Short-range Magnetic interactions in the Spin-Ice compound Ho$_{2}$Ti$_{2}$O$_{7}$

Magnetization and susceptibility studies on single crystals of the pyrochlore Ho$_{2}$Ti$_{2}$O$_{7}$ are reported for the first time. Magnetization isotherms are shown to be qualitatively similar to that predicted by the nearest neighbor spin-ice model. Below the lock-in temperature, $T^{\ast }\simeq 1.97$ K, magnetization is consistent with the locking of spins along [111] directions in a specific two-spins-in, two-spins-out arrangement. Below $T^{\ast}$ the magnetization for $B||[111]$ displays a two step behavior signalling the breaking of the ice rules.