NV^-) defect in diamond has quantum spin properties observable from cryogenic temperatures to ~1000 K. Parallel to this, SiC based divacancy (VV) complexes photoluminesce in the telecom infrared range, extending their technological applicability. Both of these spin-based quantum sensors are known to be responsive to changes in local strain, electric, magnetic, and thermal fields. Building on this foundation, we discuss recent advances of defect 3D localization in the context of improving and controlling their spatial resolution and crystalline environment. This progress is fueled by nanoimplantation and nanoscale strain-sensitive X-ray imaging techniques. The insights provided serve to better understand the defect’s lattice surroundings, guide future synthesis efforts, improve the creation efficiency, and advance the goal maintaining coherence times of the spin states.

Defect centers in diamond are promising candidates for applications such as quantum sensing, networking and computation. Previous work has experimentally identified several defects such as the NV^– and group IV related defects. However none of these color centers have shown the ideal combination of optical transitions, coherence times, and ease of fabrication and integration, motivating an ab initio search of new color centers in diamond. Towards this goal, we present first principles calculations of a new class of emitters, the group III-vacancies, which are theoretically shown to have a promising ground state structure for quantum applications, a noise insensitive optical transition, and are thermodynamically favored in intrinsic diamond. The ground state fine structure, as well as the excited electronic structure will be discussed in this talk. Further, we will show the electron-phonon coupling parameter calculations to determine the Jahn-Teller distortion, as well as the phonon sideband of the optical emission. Finally, we will discuss how the ab initio results compare with experimental quantities such as the ground state spin structure and optical emission properties.

The nitrogen vacancy (NV) center defect in diamond is emerging as a powerful quantum-enabled technology, in particular in the realm of sensing and imaging with ultra-high spatial resolution. The performance of these solid-state quantum sensors is highly dependent on their quantum coherence and charge-state stability, which are sensitive to their local environment. Surfaces are an important part of the defect's environment, in particular when targeting high spatial resolution sensing, which necessitates close proximity between the sensor and target. To identify and mitigate the deleterious environmental effects, I discuss several materials-based and quantum-control approaches. Specifically, I discuss the formation of highly-coherent NV centers via a gentle, bottom-up method of nitrogen delta-doping during chemical vapor deposition growth of diamond thin films followed by low energy (~ 150 keV) electron irradiation. I present measurements of the density and coherence properties of the NV centers formed in this way as a function of growth and irradiation parameters [1]. In the second part of the talk, I discuss the spin and charge state properties of shallow NV centers, and introduce techniques to mitigate decoherence due to paramagnetic surface spins [2] as well as charge state instabilities near surfaces [3]. These approaches to improved sensors will ultimately enable truly nanoscale spatial resolution imaging of magnetic, electric, and thermal fields in a variety of condensed matter and biological systems.

[1] “Optimizing the formation of depth-confined nitrogen vacancy center spin ensembles in diamond for quantum sensing”, T. R. Eichhorn, C. A. McLellan, A. C. Bleszynski Jayich, https://arxiv.org/abs/1901.11519

[2] "Extending the Quantum Coherence of a Near-Surface Qubit by Coherently Driving the Paramagnetic Surface Environment", Dolev Bluvstein, Zhiran Zhang, Claire A. McLellan, Nicolas R. Williams, Ania C. Bleszynski Jayich, https://arxiv.org/abs/ 1905.06405

[3] "Identifying and mitigating charge instabilities in shallow diamond nitrogen-vacancy centers”, D. Bluvstein, Z. Zhang, A. C. Bleszynski Jayich, Phys. Rev. Lett. 122, 076101 (2019)

There is currently much interest in studying quantum optical phenomena in solid state systems to realize large-scale quantum information processing applications. In addition to scalability, solid state systems can be intrinsically advantageous to atomic systems due to the vastly larger number of electrons and many-body interactions that lead to cooperative enhancement of quantum optical phenomena. One example is Dicke cooperativity, where a system of N dipoles coupled to an optical field experience an enhancement of light-matter coupling strength by a factor of N^1/2 [1]. Thus, solid state systems are particularly well-suited for studying exotic quantum optical phenomena that occur in regimes of light-matter coupling that are inaccessible to atomic systems, such as the ultrastrong coupling regime [2].

We recently demonstrated the extension of ultrastrong coupling to matter-matter coupling. Namely, we observed Dicke cooperativity between Er³⁺ electron paramagnetic resonance and a vacuum magnon field of Fe³⁺ spins in Y³⁺ doped ErFeO₃ samples, and the collectively enhanced coupling strength was in the ultrastrong coupling regime [3]. In this work, we further demonstrate matter-matter ultrastrong coupling between two magnon modes in YFeO₃. This rare earth orthoferrite is a canted antiferromagnet due to its two antiparallel spin sublattices slightly tilting towards each other, yielding a weak ferromagnetic moment. There are two distinct magnon modes in YFeO₃, referred to as the quasi-ferromagnetic (qFM) mode and the quasi-antiferromagnetic (qAFM) mode, corresponding to coherent spin precessions with terahertz (THz) frequencies. These magnons can be excited by magnetic dipolar interactions between the Fe³⁺ spins and a THz pulse, after which they precess at their Larmor frequency [4]. We studied the magnon frequency as a function of applied magnetic field strength and the direction of the magnetic field, i.e., the angle with respect to the weak ferromagnetic moment. When the applied magnetic field strength was tuned between 0 T and 30 T and the direction was not aligned with one of the crystallographic axes, anticrossing between the qFM and qAFM magnon frequencies was observed, demonstrating ultrastrong magnon-magnon coupling.

THz time-domain spectroscopy studies of YFeO₃ up to 30 T were performed using our tabletop pulsed magnet that uniquely marries strong magnetic fields and diverse optical spectroscopies [5]. We characterized magnons in YFeO₃ at different angles between the applied magnetic field and the weak ferromagnetic moment, which points along the c-axis. Specifically, we measured transmitted THz waveforms for five different samples of YFeO₃ cut such that the magnetic field was directed in the b-c plane and at an angle of 0, 20, 40, 60, and 90 degrees with respect to the c-axis. We observed clear anticrossing between the qFM and qAFM magnon frequencies as we tuned the magnetic field between 0 T and 30 T in samples with relative angles of 20, 40, and 60 degrees.

