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We address the theory of magnon-phonon interactions and compute the corresponding quasi-particle and transport lifetimes in magnetic insulators with focus on yttrium iron garnet at intermediate temperatures from anisotropy- and exchange-mediated magnon-phonon interactions, the latter being derived from the volume dependence of the Curie temperature. We find in general weak effects of phonon scattering on magnon transport and the Gilbert damping of the macrospin Kittel mode. The magnon transport lifetime differs from the quasi-particle lifetime at shorter wavelengths.
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Motivated by experimental observations, Samajdar et al. [Nature Physics 15, 1290 (2019)] have proposed that the insulating Neel state in the parent compounds of the cuprates is proximate to a quantum phase transition to a state in which Neel order coexists with semion topological order. We study the manner in which proximity to this transition can make the phonons chiral, by inducing a significant phonon Hall viscosity. We describe the spinon-phonon coupling in a lattice spinon model coupled to a strain field, and also using a general continuum theory constrained only by symmetry. We find a nonanalytic Hall viscosity across the transition, with a divergent second derivative at zero temperature.
The Phonon Hall Viscosity is the leading term evincing time-reversal symmetry breaking in the low energy description of lattice phonons. It may generate phonon Berry curvature, and can be observed experimentally through the acoustic Faraday effect and thermal Hall transport. We present a systematic procedure to obtain the phonon Hall viscosity induced by phonon-magnon interactions in magnetic insulators under an external magnetic field. We obtain a general symmetry criterion that leads to non-zero Faraday rotation and Hall conductivity, and clarify the interplay between lattice symmetry, spin-orbit-coupling, external magnetic field and magnetic ordering. The symmetry analysis is verified through a microscopic calculation. By constructing the general symmetry-allowed effective action that describes the spin dynamics and spin-lattice coupling, and then integrating out the spin fluctuations, the leading order time-reversal breaking term in the phonon effective action, i.e. the phonon Hall viscosity, can be obtained. The analysis of the square lattice antiferromagnet for a cuprate Mott insulator, Sr$_2$CuO$_2$Cl$_2$, is presented explicitly, and the procedure described here can be readily generalized to other magnetic insulators.
Motivated by the discovery of the quantum anomalous Hall effect in Cr-doped ce{(Bi,Sb)2Te3} thin films, we study the generic states for magnetic topological insulators and explore the physical properties for both magnetism and itinerant electrons. First-principles calculations are exploited to investigate the magnetic interactions between magnetic Co atoms adsorbed on the ce{Bi2Se3} (111) surface. Due to the absence of inversion symmetry on the surface, there are Dzyaloshinskii-Moriya-like twisted spin interactions between the local moments of Co ions. These nonferromagnetic interactions twist the collinear spin configuration of the ferromagnet and generate various magnetic orders beyond a simple ferromagnet. Among them, the spin spiral state generates alternating counterpropagating modes across each period of spin states, and the skyrmion lattice even supports a chiral mode around the core of each skyrmion. The skyrmion lattice opens a gap at the surface Dirac point, resulting in the anomalous Hall effect. These results may inspire further experimental investigation of magnetic topological insulators.
We theoretically investigate magnon-phonon hybrid excitations in two-dimensional ferromagnets. The bulk bands of hybrid excitations, which are referred to as magnon-polarons, are analytically shown to be topologically nontrivial, possessing finite Chern numbers. We also show that the Chern numbers of magnon-polaron bands and the number of band-crossing lines can be manipulated by an external magnetic field. For experiments, we propose to use the thermal Hall conductivity as a probe of the finite Berry curvatures of magnon-polarons. Our results show that a simple ferromagnet on a square lattice supports topologically nontrivial magnon-polarons, generalizing topological excitations in conventional magnetic systems.
Recently topological aspects of magnon band structure have attracted much interest, and especially, the Dirac magnons in Cu3TeO6 have been observed experimentally. In this work, we calculate the magnetic exchange interactions Js using the first-principles linear-response approach and find that these Js are short-range and negligible for the Cu-Cu atomic pair apart by longer than 7 Angstrom. Moreover there are only 5 sizable magnetic exchange interactions, and according to their signs and strengths, modest magnetic frustration is expected. Based on the obtained magnetic exchange couplings, we successfully reproduce the experimental spin-wave dispersions. The calculated neutron scattering cross section also agrees very well with the experiments. We also calculate Dzyaloshinskii-Moriya interactions (DMIs) and estimate the canting angle (about 1.3{deg}) of the magnetic non-collinearity based on the competition between DMIs and Js, which is consistent with the experiment. The small canting angle agrees with that the current experiments cannot distinguish the DMI induced nodal line from a Dirac point in the spin-wave spectrum. Finally we analytically prove that the sum rule conjectured in [Nat. Phys. 14, 1011 (2018)] holds but only up to the 11th nearest neighbour.
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