Thermodynamic properties of paramagnetic α - and β−Mn from first principles: The effect of transverse spin fluctuations

Abstract

First-principles-based thermodynamic modeling of cubic $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ phases of Mn represent a challenge due to their structural complexity and the necessity of simultaneous treatment of several types of disorder (electronic, magnetic, and vibrational) that have very different characteristic time scales. Here we employ mean-field theoretical models to describe the different types of disorder and then we connect each layer of theory to the others using the adiabatic principle of separating faster and slower degrees of freedom. The slowest (vibrational) degrees of freedom are treated using the Moruzzi, Janak, and Schwarz formalism [Phys. Rev. B 37, 790 (1988)] of the Debye-Gr\uneisen model parametrized based on the first-principles calculated equation of state which includes the free-energy contributions due to the fast (electronic and magnetic) degrees of freedom via the Fermi-Dirac distribution function and a mean-field theory of transverse spin fluctuations. The magnetic contribution due to transverse spin fluctuations has been computed self-consistently within the disordered local moment picture of the paramagnetic state. The obtained results for thermodynamic properties such as lattice parameter, linear thermal expansion coefficient, and heat capacity of both phases show a good agreement with available experimental data. We also tested the assumption about the nature (localized versus delocalized) of magnetic moment on site IV in $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Mn}$ and site I in $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Mn}$ on the thermodynamic properties of these two phases. Similar to the findings of experimental studies, we conclude that magnetic moment on site IV in $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Mn}$ is not of a localized character. However, a similar analysis suggests that the magnetic moment of site I in $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Mn}$ should be treated as localized.