Sub-10 nm Quantification of Spin and Orbital Magnetic Moment Across the Metamagnetic Phase Transition in FeRh Using EMCD

Electron magnetic circular dichroism (EMCD) in transmission electron microscopy (TEM) enables element-specific measurement of spin and orbital magnetic moments, analogous to X-ray magnetic circular dichroism (XMCD). While the EMCD technique offers unmatched spatial resolution, its quantitative accuracy remains under scrutiny, particularly in beam-splitter geometries with convergent probes. Here, we systematically evaluate the limits of quantitative EMCD analysis using the first-order magnetostructural transition in the functional phase-change material FeRh as a tunable magnetic reference. Unlike previous EMCD studies primarily focused on elemental ferromagnets such as Fe, we demonstrate its applicability to a correlated material exhibiting coupled structural and magnetic order. We demonstrate that the extracted orbital-to-spin moment ratio ($m_\text{L}/m_\text{S}$) remains consistent with XMCD benchmarks for TEM probes down to approximately 6 nm, thereby establishing the validity range for reliable quantification. For nm-sized probes with higher convergence angles, we observe an enhanced $m_\text{L}/m_\text{S}$, which we attribute to a combination of instrumental factors and sensitivity to nanoscale heterogeneity within the probed volume. Our results confirm that EMCD provides quantitative agreement with macroscale techniques under suitable conditions, while uniquely enabling spatially confined measurements of local magnetic moments in functional magnetic materials, and allowing the study of interfacial, defect-mediated, or phase-separated magnetism that is inaccessible to photon-based methods.