Static and dynamical signatures of Dzyaloshinskii-Moriya interactions in the Heisenberg model on the kagome lattice

Abstract

Motivated by recent experiments on Cs_22Cu_33SnF_{12}12 and YCu_{3}3(OH)_{6}6Cl_{3}3, we consider the {S=1/2}S=1/2 Heisenberg model on the kagome lattice with nearest-neighbor super-exchange JJ and (out-of-plane) Dzyaloshinskii-Moriya interaction J_DJD, which favors (in-plane) {Q=(0,0)}Q=(0,0) magnetic order. By using both variational Monte Carlo and tensor-network approaches, we show that the ground state develops a finite magnetization for J_D/J \gtrsim 0.03 \mathrm{-} 0.04JD/J≳0.03−0.04; instead, for smaller values of the Dzyaloshinskii-Moriya interaction, the ground state has no magnetic order and, according to the fermionic wave function, develops a gap in the spinon spectrum, which vanishes for J_D \to 0JD→0. The small value of J_D/JJD/J for the onset of magnetic order is particularly relevant for the interpretation of low-temperature behaviors of kagome antiferromagnets, including ZnCu_{3}3(OH)_{6}6Cl_{2}2. For this reason, we assess the spin dynamical structure factor and the corresponding low-energy spectrum, by using the variational Monte Carlo technique. The existence of a continuum of excitations above the magnon modes is observed within the magnetically ordered phase, with a broad peak above the lowest-energy magnons, similarly to what has been detected by inelastic neutron scattering on Cs_{2}2Cu_{3}3SnF_{12}12.