Temperature and pressure dependence of the optical absorption in hexagonal MnTe

Abstract

The absorption edge of hexagonal (NiAs structure) antiferromagnetic MnTe has been measured by means of light transmission experiments carried out at different temperatures in the range 16--420 K $(P=1\mathrm{bar})$ and hydrostatic pressures up to 9 GPa $(T=295\mathrm{K}).$ An indirect band gap has been found, in agreement with previous band-structure calculations, with an energy of ${E}_{\mathrm{ig}}=1.272\ifmmode\pm\else\textpm\fi{}0.013\mathrm{eV}$ at room temperature and pressure. The temperature dependence of the absorption edge is linear above the N\'eel temperature ${T}_{N}=310\mathrm{K},$ with a temperature coefficient $dE/dT=\ensuremath{-}(3.5\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\mathrm{e}\mathrm{V}/\mathrm{K}.$ Below ${T}_{N}$ an additional blueshift is found, with a maximum value of 0.1 eV at low temperatures. The temperature dependence of this anomalous shift is proportional to the square of the magnetization, a result which is consistent with previous second-order perturbation calculations. Regarding the measurements under pressure, a negative pressure coefficient with a value of $dE/dP=\ensuremath{-}(59\ifmmode\pm\else\textpm\fi{}2\mathrm{m}\mathrm{e}\mathrm{V}/\mathrm{G}\mathrm{P}\mathrm{a})$ has been found. The N\'eel temperature is known to increase with pressure in hexagonal MnTe, due to an increment of the exchange interaction, or equivalently, of the sublattice magnetization. Consequently a positive pressure shift could be expected at room temperature, derived from both the antiferromagnetic splitting of Mn $3d$ orbital and second-order electron and hole interaction with fixed Mn spins. The negative pressure coefficient has thus been interpreted as a sum of that positive contribution and a larger negative one derived from an enhanced p-d repulsion which would lead to an upwards shift of the valence-band maximum.