For magnons, the Dzyaloshinskii-Moriya interaction accounts for spin-orbit interaction and causes a nontrivial topology that allows for topological magnon insulators. In this theoretical investigation we present the bulkboundary correspondence for magnonic kagome lattices by studying the edge magnons calculated by a Green function renormalization technique. Our analysis explains the sign of the transverse thermal conductivity of the magnon Hall effect in terms of topological edge modes and their propagation direction. The hybridization of topologically trivial with nontrivial edge modes enlarges the period in reciprocal space of the latter, which is explained by the topology of the involved modes.

A magnetic bimeron is a pair of two merons and can be understood as the in-plane magnetized version of a skyrmion. Here we theoretically predict the existence of single magnetic bimerons as well as bimeron crystals, and compare the emergent electrodynamics of bimerons with their skyrmion analogues. We show that bimeron crystals can be stabilized in frustrated magnets and analyze what crystal structure can stabilize bimerons or bimeron crystals via the Dzyaloshinskii-Moriya interaction. We point out that bimeron crystals, in contrast to skyrmion crystals, allow for the detection of a pure topological Hall effect. By means of micromagnetic simulations, we show that bimerons can be used as bits of information in in-plane magnetized racetrack devices, where they allow for current-driven motion for torque orientations that leave skyrmions in out-of-plane magnets stationary.Over the last years magnetic skyrmions [ Fig. 1(a) top] [1-6] have attracted immense research interest, as these small spin textures m(r) possess strong stability, characterized by a topological charge N Sk = ±1. Skyrmions offer a topological contribution to the Hall effect [7][8][9][10][11][12][13][14][15][16][17][18], commonly measured in skyrmion crystals, and can be stabilized as individual quasiparticles in collinear ferromagnets. They can be driven by currents in thin films [6,[19][20][21][22][23][24][25][26] allowing for spintronics applicability. The stabilizing interaction in most systems is the Dzyaloshinskii-Moriya interaction (DMI) [27,28], while theoretical simulations also point to other stabilizing mechanisms, e. g. frustrated exchange interactions [29,30]. Textures with a half-integer topological charge, like merons and antimerons (or vortices and antivortices), have also been subject of intense research [31][32][33].Magnetic bimerons [34][35][36][37] [Fig.1(a) bottom] are the combination of two merons [red and blue] and can be understood as in-plane magnetized versions of magnetic skyrmions [38]. Instead of the out-of-plane component of the magnetization it is an in-plane component which is radial symmetric about the quasiparticle's center; being aligned with the saturation magnetization of the ferromagnet at the outer region of the bimeron and pointing into the opposite direction in the center. Recently, Kharkov et al. showed that isolated bimerons can be stabilized in an easy-plane magnet by frustrated exchange interactions [34]. In DMI dominated systems (as is the case for all experimentally known skyrmion-host materials) bimerons have only been shown to exist as unstable transition states [35,36].In this Rapid Communication, we show that bimerons in frustrated magnets can also be stabilized in an array, the bimeron crystal. Furthermore, we propose a structural configuration that allows for DMI stabilizing isolated bimerons and bimeron crystals. We compare fundamental properties of skyrmions and bimerons and find that both show the same topological Hall effect, whereas the bimeron allows for a pure detection, that is without supe...

Ferromagnetic insulators with Dzyaloshinskii-Moriya interaction show the magnon Hall effect, i.e., a transverse heat current upon application of a temperature gradient. In this theoretical investigation we establish a close connection of the magnon Hall effect in two-dimensional kagome lattices with the topology of their magnon dispersion relation. From the topological phase diagram we predict systems which show a change of sign in the heat current in dependence on temperature. Furthermore, we derive the high-temperature limit of the thermal Hall conductivity; this quantity provides a figure of merit for the maximum strength of the magnon Hall effect. Eventually, we compare the temperature and field dependence of the magnon Hall conductivity of the three-dimensional pyrochlore Lu 2 V 2 O 7 with experimental results.

