Frustration and Dzyaloshinsky-Moriya anisotropy in the kagome francisites Cu$_3$Bi(SeO$_3)_2$O$_2$X

TL;DR

This paper studies the complex magnetic behavior of kagome francisites Cu$_3$Bi(SeO$_3)_2$O$_2$X, revealing how frustration, Dzyaloshinsky-Moriya interactions, and quantum corrections influence their ground state and excitations.

Contribution

It introduces a minimal model including Dzyaloshinsky-Moriya interactions derived from first principles to explain the magnetic properties of kagome francisites.

Findings

Frustration causes a highly degenerate classical ground state.

Quantum corrections lift degeneracy, stabilizing a fragile canted phase.

Dzyaloshinsky-Moriya interactions are essential for explaining observed magnetic order.

Abstract

We investigate the antiferromagnetic canting instability of the spin-1/2 kagome ferromagnet, as realized in the layered cuprates Cu$_3$Bi(SeO$_3)_2$O$_2$X (X=Br, Cl, and I). While the local canting can be explained in terms of competing exchange interactions, the direction of the ferrimagnetic order parameter fluctuates strongly even at short distances on account of frustration which gives rise to an infinite ground state degeneracy at the classical level. In analogy with the kagome antiferromagnet, the accidental degeneracy is fully lifted only by non-linear 1/S corrections, rendering the selected uniform canted phase very fragile even for spins-1/2, as shown explicitly by coupled-cluster calculations. To account for the observed ordering, we show that the minimal description of these systems must include the microscopic Dzyaloshinsky-Moriya interactions, which we obtain from density-functional band-structure calculations. The model explains all qualitative properties of the kagome francisites, including the detailed nature of the ground state and the anisotropic response under a magnetic field. The predicted magnon excitation spectrum and quantitative features of the magnetization process call for further experimental investigations of these compounds.