Magnon Hall Effect Research Articles

Valley modulation and topological phase transition in Staggered Kagome Ferromagnets

Abstract Owing to its charge-free property, magnon is highly promising to achieve dissipationless transport without Joule heating and thus potentially applicable to energy-efficient devices. Here, we investigate valley magnons and associated valley modulations in a kagome ferromagnetic lattice, with the staggered exchange interaction and Dzyaloshinskii-Moriya interaction. The staggered exchange interaction breaks the spatial inversion symmetry, leading to a valley magnon Hall effect. With nonzero Dzyaloshinskii-Moriya interaction in staggered kagome lattcie, the magnon Hall effect can be observed from only one valley. Moreover, reversing the Dzyaloshinskii-Moriya interaction (D→-D) and exchange of J 1 and J 2 (J 1 ↔ J 2) can also regulate the position of the unequal valleys. With increasing Dzyaloshinskii-Moriya interaction, a series of topological phase transitions appear when two bands come to touch and split at valleys. The valley Hall effect and topological phase transitions observed in kagome magnon lattices can be realized in the thin film of the insulating ferromagnet, such as Lu2V2O7, and will extend the basis for magnonics applications in the future.

Magnon Hall effect

Hall effect is an ancient but highly potential subfield in condensed matter physics, and its origin can be traced back hundreds of years. In 1879, Hall made a momentous discovery that when a current-carrying conductor is placed in a magnetic field, the Lorentz force pushes its electrons to one side of the conductor. This intriguing phenomenon was dubbed Hall effect. Since then, a series of novel Hall effects have been discovered, including anomalous Hall effect, quantum Hall effect, spin Hall effect, topological Hall effect, and planar Hall effec. Notably, Hall effects play an important role in realizing the information transport, since it can realize the mutual conversion of current in different directions. In bosonic systems such as magnons, a series of magnon Hall effects have been found, jointly driving the development of the magnon-based spintronics. In this perspective, we review the researches of the Hall effect in magnonic system in recent years, and briefly introduce its modern semi-classical theories, including virtual electromagnetic field theory and scattering theory. Furthermore, we introduce the different magnon Hall effects and clarify the physics behind them. Finally, the prospect of magnon Hall effect is discussed.

Magnon Hall effect in antiferromagnetic lattices

Topology applied to condensed matter is an important area of research and technology, and topological magnetic excitations have recently become an active field of study. This paper presents a general discussion of magnon Hall transport in two-dimensional antiferromagnets. Although the Chern number is zero for a collinear antiferromagnet, we offer a general discussion that can be used in the more general case. First, we study the Union Jack lattice, where an effective time-reversal symmetry is broken, making the system display the magnon Hall effect. Then, we investigate the brick-wall lattice where such symmetry is present. Consequently, we have a phenomenon similar to the quantum spin Hall effect in electronic systems. Both lattices have not yet been studied from the topological point of view. The coexistence of opposite spin polarization in an antiferromagnet resembles the electron spin in various transport phenomena. We study magnon transport in the lattices mentioned above with Dzyaloshinskii-Moriya interaction and easy-axis single-ion anisotropy. We calculate the Berry curvature from the eigenvalues of the Hamiltonian. From that, we plot the spin Hall and thermal Hall conductivities, as well as the spin Nernst coefficient, as functions of the temperature. In the Union Jack lattice, we treat the effect of anharmonic interactions using a mean-field spin wave theory where the Hamiltonian becomes implicitly temperature-dependent. We determine self-consistently the renormalized dispersion and the staggered magnetization as a function of temperature. Our calculations can be applied to other antiferromagnetic lattices.

Sizable suppression of magnon Hall effect by magnon damping in Cr2Ge2Te6

Two-dimensional (2D) Heisenberg honeycomb ferromagnets are expected to have interesting topological magnon effects as their magnon dispersion can have Dirac points. The Dirac points are gapped with finite second nearest neighbor Dzyaloshinskii-Moriya interaction, providing nontrivial Berry curvature with finite magnon Hall effect. Yet, it is unknown how the topological properties are affected by magnon damping. We report the thermal Hall effect in Cr$_2$Ge$_2$Te$_6$, an insulating 2D honeycomb ferromagnet with a large Dirac magnon gap and significant magnon damping. Interestingly, the thermal Hall conductivity in Cr$_2$Ge$_2$Te$_6$ shows the coexisting phonon and magnon contributions. Using an empirical two-component model, we successfully estimate the magnon contribution separate from the phonon part, revealing that the magnon Hall conductivity was 20 times smaller than the theoretical calculation. Finally, we suggest that such considerable suppression in the magnon Hall conductivity is due to the magnon damping effect in Cr$_2$Ge$_2$Te$_6$.