The dispersion relations of magnons in ferromagnetic pyrochlores with Dzyaloshinskii-Moriya interaction is shown to possess Weyl points, i. e., pairs of topological nontrivial crossings of two magnon branches with opposite topological charge. As a consequence of their topological nature, their projections onto a surface are connected by magnon arcs, thereby resembling closely Fermi arcs of electronic Weyl semimetals. On top of this, the positions of the Weyl points in reciprocal space can be tuned widely by an external magnetic field: rotated within the surface plane, the Weyl points and magnon arcs are rotated as well; tilting the magnetic field out-ofplane shifts the Weyl points toward the center Γ of the surface Brillouin zone. The theory is valid for the class of ferromagnetic pyrochlores, i. e., three-dimensional extensions of topological magnon insulators on kagome lattices. In this Letter, we focus on the (111) surface, identify candidates of established ferromagnetic pyrochlores which apply to the considered spin model, and suggest experiments for the detection of the topological features.

Skyrmions are topologically nontrivial, magnetic quasi-particles, that are characterized by a topological charge. A regular array of skyrmions-a skyrmion crystal (SkX)-features the topological Hall effect (THE) of electrons, that, in turn, gives rise to the Hall effect of the skyrmions themselves. It is commonly believed that antiferromagnetic skyrmion crystals (AFM-SkXs) lack both effects. In this Rapid Communication, we present a generally applicable method to create stable AFM-SkXs by growing a two sublattice SkX onto a collinear antiferromagnet. As an example we show that both types of skyrmion crystals-conventional and antiferromagnetic-exist in honeycomb lattices. While AFM-SkXs with equivalent lattice sites do not show a THE, they exhibit a topological spin Hall effect. On top of this, AFM-SkXs on inequivalent sublattices exhibit a nonzero THE, which may be utilized in spintronics devices. Our theoretical findings call for experimental realization.Introduction. Skyrmions [1][2][3][4][5] are small magnetic quasiparticles, which are usually caused by the DzyaloshinskiiMoriya interaction [6,7], but they have been produced by other mechanisms [8], like frustrated exchange interactions [9], as well. While single skyrmions are envisioned to be used as "bits" in data storage devices [10][11][12][13][14][15][16][17][18][19], which provide durability of data due to topological protection [8], skyrmion crystals (SkXs)-regular arrays of skyrmions-are best known for exhibiting the topological Hall effect (THE) of electrons [20][21][22][23][24][25][26][27][28], that, in turn, gives rise to the skyrmion Hall effect (SkHE; also present in isolated skyrmions) [8,[29][30][31].From the perspective of applications in data storage devices, the SkHE is undesirable. Thus, the concept of antiferromagnetic (AFM) skyrmions has been developed [32][33][34][35]: skyrmions on two sublattices in which the spins on one sublattice are (mutually) reversed. As a result, both THE and SkHE vanish [32]. Because no periodic antiferromagnetic skyrmion crystal (AFM-SkX) is known yet, surrogate systems consisting of two skyrmion layers with opposite winding have been investigated [36,37].In this Rapid Communication, we predict the generation of stable AFM-SkXs by coupling a bipartite skyrmion material to a collinear antiferromagnetic layer (Fig. 1b). The interlayer interaction acts as staggered magnetic field, which flips the spins of the SkX on one sublattice. The approach is generally applicable, as it can turn every established phase of conventional SkXs into an AFM-SkX phase, irrespective of the skyrmion-generating mechanism. As an example, we apply the method to frustrated spins on a honeycomb lattice, i. e., two triangular sublattices that exhibit SkXs via frustrated exchange interactions (cf. Ref. 9).If both sublattices of the AFM-SkX are equivalent, there is no THE. However, we find a topological spin Hall effect (TSHE). Since the TSHE arises in a single two-dimensional layer, it is clearly distinguished from that in the surrogate system...