Spin glass and spin dynamics in a disordered Heisenberg model for rare-earth titanates

Mott insulating rare-earth titanates can display either ferromagnetic or antiferromagnetic order at low temperatures. The nature of the magnetic ground state can be controlled by chemical substitution on the rare-earth sites, which inevitably modifies the exchange constants of the material locally, in an inhomogeneous way. To capture this effect, we propose a disordered Heisenberg model to describe the chemically substituted Mott insulating rare-earth titanates. By performing systematic Monte Carlo simulations, we identify a wide range of chemical substitutions where a spin glass with a non-zero chiral glass order parameter becomes the ground state. Moreover, a robust coexistence of the magnetically ordered state with the spin and chiral glasses is also found. The dynamic spin structure factor is computed in different regions of the model and compared with neutron scattering experiments on La-doped YTiO3.