The discovery by Kane and Mele of a model of spinful electrons characterized by a Z_{2} topological invariant had a lasting effect on the study of electronic band structures. Given this, it is natural to ask whether similar topology can be found in the bandlike excitations of magnetic insulators. Time-reversal (TR) partner magnetic excitations can mimic the Kramers pairs of electrons in the Kane-Mele model but do not enjoy the same type of symmetry protection. Here, we revisit this problem in the context of the triplet excitations, which provide a faithful analog of the Kane-Mele model as long as the Hamiltonian preserves the TR×U(1) symmetry. The TR×U(1) symmetry can be thought of as a pseudo-time-reversal (PTR) symmetry that protects the Z_{2} band-topology of the triplets. We find that exchange anisotropies, typical in realistic models, break the required PTR symmetry and instantly destroy the Z_{2} band topology.

Phys. Rev. B 104, 104412 (2021)

arXiv:2012.11765

Excitations of ordered insulating magnets gain renewed interest due to their potential to realize the nontrivial topological properties discovered for weakly interacting electron systems. In this paper we go beyond these parallels and explore what else is there in the unconventional excitations of quantum magnets. We study the topologically nontrivial multiplet excitations of the antiferromagnetic spin- 1/2 kagome system with strong breathing anisotropy and Dzyaloshinskii-Moriya interaction. We show that in the chiral magnetic ground state the excitations can be characterized by a spin-1/2 doublet and a spin-3/2 quartet. With the use of magnetic field we can tune the quartet through a band touching topological phase transition, when a spin-3/2 Dirac cone is formed by the touching of four bands. In the topologically nontrivial regime the spin-3/2 bands have large Chern numbers −3, −1, 1, 3. In an open system the emerging chiral edge states naturally inherit the multipolar characters and we find novel quadrupolar edge modes.

Phys. Rev. B 99, 014408 (2019)

arXiv:1801.07950

The ultimate goal of multiferroic research is to develop new-generation nonvolatile memory devices, where magnetic bits are controlled via electric fields with low energy consumption. Here, we demonstrate the optical identification of antiferromagnetic magnetoelectric (ME) domains in LiCoPO_{4} based on the strong absorption difference of the domains. The unusual contrast in absorption is attributed to the dynamic ME effect of the spin-wave excitations. In agreement with the results of the THz spectroscopy experiments, two ME excitations were found characterized by oscillating magnetization and polarization. While the spin components precess in the same direction, there is a π phase shift between the polarization oscillations in the two different domains. This sign change in dynamic polarization is the microscopic origin of the directional anisotropy in LiCoPO_{4}, offering a route to optical distinguishing between the ME domains. The control and the optical readout of AFM/ME domains, demonstrated here, will likely promote the development of ME and spintronic devices based on AFM insulators.

Phys. Rev. Lett. 121, 057601 (2018)

arXiv:1711.08124

Exotic spin-multipolar ordering in spin transition metal insulators has so far eluded unambiguous experimental observation.
A less studied, but perhaps more feasible fingerprint of multipole character emerges in the excitation spectrum in the form of quadrupolar transitions.
Such multipolar excitations are desirable as they can be manipulated with the use of light or electric field and can be captured by means of conventional experimental techniques.
Here we study single crystals of multiferroic Sr_{2}CoGe_{2}O_{7}, and observe a two-magnon spin excitation appearing above the saturation magnetic field in electron spin resonance (ESR) spectra.
Our analysis of the selection rules reveals that this spin excitation mode does not couple to the magnetic component of the light, but it is excited by the electric field only, in full agreement with the theoretical calculations.
Due to the nearly isotropic nature of Sr_{2}CoGe_{2}O_{7}, we identify this excitation as a purely spin-quadrupolar two-magnon mode.

Phys. Rev. B 96, 214406 (2017)

arXiv:1702.04158

We formulate and study a spin-orbital model for a family of cubic double perovskites with d^{1} ions occupying a frustrated fcc sublattice. A variational approach and a complementary analytical analysis reveal a rich variety of phases emerging from the interplay of Hund’s rule and spin-orbit coupling. The phase digram includes noncollinear ordered states, with or without a net moment, and, remarkably, a large window of a nonmagnetic disordered spin-orbit dimer phase. The present theory uncovers the physical origin of the unusual amorphous valence bond state experimentally suggested for Ba_{2}*B*MoO_{6}(*B*=Y, Lu) and predicts possible ordered patterns in Ba_{2}*B*OsO_{6}(*B*=Na, Li) compounds.

