Neutron Scattering Study of the Spin Correlation in the Spin Ice System Ho ₂Ti ₂O ₇

Intensity distribution of the neutron magnetic scattering has been taken in the reciprocal space of a single crystal of the "spin ice" system Ho ₂Ti ₂O ₇ at the elastic energy position in the temperature (T) region between 0.4 K and 50 K. The short range magnetic correlation becomes appreciable with decreasing T at around 30 K. The freezing of the moment system takes place at around 1.5 K with decreasing T. Based on the mean field treatment of the moment system, the distribution of the observed intensity has been reproduced, where the dipolar interaction is confirmed to be primarily important for the determination of the magnetic correlation. Simple calculations of the scattering intensity carried out by using a cluster of 25 moments of Ho ³⁺ ions indicate that there are many types of the moment arrangement within a cluster which have almost degenerated energies, indicating that the system cannot uniquely select the correlation pattern down to rather low temperature, and before going to the lowest energy state, the system undergoes the gradual slowing down to the glassy state.