Pinch points and Kasteleyn transitions in kagome ice

Complex disordered states-from liquids and glasses to exotic quantum matter-are ubiquitous in nature. Their key properties include finite entropy, power-law correlations and emergent organizing principles. In spin ice, spin correlations are determined by the 'ice rules' organizing principle that stabilizes a magnetic state with the same zero-point entropy as water ice. The entropy can be manipulated with great precision by an applied magnetic field: when directed along the three-fold crystallographic axis, the field produces a state of finite entropy, known as kagome ice. Here, we investigate the spin-ice material Ho2Ti2O7 by tilting the magnetic field slightly away from that axis. We thus realize a classic statistical system named after Kasteleyn, in which the entropy of a critical phase can be continuously tuned. Our neutron scattering experiments reveal how this process occurs at a microscopic level.