Using the Herrmann model, we calculated the qFM and qAFM magnon frequencies for our experimental geometry [6]. The applied magnetic field breaks the symmetries of the two modes, and the mixing of these modes causes anticrossing. We found excellent agreement between experimentally measured and calculated frequencies. Most importantly, the vacuum Rabi splitting was found to be a sizeable fraction of the resonance frequency, showing that the qFM and qAFM magnon-magnon coupling strength is in the ultrastrong coupling regime.

[1] R. H. Dicke, Phys. Rev. 93, 99 (1954).
[2] P. Forn-Diaz et al., Rev. Mod. Phys. 91, 025005 (2019).
[3] X. Li et al., Science 361, 794 (2018).
[4] Z. Jin et al., Phys. Rev. B 87, 094422 (2013).
[5] G. T. Noe II et al., Rev. Sci. Instr. 84, 123906 (2013).
[6] G. F. Herrmann, J. Phys. Chem. Solids 24, 597 (1963).

To build hybrid quantum interfaces based on magnons, it will be important to optimise the coupling strength to both optical and microwave fields. While magnons can be routinely coupled to microwave photons in a coherent way, there is still a long way to go to achieve similarly strong coupling in the optical domain. This is because the strength of magneto-optical interactions through the Faraday effect are typically very weak. In order to strengthen the magneto-optical interaction, the magnetic material can be embedded in a high quality-factor optical cavity. Such devices have been used to demonstrate that the scattering of optical photons with magnons can be significantly enhanced [1]. I will present our measurements on resonant magnon scattering in yttrium iron garnet, and discuss whether the limit of strong coupling can be achieved. In addition, optimizing the optical coupling requires reducing the volume of magnetic material. Although this is in conflict with the requirements for strong microwave coupling, we have shown the coupling strength can be maintained through the use of low-impedance microwave resonators [2].

[1] Selection rules for cavity-enhanced Brillouin light scattering from magnetostatic modes, J. A. Haigh, N. J. Lambert, S. Sharma, Y. M. Blanter, G. E. W. Bauer, and A. J. Ramsay, PRB 97, 214423 (2018).
[2] Low-impedance superconducting microwave resonators for strong coupling to small magnetic mode volumes, L. McKenzie-Sell, J. Xie, C.-M. Lee, J. W. A. Robinson, C. Ciccarelli, and J. A. Haigh, PRB 99, 140414 (2019).

Over the past few years, it has become possible to control the magnetic order of materials on timescales smaller than a picosecond, promising application in advanced data storage and data processing in spintronic devices. One ingredient is the coherent excitation of spin waves, which can be achieved by driving the spins with the magnetic or electric field components of an ultrashort light pulse. The basic interaction of light with a magnetic material is described by the opto-magnetic effects, of which the most prominent examples are the inverse Faraday and inverse Cotton-Mouton effects. There, the irradiated light acts as an effective magnetic field on the spins of the magnetic ions in the material, and coherent collective precession of the spins is induced via an impulsive stimulated Raman scattering mechanism [1,2].

Here, we present an alternative route of exciting coherent spin waves by coupling the magnetic degrees of freedom to the crystal lattice. We introduce the phenomenology of the analog magneto-phononic and phono-magnetic effects, in which coherently excited vibrational quanta take the place of the light quanta. Here, the coherent lattice vibrations couple to the magnetic order through the spin-phonon coupling, and the underlying mechanism is ionic Raman scattering, which had been proposed already half a century ago, and has only been demonstrated within this decade in the context of nonlinear phononics. The mechanism is less dissipative and reduces parasitic electronic effects compared to impulsive stimulated Raman scattering due to the lower energy of the excitation at mid-infrared wavelengths compared to visible light. Using density functional theory calculations in combination with phenomenological modeling for the paradigm antiferromagnet nickel oxide (NiO), we show that the phono-magnetic effects can potentially overcome the efficiency of the established opto-magnetic effects [3].

[1] Kalashnikova, Kimel, and Pisarev, Phys.-Usp. 58, 969 (2015)
[2] Nemec, Fiebig, Kampfrath, and Kimel, Nat. Photonics 14, 299 (2018)
[3] Juraschek, Stepanow, Narang, and Spaldin, in preparation

The solid-state maser, invented in the 1950s, had a much less impressive career than its younger sibling the laser, mainly due to its dependence on cryogenic refrigeration and high-vacuum systems. Despite this, masers found niche application in deep-space communications and radio astronomy due to their unparalleled performance as low-noise amplifiers and oscillators.

In 2012, the first room- temperature solid-state maser was demonstrated, employing an high-Q cavity coupled ensemble of inverted triplet states in photo-excited pentacene molecules doped into a p-terphenyl host [1].

Since then, this new class of maser has been dramatically miniaturized [2], characterized on nanosecond timescales [3] and shown to exhibit Rabi oscillations and normal-mode splitting, hallmarks of the strong-coupling regime of cavity quantum electrodynamics [4]. Unfortunately, the p-terphenyl host is volatile, has very poor thermal properties and unfavourable triplet sublevel decay rates – so that only pulsed operation lasting less than a millisecond has been observed to date. Alternative inorganic materials containing spin-polarizable defects such as diamond nitrogen-vacancy (NV) centres and [5,6] and vacancies in silicon carbide [7] have been proposed due to their slow spin-lattice relaxation and spin dephasing rates. These materials have the additional advantage of excellent thermal and mechanical properties.

