Low temperature specific heat of frustrated antiferromagnet HoInCu$_{4}$*

We present low temperature specific heat measurements of single crystal HoInCu$_{4}$, down to 35 mK and in magnetic field up to 12 Tesla. Ho atoms are arranged in an FCC lattice of the edge-sharing tetrahedra, and undergo an antiferromagnetic ordering at $T_{N}=$0.76 K, with the frustration parameter $f =-\Theta_{\mathrm{CW}}$/T$_{\mathrm{N}}$ of 14.3 [1]. Magnetic AF order is suppressed in field $H_{0} \approx $ 4 T. The low temperature Schottky anomaly due to Ho evolves smoothly as a function of field through $H_{0}$ and $T_{N}$. The peak value of the anomaly remains roughly constant from 0 T to 12 T. The temperature of the anomaly's peak remains constant at $T_{Sch} \approx $ 170 mK for \textit{H\textless H}$_{0}$, and gradually increases above $H_{0}$ up to 300 mK at 12 T. This indicates a complete ordering of Ho spins in zero field as well as an increasing moment on Ho once the AF order is suppressed. The measured entropy of HoInCu$_{\mathrm{4}}$ at 12 T and 2K is 17.32 J/mol-K $\approx $ Rln8 expected for an I$=$7/2 nuclear spin of Ho. \\[4pt] [1] V. Fritsch, J. D. Thompson, and J. L. Sarrao, ``Spin and orbital frustration in $R$InCu4 ($R=$Gd, Dy, Ho, and Er)'', PRB \textbf{71}, 132401 (2005).