Topological magnons in the honeycomb-kagome lattice

Materials with magnon Hall effect have potential applications in the field of spintronics and magnonics. The experimental observations of the magnon Hall effect in three-dimensional pyrochlore ferromagnets and two-dimensional kagome ferromagnets inspired the search for topological magnons in various lattice structures. The honeycomb-kagome (HK) lattice (also known as the edge-centered honeycomb lattice) can be seen as the combination of the honeycomb and kagome lattices. Hence, the Dzyaloshinskii–Moriya (DM) interaction is allowed and topological magnons are expected in the HK lattice, as the cases in the honeycomb and the kagome lattices alone. Here, we study the topological magnons in the HK lattice by calculating its band structure, Chern number, edge states and thermal Hall conductivity. It is shown that there are rich topological phases and phase transitions with the tuning of the model parameters. The finite thermal Hall conductivity induced by the DM interaction also has interesting behaviors, which are related to the topological phase transitions.

Quantum entanglement and magnon Hall effect on the Lieb lattice model

Entanglement of magnons in the nearest-neighbor Heisenberg model on Lieb lattice (LL) with out-of-plane Dzyaloshinskii–Moriya (DM) antisymmetric spin coupling and external magnetic field is studied. We obtain the behavior of the von Neumann entropy (VN) and concurrence as a function of the DM strength, analyzing the effect of magnon bands on quantum entanglement . Furthermore, the quantum correlations in some fermions models such as the two-dimensional non-Hermitian model (NH) on LL lattice and the tight-binding model (TB) on the LL lattice have been also analyzed. The effect of opening of the gap in the spectrum in these models generates an effect on the entanglement quantifiers as von Neumann entropy, concurrence and negativity. • Quantum entanglement on two-dimensional Lieb lattice is studied. • von Neumann entropy, concurrence and entanglement negativity are studied. • Influence of magnon bands on entanglement is investigated.

Topology dependence of skyrmion Seebeck and skyrmion Nernst effect

We explore the dynamics of skyrmions with various topological charges induced by a temperature gradient in an ultra-thin insulating magnetic film. Combining atomistic spin simulations and analytical calculations we find a topology-dependent skyrmion Seebeck effect: while skyrmions and antiskyrmions move to the hot regime, a topologically trivial localized spin structure moves to the cold regime. We further reveal the emergence of a skyrmion Nernst effect, i.e. finite, topology-dependent velocities transverse to the direction of the temperature gradient. These findings are in agreement with accompanying simulations of skyrmionic motion induced by monochromatic magnon currents, allowing us to demonstrate that the magnonic spin Seebeck effect is responsible for both, skyrmion Seebeck and Nernst effect. Furthermore we employ scattering theory together with Thiele’s equation to identify linear momentum transfer from the magnons to the skyrmion as the dominant contribution and to demonstrate that the direction of motion depends on the topological magnon Hall effect and the topological charge of the skyrmion.

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.

Theory for electrical detection of the magnon Hall effect induced by dipolar interactions

We derive the anomalous Hall contributions arising from dipolar interactions to diffusive spin transport in magnetic insulators. Magnons, the carriers of angular momentum in these systems, are shown to have a non-zero Berry curvature, resulting in a measurable Hall effect. For yttrium iron garnet (YIG) thin films we calculate both the anomalous and magnon spin conductivities. We show that for a magnetic field perpendicular to the film the anomalous Hall conductivity is finite. This results in a non-zero Hall signal, which can be measured experimentally using Permalloy strips arranged like a Hall bar on top of the YIG thin film. We show that electrical detection and injection of spin is possible, by solving the resulting diffusion-relaxation equation for a Hall bar. We predict the experimentally measurable Hall coefficient for a range of temperatures and magnetic field strengths. Most strikingly, we show that there is a sign change of the Hall coefficient associated with increasing the thickness of the film.

Topological magnonics

Spin waves, whose quanta are called magnons, are propagating excitations of magnetic materials. Magnonics is an emerging field of modern condensed matter physics that aims to study and utilize the properties and behaviors of magnons. The topological magnon band is an interesting topic of magnonics, and nontrivial topology is usually accompanied with many exotic phenomena such as emergence of robust edge states and the magnon Hall effect. In this Tutorial, using a honeycomb ferromagnet as a prototypical platform, we pedagogically demonstrate how to compute the magnon spectra and the topological invariants characterizing the topology of the magnon bands. We also briefly discuss some numerical techniques.

