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 super -exchange J and (out-of-plane) Dzyaloshinskii-Moriya interaction JD, 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 JD/J greater than or similar to 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 JD -> 0. The small value of JD/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 Cs2Cu3SnF12.