Giant octupole moment in magnetic multilayers

TL;DR

This paper introduces a method to quantify multipole contributions in the anomalous Hall effect, revealing a dominant octupole component in multilayers and demonstrating control over it through interface and magnetic reconfiguration.

Contribution

The study presents a novel technique to analyze multipole moments in magnetic effects, especially octupole contributions, in non-periodic systems like multilayers.

Findings

Octupole-dominated anomalous Hall effect observed in multilayers.

Conventional contributions include significant octupole components.

Control over octupole effects achieved via interface and magnetic reconfiguration.

Abstract

Multipole moments serve as order parameters for characterizing higher-order magnetic effects in momentum space, providing a framework to describe diverse magnetic responses by extending the concept of magnetism. In this letter, we introduce a methodology to quantitatively determine the multipole moment contributions in anomalous Hall effect through angle-dependent anomalous Hall current, with explicit incorporation of discrete crystal symmetries. Our technique uniquely enables the investigation of octupole contribution in non-periodic systems, particularly at interfaces and surfaces. Typically, in (Ag$_{2}$Fe$_{5}$)$_{n}$ multilayers with quantum-well-engineered $k$-point selectivity, we observe an octupole-dominated anomalous Hall effect in conventional ferromagnetic materials, through first-principles calculations. These results fundamentally challenge the existing theoretical understanding of the anomalous Hall effect, showing that even the conventional contribution arises not only from the dipole moment (net magnetization). Furthermore, we establish practical control over the octupole contribution through two distinct approaches: interface engineering and magnetic ordering reconfiguration, opening new possibilities for manipulating higher-order transport effects.