Phys. Rev. Lett. 118, 217202 (2017)

arXiv:1611.00646

Complex low-temperature-ordered states in chiral magnets are typically governed by a competition between multiple magnetic interactions. The chiral-lattice multiferroic Cu_{2}OSeO_{3} became the first insulating helimagnetic material in which a long-range order of topologically stable spin vortices known as skyrmions was established. Here we employ state-of-the-art inelastic neutron scattering to comprehend the full three-dimensional spin-excitation spectrum of Cu_{2}OSeO_{3} over a broad range of energies. Distinct types of high- and low-energy dispersive magnon modes separated by an extensive energy gap are observed in excellent agreement with the previously suggested microscopic theory based on a model of entangled Cu4 tetrahedra. The comparison of our neutron spectroscopy data with model spin-dynamical calculations based on these theoretical proposals enables an accurate quantitative verification of the fundamental magnetic interactions in Cu_{2}OSeO_{3} that are essential for understanding its abundant low-temperature magnetically ordered phases.

Nat. Commun. 7, Article number: 10725 (2016)

arXiv:1509.02432

A promising route to tailoring the electronic properties of quantum materials and devices rests on the idea of orbital engineering in multilayered oxide heterostructures. Here we show that the interplay of interlayer charge imbalance and ligand distortions provides a knob for tuning the sequence of electronic levels even in intrinsically stacked oxides. We resolve in this regard the d-level structure of layered Sr_{2}IrO_{4} by electron spin resonance. While canonical ligand-field theory predicts g_{||}-factors less than 2 for positive tetragonal distortions as present in Sr_{2}IrO_{4}, the experiment indicates g_{||} is greater than 2. This implies that the iridium d levels are inverted with respect to their normal ordering. State-of-the-art electronic-structure calculations confirm the level switching in Sr_{2}IrO_{4}, whereas we find them in Ba_{2}IrO_{4} to be instead normally ordered. Given the nonpolar character of the metal-oxygen layers, our findings highlight the tetravalent transition-metal 214 oxides as ideal platforms to explore d-orbital reconstruction in the context of oxide electronics.

Nat. Commun. 6, Article number: 7306 (2015)

arXiv:1604.07780

We theoretically study coherent subharmonic (multiphoton) transitions of a harmonically driven spin. We consider two cases: magnetic resonance (MR) with a misaligned, i.e., nontransversal, driving field, and electrically driven spin resonance (EDSR) of an electron confined in a one-dimensional, parabolic quantum dot, subject to Rashba spin-orbit interaction. In the EDSR case, we focus on the limit where the orbital level spacing of the quantum dot is the greatest energy scale. Then, we apply time-dependent Schrieffer-Wolff perturbation theory to derive a time-dependent effective two-level Hamiltonian, allowing us to describe both MR and EDSR using the Floquet theory of periodically driven two-level systems. In particular, we characterize the fundamental (single-photon) and the half-harmonic (two-photon) spin transitions. We demonstrate the appearance of two-photon Rabi oscillations, and analytically calculate the fundamental and half-harmonic resonance frequencies and the corresponding Rabi frequencies. For EDSR, we find that both the fundamental and the half-harmonic resonance frequencies change upon increasing the strength of the driving electric field, which is an effect analogous to the Bloch-Siegert shift known from MR. Remarkably, the drive-strength-dependent correction to the fundamental EDSR resonance frequency has an anomalous, negative sign, in contrast to the corresponding Bloch-Siegert shift in MR which is always positive. Our analytical results are supported by numerical simulations, as well as by qualitative interpretations for simple limiting cases.

Phys. Rev. B 92, 054422 (2015)

arXiv:1504.06081

SrCu_{2}(BO_{3})_{2} is the archetypal quantum magnet with a gapped dimer-singlet ground state and triplon excitations. It serves as an excellent realization of the Shastry–Sutherland model, up to small anisotropies arising from Dzyaloshinskii–Moriya interactions. Here we demonstrate that these anisotropies, in fact, give rise to topological character in the triplon band structure. The triplons form a new kind of Dirac cone with three bands touching at a single point, a spin-1 generalization of graphene. An applied magnetic field opens band gaps resulting in topological bands with Chern numbers +/-2. SrCu_{2}(BO_{3})_{2} thus provides a magnetic analogue of the integer quantum Hall effect and supports topologically protected edge modes. At a threshold value of the magnetic field set by the Dzyaloshinskii–Moriya interactions, the three triplon bands touch once again in a spin-1 Dirac cone, and lose their topological character. We predict a strong thermal Hall signature in the topological regime.

Nat. Commun. 6, Article number: 6805 (2015)

arXiv:1406.1163

The recent discovery of skyrmions in Cu_{2}OSeO_{3} has established a new platform to create and manipulate skyrmionic spin textures. We use high-field electron spin resonance with a terahertz free-electron laser and pulsed magnetic fields up to 64 T to probe and quantify its microscopic spin-spin interactions. In addition to the previously observed long-wavelength Goldstone mode, this technique probes also the high-energy part of the excitation spectrum which is inaccessible by standard low- frequency electron spin resonance. Fitting the behavior of the observed modes in magnetic field to a theoretical framework establishes experimentally that the fundamental magnetic building blocks of this Skyrmionic magnet are rigid, highly entangled and weakly coupled tetrahedra.

