Magnon Thermal Hall Effect Research Articles

Intrinsic second-order magnon thermal Hall effect

In this paper, we study the intrinsic contribution of nonlinear magnon thermal Hall Effect. We derive the intrinsic second-order thermal Hall conductivity of magnon by the thermal scalar potential method and the thermal vector potential method. We find that the intrinsic second-order magnon thermal Hall conductivity is related to the thermal Berry-connection polarizability. We apply our theory to the monolayer ferromagnetic Hexagonal lattice, and we find that the second-order magnon thermal Hall conductivity can be controlled by changing Dzyaloshinskii–Moriya strength and applying strain.

Topological band engineering and tunable thermal Hall effect in trimerized Lieb lattice ferromagnets

We theoretically study the topological properties of magnons and the relevant magnon thermal Hall effect in trimerized Lieb lattice ferromagnets in the presence of next-nearest-neighbor Dzyaloshinskii-Moriya interactions. By calculating the magnon band structures and their Chern numbers with the linear spin-wave theory, we show that the system can undergo a phase transition between a magnonic topological insulator phase and a magnonic trivial insulator phase. The main results are presented in the form of topological phase diagrams, where the Chern numbers or magnon thermal Hall conductivity are shown as a function of the two lattice trimerization parameters. We find a sharp change of the thermal Hall conductivity across the critical point of phase transformations associated with topological nontrivial edge states. The behaviors reflect that the existence of trimerizations breaks the C4 rotational symmetry of the Lieb lattice. Finally, we show that our theoretical predictions could be experimentally realized in high-temperature cuprate superconductors or organic magnetic materials. Published by the American Physical Society 2024

Tuning bulk topological magnon properties with light-induced magnons

Although theoretical modeling and inelastic neutron scattering measurements have indicated the presence of topological magnon bands in multiple quantum magnets, experiments remain unable to detect a signal of the magnon thermal Hall effect in the quantum magnets, which is a consequence of magnons condensation at the bottom of the bands following Bose-Einstein statistics as well as the concentration of Berry curvature at the higher energies. In recent work, Malz et al. [Nat. Commun. 10, 3937 (2019)] have shown that topological magnons in edge states in a finite sample can be amplified using tailored electromagnetic fields. We extend their approach by showing that a uniform electromagnetic field can selectively amplify magnons with finite Berry curvature by breaking the inversion symmetry of a lattice. Using this approach, we demonstrate the generation of bulk topological magnons in a Heisenberg ferromagnet on the breathing kagome lattice and the consequent amplification of the thermal Hall effect.

Intrinsic magnon Nernst effect in pyrochlore iridate thin films

We theoretically study the magnon spin thermal transport using a strong coupling approach in pyrochlore iridate trilayer thin films grown along the [111] direction. As a result of the Dzyaloshinskii-Moriya interaction (DMI), the spin configuration of the ground state is an all-in/all-out ordering on neighboring tetrahedra of the pyrochlore lattice. In such a state, the system has an inversion symmetry and a Nernst-type thermal spin current response is well defined. We calculate the temperature dependence of the magnon Nernst response with respect to the magnon band topology controlled by the spin-orbit coupling parameters and observe topologically protected chiral edge modes over a range of parameters. Our study complements prior work on the magnon thermal Hall effect in thin-film pyrochlore iridates and suggests that the [111] grown thin-film pyrochlore iridates are a promising candidate for thermal spin transport and spin caloritronic devices.

Topological Weyl magnons and thermal Hall effect in layered honeycomb ferromagnets

In this work, we study the topological properties and magnon Hall effect of a three-dimensional ferromagnet in the ABC stacking honeycomb lattice, motivated by the recent inelastic neutron scattering study of $\mathrm{Cr}{\mathrm{I}}_{3}$. We show that the magnon band structure and Chern numbers of the magnon branches are significantly affected by the interlayer coupling ${J}_{c}$, which moreover has a qualitatively different effect in the ABC stacking compared to the AA stacking adopted by other authors. The nontrivial Chern number of the lowest magnon band is stabilized by the next-nearest-neighbor Dzyaloshinskii-Moriya interaction in each honeycomb layer, resulting in the hopping term similar to that in the electronic Haldane model for graphene. However, we also find several gapless Weyl points, separating the nonequivalent Chern insulating phases, tuned by the ratio of the interlayer coupling ${J}_{c}$ and the third-neighbor Heisenberg interaction ${J}_{3}$. We further show that the topological character of magnon bands results in nonzero thermal Hall conductivity, whose sign and magnitude depend on ${J}_{c}$ and the intralayer couplings. Since the interlayer coupling strength ${J}_{c}$ can be easily tuned by applying pressure to the quasi-2D material such as $\mathrm{Cr}{\mathrm{I}}_{3}$, this provides a potential route to tuning the magnon thermal Hall effect in an experiment.

