Ordering phenomena of spin trimers accompanied by large geometrical Hall effect

TL;DR

This paper investigates the ordering of spin trimers in a breathing kagomé lattice compound, revealing how their scalar spin chirality induces a large geometrical Hall effect that can be controlled by an external magnetic field.

Contribution

It demonstrates the ordering phenomena of spin-trimer scalar spin chirality and its impact on the geometrical Hall effect in a specific compound, highlighting tunable topological magnetic states.

Findings

Spin trimers exhibit non-coplanar spin structures with local chirality.

External magnetic fields can switch the chirality and magnetic order of spin trimers.

Large changes in the geometrical Hall effect are observed with magnetic field adjustments.

Abstract

The wavefuntion of conduction electrons moving in the background of a non-coplanar spin structure can gain a quantal phase - Berry phase - as if the electrons were moving in a strong fictitious magnetic field. Such an emergent magnetic field effect is approximately proportional to the solid angle subtended by the spin moments on three neighbouring spin sites, termed the scalar spin chirality. The entire spin chirality of the crystal, unless macroscopically canceled, causes the geometrical Hall effect of real-space Berry-phase origin, whereas the intrinsic anomalous Hall effect (AHE) in a conventional metallic ferromagnet is of the momentum-space Berry-phase origin induced by relativistic spin-orbit coupling (SOC). Here, we report the ordering phenomena of the spin-trimer scalar spin chirality and the consequent large geometrical Hall effect in the breathing kagom\'e lattice compound Dy$_3$Ru$_4$Al$_{12}$, where the Dy$^{3+}$ moments form non-coplanar spin trimers with local spin chirality. Using neutron diffraction, we show that the local spin chirality of the spin trimers as well as its ferroic/antiferroic orders can be switched by an external magnetic field, accompanying large changes in the geometrical Hall effect. Our finding reveals that systems composed of tunable spin trimers can be a fertile field to explore large emergent electromagnetic responses arising from real-space topological magnetic orders.