In this talk I will discuss the development of the organic pentacene solid-state room-temperature maser and how the quest for continuous operation naturally led towards diamond and nitrogen-vacancy centres. I will report on the recently reported continuous-wave room-temperature maser based on optically pumped charged nitrogen-vacancy (NV) defect centres in diamond [8]. I will also discuss prospects for the macroscopic quantum (Dicke) states and multipartite entanglement supported by masers [4,9] and the immediate challenges

[1] M. Oxborrow, J. D. Breeze, N. Alford, Nature, 488, pp. 353–356 (2012)
[2] J. Breeze et al, Nature Communications, 6 (2015)
[3] E. Salvadori, J.D. Breeze et al, Scientific Reports, 7, 41836 (2017)
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[7] H. Kraus et al, Nature Physics, 10, pp. 157–162 (2014)
[8] J.D. Breeze et al, Nature, 555, pp. 493–496 (2018)
[9] R.-B. Liu, Nature News & Views, 555 (2018)

The study of quantum coherent magnonic interactions relies implicitly on the ability to excite and exploit long lived spin wave excitations in a magnetic material. That requirement has led to the nearly universal reliance on yttrium iron garnet (YIG), which for half a century has reigned as the unchallenged leader in high-Q, low-loss magnetic resonance, and more recently in the exploration of coherent quantum coupling between magnonic and spin or superconducting degrees of freedom. Surprisingly, the organic-based, ferrimagnetic coordination compound vanadium tetracyanoethylene (V[TCNE]_x~2) (T_c > 600 K) has recently emerged as a compelling alternative to YIG. Since V[TCNE]_x~2 is deposited via chemical vapor deposition (CVD) at 50° C, it can be conformally deposited on a wide variety of substrates with Q rivaling the very best YIG films, which must be grown epitaxially on GGG substrates at temperatures over 800° C. Recent studies on V[TCNE]_x~2 reveal ultra-low damping (α = 7.96 × 10^-5) in thin films, as well as the ability to pattern microstructures (via standard lithographic techniques) exhibiting high-Q resonances (Q ~ 8000) with narrow peak-to-peak FMR linewidths (0.5 Oe at 9.86 GHz), making V[TCNE]_x~2 an exciting candidate material for studying quantum coherent magnonic interactions. In that context, a deeper understanding of the magnonic properties of V[TCNE]_x~2 has the potential to substantially impact key applications in coherent magnonics. Here, we present experimental measurements of the longitudinal spin Seebeck effect (LSSE) in V[TCNE]_x~2 thin films, with spin Seebeck resistance (SSR) comparable to the very best YIG/Pt heterostructures. Further, these spin-thermal measurements provide insight into magnonic properties of V[TCNE]_x~2, such as the magnon density of states, magnon spin diffusion length, and magnon-phonon coupling. These properties are central to the design and fabrication of future generations of quantum coherent devices, and will help to guide the development of this emerging class of highly coherent magnetic materials.

The quantum regime of magnonics has been recently explored thanks to the strong and coherent interaction engineered between a superconducting qubit and the uniform magnetostatic mode, or Kittel mode, of a spherical ferrimagnetic crystal of yttrium iron garnet (YIG) [1-4]. With this architecture of quantum magnonics, single quanta of collective spin excitations, called magnons, have been resolved by using the qubit as a quantum sensor when the hybrid system reaches the strong dispersive regime [3, 4]. Here, we use this strong dispersive interaction to demonstrate novel protocols for quantum-enhanced sensing of magnons in a ferromagnetic crystal. First, we demonstrate a magnon detection sensitivity of about 10^-3 magnons/√Hz by using a simple quantum sensing protocol that relies on the dephasing of the qubit from the presence of magnons in the ferromagnetic crystal. In a second experiment, we entangle the Kittel mode with the qubit through a conditional excitation of the qubit, which we use to demonstrate the single shot detection of a single magnon with a detection efficiency of about 69%. This demonstration brings the equivalent of the single photon detector to the field of magnonics. Furthermore, using this conditional qubit excitation, we can perform tomography measurements of the vacuum and coherent states of the Kittel mode and thereby study the dynamics of magnons in the quantum regime. These measurements have enabled us to confirm the absence of a significant pure dephasing mechanism for the Kittel mode of YIG in the quantum regime. Finally, we discuss our progress towards preparing and characterizing quantum states of magnons, as well as our investigation regarding the origin of losses of the Kittel mode in the quantum regime [2, 5].

[1] Y. Tabuchi et al., Science 349, 405 (2015).
[2] Y. Tabuchi et al., Comptes Rendus Physique 17, 729 (2016).
[3] D. Lachance-Quirion et al., Science Advances 3, e1603150 (2017).
[4] D. Lachance-Quirion et al., Applied Physics Express, 12, 070101 (2019).
[5] Y. Tabuchi et al., Physical Review Letters 113, 083603 (2014).

Through the application of a rf magnetic field in ferrimagnetic materials it becomes possible to create magnetostatic spin waves [1,2]. These collective excitations have been recently getting attention due to their applicability in both devices and fundamental research, which stems from the their long spin lifetimes and absence of ohmic losses. In this work we obtain the magnetostatic resonant modes of a ferrimagnetic V[TCNE]_x≈2 disk [3] on top of a diamond substrate. Most importantly, we calculate analytically the spectrum, the fringe field and the magnetization obtained through the pinning condition at both top and bottom disk surfaces. In addition, we also perform the relaxation of the pinning condition and analyze its consequences in the spectrum, fringe fields and magnetization. We present our results for two different magnetic field directions: in plane and out of plane of the disk. The material is based on work supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under Award Number DE-SC0019250.


[1] R. W. Damon and J. R. Eshbach, J. Phys. Chem. Solids 19, 308 (1961).
[2] R. W. Damon and H. van de Vaart, Journal of Applied Physics 36, 11 (1965)
[3] Na Zhu, Xufeng Zhang, I. H. Froning, Michael E. Flatté, E. Johnston-Halperin and Hong X. Tang., Applied Physics Letters 109, 082402 (2016)

The ferromagnet yttrium iron garnet (YIG) has attracted a considerable attention for studying quantum magnonics for the advantages such as long spin lifetime [1], narrow ferromagnetic linewidth (FMR), low Gilbert damping constant [2] and high Q factor [3]. However, a specific superlattice substrate gadolinium gallium garnet (GGG) is required to fabricate high quality YIG thin films [4], preventing the broad application of YIG such as with silicon. Recent studies have revealed that an organic based ferrimagnet, V[TCNE]_x~2 is an excellent alternative to YIG. High quality V[TCNE]_x~2 can be grown on various flexible substrates such as glass, quartz and Si wafer using low temperature CVD [5]. This suggests that V[TCNE]_x~2 is an attractive magnonic media with the same advantages as YIG [6-8].
Here, we present the dispersion relations and linewidths of quasi one-dimensional and two-dimensional periodic magnonic crystals of V[TCNE]_x~2 calculated by using Landau-Lifshitz-Gilbert (LLG) formalism [9]. For the one-dimensional magnonic crystals, periodic layers of two alternating materials is studied. For the two-dimensional magnonic crystals, we considered infinitely long cylinders embedded in a host material forming a square lattice periodic structure. In both cases, V[TCNE]_x~2 combined with well known ferromagnets such as YIG and cobalt are considered. We focus on unit cells with a lattice constant of a=100nm in an external dipolar field of H₀μ₀=0.1T. Our results can be extended to investigate other properties of V[TCNE]_x~2 such as spin wave propagation and their applications.
We acknowledge support from NSF EFRI NewLAW under Award No. EFMA-1741666.

