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

TL;DR

EMCD in TEM offers element-specific measurements of spin and orbital moments with nanometer-scale spatial resolution, but its quantitative reliability in beam-splitter geometries requires systematic benchmarking. This study uses the AF–FM metamagnetic transition in FeRh as a tunable reference to test EMCD limits in a correlated material, employing both TEM- and STEM-based probes and comparing to XMCD via sum rules for the $L_{3}$ and $L_{2}$ edges. They find quantitative agreement with XMCD for TEM probes down to about $6$ nm, with $m_{\text{L}}/m_{\text{S}}$ around $0.026\pm0.005$, while sub-6 nm, highly convergent probes produce larger values up to $0.17\pm0.01$ due to instrumental factors and nanoscale heterogeneity. The work establishes EMCD as a robust nanoscale magnetometry tool capable of imaging local spin and orbital moments and studying interfacial, defect-mediated, or phase-separated magnetism inaccessible to photon-based methods.

Abstract

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.

Figures (7)

• Figure 1: FeRh system and studied specimen geometry (a) Schematic of the AF-FM transition in FeRh, showing atomic positions and magnetic moments on Fe and Rh atoms. (b) Temperature-dependent magnetization during heating and cooling for the 25-nm-film on MgO before detachment. (c) Sample preparation: epitaxial FeRh grown on MgO, followed by selective MgO etching in Na$_2$EDTA to release the FeRh film, which is then collected on a Cu TEM grid.
• Figure 2: AF-FM phase transition in LTEM. (a) Schematic illustration of the pretilted freestanding FeRh (red box) illuminated by electron beam, with expected Fresnel contrast at AF–FM phase boundaries and FM domain walls. (b) In situ LTEM images showing the nucleation and growth of the FM phase during heating. (c) Corresponding retraction of the FM phase upon cooling, revealing the spatial evolution of the magnetic first-order phase transition.
• Figure 3: EMCD in freestanding FeRh. (a) Schematic of EMCD detection using parallel beam and convergent beam configurations. (b) Simulated relative EMCD signal as a function of sample thickness for a conventional experimental setup, showing optimal signal near 25 nm at 300 keV. (c) Experimental diffraction patterns with marked aperture positions used for dichroic signal acquisition on 25-nm-thick freestanding FeRh films. (d) EMCD spectra measured in the AF phase (300 K) for both configurations, showing weak noise-like differences. (e) EMCD spectra in the FM phase (425–450 K), showing pronounced dichroic contrast.
• Figure 4: Probe-size dependence of Fe magnetic moments in FeRh from EMCD. Evaluated orbital-to-spin moment ratio ($m_\text{L}/m_\text{S}$) as a function of electron probe size. The red curve indicates the corresponding convergence angle of the beam. EMCD results are compared with reference XMCD values from Stamm et al.Stamm2008Antiferromagnetic-ferromagneticDichroism, showing good agreement for probe diameters larger than $\sim$6 nm in TEM mode. For smaller, highly convergent STEM probes, $m_\text{L}/m_\text{S}$ changes sharply, indicating limitations of quantitative extraction.
• Figure 5: Interlink between XMCD and the beam splitter EMCD method. (a) Schematic of core level spin-orbit coupled electron transitions excited by different handedness circular polarized X-rays. (b) Example X-ray absorption spectra (XAS) and difference (XMCD) spectrum for Co. Adapted from vanderLaan2014X-rayMagnetism. (c) Schematic of the beam splitter method for EMCD and Thales circle diagram. Adapted from Schattschneider2006.