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The magnetic toroidal monopole, a time-reversal-odd scalar, has attracted attention through its characteristic responses, such as electric-field-induced nonreciprocal directional dichroism observed in Co$_2$SiO$_4$. However, its evaluation…
Working in the Wannier representation, we derive an expression for the orbital magnetization of a periodic insulator. The magnetization is shown to be comprised of two contributions, an obvious one associated with the internal circulation…
We present a thorough density functional theory study of the magneto-electric (ME) effect in Cr$_{2}$O$_{3}$. The spin-lattice ME tensor $\alpha$ was determined in the low-field and spin flop (SF) phases, using the method of dynamical…
Using first-principles calculations, we explore the magnetoelectric properties of the room-temperature multiferroic crystal BiCoO$_3$. We use both applied magnetic field and finite-difference techniques to show that BiCoO$_3$ is…
We present a phenomenological model for magnetoelectricity in multiferroic materials. The distinctive feature of the model is a two-component complex order parameter that encodes the electric polarization, along with a direct coupling…
The contribution of magnetoelectric effect to Landau--Lifshitz-Gilbert equation is considered in case when medium polarization is caused by parallel component of neighboring spins. The result is presented for ferromagnetic and…
The large spin orbit coupling in topological insulators results in helical spin-textured Dirac surface states that are attractive for topological spintronics. These states generate an efficient spin-orbit torque on proximal magnetic moments…
Electric field control of magnetism in solids, i.e. the converse magnetoelectricity, is highly desired for applications of scalable energy-efficient logic devices. However, it is not only a technical challenge but also a scientific paradox,…
Strongly correlated analogues of topological insulators have been explored in systems with purely on-site symmetries, such as time-reversal or charge conservation. Here, we use recently developed tensor network tools to study a quantum…
The exchange-driven contribution to the magnetoelectric susceptibility $\hat\alpha$ is formulated using a microscopic model Hamiltonian coupling the spin degrees of freedom to lattice displacements and electric field, which may be…
Topological boundary modes, a hallmark of quantum topological phases, remarkably occur in classical mechanical systems through an interesting correspondence with the quantum case. Here, we explore the Maxwell lattice frustrated Mott…
Condensed matter systems admit topological collective excitations above a trivial ground state, an example being Chern insulators formed by Dirac bosons with a gap at finite energies. However, in contrast to electrons, there is no…
We derive an exact expression for the orbital magnetization of electrons with short-range interactions (such as density-density interactions) in terms of exact zero-frequency response functions of the zero-field system. The result applies…
In this Book Chapter (invited) we briefly review the basic concepts defining topological insulators and focus on elaborating on the key experimental results that revealed and established their symmetry protected (SPT) topological nature. We…
We theoretically study the emergence of topological magnons in electron-magnon coupled systems. The magnon dispersion in a ferromagnet usually possesses an effective time reversal symmetry in the absence of Dzyaloshinskii-Moriya (DM)…
We present topological features of the magnetic response (orbital and spin) of a two-dimensional degenerate and non interacting electron gas due to inhomogeneous applied magnetic fields. These issues are analysed from the point of view of…
Fascinating phenomena have been known to arise from the Dirac theory of relativistic quantum mechanics, which describes high energy particles having linear dispersion relations. Electrons in solids usually have non-relativistic dispersion…
The interface between a topological insulator and a ferromagnetic insulator exhibits an interesting interplay of topological Dirac electrons and magnetism. As has been shown recently, the breaking of time-reversal invariance by magnetic…
Spin-orbit coupled materials have attracted revived prominent research interest as of late, especially due their direct connection with topological notions. Arguably, a hallmark of this pursuit is formed by the concept of the topological…
Magnetics, ferroelectrics and multiferroics have attracted great attentions because they are not only extremely important for investigating fundamental physics, but also have important applications in information technology. Here, recent…