Specific Heat of the Kagome Antiferromagnet Herbertsmithite in High Magnetic Fields

Measuring the specific heat of herbertsmithite single crystals in high magnetic fields (up to 34 T) allows us to isolate the lowerature kagome contribution while shifting away extrinsic Schottky-like contributions. The kagome contribution follows an original power law Cp(T→0)∝Tα with α∼1.5 and is found to be field independent between 28 and 34 T for temperatures 1≤T≤4 K. These are serious constraints when it comes to replication using lowerature extrapolations of higherature series expansions. We manage to reproduce the experimental observations if about 10% of the kagome sites do not contribute. Between 0 and 34 T, the computed specific heat then has a minute field dependence supporting an algebraic temperature dependence in zero field, typical of a critical spin-liquid ground state. The need for an effective dilution of the kagome planes is discussed and is likely linked to the presence of copper ions on the interplane zinc sites. At very low temperatures and moderate fields, we also report some small field-induced anomalies in the total specific heat and start to elaborate on a phase diagram.