[1] E. G. Spencer, R. C. LeCraw, and R. C. Linares, Jr, Phys Rev. 123, 1937 (1961).
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[9] G. Sietsema, T. Liu, M. E. Flatté, SPIN, 7, 1740012 (2017).

Quantum teleportation is essential to the development of many aspects of quantum information science (QIS). Toward this goal, we demonstrate electron spin state teleportation in an ensemble of covalent organic donor-acceptor-stable radical (D-A-R^.) molecules. Following preparation of a specific electron spin state on R^. in a magnetic field using a microwave pulse, photoexcitation of A results in the formation of an entangled electron spin pair D^.+-A^.-. The spontaneous ultrafast chemical reaction D^.+-A^.--R^. -> D^.+-A-R^- constitutes the Bell state measurement step necessary to carry out spin state teleportation. Quantum state tomography of the R^. and D^.+ spin states using pulse electron paramagnetic resonance spectroscopy shows that the spin state of R^. is teleported to D^.+ with high fidelity. This result affords the possibility that chemical synthesis can create complex nanostructures for QIS applications.

On-chip integration of patterned, low-loss magnetic materials and magnon cavities into microwave devices and circuits presents many challenges due to the specific conditions that are required to grow ferrite materials, driving the need for flip-chip and other indirect fabrication techniques. The low-loss (α = (3.98±0.22)×10^-5), room-temperature ferrimagnetic coordination compound vanadium tetracyanoethylene (V[TCNE]_x) is a promising new material for these applications that is potentially compatible with semiconductor processing. Here we present the deposition, patterning, and characterization of V[TCNE]_x thin films with lateral dimensions ranging from 1 micron to several millimeters. We employ electron-beam lithography and liftoff using an aluminum encapsulated poly(methyl methacrylate), poly(methyl methacrylate-methacrylic acid) copolymer bilayer (PMMA/P(MMA-MAA)) on sapphire and silicon. This process can be trivially extended to other common semiconductor substrates. Films patterned via this method maintain low-loss characteristics down to 25 microns with only a factor of 2 increase down to 5 microns. A rich structure of thickness and radial confined spin wave modes reveals the quality of the patterned films. Further fitting, simulation, and analytic analysis providing an exchange constant, A_ex = (2.2±0.5)×10^-15 J/m, as well as insights into the mode character and surface spin pinning. Below a micron, the deposition is non-conformal which leads to interesting and potentially useful changes in morphology. This work establishes the versatility of V[TCNE]_x for applications requiring highly coherent magnetic excitations ranging from microwave communication to quantum information.

Noncollinear magnetic textures give rise to interesting charge and spin transport properties, and allow for control of magnetism using small electric currents. While these textures have been observed in a number of bulk materials and in thin films, realizing non-collinear magnetism in heterostructures presents new avenues to control their properties using tailored interfaces and gate electric fields. We have discovered noncollinear magnetism in superlattices comprised of two metallic perovskites, La₂/3Sr₁/3MnO₃ (LSMO) and LaNiO₃ (LNO). The superlattices are synthesized using oxide molecular beam epitaxy and characterized with a variety of means, including x-ray and neutron scattering. We find that the angle between the magnetization of the LSMO layers varies in an oscillatory manner with the thickness of the intervening LNO. We demonstrate a memory device in one such superlattice, where the magnetic state of the noncollinear magnetism is reversibly switched between different orientations using a small magnetic field and read out in real time using a combination of the anomalous Nernst effect and anisotropic magnetoresistance measurements. Finally, we discuss the growth and characterization of additional complex-oxide-based systems and devices, such as LaVO₃.

Iridates are of great importance to investigate the realization of exotic quantum phenomena generated by non-negligible spin-orbit coupling. The strontium-based iridates, with the perovskite structure and a valence band derived from the 5d orbitals of Ir, exhibit electronic and magnetic ground states resulting from the subtle interplay of spin-orbit coupling, electron-electron correlation and dimensionality. Therefore, they are highly susceptible to small changes in the relative strength of the different interactions. In the Ruddlesden-Popper series Sr_m+1Ir_mO_3m+1 (m=1,2, … ∞), the two-dimensional compounds, m = 1 and 2, present an antiferromagnetic (AF) Mott insulating ground state, with canted planar and out of plane AF orderings, respectively. Conversely, the three-dimensional SrIrO3 is semi-metallic, non-magnetic and shows non-trivial topological features. Here, based on a multi-fold approach relying on magneto-transport measurements and first-principles calculations, we demonstrate the reversible tuning of the magnetic and electric ground state of thin SrIrO₃ films by external electric fields. Ultra-thin epitaxial SrIrO3 films grown on SrTiO₃ exhibit thickness dependent metal-insulator and associated magnetic transitions. Its ground state evolves from a magnetic insulator, for 1 or 2 unit cell (u.c.), to a paramagnetic semi-metal, for n > 3 u.c. thicknesses. Moreover, for the thicker metal films, an electric field perpendicular to the film drives a metal-insulator and a simultaneous paramagnetic to weak ferromagnetic transition. We explore the transitions in ultra-thin layers of SrIrO₃, 3 < n < 8 u.c., by electric double layer techniques, which employ ionic liquid as gate dielectric, and prove that the metal-insulator and magnetic transitions are reversible. In addition, we show that the weak ferromagnetic behavior induced by the electric field arises from an underlying canted AF order within the basal plane. The orbital and spin moment canting rigidly tracks the staggered rotations of the IrO6 octahedra, which results in out-of-plane ferromagnetic spin components induced by the Dzyaloshinskii–Moriya interaction. We discuss the role of the orbital magnetism and Rashba spin-orbit interaction -due to the breaking of inversion symmetry- in the stabilization of the magnetic insulator state. The electric field, via the Rashba interaction, promotes a moment reorientation of the disordered paramagnetic state, which is at the root of the metal-insulator transition. This novel behavior is a consequence of the unique character of the semi-metallic SrIrO₃ ground state, it illustrates the exotic spin interactions in iridates and points to a new paradigm for device structures in which magnetic states are reversibly manipulated by electric fields.

