Magneto-elastic effects and thermodynamic properties of ferromagnetic hcp Co

Using first principles projector augmented wave (PAW) potential method, the magneto-elastic effects and thermodynamic properties of ferromagnetic hcp Cobalt at high pressure and temperature are investigated. The calculated elastic constants from PBE+U method demonstrate a noticeable improvement with regard to experimental data. Various physical quantities under high pressure also present significant improvements, such as the bulk modulus, shear modulus, Young׳s modulus, Debye temperature, various sound velocities and the normalized acoustic velocities in the meridian plane. That is due to the fact that Cobalt system possesses large correlation effects. Meanwhile, the phonon dispersion curves are in excellent agreement with experimental data. It is not observed any anomaly or instability under compression. However, according to the E2g-phonon frequencies, the obtained pressure variation of C44 elastic modulus also suggests that the system has miraculous magneto-elastic effects. Moreover, the pressure and temperature dependence of thermodynamic properties are derived within the quasi-harmonic approximation for the first time. The obtained Grüneisen ratio, Anderon–Grüneisen parameter and the volume dependence of Grüneisen ratio display manifestly temperature and pressure dependences.