Figure 5: The response of Eu spin alignment with applied H-field in the ETO film on LSAT with and without E-field.

(a) Energy scans through the Eu L_II edge at the (003)_ETO reflection with ±1.2 T showing the maximum interference effect at full saturation between the magnetic and charge scattering amplitudes. The sign of the magnetic amplitude switches with the H-field direction altering the interference effect. (b) The linear XRIS-H-field dependence is presented by plotting the scattering amplitude at the line indicated energy in (a). The arrows illustrate the spin reorientation of the Eu ions with H-field and the inset shows the measurement (π–π) geometry. The error bars represent the s.d. (c) The energy dependence of the intensity difference between ±0.1 T across the resonance edge with and without E-field application (1 × 10⁵ V cm⁻¹). The solid line in the top panel is a scaled version of the ±1.2 T data set. The charge–magnetic interference phenomenon is eliminated with E-field. (c—Inset) A microscopic cartoon model of the Eu spin arrangement with and without E-field. Naturally, the G-AFM-ordered Eu spins coherently cant towards the external H-field direction; however, with applied E-field, the near magnetic degenerate states likely induce a collinear mixed AFM–FM phase devoid of long-range magnetic ordering. While the FM regions produce insufficient coherency themselves, by pining neighbouring AFM spin orientations along the applied H-field direction they inhibit spin canting and in effect mute the interference effect. S.d. errors are propagated for the difference measurements.