  The transition metal pnictide CrAs exhibits superconductivity in the vicinity
of a helimagnetic phase, where it has been found that the propagation vector is
parallel to the c axis and the magnetic moments lie in the ab plane. Here we
use ab initio calculations to study the magnetic interactions in the material.
Mapping onto a Heisenberg Hamiltonian, we calculate the magnetic exchanges by
using LDA+U calculations and we unveil the origin of the magnetic frustration.
Finally, we reproduce the double helix magnetic order with a propagation vector
Q = (0, 0, 0.456) and we obtain the magnetic transition temperature TN through
Monte-Carlo simulations of the specific heat. Due to the limitations of the use
of the Heisenberg Hamiltonian for itinerant magnetic systems, the theoretical
TN underestimated the experimental value of the pure CrAs. However, our results
are in good agreement with those found for the alloy CrAs0.5Sb0.5 belonging to
the same space group, showing that our result can describe this material class.
