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This article presents a survey of many nontrivial effects connected with the coupling of electric and magnetic degrees of freedom in solids -- the field initiated by I.~E.~Dzyaloshinskii in 1959. I briefly consider the main physics of…
The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling $\theta$, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous…
The transport on top of a periodic two-dimensional hexagonal magnetic pattern of (i) a single macroscopic steel sphere, (ii) a doublet of wax/magnetite composite spheres, and (iii) an immiscible mixture of ferrofluid droplets with a…
The article describes a topological theory of quasiperiodic functions on the plane. The development of this theory was started (in different terminology) by the Moscow topology group in early 1980s. It was motivated by the needs of solid…
We extend the spherical tensorial formalism for polarization to the treatment of electric- and magnetic-multipole transitions of any order. We rely on the spherical-wave expansion to derive the tensor form of the operator describing the…
Recent Lorentz transmission electron microscopy experiments have revealed a variety of noncollinear spin textures including topological magnetisms such as skyrmions, biskyrmions and multiple skyrmions in thin-plate magnetic samples of e.g.,…
In this paper we predict that the magnetoelectric response of two-dimensional (2D) antiferromagnets is determined by the topology of the ground state. This topological magnetoelectric response, encoded in the spin magnetoelectric…
Magnetic topological semimetals (TSMs) are topological quantum materials with broken time-reversal symmetry (TRS) and isolated nodal points or lines near the Fermi level. Their topological properties would typically reveal from the…
Cupric oxide is multiferroic at unusual high temperatures. From density functional calculations we find that the low-T magnetic phase is paraelectric and the higher-T one ferroelectric, with a size and direction of polarization in good…
Based on our experimental and theoretical studies, we report the identification of the quaternary Heusler alloy, CoRuVSi as a new member of the recently discovered spin semimetals class. Spin polarised semimetals possess a unique band…
We conducted a high-throughput search for topological magnetic materials on 522 new, experimentally reported commensurate magnetic structures from MAGNDATA, doubling the number of available materials on the Topological Magnetic Materials…
Multifunctional materials can exhibit emergent behavior from the coupling of two or more different properties. For example, coupling between magnetic and ferroelectric order enables electrical control of the magnetic state, enabling for…
The occurence of spin-polarization at ZrO$_{2}$, Al$_{2}$O$_{3}$ and MgO surfaces is proved by means of \textit{ab-initio} calculations within the density functional theory. Large spin moments, as high as 1.56 $\mu_B$, develop at O-ended…
Materials with strongly correlated electrons exhibit physical properties that are often difficult to predict as they result from the interactions of large numbers of electrons combined with several quantum degrees of freedom. The layered…
The realization of multiferroicity in 2D nanomaterials is crucially important for designing advanced nanoelectronic devices such as non-volatile multistate data storage. In this work, the coexistence of ferromagnetism and ferroelectricity…
Topological semimetals exhibit band crossings near the Fermi energy, which are protected by the nontrivial topological character of the wave functions. In many cases, these topological band degeneracies give rise to exotic surface states…
We report observation of surface-defect-induced room temperature multiferroicity - surface ferromagnetism ($M_S$ at 50 kOe $\sim$0.005 emu/g), ferroelectricity ($P_R$ $\sim$2 nC/cm$^2$), and significantly large magnetoelectric coupling…
Binary ferroelectric nitrides are promising materials for information technologies and power electronics. However, polarization switching in these materials is highly unusual. From the structural perspective, polarization reversal is…
The past years have seen rapid progress in the classification of topological materials. These diagnostical methods are increasingly getting explored in the pertinent context of magnetic structures. We report on a general class of electronic…
The past decades have witnessed a transformation in characterizing condensed matter systems with topology. Aided by a refined understanding of topological band structures with crystalline symmetries that has emerged recently, many…