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The antiferromagnetic semiconductor MnTe has recently attracted attention for spintronics and high-performance thermoelectric applications. However, little is known about its vibrational and thermal transport properties and how these might relate to the electronic and magnetic structure, particularly as related to Mn orbital correlations. Here, we calculate a physically justified Coulomb correlation parameter within the framework. We couple this framework with the Heisenberg Hamiltonian and first-principles Boltzmann transport to understand the magnetic, vibrational, and phonon thermal transport properties of MnTe. We also perform inelastic neutron and nuclear inelastic x-ray scattering measurements of the total and partial phonon density of states, respectively. Very good agreement is obtained with the measured and calculated phonon density of states, and with available measurements for the band …