Thermal Hall effect from a two-dimensional Schwinger boson gas with Rashba spin-orbit interaction: Application to ferromagnets with in-plane Dzyaloshinskii-Moriya interaction

Recently, uncovering the sources of thermal Hall effect in insulators has become an important issue. In the case of ferromagnetic insulators, it is well known that Dzyaloshinskii-Moriya (DM) interaction can induce magnon thermal Hall effect. Specifically, the DM vector parallel to the magnetization direction induces complex magnon hopping amplitudes, so that magnons act as if they feel Lorentz force. However, the DM vector which is orthogonal to the magnetization direction has hitherto been neglected as a possible source of magnon thermal Hall effect. This is because they play no role in the linear spin wave theory, an often invoked approximation when computing the magnon thermal Hall effect. Here, we challenge this expectation by presenting the self-consistent Schwinger-boson mean field study of two-dimensional magnets with ferromagnetic Heisenberg interaction and in-plane DM interaction. We find that the relevant Schwinger-boson mean field Hamiltonian takes the form of two-dimensional electron gas with Rashba spin-orbit interaction, which is known to show anomalous Hall effect, spin Hall effect, and Rashba-Edelstein effect, whose thermal counterparts also appear in our system. Importantly, the thermal Hall effect can be induced when out-of-plane magnetic field is applied, and persists even when the magnetic field is large, so that the spins are significantly polarized, and the linear spin wave theory is expected to be a reasonable approximation. Since the linear spin wave theory predicts vanishing thermal Hall effect, our result implies that linear spin wave is not a sufficient approximation, and that magnon-magnon interaction must be taken into account to predict the correct thermal Hall conductivity.

Non-Hermiticity and topological invariants of magnon Bogoliubov–de Gennes systems

Abstract Since the theoretical prediction and experimental observation of the magnon thermal Hall effect, a variety of novel phenomena that may occur in magnonic systems have been proposed. We review recent advances in the study of topological phases of magnon Bogoliubov–de Gennes (BdG) systems. After giving an overview of previous works on electronic topological insulators and the magnon thermal Hall effect, we provide the necessary background for bosonic BdG systems, with particular emphasis on their non-Hermiticity arising from the diagonalization of the BdG Hamiltonian. We then introduce definitions of $$ \mathbb{Z}_2 $$ topological invariants for bosonic systems with pseudo-time-reversal symmetry, which ensures the existence of bosonic counterparts of “Kramers pairs.” Because of the intrinsic non-Hermiticity of bosonic BdG systems, these topological invariants have to be defined in terms of the bosonic Berry connection and curvature. We then introduce theoretical models that can be thought of as magnonic analogs of two- and three-dimensional topological insulators in class AII. We demonstrate analytically and numerically that the $$ \mathbb{Z}_2 $$ topological invariants precisely characterize the presence of gapless edge/surface states. We also predict that bilayer CrI$$_3$$ with a particular stacking would be an ideal candidate for the realization of a two-dimensional magnon system characterized by a nontrivial $$ \mathbb{Z}_2 $$ topological invariant. For three-dimensional topological magnon systems, the magnon thermal Hall effect is expected to occur when a magnetic field is applied to the surface.

Magnon valley Hall effect in CrI3 -based van der Waals heterostructures

Magnonic excitations in the two-dimensional (2D) van der Waals (vdW) ferromagnet CrI3 are studied. We find that bulk magnons exhibit a non-trivial topological band structure without the need for Dzyaloshinskii-Moriya (DM) interaction. This is shown in vdW heterostructures, consisting of single-layer CrI3 on top of different 2D materials as MoTe2, HfS2 and WSe2. We find numerically that the proposed substrates modify substantially the out-of-plane magnetic anisotropy on each sublattice of the CrI3 subsystem. The induced staggered anisotropy, combined with a proper band inversion, leads to the opening of a topological gap of the magnon spectrum. Since the gap is opened non-symmetrically at the K+ and K- points of the Brillouin zone, an imbalance in the magnon population between these two valleys can be created under a driving force. This phenomenon is in close analogy to the so-called valley Hall effect (VHE), and thus termed as magnon valley Hall effect (MVHE). In linear response to a temperature gradient we quantify this effect by the evaluation of the temperature-dependence of the magnon thermal Hall effect. These findings open a different avenue by adding the valley degrees of freedom besides the spin, in the study of magnons.

