Static Spin Disorder and Field-Induced Low Dimensionality in the Spin Ice Phase of Ho$_2$Ti$_2$O$_7$

The pyrochlore magnet Ho$_2$Ti$_2$O$_7$ displays a disordered, geometrically frustrated state at low temperature known as ``Spin Ice.'' This short-range correlated magnetic state is so named because it maps onto the proton-disorder problem in water ice. Unique to spin ice, as opposed to water ice, is the tunable parameter of applied magnetic field, which allows a new dimension of its phase behavior to be studied [Fennell et.al, PRB 72, 224411(2005)]. We report time-of-flight neutron scattering experiments probing the magnetic field-induced behavior of Ho$_2$Ti$_2$O$_7$ with the field applied along a crystallographic [110] direction. These results show elastic short-range correlations in Ho$_2$Ti$_2$O$_7$ in zero field, and a decomposition of the pyrochlore lattice into two orthogonal sets of weakly interacting chains in the presence of a [110] magnetic field. One of these subsystems of the pyrochlore lattice undergoes a 3D to 1D crossover with applied field. We compare our results with expectations for a dipolar spin ice model, and with recent results for the antiferromagnetic sister compound Tb$_2$Ti$_2$O$_7$.