Spontaneous spin ordering of Dirac spin liquid in a magnetic field

TL;DR

This paper investigates how a magnetic field induces spontaneous spin ordering in the Dirac spin liquid state of Kagome antiferromagnets, predicting a universal magnetization scaling and suggesting experimental detection methods.

Contribution

It demonstrates the instability of the Fermi pocket state to a Landau level state with spontaneous in-plane magnetization in a Dirac spin liquid under magnetic field.

Findings

Landau level state breaks spin rotation symmetry.

Magnetization scales as M ~ B^α with a universal exponent.

Proposes experimental detection in Herbertsmithite.

Abstract

The Dirac spin liquid was proposed to be the ground state of the spin-1/2 Kagome antiferromagnets. In a magnetic field $B$, we show that the state with Fermi pocket is unstable to the Landau level (LL) state. The LL state breaks the spin rotation around the axis of the magnetic field. We find that the LL state has an in-plane 120$^{\circ}$ $q=0$ magnetization $M$ which scales with the external field $M\sim B^{\alpha}$, where $\alpha$ is an intrinsic calculable universal number of the Dirac spin liquid. We discuss the related experimental implications which can be used to detect the possible Dirac spin liquid phase in Herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$.