Asymmetric ferromagnetic criticality in pyrochlore ferromagnet Lu2V2O7

We study the ferromagnetic criticality of the pyrochlore magnet Lu2V2O7 at the ferromagnetic transition TC≈70K from the isotherms of magnetization M(H) via an iteration process and the Kouvel-Fisher method. The critical exponents associated with the transition are determined: β = 0.32(1), γ = 1.41(1), and δ=5.38. The validity of these critical exponents is further verified by scaling all the M(H) data in the vicinity of TC onto two universal curves in the plot of M/|ε|β versus H/|ε|β+γ, where ε=T/TC-1. The obtained β and γ values show asymmetric behaviors on the T<TC and the T>TC sides, and are consistent with the predicted values of 3D Ising and cubic universality classes, respectively. This makes Lu2V2O7 a rare example in which the critical behaviors associated with a ferromagnetic transition belong to different universality classes. We describe the observed criticality from the Ginzburg-Landau theory with the quartic cubic anisotropy that microscopically originates from the anti-symmetric Dzyaloshinskii-Moriya interaction as revealed by recent magnon thermal Hall effect and theoretical investigations.

Consideration of thermal Hall effect in undoped cuprates

A recent observation of thermal Hall effect of magnetic origin in underdoped cuprates calls for critical re-examination of low-energy magnetic dynamics in undoped antiferromagnetic compound on square lattice, where traditional, renormalized spin-wave theory was believed to work well. Using Holstein-Primakoff boson formalism, we find that magnon-based theories can lead to finite Berry curvature in the magnon band once the Dzyaloshinskii-Moriya spin interaction is taken into account explicitly, but fail to produce non-zero thermal Hall conductivity. Assuming accidental doping by impurities and magnon scattering off of such impurity sites fails to predict skew scattering at the level of Born approximation. Local formation of skyrmion defects is also found incapable of generating magnon thermal Hall effect. Turning to spinon-based scenario, we write down a simple model by adding spin-dependent diagonal hopping to the well-known {\pi}-flux model of spinons. The resulting two-band model has Chern number in the band structure, and generates thermal Hall conductivity whose magnetic field and temperature dependences mimic closely the observed thermal Hall signals. In disclaimer, there is no firm microscopic basis of this model and we do not claim to have found an explanation of the data, but given the unexpected nature of the experimental observation, it is hoped this work could serve as a first step towards reaching some level of understanding.

Magnonic Floquet Quantum Spin Hall Insulator in Bilayer Collinear Antiferromagnets

We study irradiated two-dimensional insulating bilayer honeycomb ferromagnets and antiferromagnets coupled antiferromagnetically with a zero net magnetization. The former is realized in the recently synthesized bilayer honeycomb chromium triiodide CrI3. In both systems, we show that circularly-polarized electric field breaks time-reversal symmetry and induces a dynamical Dzyaloshinskii-Moriya interaction in each honeycomb layer. However, the resulting bilayer antiferromagnetic system still preserves a combination of time-reversal and space-inversion ({bf{P}}{bf{T}}) symmetry. We show that the magnon topology of the bilayer antiferromagnetic system is characterized by a {{bf{Z}}}_{{bf{2}}} Floquet topological invariant. Therefore, the system realizes a magnonic Floquet quantum spin Hall insulator with spin filtered magnon edge states. This leads to a non-vanishing Floquet magnon spin Nernst effect, whereas the Floquet magnon thermal Hall effect vanishes due to {bf{P}}{bf{T}} symmetry. We study the rich {{bf{Z}}}_{{bf{2}}} Floquet topological magnon phase diagram of the system as a function of the light amplitudes and polarizations. We further discuss the great impact of the results on future experimental realizations.

