Simulating Microwave-Controlled Spin Imaging with Free-Space Electrons

TL;DR

This paper develops a theoretical framework for Spin Resonance Spectroscopy in transmission electron microscopy, enabling atomic-scale spin imaging through microwave-controlled electron interactions and phase shift detection.

Contribution

It introduces a novel theoretical model combining microwave fields with TEM for state-selective spin imaging at the atomic level, bridging spin spectroscopy and high-resolution imaging.

Findings

Detectable phase shifts from individual electron spins in TEM images.

Differential measurements can extract local resonance frequencies.

Imaging conditions optimized for maximum SNR using Fisher Information.

Abstract

Coherent spin resonance techniques, such as nuclear and electron spin resonance spectroscopy, have revolutionized non-invasive imaging by providing spectrally resolved information about spin dynamics. Motivated by the recent emergence of electron microscopy methods capable of sensing microwave-excitations, we establish a theoretical framework for Spin Resonance Spectroscopy (SRS) in transmission electron microscopy (TEM). This technique combines microwave pump fields with focused electron probe beams to enable state-selective spin imaging at the atomic scale. Using scattering theory, we model the interaction between free-space electrons and electron spin systems, capturing both elastic and inelastic processes. The strongest effect of the spin system on the free electron is a magnetic phase shift. Our simulations demonstrate that phase shifts from individual electron spins are detectable in both image mode and diffraction mode. In principle, differential measurements under microwave control allow the extraction of local resonance frequencies that are influenced by the surrounding spin environment. By evaluating the Classical Fisher Information (CFI), we identify imaging conditions that maximize the signal-to-noise ratio (SNR), showing how defocus and beam width affect the measurement sensitivity. These findings establish a foundation for integrating SRS with high-resolution TEM, bridging spin spectroscopy and atomic-scale imaging, and enabling new capabilities in quantum spin research and nanoscale materials characterization.