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

Motivated by recent experiments on Cs₂Cu₃SnF₁₂ and YCu₃(OH)₆Cl₃, we consider the S = 1/2 Heisenberg model on the kagome lattice with nearest-neighbor superexchange J and (out-of-plane) Dzyaloshinskii-Moriya interaction J_D, which favors (in-plane) 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 ≳ 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 → 0. The small value of J_D / J for the onset of magnetic order is particularly relevant for the interpretation of low-temperature behaviors of kagome antiferromagnets, including ZnCu₃(OH)₆Cl₂. 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 Cs₂Cu₃SnF_12.