This work was supported by the Spanish Ministerio de Ciencia e Innovación through MINECO/FEDER Grants MAT2015-66888-C3-1R and RTI2018-097895-B-C41.

Thermal expansion is an important consideration in many applied fields ranging from large-scale infrastructure building to high-precision instrumentation. Starting from the discovery of isotropic negative thermal expansion (NTE) in ZrW₂O₈ by Sleight, et al. in 1996 [1], NTE has been an intensely studied material phenomenon. For NTE, one, two, or all three dimensions of the material shrink with increasing temperature, which is counter to both our intuition and experience. NTE is believed to be connected with various origins, such as geometrical flexibility, ferroelectricity and magnetism [2]. Such connections then provide potential routes for controlling the thermal expansion utilizing NTE materials. Specifically concerning the superexchange driven NTE, increasing of atomic distances is beneficial for reducing the on-site Coulomb repulsion (through reducing, e.g. the p-d orbital overlapping) and therefore is potentially accounting for the expanding of lattice as T decreases (i.e. NTE). However, the lattice expansion in turn tends to reduce the magnetic coupling. Therefore, it brings in an outstanding question – how the interplay between superexchange interaction and lattice expansion proceeds as T decreases. Concerning the implication for tuning NTE of superexchange systems in general sense, it is important to resolve such a question. To this aim, we revisit the superexchange involved anisotropic NTE of CuO [3].

The negative thermal expansion (NTE) in CuO is explained via electron-transfer-driven superexchange interaction. The elusive connection between the spin-lattice coupling and NTE of CuO is investigated by neutron scattering and principal strain axes analysis. The density functional theory calculations show as the temperature decreases, the continuously increasing electron transfer accounts for enhancing the superexchange interaction along – the principal NTE direction. It is further rationalized that only when the interaction along is preferably enhanced to a certain level compared to the other competing antiferromagnetically exchange pathways can the corresponding NTE occur. Outcomes from this work have implications for controlling the thermal expansion through superexchange interaction, via, for example, optical manipulation, electrons or holes doping, etc.

References
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Heusler compounds have been predicted and experimentally shown to exhibit novel electronic and magnetic properties, such as half-metallic ferromagnetism, semiconducting and superconducting. The spin dependent transport across ferromagnet/semiconductor or ferromagnet/insulator interfaces depends critically on their structure and electronic properties, which include the semiconductor doping beneath the ferromagnetic contact, as well as the contact metallization. Interfacial reactions, the formation of non-magnetic interlayers, and conductivity mismatch have been attributed to low spin injection efficiency. In the case of epitaxial Fe₃Ga/GaAs(001) interfaces, the interface reconstruction was found to depend on the GaAs(001) surface reconstruction and the Fe₃Ga growth conditions. Co₂MnSi is predicted to be half-metallic and we have demonstrated record high spin accumulation at Co₂MnSi/GaAs(001) interfaces in lateral spin transport device structures and also investigated electronic structure tuning with Co₂(Mn,Fe)Si/GaAs(001) heterostructures. The variation in the spin polarization in the GaAs is consistent with the Fermi level increasing in the Co₂(Mn,Fe)Si films with the increase in the number of valence electrons per formula unit with the addition of Fe. This results in a sign change in the spin polarization between Co₂MnSi and Co₂FeSi contacts.
The magnetic damping and magnetoresistance were found to depend on the composition of Co_2-xMn_1+xSi films grown on MgO(001). Current-induced spin-orbit torque in Co₂FeAl/Pt ultrathin bilayers have been investigated as a function of temperature. By substituting Fe for Ti, the half-Heusler CoTiSb can be controllably tuned from a semiconductor to ferromagnetic metal. We have also demonstrated, by both angle-resolved photoemission and magnetotransport measurements, Fermi level tuning of topological PtLuSb by substituting Au for Pt, which results in control of the dominant carrier type and density.
Using a combination of molecular beam epitaxy and in-situ scanning tunneling microscopy and x-ray photoelectron spectroscopy, we have investigated the surface atomic structure, the interface formation and growth mechanisms. Ab-initio theory and ex-situ transmission electron microscopy studies corroborate the Heusler/semiconductor interfacial atomic structure.
In this presentation, I will discuss the molecular beam epitaxial growth and tuning of properties of Heusler compounds with emphasis for spintronic and hybrid quantum interfaces.

Antiferromagnets with zero net magnetic moment, strong anti-interference and ultrafast switching speed have potential competitiveness in high-density data storage. Electrical switching of antiferromagnets is at the heart of their device application [1,2]. The antidamping torque-induced switching of Néel order is attained in a biaxial antiferromagnetic insulator NiO and metal Mn₂Au, which is manifested electrically via spin Hall magnetoresistance in NiO/Pt bilayers [3] as well as a combination of anisotropic magnetoresistance and spin Hall magnetoresistance in Mn₂Au/Pt bilayers [4]. The antiferromagnetic moments are switched towards the current direction, different from the vertical configuration in the fieldlike torque scenario in a Mn₂Au single layer [5]. Electric field is used to switch the magnetic moment of Mn₂Au films grown on piezoelectric Pb(Mg_1/3Nb_2/3)_0.7Ti_0.3O₃ (PMN-PT) (011) substrates. When the electric field is swept, the easy axis of Mn₂Au is switched between [100] and [0 1] directions of PMN-PT (011) at room temperature, exhibiting a butterfly-like swithing feature. This feature indicates that the underlying mechanism is the electric field-induced ferroelastic strain. Such a transition of the easy axis leads to the change of threshold current for the field-like torque switching of Mn₂Au [6]. Recently, we also realize a bulk spin-orbit torque in ferrimagnetic CoTb, and provides a possible mechanism to explain this unusual phenomenon. Electrical switching of antiferromagnetic and ferrimagnetic moments pave the way for all-electrical writing and readout in antiferromagnetic spintronics.
I am grateful to the contribution by Prof. Yaroslav Tserkovnyak, Dr. Jia Zhang, Dr. Ran Cheng, Prof. Yonggang Zhao, and Dr. Wanjun Jiang.
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The global centrosymmetry plus broken sublattice inversion symmetry crystal structure of antiferromagnetic (AFM) Mn₂Au result in the Néel spin-orbit torque (NSOT) switching of its Néel vector direction. In this talk, I will present our recent progress on the spin-charge conversion and spin-orbit torques generated by Mn₂Au films, where its special crystal structure is strongly invovled. Current-induced spin-orbit torques generated by Mn₂Au was measured in Mn₂Au/Permalloy bilayers with the spin-torque ferromagnetic resonance (ST-FMR). Unlike the spin-charge conversion in generally used heavy metal/ferromagnetic metal and AFM/ferromagnetic metal bilayers, we find that besides a spin polarization along transverse direction (y-axis), in Mn₂Au films there is a spin polarization along the film normal direction (z-axis), which is perpendicular to the charge current (x-axis). The AFM Mn₂Au broken sublattice inversion symmetry crystal structure induced unusual spin polarization along the film normal direction and subsequent in-plane field-like torque. The film thickness and angular dependence of the spin polarization along z-axis are thoroughly investigated. Our observation adds a different dimension to spin-orbit torque.