Phys. Rev. Lett. 113, 157205 (2014)

arXiv:1404.7319

We studied spin excitations in the magnetically ordered phase of the noncentrosymmetric Ba_{2}CoGe_{2}O_{7} in high magnetic fields up to 33 T. In the electron spin resonance and far infrared absorption spectra we found several spin excitations beyond the two conventional magnon modes expected for such a two- sublattice antiferromagnet. We show that a multiboson spin-wave theory describes these unconventional modes, including spin-stretching modes, characterized by an oscillating magnetic dipole and quadrupole moment. The lack of inversion symmetry allows each mode to become electric dipole active. We expect that the spin-stretching modes can be generally observed in inelastic neutron scattering and light absorption experiments in a broad class of ordered S > 1/2 spin systems with strong single-ion anisotropy and/or noncentrosymmetric lattice structure.

Phys. Rev. Lett. 108, 257203 (2012)

arXiv:1202.3996

We investigate the spin induced polarization in the multiferroic compound Ba_{2}CoGe_{2}O_{7} using variational and finite-temperature mean field approaches, with the aim to reproduce the peculiar behavior of the induced polarization in a magnetic field observed experimentally in Murakawa et al. The compound is usually described by a spin-3/2 Heisenberg model extended with easy-plane anisotropy and Dzyaloshinskii-Moriya (DM) interaction. By applying a magnetic field parallel to the [110] axis, three phases can be distinguished in this model: (i) At high magnetic field, we find a partially magnetized phase with spins parallel to the fields and uniform polarization. (ii) Below a critical field, the ground state is a twofold-degenerate canted antiferromagnet, where the degeneracy can be lifted by a finite DM interaction. (iii) At zero field, a U(1) symmetry-breaking phase takes place, exhibiting a Goldstone mode. We find that extending the Hamiltonian with an antiferroelectric term results in the appearance of a canted ferrimagnetic phase for h~1 T. This phase is characterized by a finite staggered polarization, as well as by a magnetization closing a finite angle with the applied field leading to torque anomalies.

Phys. Rev. B 84, 224419 (2011)

arXiv:1110.0788

We consider effect of exchange and easy- plane anisotropies on the formation of magnetization plateaus and supersolid phases in spin-3/2 system on unfrustrated bipartite lattices. In the Ising limit, when the off-diagonal exchange interaction J is zero, the phase diagram in magnetic field is characterized by magnetization plateaus that are either translationally invariant or have a two-sublattice order, with phase boundaries that are macroscopically degenerate. We showed that when the off-diagonal exchange interaction J becomes finite this degeneracy is lifted and new gapless superfluid and supersolid phases emerge. All the plateaus continuously evolve from the Ising limit, and the degeneracy of the boundaries in the Ising limit gives a hint on the order of the phase transition and on the nature of the gapless state. Not surprisingly, our variational calculation shows that the supersolid phases are concentrated around the plateaus that break the translational symmetry. The variational approach is complemented by a density matrix renormalization group study of a one-dimensional chain and exact diagonalization on small clusters of a square lattice. The studied model may serve as a minimal model for Ba_{2}CoGe_{2}O_{7}, and we believe that the vicinity of the uniform 1/3 plateau in the model parameter space can be observed as an anomaly in the measured magnetization curve.

Phys. Rev. B 84, 184427 (2011)

arXiv:1109.4078

We studied the magnetic properties of SrCu_{2}(BO_{3})_{2} based on the Shastry–Sutherland model extended with anisotropies. The possible form of the anisotropies, such as the Dzyaloshinskii-Miriya (DM) interactions and the g-tensor anisotropy, follow from the symmetry properties of the material.
We used a bond-factorized form of the variational wave function to study the effect of the anisotropies on the ground-state properties in phases that are compatible with the crystallographic unit cell comprising two orthogonal dimers in the presence of an external magnetic field.
We have found that in the less symmetrical, low-temperature structure of SrCu_{2}(BO_{3})_{2}, the finite intra-dimer DM interaction gives rise to an admixture of triplet and the singlet states changing the dimer singlet phase.
To study the effect of anisotropies on excitation spectra we developed a bond-wave formalism based on the bosons representing the entangled states of the dimers. With this approach we recovered the experimentally measured electron spin resonance spectra for a physically reasonable set of parameters.

Phys. Rev. B 83, 024413 (2011)
arXiv:1010.4476