  Equation of state for chromium nitride has been debated in the literature in
connection with a proposed collapse of its bulk modulus following the pressure
induced transition from the paramagnetic cubic phase to the antiferromagnetic
orthorhombic phase [F. Rivadulla et al., Nat Mater 8, 974 (2009); B. Alling et
al., Nat Mater 9, 283 (2010)]. Experimentally the measurements are complicated
due to the low transition pressure, while theoretically the simulation of
magnetic disorder represent a major challenge. Here a first-principles method
is suggested for the calculation of thermodynamic properties of magnetic
materials in their high temperature paramagnetic phase. It is based on
ab-initio molecular dynamics and simultaneous redistributions of the disordered
but finite local magnetic moments. We apply this disordered local moments
molecular dynamics method to the case of CrN and simulate its equation of
state. In particular the debated bulk modulus is calculated in the paramagnetic
cubic phase and is shown to be very similar to that of the antiferromagnetic
orthorhombic CrN phase for all considered temperatures.
