Benjamin E Atkinson, Nicholas F Chilton
Tau2 is a Python reimplementation and development of our code Tau, which calculates magnetic relaxation rates via the one-phonon (Orbach and direct) and two-phonon Raman-I mechanisms. It is substantially faster than Tau, by a factor of up to 12,000 times for Raman-I rates, and is more numerically accurate due to careful design of the integration grid. The most important optimization is that Raman rates are calculated via the calculation of a temperature-independent "Raman spectral density", which avoids recalculation of the expensive sum over phonon pairs for each temperature. Tau2 takes advantage of just-in-time compilation with Numba to minimize the overheads of the interpreted Python language. The improved algorithm drastically reduces the cost of calculating magnetic relaxation rates, making the computational cost of routine rate calculations trivial, and allows for simulation of far larger spin systems, which would not previously have been feasible.