The transition metal monopnictides TaAs, NbAs, TaP, and NbP have been well-studied in the past few years since they were first predicted and experimentally confirmed to be Weyl semimetals. Much work has been done in further characterization of these materials and probing of additional Weyl physics signatures, including studies of both linear and nonlinear optics. However, some of the microscopics of these systems relevant to designing complex device architectures utilizing the Weyl nodes' linear dispersion in the bulk of the crystal are still not fully understood. In this talk, we address the temperature dependence of the linear optical responses in TaAs and NbAs. We present the real and imaginary parts of an experimentally relevant complex dielectric function for these materials as functions of frequency, temperature, and polarization direction, incorporating scattering rates calculated from first principles. From these we also present linear optical conductivity predictions which agree well with experiment where experiment exists for TaAs. Finally, we examine the effect of chemical potential on the optical conductivity, which can be used to understand the role of the Weyl nodes in these optical responses.

[1] Garcia, C. A. C., Coulter, J. & Narang, P. (in preparation).
[2] Coulter, J., Osterhoudt, G. B., Garcia, C. A. C., Wang, Y., Plisson, V., Shen, B., Ni, N., Burch, K. S. & Narang, P. (2019). arXiv preprint arXiv:1903.07550.

Topological insulators, Weyl and Dirac semimetals and new Fermions are new quantum states of matter, which have attracted considerable interest from the condensed matter community. Heusler compounds are a remarkable class of materials which exhibit a wide range of extraordinary multi-functionalities including tunable topological insulators, half metallic ferromagnets and non collinear topological spin structures [1]. The required band inversion has already been unambiguously identified by angle-resolved photoemission (ARPES) and transport [2, 3]. Weyl and Dirac semimetals open up new research directions and applications that result from the large Berry phases that they exhibit: these lead to giant anomalous Hall effect (AHE), giant anomalous Nernst and spin Hall effects (SHE) and topological spin structures [4]. Examples discussed in the talk are Mn3Sn, Co3Sn2S2 and Co2MnGa. In the 2D limited we propose a Quantum anomalous Hall effect for Co3Sn2S2 [5, 6]. However the number of correlated materials with topological properties is limited. With Ta2Se8I a material with a competition between a Weyl semimetal and a charge density wave might open a new field “axion insulators” [7]

[1] Graf, et al., Progress in Solid State Chemistry 39 1 (2011)
[2] Liu, et al., Nature Communication 7, 12924 (2016)
[3] Belopolski, Manna, et al., Science accepted (2019) preprint arXiv:1712.09992
[4] Manna, et al., Nature Reviews Materials 3 (2018) 244 preprint arXiv:1802.02838v1
[5] Xu, et al., Physical Review B 97 (2018) 235416 preprint arXiv:1801.0013
[6] Liu, et al., Nature Physics 14 (2018) 1125 preprint arXiv:1712.06722
[7] Gooth, et al., arXiv:1906.04510

The optical properties of transition metal dichalcogenide (TMD) monolayers (MLs) are dominated by excitons, electron and hole pairs bound by Coulomb attraction [1]. In this talk we report recent results on linear and non-linear optical spectroscopy of these atomically thin semiconductors for applications in optoelectronics and spintronics. We discuss fundamental parameters such as the optical bandgap and the photoluminescence emission time and yield that can be tuned by changing the dielectric environment of the monolayers and using different substrate materials and heterostructure fabrication techniques [2,3]. We discuss the polarization dynamics of excitons and resident carriers in different TMD materials giving access to spin and valley physics, governed by very different physical processes in the case of excitons as compared to resident carriers [4].
[1] G. Wang et al, Reviews of Modern Physics 90 (2), 021001 (2018)
[2] M Goryca et al, arXiv:1904.03238
[3] H.H. Fang et al, arXiv:1902.00670
[4] M.M. Glazov et al, arXiv:1904.02674

Greater control of nuclear spin polarization could provide breakthroughs in both classical and quantum information storage and processing. In this talk, I will describe optical pump-probe techniques that generate and measure an electron spin polarization that persists over several laser pulse repetition periods in a gallium arsenide epilayer. Spins excited from successive laser pulses interfere, either constructively or destructively, depending on the Larmor spin precession frequency, which is determined by both the applied magnetic field and nuclear Overhauser field, and we demonstrate a dynamic nuclear polarization that actively responds to the external magnetic field sweep direction, sweep rate, and magnitude of transverse electron spin polarization [1]. We show that the electron-nuclear spin system retains memory of the external field history, including interruptions and reversals in magnetic field sweeps.
[1] “Observation of magnetic field sweep direction dependent dynamic nuclear polarization under periodic optical electron spin pumping,” M. Macmahon, J. R. Iafrate, M. J. Dominguez, and V. Sih, Phys. Rev. B 99, 075201 (2019).