Photo-induced Floquet Weyl magnons in noncollinear antiferromagnets

We study periodically driven insulating noncollinear stacked kagome antiferromagnets with a conventional symmetry-protected three-dimensional (3D) in-plane 120° spin structure, with either positive or negative vector chirality. We show that the symmetry protection of the in-plane 120° spin structure can be broken in the presence of an off-resonant circularly or linearly polarized electric field propagating parallel to the in-plane 120° spin structure (say along the x direction). Consequently, topological Floquet Weyl magnon nodes with opposite chirality are photoinduced along the kx momentum direction. They manifest as the monopoles of the photoinduced Berry curvature. We also show that the system exhibits a photoinduced magnon thermal Hall effect for circularly polarized electric field. Furthermore, we show that the photoinduced chiral spin structure is a canted 3D in-plane 120° spin structure, which was recently observed in the equilibrium noncollinear antiferromagnetic Weyl semimetals Mn3Sn/Ge. Our result not only paves the way towards the experimental realization of Weyl magnons and photoinduced thermal Hall effects, but also provides a powerful mechanism for manipulating the intrinsic properties of 3D topological antiferromagnets.

Topological magnon nodal lines and absence of magnon spin Nernst effect in layered collinear antiferromagnets

We propose the existence of a symmetry-protected topological Dirac nodal-line (DNL) magnonic phase in layered honeycomb collinear antiferromagnets even in the presence of spin-orbit Dzyaloshinskii-Moriya interaction. We show that the magnon spin Nernst effect, predicted to occur in strictly two-dimensional (2D) honeycomb collinear antiferromagnets cancels out in the layered honeycomb collinear antiferromagnets. In other words, the magnon spin Nernst effect in each 2D antiferromagnetic layer cancels out the succeeding layer. Hence, the Berry curvature vanishes in the entire Brillouin zone due to the combination of time-reversal and space-inversion symmetry. However, upon symmetry breaking by an external magnetic field, we show that a non-vanishing Berry curvature and Chern number protected topological magnon bands are induced in the non-collinear spin structure. This leads to an experimentally accessible magnon thermal Hall effect in the symmetry-broken topological DNL magnonic phase of layered honeycomb antiferromagnets. We propose that the current predicted results can be experimentally investigated in the layered honeycomb antiferromagnets CaMn2Sb2, BaNi2V2O8, and Bi3Mn4O12(NO3).

Thermal Hall effect in noncollinear coplanar insulating antiferromagnets

We establish theoretically a thermal Hall effect of collective magnetic excitations in noncollinear but coplanar antiferromagnets. In agreement with superordinate symmetry arguments for linear transport tensors, our findings demonstrate that neither a ferromagnetic moment, nor a magnetic field, nor a scalar spin chirality are indispensable for a magnon thermal Hall effect. Similar to the electronic anomalous Hall effect, the two necessary requirements are broken effective time-reversal symmetry and a magnetic point group compatible with ferromagnetism. As an example, we construct a minimal model for an antiferromagnet on the kagome lattice with the coplanar negative vector chiral order. In the presence of in-plane Dzyaloshinskii-Moriya interactions, the coplanar order stays intact but both magnon band gaps and a nonzero Berry curvature develop. This coplanar magnet realizes an antiferromagnetic magnon Chern insulator with a nonzero thermal Hall effect. We propose cadmium kapellasite ${\mathrm{CdCu}}_{3}{(\mathrm{OH})}_{6}{({\mathrm{NO}}_{3})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$ as an approximate material realization.

Magnon thermal Hall effect in kagome antiferromagnets with Dzyaloshinskii-Moriya interactions

We theoretically study magnetic and topological properties of antiferromagnetic kagome spin systems in the presence of both in- and out-of-plane Dzyaloshinskii-Moriya interactions. In materials such as the iron jarosites, the in-plane interactions stabilize a canted noncollinear "umbrella" magnetic configuration with finite scalar spin chirality. We derive expressions for the canting angle, and use the resulting order as a starting point for a spin-wave analysis. We find topological magnon bands, characterized by non-zero Chern numbers. We calculate the magnon thermal Hall conductivity, and propose the iron jarosites as a promising candidate system for observing the magnon thermal Hall effect in a noncollinear spin configuration. We also show that the thermal conductivity can be tuned by varying an applied magnetic field, or the in-plane Dzyaloshinskii-Moriya strength. In contrast with previous studies of topological magnon bands, the effect is found to be large even in the limit of small canting.