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arXiv:1110.6229 · Physical Review B

Spatially anisotropic kagome antiferromagnet with Dzyaloshinskii-Moriya interaction

Vladimir A. Zyuzin, Gregory A. Fiete

Published Mar 27, 2012• 8 citations
arXivHTMLPDF

Abstract

We theoretically study the spatially anisotropic spin-1/2 kagome antiferromagnet with a Dzyaloshinskii-Moriya (DM) interaction using a renormalization-group analysis in the quasi-one-dimensional limit. We identify the various temperature and energy scales for ordering in the system. For a very weak DM interaction, we find a low-temperature spiral phase with the plane of the spiral selected by the DM interaction. This phase is similar to a previously identified phase in the absence of the DM interaction. However, above a critical DM interaction strength we find a transition to a phase with coexisting antiferromagnetic and dimer order, reminiscent of one-dimensional antiferromagnetic systems with a uniform DM interaction. Our results help shed light on the fate of two-dimensional systems with both strong interactions and significant spin-orbit coupling.

DOI
10.1103/physrevb.85.104417

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We theoretically study the spatially anisotropic spin-1/2 kagome antiferromagnet with a Dzyaloshinskii-Moriya (DM) interaction using a renormalization-group analysis in the quasi-one-dimensional limit. We identify the various temperature and energy scales for ordering in the system. For a very weak DM interaction, we find a low-temperature spiral phase with the plane of the spiral selected by the DM interaction. This phase is similar to a previously identified phase in the absence of the DM interaction. However, above a critical DM interaction strength we find a transition to a phase with coexisting antiferromagnetic and dimer order, reminiscent of one-dimensional antiferromagnetic systems with a uniform DM interaction. Our results help shed light on the fate of two-dimensional systems with both strong interactions and significant spin-orbit coupling.
Using the density-matrix renormalization-group algorithm (DMRG) and a finite-size scaling analysis, we study the properties of the one-dimensional completely-anisotropic spin-1/2 XYZ model with Dzyaloshinsky-Moriya (DM) interactions. The model shows a rich phase diagram: depending on the value of the coupling constants, the system can display different kinds of ferromagnetic order and Luttinger-liquid behavior. Transitions from ferromagnetic to Luttinger-liquid phases are first order. We thoroughly discuss the transition between different ferromagnetic phases, which, in the absence of DM interactions, belongs to the XX universality class. We provide evidence that the DM exchange term turns out to split this critical line into two separated Ising-like transitions and that in between a disordered phase may appear. Our study sheds light on the general problem of strongly-interacting spin-orbit-coupled bosonic gases trapped in an optical lattice and can be used to characterize the topological properties of superconducting nanowires in the presence of an imposed supercurrent and of interactions.
A preponderance of evidence suggests that the ground state of the nearest-neighbor S=1/2S=1/2S=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, ${D}_{c}/J\ensuremath{\simeq}0.012(2)$, 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.
We have studied the phase diagram of the one dimensional XXZ model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points, critical point and the scaling of coupling constants. This model has three phases, ferromagnetic, spin-fluid and Néel phases which are separated by a critical line which depends on the DM coupling constant. We have shown that the staggered magnetization is the order parameter of the system and investigated the influence of DM interaction on the chiral ordering as a helical magnetic order.
We study the quasi-one-dimensional limit of the spin-1/2 quantum Heisenberg antiferromagnet on the kagome lattice. The lattice is divided into antiferromagnetic spin chains (exchange JJJ) that are weakly coupled via intermediate ``dangling'' spins (exchange ${J}^{\ensuremath{'}}$). Using one-dimensional bosonization, renormalization-group methods, and current algebra techniques, the ground state is determined in the limit ${J}^{\ensuremath{'}}⪡J$. We find that the dangling spins and chain spins form a spiral with O(1)O(1)O(1) and $O({J}^{\ensuremath{'}}/J)$ static moments, respectively, atop of which the chain spins exhibit a smaller $O[{({J}^{\ensuremath{'}}/J)}^{2}]$ antiferromagnetically ordered component along the axis perpendicular to the spiral plane.
The Dzyaloshinskii-Moriya (DM) interaction in magnetic models is the result of a combination of superexchange and spin-orbital coupling, and it can give rise to rich phase-transition behavior. In this paper, we study ferromagnetic XY models with the DM interaction on two-dimensional L×L square lattices using a hybrid Monte Carlo algorithm. To match the incommensurability between the resultant spin structure and the lattice due to the DM interaction, a fluctuating boundary condition is adopted. We also define a different kind of order parameter and use finite-size scaling to study the critical properties of this system. We find that a Kosterlitz-Thouless-like phase transition appears in this system and that the phase-transition temperature shifts toward higher temperature with increasing DM interaction strength.
Dzyaloshinskii–Moriya (DM) interactions cause many interesting physical features, such as topologically nontrivial magnetic skyrmions and chiral domain walls. These interactions become more pronounced in low-dimensional systems. We investigated a one-dimensional Heisenberg spin-1/2 chain with an asymmetric DM interaction. The results show that, upon applying a nonzero DM interaction, the Néel ground state transitions to a spin chiral phase. Moreover, using the mean-field approximation, we obtain the dispersion of the energy spectrum, from which the z-axis spin chirality is calculated as a function of the strength of the DM interaction for low-lying excitations. The results indicate that the DM interaction facilitates chirality for Dz ≤ J and induces a spin-gapped chiral state.