  The dynamical and thermodynamic phase stabilities of the stoichiometric
compound CrN including different structural and magnetic configurations are
comprehensively investigated using a first-principles density-functional-theory
(DFT) plus U approach in conjunction with experimental measurements of the
thermal expansion. Comparing DFT and DFT+U results with experimental data
reveals that the treatment of electron correlations using methods beyond
standard DFT is crucial. The non-magnetic face-centered cubic B1-CrN phase is
both, elastically and dynamically unstable, even under high pressure, while CrN
phases with non-zero local magnetic moments are predicted to be dynamically
stable within the framework of the DFT+U scheme. Furthermore, the impact of
different treatments for the exchange-correlation (xc)-functional is
investigated by carrying out all computations employing the local density
approximation and generalized gradient approximation. To address
finite-temperature properties, both, magnetic and vibrational contributions to
the free energy have been computed employing our recently developed spin-space
averaging method. The calculated phase transition temperature between
low-temperature antiferromagnetic and high-temperature paramagnetic (PM) CrN
variants is in excellent agreement with experimental values and reveals the
strong impact of the choice of the xc-functional. The temperature-dependent
linear thermal expansion coefficient of CrN is experimentally determined by the
wafer curvature method from a reactive magnetron sputter deposited single-phase
B1-CrN thin film with dense film morphology. A good agreement is found between
experimental and ab initio calculated linear thermal expansion coefficients of
PM B1-CrN. Other thermodynamic properties, such as the specific heat capacity,
have been computed as well and compared to previous experimental data.
