  We propose new semi-implicit numerical methods for the integration of the
stochastic Landau-Lifshitz equation with built-in angular momentum
conservation. The performance of the proposed integrators is tested on the 1D
Heisenberg chain. For this system, our schemes show better stability properties
and allow us to use considerably larger time steps than standard explicit
methods. At the same time, these semi-implicit schemes are also of comparable
accuracy to and computationally much cheaper than the standard midpoint
implicit method. The results are of key importance for atomistic spin dynamics
simulations and the study of spin dynamics beyond the macro spin approximation.