Magnonic Su-Schrieffer-Heeger model in honeycomb ferromagnets

Topological electronics has extended its richness to non-electronic systems where phonons and magnons can play the role of electrons. In particular, topological phases of magnons can be enabled by the Dzyaloshinskii-Moriya interaction (DMI) which acts as an effective spin-orbit coupling. We show that besides DMI, an alternating arrangement of Heisenberg exchange interactions critically determines the magnon band topology, realizing a magnonic analog of the Su-Schrieffer-Heeger model. On a honeycomb ferromagnet with perpendicular anisotropy, we calculate the topological phase diagram, the chiral edge states, and the associated magnon Hall effect by allowing the relative strength of exchange interactions on different links to be tunable. Including weak phonon-magnon hybridization does not change the result. Candidate materials are discussed.

Experimental evidence consistent with a magnon Nernst effect in the antiferromagnetic insulator MnPS3

A magnon Nernst effect, an antiferromagnetic analogue of the magnon Hall effect in ferromagnetic insulators, has been studied experimentally for a layered antiferromagnetic insulator MnPS3 in contact with two Pt strips. Thermoelectric voltage in the Pt strips grown on MnPS3 single crystals exhibits non-monotonic temperature dependence at low temperatures, which cannot be explained by electronic origins in Pt but can be ascribed to the inverse spin Hall voltage induced by a magnon Nernst effect. Control of antiferromagnetic domains in the MnPS3 crystal by magnetoelectric cooling is found to modulate the low-temperature thermoelectric voltage in Pt, which corroborates the emergence of the magnon Nernst effect in Pt|MnPS3 hybrid structures.

Noncollinear antiferromagnetic Haldane magnon insulator

In this paper, we present a comprehensive study of topological magnon bands and thermal Hall effect in non-collinear antiferromagnetic systems on the honeycomb lattice with an intrinsic Dzyaloshinskii-Moriya interaction. We theoretically show that the system possesses topological magnon bands with Chern number protected edge modes accompanied by a nonzero thermal magnon Hall effect. These features result from non-collinearity of the magnetic moments due to an applied out-of-plane magnetic field. Our results provide an experimental clue towards the realization of topological magnon transports in honeycomb antiferromagnetic compounds such as XPS3 (X = Mn,Fe) and α-Cu2V2O7.

Topological magnon bands in ferromagnetic star lattice

The experimental observation of topological magnon bands and thermal Hall effect in a kagomé lattice ferromagnet Cu(1–3, bdc) has inspired the search for topological magnon effects in various insulating ferromagnets that lack an inversion center allowing a Dzyaloshinskii–Moriya (DM) spin–orbit interaction. The star lattice (also known as the decorated honeycomb lattice) ferromagnet is an ideal candidate for this purpose because it is a variant of the kagomé lattice with additional links that connect the up-pointing and down-pointing triangles. This gives rise to twice the unit cell of the kagomé lattice, and hence more interesting topological magnon effects. In particular, the triangular bridges on the star lattice can be coupled either ferromagnetically or antiferromagnetically which is not possible on the kagomé lattice ferromagnets. Here, we study DM-induced topological magnon bands, chiral edge modes, and thermal magnon Hall effect on the star lattice ferromagnet in different parameter regimes. The star lattice can also be visualized as the parent material from which topological magnon bands can be realized for the kagomé and honeycomb lattices in some limiting cases.

Thermal Hall Effect of Magnons

We review recent developments in theories and experiments on the magnon Hall effect. We derive the thermal Hall conductivity of magnons in terms of the Berry curvature of magnonic bands. In addition to the Dzyaloshinskii–Moriya interaction, we show that the dipolar interaction can make the Berry curvature nonzero. We mainly discuss theoretical aspects of the magnon Hall effect and related theoretical works. Experimental progress in this field is also mentioned.

Spin Chirality and Hall-Like Transport Phenomena of Spin Excitations

Experimental and theoretical aspects of Hall-type transport of spins in magnetic insulators are reviewed, with emphasis on their spin chirality origin. A general formalism for linear response theory of thermal Hall transport in the spin model is developed, which can be applied to both the magnon and the paramagnetic, spin-liquid regimes. Recent experiments on magnon-mediated thermal Hall transport in the two-dimensional kagome, and three-dimensional pyrochlore ferromagnetic insulators are reviewed in light of the multi-band magnon theory of Hall transport, and compared to the more mysterious thermal Hall transport found in the putative quantum spin ice material. As realizations of spin-chirality driven magnon transport in the real space, we review the general theory of emergent gauge fields governing the magnon dynamics in the textured magnet, and discuss its application to the magnon-Skyrmion scattering problem. Topological magnon Hall effect driven by the Skyrmion texture is discussed.