Te₂ molecules in ZnSe form a quantum defect that offers advantageous characteristics, including a high optical uniformity due to its atomic nature and a strong optical dipole moment matching those from semiconductor nanostructures, for the development of efficient spin-photon interfaces for applications in quantum optics, communications and networks.
In this work, we demonstrate that excitons-polaritons generated in the ZnSe host material can be used to deterministically control the emission characteristics of excitons and trions bound to a single Te₂ molecule.
In particular, the emission efficiency is increased by two orders of magnitude, indicating a very efficient coupling between free excitons and Te2 bound states.
Scanning the free-exciton band with a narrow-frequency tunable laser over the free exciton spectral region reveals strong in-phase oscillations with a period of about 1 meV in the bound exciton emission intensity, emission energy, and emission linewidth. These modulations are explained by the strong coupling naturally occurring in ZnSe between photons and free-excitons, or exciton-polaritons.
This type of cooperative process whereby a host excitation is used to control the behavior of a single emitter has never been reported before. It allows deterministically controlling the emission properties and enables the development of new coherent control scheme, such as the rotation of spins without the need for an external magnetic field.

Te₂ molecules in ZnSe form an isoelectronic center capable of binding a single hole, an exciton, a positively charged exciton, or a biexciton. This defect offers two advantageous characteristics for the development of spin-photon interfaces for applications in quantum optics, communications and networks. It provides the optical uniformity of atomic defects composed of a few atoms, like NV or other color centers in diamond, and the remarkable optical dipole moments found in semiconductor nanostructure.

In this work, we perform resonant excitation on a single Te₂ molecule in ZnSe. Resonant excitation reveals the intrinsic absorption linewidth of exciton and trion states. It is found that the addition of ultra weak non-resonant above band gap excitation can be used to stabilize the environment by reducing charge fluctuations, thereby allowing the measurement of much narrower absorption linewidths. Resonant excitation also reveals the participation of several bulk phonons along with phonons that have been reported in ZnSe. They are associated with localized phonons bound to the Te₂ molecule. In addition, resonant excitation on single Te₂ molecules reveals exciton tunneling to a nearby Te2 molecule. Tunneling efficiency depends sensitively of the energetic separation, the respective orientation of the two molecules and the angular nature of the optical excited and detected exciton wavefunctions.
These results pave the way towards resonant fluorescence and quantum optics with atomic-sized defects in semiconductor materials.

The magnetic proximity effect (MPE)[1], which occurs due to the magnetic coupling within a few monolayers at the interface of two magnetically dissimilar layers, is effective in incorporating magnetic effects into nonmagnetic (NM) materials. In particular, the MPE at ferromagnetic (FM)/NM interfaces, where the NM layer is a material with strong spin-orbit coupling—typically a heavy metal, topological insulator, or two-dimensional electron gas (2DEG) with a strong Rashba effect—, has attracted much attention as promisingly open routes toward realizing Majorana fermions without using a strong magnetic field. However, the magnetic coupling at the FM/NM interface is typically a short range (~1 nm), which limits the strength of the MPE and hinders the ability of electrical gating of the effect.
Here, we show that the magnetic coupling range of MPE in a NM/FM bilayer can be dramatically enhanced, at least by two orders of magnitude, to several tens of nm on the NM side by using a semiconductor quantum well (QW) as the NM layer. The bilayers under study consist of InAs (thickness t = 15 - 40 nm)/(Ga,Fe)Sb (15 nm, 20% Fe) grown on AlSb buffer/semi-insulating GaAs (100) substrates by molecular beam epitaxy. This bilayer system has several unique properties that are particularly suitable for demonstrating MPE: i) (Ga,Fe)Sb is a p-type ferromagnetic semiconductor (FMS) with a high Curie temperature T_C (> 300 K)[2,3], while InAs QW is a typical Rashba 2DEG system with high electron mobility. ii) The lattice mismatch between InAs and (Ga,Fe)Sb is only ~0.1%; thus, high-quality heterostructures can be epitaxially grown. iii) InAs/(Ga,Fe)Sb is a type-III heterostructure, i.e., the conduction band bottom of InAs is lower than the valence band top of (Ga,Fe)Sb at the NM/FM interface, which enables large penetration of the electron wavefunction into the (Ga,Fe)Sb side. iv) The resistivity of the (Ga,Fe)Sb layer is two orders of magnitude higher than that of the InAs 2DEG, particularly at low temperature. Therefore, the electrical transport in these bilayers is dominated (> 99%) by the InAs 2DEG. We fabricate field-effect transistor structures on these InAs/(Ga,Fe)Sb bilayers, and measure magnetotransport properties using a standard four-terminal method.
We demonstrate that a new giant magnetoresistance (~80% at 14 T), which we call proximity magnetoresistance (PMR), is induced in the InAs 2DEG due to the MPE from the neighbouring (Ga,Fe)Sb layer. This PMR is two orders of magnitude larger, and its dependence on the magnetic field direction has a unique symmetry, which is different from the MR observed in other NM/FM bilayers reported to date. The PMR magnitude can be controlled over one order of magnitude by a gate voltage V_g. These results are explained by the penetration of the InAs 2DEG wavefunction into (Ga,Fe)Sb, which is effectively modulated by V_g. By fitting our modified Khosla-Fischer model to these PMR data, we find that a spontaneous spin splitting ΔE is induced in the InAs channel by the MPE from (Ga,Fe)Sb. The magnitude of ΔE is largely modulated from 0.17 to 3.8 meV when applying V_g between ± 3V. In principle, this gate-controlled spin splitting and the new PMR provide a mechanism to locally access Majorana fermions in InAs-based Josephson junctions[4], and introduce a new concept of magnetic-gating spin transistors in which the NM channel current is modulated by both electrical and magnetic means[5].

This work was partly supported by Grants-in-Aid for Scientific Research (Nos. 16H02095, 17H04922, 18H05345), the CREST Program (JPMJCR1777) of JST, Yazaki Foundation for Science & Technology, and Spin-RNJ.

