  We present a theoretical scheme to calculate the elastic constants of
magnetic materials in the high-temperature paramagnetic state. Our approach is
based on a combination of disordered local moments picture and ab initio
molecular dynamics (DLM-MD). Moreover, we investigate a possibility to enhance
the efficiency of the simulations of elastic properties using recently
introduced method: symmetry imposed force constant temperature dependent
effective potential (SIFC-TDEP). We have chosen cubic paramagnetic CrN as a
model system. This is done due to its technological importance and its
demonstrated strong coupling between magnetic and lattice degrees of freedom.
We have studied the temperature dependent single-crystal and polycrystalline
elastic constants of paramagentic CrN up to 1200 K. The obtained results at T=
300 K agree well with the experimental values of polycrystalline elastic
constants as well as Poisson ratio at room temperature. We observe that the
Young's modulus is strongly dependent on temperature, decreasing by ~14% from
T=300 K to 1200 K. In addition we have studied the elastic anisotropy of CrN as
a function of temperature and we observe that CrN becomes substantially more
isotropic as the temperature increases. We demonstrate that the use of Birch
law may lead to substantial errors for calculations of temperature induced
changes of elastic moduli. The proposed methodology can be used for accurate
predictions of mechanical properties of magnetic materials at temperatures
above their magnetic order-disorder phase transition.
