Determination of spin chirality using x-ray magnetic circular dichroism

Gerrit van der Laan

doi:10.1103/physrevb.104.094414

Abstract

A 3-fold symmetric kagome lattice that has negative spin chirality can give a non-zero x-ray magnetic circular dichroism (XMCD) signal, despite that the total spin moment amounts to zero. This is explained by a hitherto unnoticed rule for the rotational symmetry invariance of the XMCD signal. A necessary condition is the existence of an anisotropic XMCD signal for the local magnetic atom, which can arise from a spin anisotropy either in the ground state or the final state. The angular dependence of the XMCD as a function of the beam direction has an unusual behavior. The maximum dichroism is not aligned along the spin direction, but depends on the relative orientation of the spin with respect to the atomic orientation. Therefore, different geometries can result in the same angular dependence, and the spin direction can only be determined if the atomic orientation is known. The consequences for the x-ray magneto-optical sum rules are given. The integrated XMCD signals are proportional to the anisotropy in the orbital moment and the magnetic dipole term, where the isotropic spin moment drops out.

Highlights

X-ray magnetic circular dichroism (XMCD) has become a versatile technique to interrogate ferro- and ferrimagnetic magnetic materials [1]
From the viewpoint of XMCD several questions remain to be addressed: What is the origin of the nonzero XMCD in the threefold symmetric AFM structure? Is this effect present for other n-fold AFM structures, notably skyrmions? Can the XMCD be used to deduce the spin direction? What roles are played by the orbital moment and the magnetic dipole term of the atoms? These questions will be answered in the following
Anisotropic spectra for an isotropic ground state have been reported for Ti 3d0 →. It is shown most generally using a straightforward analytical derivation as well as by graphical illustration that a triangular structure with negative spin chirality allows the existence of a nonzero total XMCD, despite the fact that the total spin moment vanishes

Summary

INTRODUCTION

X-ray magnetic circular dichroism (XMCD) has become a versatile technique to interrogate ferro- and ferrimagnetic magnetic materials [1]. The scalar spin chirality is closely related to the emergent magnetic field, a natural concept in the geometric theories of the Hall effect and orbital magnetization [11] It requires a noncoplanar rather than a noncollinear magnetic structure [12]. The Néel temperature TN ≈ 430 K, the combination of intersite AFM and Dzyaloshinskii-Moriya interactions leads to a 120◦ spin structure with a uniform negative spin chirality of the in-plane Mn moments because of geometrical frustration. It exhibits a large anomalous Hall conductivity [18] and magneto-optic Kerr effect (MOKE) [19] despite the absence of a net magnetic moment. From the viewpoint of XMCD several questions remain to be addressed: What is the origin of the nonzero XMCD in the threefold symmetric AFM structure? Is this effect present for other n-fold AFM structures, notably skyrmions? Can the XMCD be used to deduce the spin direction? What roles are played by the orbital moment and the magnetic dipole term of the atoms? These questions will be answered in the following

Angular dependence

General derivation

Unit cell with multifold axis

Orbital moment

Magnetic dipole term

CONCLUSIONS