Equation of state of paramagnetic CrN from ab initio molecular dynamics

The 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., Nature Mater. 8, 947 (2009) (http://dx.doi.org/10.1038/nmat2549); B. Alling et al., Nature Mater. 9, 283 (2010) (http://dx.doi.org/10.1038/nmat2722)]. Experimentally the measurements are complicated due to the low transition pressure, while theoretically the simulation of magnetic disorder represents 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.