Chiral fluctuations in triangular antiferromagnets at $T⪡T_N$

Chiral fluctuations in triangular antiferromagnets (TAFs) at $T⪡T_N$ are studied theoretically. The case of a ferromagnetic interaction along the $c$ axis (which is directed perpendicular to the plane of the lattice), Dzyaloshinskii-Moriya interaction $\mathbf{D}\Vert c$ and a weak magnetic field $\mathbf{H}\Vert c$, is considered in detail. Previously, this model has been proposed to describe quantum TAF $\mathrm{Cs}\mathrm{Cu}{\mathrm{Cl}}_3$. Expressions for dynamical chirality (DC) are derived within the linear spin-wave approximation. In contrast to nonfrustrated antiferromagnets, DC is found to be nonzero even at $D,H=0$ in a one-domain sample. We argue that this unusual behavior stems from the fact that a ground state of $XY$ and Heisenberg TAFs is characterized by an axial vector along which DC is directed.

Figure 1

(a) and (b) 120° spin structures of an elementary triangle with positive and negative chirality, respectively; (c) and (d) Two inequivalent 120° spin structures of a triangular antiferromagnet, which differ from one another by chiralities of each triangle. They are described by Eq. (2) with the same $\mathbf{a}$ and $\mathbf{b}$ and with antiferromagnetic vectors ${\mathbf{k}}_0$ and $-{\mathbf{k}}_0$, respectively. These configurations are referred to in the text as $(+{\mathbf{k}}_0)$ and $(-{\mathbf{k}}_0)$, respectively.

Figure 2

The reciprocal chemical lattice (RCL) (open circles) and the reciprocal magnetic lattice (RML) (black dots). The inner (white) hexagon is the first Brillouin zone (BZ) of RML. The outer hexagon defines the edge of the second BZ of RML and, simultaneously, the first BZ of RCL. Antiferromagnetic vectors ${\mathbf{k}}_0^{\left(1\right)},{\mathbf{k}}_0^{\left(2\right)}$, and ${\mathbf{k}}_0^{\left(3\right)}$ are also presented. They are equivalent up to vectors of RCL. Also shown are two parts of the second BZ of RML, which can be reduced to the first BZ by shifting on ${\mathbf{k}}_0$ (dark-colored region) and $-{\mathbf{k}}_0$ (light-colored region).