Ordering of charge/spin/orbital degrees of freedom in complex materials accompanies domains and domain walls associated with the directional variants (Z_m) and also antiphases (Z_n). It has been recently realized that nontrivial Z_mxZ_n topology can exists in large-scale real-space configurations of domains and domains walls of complex materials. Furthermore, the vertices where domain walls merge can be considered as topological defects with well-defined vorticities (Z_l vortices). We will discuss the recently-discovered examples of Z_mxZ_n domains and Z_l vortices in complex materials.

I will discuss a recently proposed form of hidden order -- the magnetoelectric monopole -- and its relationship to a material's magnetoelectric response. Using density functional calculations for the Li transition metal phosphate series, LiMPO₄, with M = Mn, Fe, Co and Ni, I will show that materials with the same overall antiferromagnetic ordering can have distinct ferromonopolar or antiferromonopolar orderings, that lead to different, and in principle measureable, magnetoelectric responses. The current status and open questions in both the theoretical formalism and experimental verification will be outlined.
Monopole-based formalism for the diagonal magnetoelectric response, N. A. Spaldin, M. Fechner, E. Bousquet, A. Balatsky and L. Nordstrom, Phys. Rev. B 88, 094429 (2013).
Magnetic field generated by a charge in a uniaxial magnetoelectric material, M. Fechner, N. A. Spaldin and I. E. Dzyaloshinskii, Phys. Rev. B 89, 184415 (2014).

Room temperature multiferroics has been a frontier research field by manipulating spin-driven ferroelectricity or charge-order-driven magnetism. A new family of charge-transfer crystals based on electron donor and acceptor assembly - exhibiting simultaneous spin ordering - are drawing significant interests for the development of all-organic magnetoelectric multiferroics. Here, we report that a remarkable anisotropic magnetization and room temperature multiferroicity can be achieved through assembly of thiophene donor and fullerene acceptor. The crystal motif directs the dimensional and compositional control of charge-transfer networks that could switch magnetization under external stimuli, thereby opening up a new class of all-organic nanoferronics.

Layered perovskites are emerging as an interesting player in the field of multiferroicity and beyond. Several examples of exotic behavior have been predicted [1-4] in the family A_nB_nO_3n+2, which exhibits a natural internal stacking in blocks of n octahedra along a (110) direction.
The n=4 case is usually a band insulator, frequently ferroelectric by way of a unusual uncompensated-rotation mechanism; magnetic doping or substitution thus offers an opportunity for multiferroicity. We exemplify this case with a) the weak ferromagnet La₂Mn₂O₇, with its anomalously large linear magnetoelectric coupling [2], and b) V-doped La₂Ti₂O₇ [2,3], a ferroelectric ferromagnet exhibiting magnetization inversion upon polarization inversion - the quintessential magnetoelectric effect.
The n=5 material is a strongly anisotropic metal which seems to sustain a polarization in some cases. Our showcase is the first known native ferroelectric metal, Bi₅Ti₅O₁₇, a n=5 system, which exhibits coexisting metallicity and spontaneous polarization, as well as -with some tweaking via delta doping still being investigated- a depolarizing field in a finite system [1]. (we are considering the possibility that this material may possibly turn out to be an example of hyperferroelectric.)
Finally, the layered structural pattern naturally lends itself to the combination of, for example, n=4 and n=5 materials to form functional. We are currently exploring the relation and interaction of the various degrees of freedom in a n=4/n=5 superlattice where both constituents are polarized.
[1] A. Filippetti, V. Fiorentini, F. Ricci, P. Delugas, and J. Iniguez: Prediction of a native ferroelectric metal, submitted.
[2] M. Scarrozza, M. B. Maccioni, G. M. Lopez, and V. Fiorentini, Topological multiferroics, Phase Trans.88, doi:10.1080/01411594.2014.986731 (2015)
[3] M. Scarrozza, A. Filippetti, and V. Fiorentini: Ferromagnetism and orbital order in a topological ferroelectric, Phys. Rev. Lett. 109, 217202 (2012)
[4] M. B. Maccioni, A. Filippetti, V. Fiorentini, F. Ricci, and J. Iniguez: Multiply-polarized perovskite superlattices, in preparation

The functionality of any ferroic material depends on its domains. Consequently, their shape and manipulation in external fields are of major interest. In compounds uniting magnetic and electric order in the same phase, the magnetoelectric coupling on the level of the domains is, however, largely unexplored. For such so-called multiferroics it is therefore not known how exactly the electric or magnetic fields affect the multiferroic domains and their walls. In my talk I will discuss this issue and focus on the influence of the multiferroic order on the ferroelectric state and its domain walls. Examples will be: (i) multiferroics with geometric ferroelectricity like hexagonal YMnO₃ where topological requirements lead to domain walls with anisotropic conductance [1]; (ii) multiferroics with magnetically induced ferroelectricity like MnWO₄ or TbMnO₃ where the electric polarization within the wall is expected to rotate instead of passing through zero, as in conventional displacive ferroelectrics [2, 3]; (iii) multiferroics with strain-induced ferroelectricity like SrMnO₃ where the interplay of strain and oxygen vacancies leads to polar state in which domain walls act as insulating boundaries to the conducting domains [4].
[1] D. Meier et al., Nature Materials 11, 284 (2012)
[2] N. Leo et al., Nature Comm. 6, 6661 (2015)
[3] M. Matsubara, S. Manz et al., Science 348, 1112 (2015)
[4] C. Becher et al., Nature Nanotech. 10, DOI: 10.1038/NNANO.2015.108 (2015