Magnon Hall effect without Dzyaloshinskii–Moriya interaction

Topological magnon bands and magnon Hall effect in insulating collinear ferromagnets are induced by the Dzyaloshinskii–Moriya interaction (DMI) even at zero magnetic field. In the geometrically frustrated star lattice, a coplanar/noncollinear magnetic ordering may be present due to spin frustration. This magnetic structure, however, does not exhibit topological magnon effects even with DMI in contrast to collinear ferromagnets. We show that a magnetic field applied perpendicular to the star plane induces a non-coplanar spin configuration with nonzero spin scalar chirality, which provides topological effects without the need of DMI. The non-coplanar spin texture originates from the topology of the spin configurations and does not need the presence of DMI or magnetic ordering, which suggests that this phenomenon may be present in the chiral spin liquid phases of frustrated magnetic systems. We propose that these anomalous topological magnon effects can be accessible in polymeric iron (III) acetate—a star-lattice antiferromagnet with both spin frustration and long-range magnetic ordering.

Berry curvature and various thermal Hall effects

Applying the approach of semiclassical wave packet dynamics, we study various thermal Hall effects where carriers can be electron, phonon, magnon, etc. A general formula of thermal Hall conductivity is obtained to provide an essential physics for various thermal Hall effects, where the Berry phase effect manifests naturally. All the formulas of electron thermal Hall effect, phonon Hall effect, and magnon Hall effect can be directly reproduced from the general formula. It is also found that the Strěda formula can not be directly applied to the thermal Hall effects, where only the edge magnetization contributes to the Hall effects. Furthermore, we obtain a combined formula for anomalous Hall conductivity, thermal Hall electronic conductivity and thermal Hall conductivity for electron systems, where the Berry curvature is weighted by a different function. Finally, we discuss particle magnetization and its relation to angular momentum of the carrier, change of which could induce a mechanical rotation; and possible experiments for thermal Hall effect associated with a mechanical rotation are also proposed.

Magnon Hall effect in AB-stacked bilayer honeycomb quantum magnets

Motivated by the fact that many bilayer quantum magnets occur in nature, we generalize the study of thermal Hall transports of spin excitations to bilayer magnetic systems. It is shown that bilayer magnetic systems can be coupled either ferromagnetically or antiferromagnetically. We study both scenarios on the honeycomb lattice and show that the system realizes topologically nontrivial magnon bands induced by alternating next-nearest-neighbour Dzyaloshinsky-Moriya interaction (DMI). As a result, the bilayer system realizes both magnon Hall effect and magnon spin Nernst effect. We show that antiferromagnetically coupled layers differ from ferromagnetically coupled layers by a sign change in the conductivities as the magnetic field is reversed. Furthermore, Chern number protected magnon edge states are observed and propagate in the same direction on the top and bottom layers in ferromagnetically coupled layers, whereas the magnon edge states propagate in opposite directions for antiferromagnetically coupled layers.

Topological honeycomb magnon Hall effect: A calculation of thermal Hall conductivity of magnetic spin excitations

Quite recently, the magnon Hall effect of spin excitations has been observed experimentally on the kagome and pyrochlore lattices. The thermal Hall conductivity κxy changes sign as a function of magnetic field or temperature on the kagome lattice, and κxy changes sign upon reversing the sign of the magnetic field on the pyrochlore lattice. Motivated by these recent exciting experimental observations, we theoretically propose a simple realization of the magnon Hall effect in a two-band model on the honeycomb lattice. The magnon Hall effect of spin excitations arises in the usual way via the breaking of inversion symmetry of the lattice, however, by a next-nearest-neighbour Dzyaloshinsky-Moriya interaction. We find that κxy has a fixed sign for all parameter regimes considered. These results are in contrast to the Lieb, kagome, and pyrochlore lattices. We further show that the low-temperature dependence on the magnon Hall conductivity follows a T2 law, as opposed to the kagome and pyrochlore lattices. These results suggest an experimental procedure to measure thermal Hall conductivity within a class of 2D honeycomb quantum magnets and ultracold atoms trapped in a honeycomb optical lattice.