Abstract
At low temperatures, a spin ice enters a Coulomb phase - a state with algebraic correlations and topologically constrained spin configurations. In Ho2Ti2O7, we have observed experimentally that this process is accompanied by a non-standard temperature evolution of the wave vector dependent magnetic susceptibility, as measured by neutron scattering. Analytical and numerical approaches reveal signatures of a crossover between two Curie laws, one characterizing the high temperature paramagnetic regime, and the other the low temperature topologically constrained regime, which we call the spin liquid Curie law. The theory is shown to be in excellent agreement with neutron scattering experiments. On a more general footing, i) the existence of two Curie laws appears to be a general property of the emergent gauge field for a classical spin liquid, and ii) sheds light on the experimental difficulty of measuring a precise Curie-Weiss temperature in frustrated materials; iii) the mapping between gauge and spin degrees of freedom means that the susceptibility at finite wave vector can be used as a local probe of fluctuations among topological sectors.
Highlights
There are indications [1,2,3,4,5,6,7,8,9,10] that condensed matter physics is leaving the drought in which experimental candidates for quantum spin-liquid states are scarce
Theory and experiment agree for bulk quantities and at large scattering wave vectors, but differences at small wave vectors indicate that the classical spin-ice states are not populated at low temperatures
Main contenders for future spin-liquid materials are quantum versions of the well-known ‘‘spin ices,’’ where quantum fluctuations [11,12,13,14] of the classically degenerate spin-ice state could lead to a collective paramagnetic phase with such exotic features as emergent gauge symmetry or charge or spin fractionalization [15,16]
Summary
There are indications [1,2,3,4,5,6,7,8,9,10] that condensed matter physics is leaving the drought in which experimental candidates for quantum spin-liquid states are scarce. In the case of gapless spin liquids, entanglement entropy cannot be so used to classify the emergent topology This is unfortunate for the quantum spin ices, which, due to the nature of the underlying classical gauge structure, most likely fall into this category [3]. The correlations induced by local constraints were discussed in systems on the kagome lattice with both discrete [22] and continuous symmetry [23] and for frustrated antiferromagnets with a pyrochlore structure [24,25,26] In these theoretical models, the physics of the ‘‘Coulomb phase,’’ with dipolar correlations showing up as pinch-point singularities in reciprocal space [27,28,29], is universally present.
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