Thermal transport in CuCr2X4 ( X=S , Se, Te): Experiment and ab initio calculations

We present a combined experimental and theoretical study of the longitudinal and transverse thermoelectric properties of ferrimagnetic spinels $\mathrm{Cu}{\mathrm{Cr}}_{2}{X}_{4}$ ($X=\mathrm{S}$, Se, Te). The thermoelectric power of all studied phases is positive and consists of two contributions; an almost linear diffusive thermopower observed at high temperature, and a strong enhancement below ${T}_{C}$ attributed to magnon drag. The diffusive part of thermopower and resistivity decreases from $X=\mathrm{S}$ to Te, whereas the magnon drag enhancement is the biggest for $X=\mathrm{Se}$, which has also the highest ${T}_{C}$. The thermopower was calculated by DFT method using GGA, $\mathrm{GGA}+U, \mathrm{GGA}+\text{oeeHyb}$, and mBJ potentials. A good agreement with the experimental thermopower was achieved using GGA potential for $X=\mathrm{S}$ and with mBJ potential for $X=\mathrm{Te}$. The mBJ potential, which was designed for $sp$-type semiconductors, better describes the valence bands of $\mathrm{Cu}{\mathrm{Cr}}_{2}{\mathrm{Te}}_{4}$ that exhibit stronger $sp$-orbitals character than sulfide and selenide. The anomalous Nernst effect (ANE) is negative at room temperature for all phases, the highest absolute value $\ensuremath{\sim}1.5 \ensuremath{\mu}\mathrm{V}$/K is observed for $X=\mathrm{Te}$ and Se around room temperature, whereas ANE for $X=\mathrm{S}$ is much smaller. A sign change of ANE to positive is observed at 285 K for $X=\mathrm{S}$ and at 65 K for $X=\mathrm{Se}$. The trend of anomalous Nernst conductivity is reproduced by Berry phase calculations if the renormalization of the bands due to the strong correlation effects is taken into account.