Specific Heat of the Kagome Antiferromagnet Herbertsmithite in High Magnetic Fields

TL;DR

This study measures the specific heat of herbertsmithite in high magnetic fields, revealing a field-independent power-law behavior consistent with a critical spin liquid state and suggesting about 10% site dilution affects the kagome lattice.

Contribution

It provides the first detailed high-field specific heat measurements of herbertsmithite, demonstrating a field-independent power-law and proposing a model with site dilution to explain the data.

Findings

Kagome contribution follows a T^{1.5} power law at low temperatures.

Specific heat is field-independent between 28 and 34 T.

Evidence of a critical spin liquid ground state supported by minimal field dependence.

Abstract

Measuring the specific heat of herbertsmithite single crystals in high magnetic fields (up to $34$ T) allows us to isolate the low-temperature kagome contribution while shifting away extrinsic Schottky-like contributions. The kagome contribution follows an original power law $C_{p}(T\rightarrow0)\propto T^{\alpha}$ with $\alpha\sim1.5$ and is found field-independent between $28$ and $34$ T for temperatures $1\leq T\leq4$ K. These are serious constrains when it comes to replication using low-temperature extrapolations of high-temperature 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 has a minute field dependence then 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 a phase diagram.