In recent years, attempts towards electric-field control of magnetism has aroused significant interest in the field of spintronics dealing with various systems such as metals, diluted magnetic semiconductors, and multiferroics, because of its potential for future energy efficient electronic devices. In the case of magnetoelectric multiferroics, the electric-field control of magnetism has been demonstrated in various composite systems such as ferromagnetic(FM)/piezoelectric, FM/magnetoelectric, and FM/multiferroic heterostructures. Furthermore, the electric-field control of magnetic properties has also been demonstrated in several single-phase multiferroics. However, such a control can be realized only far below room temperature in most of single-phase multiferroics.
As for single-phase magnetoelectrics, only a few compounds (e.g., Cr₂O₃) exhibit magnetoelectric effects at room temperature. In 2010, however, it has been found that polycrystalline samples of Z-type hexaferrite Sr₃Co₂Fe₂₄O₄₁ showing a complex conical spiral magnetic structure exhibit a direct magnetoelectric (ME) effect, i.e., the change in electric polarization by a magnetic field, up to 400 K. More lately, it has been reported the converse ME effects, that is, the change in magnetization by applying an electric field, in single crystals of Z-type (Ba,Sr)₃Co₂Fe₂₄O₄₁ around room temperature. The microwave permeability changes due to the application of DC electric fields have also been observed in Sr₃Co₂Fe₂₄O₄₁ hexaferrite slabs at room temperature. Thus, the ME effect in single-phase magnetoelectrics is now going to the room-temperature operation. These results suggest a potential for electric-filed-control electronic devices using the converse ME effect in single-phase magnetoelectrics. In this presentation, we report on our recent activity to pursue single-phase room-temperature magnetoelectrics.
This work has been done in collaboration with K. Haruki, K. Okumura, A. Iyama, Y. Yoshimori, H. Ueda, K. Kimura, S. Hirose, and Y. Tanaka.

Perovskite type structured ferroelectric materials such as BaTiO₃ and Pb(Zr,Ti)O₃ are used for memory, sensor and various applications since they are found around 70 years ago. For good or but, these materials have been still used because of their superior ferroelectricity, piezoelectricity and their related multiferroic properties. Overcoming this situation, we suggest novel ferroelectric/ferrimagnetic ScFeO₃ which has GaFeO₃-type (ε-type) crystal structure classified as polar Pna2₁ space group. ε-ScFeO₃ epitaxial thin films were prepared on (111)SrTiO₃ single crystal substrates by pulsed laser deposition. Growth of metastable ε-ScFeO₃ phase was controlled by film preparation technique. Polarization-electric field loops were measured at room temperature using Pt/ε-ScFeO₃/SrRuO₃ capacitor structure. Saturation polarization of 5 mu;C/cm₂ was observed at 100 Hz. We also carried out first principle calculation for investigation of switching mechanism in GaFeO₃-type structure. Novel polarization switching system was considered through paraelectric phase with lower activation energy of 0.1-0.15 eV than that with reported value of 0.5 eV at Pnna phase. This result suggests that polarization switching should be occured by electric field. Magnetic and multiferroic properties of ε-ScFeO₃ will be discussed.

Multiferroic hexagonal manganites possess intriguing domain patterns and potential applications. The improper ferroelectrics YMnO₃ has six domain variants, which can cycle around vortex and antivortex cores, so called “topological defects”. The vortex, antivortex, and connections between them form two types of domain networks, type-I without and type-II with applied electric fields. Here we employ the phase-field method to investigate the vortex-antivortex evolution in type-I networks and the transition from type-I to type-II networks. The predictions are shown to have excellent agreements with experimental observations. It is found that type-I networks process log-normal statistical distributions (the logarithms of the variable is normally distributed), whereas Type-II shows scale-free power-law distributions with the exponent of ~2. A “proportionate growth” mechanism during the transition between two types of networks is shown to be responsible for the emergence of the scale-free network.

BiMnO3 is the only transition-metal perovskite oxide that is insulating and shows strong ferromagnetism in bulk. This distinctive behavior would make it a promising candidate as a magnetoelectric multiferroic if it was also a polar material, but experiments have shown that bulk BiMnO3 has either a very small polarization (below 0.1mu;C/cm2) or, most likely, that it is a paraelectric. There is also experimental evidence that the polarization in BiMnO3 films grown on SrTiO3 can be as high as 20mu;C/cm2. Despite the interest in these behaviors, the diagram of BiMnO3 as a function of epitaxial strain has remained largely unexplored. Here, we use first-principles to predict that, both under enough compressive and tensile epitaxial strain, BiMnO3 films are ferroelectric with a giant polarization around 100mu;C/cm2. The phases displayed by the films are similar to those experimentally found for BiFeO3 in similar conditions—at compressive strains, the film is supertetragonal with a large component of the polarization pointing out of plane, while at tensile strains the polarization points mostly in plane. As in BiFeO3 films, these phases are antiferromagnetic—the orbital ordering responsible for ferromagnetism in BiMnO3 is absent in the polar phases. Our calculations also show that the band gap of some of these BiMnO3 films is substantially smaller than gaps typically found in ferroelectric oxides, suggesting it may be a suitable material for photovoltaic applications.

In this work, HoCrO₃ and Fe substituted HoCrO₃ (HoCr_0.7Fe_0.3O₃) powders and thin films were synthesized via a solution route. The phase purity and structural properties were examined by Raman spectroscopy and Rietveld refinement of the x-ray diffraction data. The dc magnetic measurement indicates that the ordering temperatures of Cr³⁺ are 140 K and 174 K for HoCrO₃ and HoCr_0.7Fe_0.3O₃, respectively. By fitting the temperature dependent susceptibility data of the powder samples in the paramagnetic region with the Curie-Weiss fit, the effective magnetic moment were determined to be 11.67mu;_B and 11.30mu;_B for the HoCrO₃ and HoC