Thermal conductivity of spinel MnV$_{2}$O$_{4}$ with doping

Spinel MnV$_{2}$O$_{4}$ exhibits a structural phase transition and ferrimagnetic ordering simultaneously at 57 K. The crystal symmetry in the low-temperature phase obtained by the x-ray diffraction of a single crystal indicates an antiferro-orbital ordering of V $t_{2g}$ states [1]. It was also found that Al doping into the V site suppresses the orbital-ordering temperature ($T_{\rm oo}$) but barely affects the ferrimagnetic-ordering temperature ($T_{\rm N}$); thus two transition temperatures are separated in the Al-doped samples. We measured the thermal conductivity of Mn(V$_{1-x}$Al$_{x}$)$_{2}$O$_{4}$, and found that thermal conductivity sharply increases (thermal resistivity decreases) below $T_{\rm oo}$. It was also found that, with applied magnetic field, thermal resistivity increases above $T_{\rm oo}$ but decreases below $T_{\rm oo}$. These results indicate that thermal conductivity is dominated by the fluctuation of orbital ordering. [1] T. Suzuki {\em et al.}, Phys. Rev. Lett. 98, 127203 (2007).