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Register a new userTopological magnons in a kagome lattice spin system with $XXZ$ and Dzyaloshinskii-Moriya interactions
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We study the phases of a spin system on the Kagome lattice with nearest-neighbor $XXZ$ interactions with anisotropy ratio $Delta$ and Dzyaloshinsky-Moriya interactions with strength $D$. In the classical limit where the spin $S$ at each site is very large, we find a rich phase diagram of the ground state as a function of $Delta$ and $D$. There are five distinct phases which correspond to different ground state spin configurations in the classical limit. We use spin wave theory to find the bulk energy bands of the magnons in some of these phases. We also study a strip of the system which has infinite length and finite width; we find modes which are localized on one of the edges of the strip with energies which lie in the gaps of the bulk modes. In the ferromagnetic phase in which all the spins point along the $+ hat z$ or $- hat z$ direction, the bulk bands are separated from each other by finite energy gaps. This makes it possible to calculate the Berry curvature at all momenta, and hence the Chern numbers for every band; the number of edge states is related to the Chern numbers. Interestingly, we find that there are four different regions in this phase where the Chern numbers are different. Hence there are four distinct topological phases even though the ground state spin configuration is identical in all these phases. We calculate the thermal Hall conductivity of the magnons as a function of the temperature in the above ferromagnetic phase; we find that this can distinguish between the various topological phases. These results are valid for all values of $S$.In the other phases, there are no gaps between the different bands; hence the edge states are not topologically protected.
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The kagome lattice sits at the crossroad of present research efforts in quantum spin liquids, chiral phases, emergent skyrmion excitations and anomalous Hall effects to name but a few. In light of this diversity, our goal in this paper is to build a unifying picture of the underlying magnetic degrees-of-freedom on kagome. Motivated by a growing mosaic of materials, we especially consider a broad range of nearest-neighbour interactions consisting of Dzyaloshinskii-Moriya as well as anisotropic ferro$-$ and antiferromagnetic coupling. We present a three-fold mapping on the kagome lattice which transforms the celebrated Heisenberg antiferromagnet and XXZ model onto two lines of time-reversal invariant Hamiltonians. The mapping is exact for classical and quantum spins alike, i.e. it preserves the energy spectrum of the original Heisenberg and XXZ models. As a consequence, at the classical level, all phases have an extensive ground-state degeneracy. These ground states support a variety of phenomena such as ferromagnetically induced pinch points in the structure factor and the possibility for spontaneous scalar chirality. For quantum spin$-1/2$, the XXZ model has been recently shown to be a quantum spin liquid. Applying our three-fold mapping to the XXZ model gives rise to a connected network of quantum spin liquids, centered around a paragon of quantum disorder, namely the Ising antiferromagnet. We show that this quantum disorder spreads over an extended region of the phase diagram at linear order in spin wave theory, which overlaps with the parameter region of Herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$. We conclude this work by discussing the connection of our results to the chiral spin liquids found on kagome with further nearest-neighbour interactions, and to the recently synthesized ternary intermetallic materials.
A preponderance of evidence suggests that the ground state of the nearest-neighbor $S = 1/2$ antiferromagnetic Heisenberg model on the kagome lattice is a gapless spin liquid. Many candidate materials for the realization of this model possess in addition a Dzyaloshinskii-Moriya (DM) interaction. We study this system by tensor-network methods and deduce that a weak but finite DM interaction is required to destabilize the gapless spin-liquid state. The critical magnitude, $D_c/J simeq 0.012(2)$, lies well below the DM strength proposed in the kagome material herbertsmithite, indicating a need to reassess the apparent spin-liquid behavior reported in this system.
The influence of the Dzyaloshinskii-Moriya interaction in ultra-thin ferromagnetic films and chiral magnonic crystals on the behavior of spin waves is reviewed. During the last decade, it has been shown, both theoretically and experimentally, that this anisotropic exchange interaction produces non-reciprocal features on the spin-wave spectrum of a magnetic system, a phenomenon that occurs both for bulk and interfacial Dzyaloshinskii-Moriya coupling. More recently, the concept of a chiral magnonic crystal has been introduced, where the interfacial Dzyaloshinskii-Moriya interaction is periodic. The effect of this periodicity include additional features such as flat bands, indirect gaps, and an unusual spin-wave evolution.
We study in this paper magnetic properties of a system of quantum Heisenberg spins interacting with each other via a ferromagnetic exchange interaction J and an in-plane Dzyaloshinskii-Moriya interaction D. The non-collinear ground state due to the competition between J and D is determined. We employ a self-consistent Greenfunction theory to calculate the spin-wave spectrum and the layer magnetizations at finite T in two and three dimensions as well as in a thin film with surface effects. Analytical details and the validity of the method are shown and discussed.
Vortex states in magnetic nanodisks are essentially affected by surface/interface induced Dzyaloshinskii-Moriya interactions. Within a micromagnetic approach we calculate the equilibrium sizes and shape of the vortices as functions of magnetic field, the material and geometrical parameters of nanodisks. It was found that the Dzyaloshinskii-Moriya coupling can considerably increase sizes of vortices with right chirality and suppress vortices with opposite chirality. This allows to form a bistable system of homochiral vortices as a basic element for storage applications.
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