References: [1] I. Zutic et al., Materials Today 22, 85-107 (2019). [2] N. T. Tu et al. Appl. Phys. Lett. 108, 192401 (2016). [3] S. Goel et al., Phys. Rev. Mater. 3, 084417 (2019). [4] J. D. Sau et al. Phys. Rev. Lett. 104, 040502 (2010). [5] K. Takiguchi, L. D. Anh et al., Nature Phys.(2019). https://doi.org/10.1038/s41567-019-0621-6

There is currently a great deal of interest in the research field of superconducting spintronics [1]. In particular, the generation of spin-polarised (triplet) Cooper-pairs is a central topic. Long-range transportation of triplet Cooper-pairs, compared to singlet Cooper-pairs within a neighbouring ferromagnet, has been measured in a number of magnetic Josephson junctions with spatially inhomogeneous magnetisation [1,2]. We have demonstrated generation of the triplet Cooper-pairs spin currents and detection by spin pumping experiments in Pt/Nb/NiFe samples [3]. The observed enhancement of spin relaxation (or Gilbert damping) in this case implies that when Nb turns superconducting, a spin channel opens allowing spin-pumped magnons in NiFe to be dissipated at the Pt sink layer. This is in stark contrast to the picture of singlet Cooper-pairs which are unable to carry away any angular momentum, leading to the reduction of Gilbert damping below Tc. A proposed driving mechanism is the interaction of the spin-orbit coupling in Pt and the magnetic exchange interaction through the Nb layer. In this presentation, we will show our study of applying the same measurement techniques to other material systems. Of particular interest is an Fe/Cr interface where spin-glass states are formed to generate spin misalignments [4]. We will describe how the Gilbert damping parameter behaves below and above Tc and the implications for spin transport through the Fe/Cr/Nb interfaces, in terms of the triplet Cooper-pair generation.

[1] J. Linder & J. W. A. Robinson, Nature Phys. 11, 307 (2015).
[2] R. S. Keizer et al., Nature 439, 825 (2006).
[3] K-R Jeon et. al., Nature Materials 17 499-503 (2018).
[4] J. W. A. Robinson et. al., Physical Review B 89, 104505 (2014).

Spin selectivity in a ferromagnet results from a difference in the density of up- and down-spin electrons at the Fermi energy as a consequence of which the scattering rates depend on the spin-orientation of electrons. This property is utilized in spintronics to control the flow of electrons by ferromagnets in a ferromagnet/normal metal/ferromagnet pseudo spin-valve.
The feasibility of superconducting spintronics depends on a spin-sensitivity of ferromagnets to the spin of equal-spin triplet Cooper pairs generated at superconductor(S)/ferromagnet(F) heterostructures with magnetic inhomogeneity at the S/F interface (1). In this talk we report Nb/Cr/Fe/Cu/Fe/Cr/Nb triplet Josephson junctions in which Cr/Fe interfaces act as triplet generators (2) and where the magnetization-alignment between the Fe layers controls the critical current (I_c). Furthermore, we will discuss equivalent junctions in which the central layer of Cu is substituted for a 10-40 nm thick layer of superconducting Nb; in these junctions we observe a suppression of I_c below the critical temperature of the central Nb layer indicating a blocking of triplet pairs by the Nb singlet density of states.
1. J. Linder & J. W. A. Robinson, Nature Physics 11, 307–315 (2015).
2. J. W. A. Robinson, N. Banerjee, M. G. Blamire, Phys. Rev. B 89, 104505 (2014).

The superconducting equivalent of giant magnetoresistanceinvolves placing a thin-film superconductor between two ferromagnetic layers.¹A change of magnetization-alignment in such a superconducting spin-valve from parallel (P) to antiparallel (AP) creates a positive shift in the superconducting transition temperature [ΔΤ_c=Τ_c(P)-Τ_c(AP)]due to an interplay of the magnetic exchange energy and the superconducting condensate. The magnitude of ΔΤ_cscales inversely with the superconductor thickness (d_S) and is zero when d_S exceeds the superconducting coherence length (ξ). In this talk I will discuss a superconducting spin-valve effect involving a different underlying mechanism in which magnetization-alignment and ΔΤ_care determined by the nodal quasiparticle-excitation states on the Fermi surface of the d-wave superconductor YBa₂Cu₃O_7-δ(YBCO) grown between the insulating ferromagnet Pr_0.8Ca_0.2MnO₃. We observe ΔΤ_cvalues of 2 K with ΔΤ_c oscillating with d_S over a length scale exceeding 100 ξand, for particular values of d_S, we find that the superconducting state reinforces an antiparallel magnetization-alignment. The rults pave the way for all-oxide superconducting memory² in which superconductivity modulates the magnetic state.

1. P. G. de Gennes, Phys. Lett.23, 10–11 (1966).
2. J Linder & JWA Robinson, Nature Physics11, 307–315 (2015)

The epitaxial integration of functional oxides on conventional semiconductors using advanced molecular beam epitaxy opens new opportunities for coupling their unique properties with semiconductors for post-CMOS computing paradigms. Here we explore spin-dependent phenomena in Permalloy-BaTiO₃-Germanium heterostructures and demonstrate an interesting correlation between charge transport and magneto-resistive response across the crystalline BaTiO₃-Germanium interface. In the quantum tunneling charge transport region, we observe Hanle and inverted Hanle effect with a full width at half maximum of ~100 mT. The single Hanle peak evolves into a superposition of two peaks with opposite polarity and distinct linewidth when impurity-assisted charge transport becomes dominant. Our result serves as a step towards understanding the origin of the magnetoresistance in oxide tunnel junctions.

It has been shown that the anomalous Hall effect can be observed in platinum films deposited on a ferromagnetic insulator which implies the existence of a magnetic proximity effect [1]. One of the key features of ferromagnetic metals is a net spin polarization of the carriers at the Fermi energy which enable the functionality of spintronic devices. In this presentation we show that spin polarized carriers are indeed present in Pt films of various thicknesses that were deposited on magnesium aluminum ferrite (MAFO) using point contact Andreev scattering [2]. The results were obtained by extracting conductance vs. voltage data from I-V curves taken through contacts formed by driving a sharpened superconducting Nb tip into the Pt/MAFO samples. The resulting spectra were then analysed using a modified BTK theory of supercurrent conversion at a normal/superconductor interface to obtain the values of the transport spin polarization.

The authors acknowledge the support of the Basic Research Office of the Assistant Secretary of Defense for Reserch and Engineering under the Laboratory University Collaboration Initiative (LUCI) andVannevar Bush Faculty Fellowship (funded by the Office of Naval Research through grant N00014-15-1-0045).

References
1. Z. Wang, C. Tang, R. Sachs, Y. Barlas, and J. Shi, Phys. Rev. Lett. 114, 016603 (2015).

2. R. J. Soulen, Jr., J. M. Byers. M. S. Osofsky, B. Nadgorny, T. Ambrose, S. F. Cheng, P. R. Broussard, C. T. Tanaka, J. Nowak, J. S. Moodera, A. Barry, and J. M. D. Coey, Science 282, 85 (1998).