Thermal Hall effect and topological edge states in a square-lattice antiferromagnet

Abstract

We show that the two dimensional spatial inversion-symmetry (SIS) broken square lattice antiferromagnet with easy-plane spin anisotropy exhibits a thermal Hall effect and the edge modes characterized by the Z2 topological invariant. These topological properties require a nonzero Berry curvature, and its origin is ascribed to the Dzyaloshinskii-Moriya (DM) interactions or the noncoplanar magnetic ordering generating a U(1) gauge field that couples to the kinetic motion of magnons. Although this picture is established in ferromagnets on the kagome and pyrochlore lattices, it does not apply to our square lattice model since such gauge field cancels out in an edge shared geometry. Instead, our case has an analogy with the anomalous Hall effect of Rashba electronic system where the spin orbit coupling generates an SU(2) gauge field. The two species of magnons defined on antiferromagnetic sublattices can be regarded as the pseudo-spin degrees of freedom of magnons. The DM interactions that emerge due to the SIS breaking serve as a pseudo-spin orbit coupling of magnons and generate a Berry curvature, when the direction of the magnetic moments is properly controlled by the magnetic field. The thermal Hall conductivity of our antiferromagnet shows rapid growth in temperature T beyond the power-law, reflecting the almost gapless low energy branch of the antiferromagnet, which distinctively differs from the T 7/2 -dependence in the pyrochlore ferromagnets. The present system serves as a standard model for the noncentrosymmetric crystals Ba2MnGe2O7 and Ba2CoGe2O7. arXiv:1805.05872v3 [cond-mat.mtrl-sci]

Excitation of magnon spin photocurrents in antiferromagnetic insulators

“…For illustration, we consider a two dimensional antiferromagnet where electromagnetic wave polarized in the x-direction is traveling along the y-direction with a wave number k. There are many possibilities of DMI configurations in a two-dimensional (2D) system, with some being summarized in Ref. 54. We describe these configurations by modifying the fist term in the Hamiltonian such that a phase term and effective interaction appear, J ij →J ij exp(iϕ ij ).…”

All‐Electrical Magnon Transport Experiments in Magnetically Ordered Insulators

“…There is a growing number of theoretical concepts already out exploiting this equivalent nature, predicting, for example, the existence of topological magnon states in AFIs or emergent spin-orbit coupling effects in magnon transport. [37,154,[163][164][165][166][167][168][169][170] First experiments on magnon transport via all-electrical means in AFIs were fully compatible with a simple diffusive magnon spin transport, where the injected spin orientation is maintained within the AFI. [71,[77][78][79] However, within the past year, new experiments emerged, which confirm the electronic transport analogy via the observation of the magnon Hanle effect in easy-plane AFIs.…”

“…It is also possible to combine these two different magnon modes and form linearly polarized magnon modes carrying zero spin. We can describe these pairs of magnons and their superpositions via a pseudospin [37,165,167,[169][170][171] quite similar to the spin of an electron (see Figure 6). In the description used here, the detected spin in our all-electrical magnon transport experiments corresponds to the z-component of the pseudospin.…”

Topological excitations in quasi two-dimensional quantum magnets with weak interlayer interactions

“…Quantum magnets are particularly promising since they have for long been a versatile platform to realise complex quantum states of matter including bosonic analogs of novel fermionic phases. The wide range of available quantum magnets with different lattice geometries and the ability to tune their properties readily by external magnetic field make them ideal testbed for realising bosonic analogs of topological states of matter [63,227,54,193,228,89,68,70,229,230,231,232,233,234 [1,87,88]. In this work, we have used experimentally determined Hamiltonian parameters [235] for the microscopic model that have been demonstrated to reproduce faithfully the experimentally observed behavior of the material [87].…”

“…The nature of DM-interaction chosen for the study(Fig To study low energy excitations (magnons) above the magnetic ground state, we have used the linearized HP transformation [63,67]. The HP transformation is a versatile and extensively used approach to study low energy magnons [192,193,63,54,180,67,173,71,68]. In this work, we have extended the HP approach to study magnon excitations above complex magnetic orders with longer periodicity.…”