Probing spin fractionalization with ESR-STM absolute magnetometry

TL;DR

This paper demonstrates how ESR-STM can directly measure the magnetic properties of fractionalized edge spins in Haldane chains, enabling unambiguous detection of their fractional magnetic moments and localization lengths.

Contribution

It introduces a method to map stray fields from edge spins using ESR-STM and invert the Biot-Savart law to determine their magnetic moments and localization.

Findings

Successful mapping of stray magnetic fields from edge spins

Method to invert Biot-Savart law for magnetization extraction

Unambiguous measurement of fractional magnetic moments

Abstract

The emergence of effective $S=1/2$ spins at the edges of $S=1$ Haldane spin chains is one of the simplest examples of fractionalization. Whereas there is indirect evidence of this phenomenon, direct measurement of the magnetic moment of an individual edge spin remains to be done. Here we show how scanning tunnel microscopy electron-spin resonance (ESR-STM) can be used to map the stray field created by the fractional $S=1/2$ edge spin and we propose efficient methods to invert the Biot-Savart equation, obtaining the edge magnetization map. This permits one to determine unambiguously the two outstanding emergent properties of fractional degrees of freedom, namely, their fractional magnetic moment and their localization length $\xi$.