Electric-field-induced X-ray Nonreciprocal Dichroism in Hematite

Abstract

Hematite (alpha-Fe2O3) is a prototypical room temperature antiferromagnet whose time-reversal-odd magnetic structure has recently attracted renewed attention. While such magnetic symmetry can be characterized in terms of higher-order multipoles beyond the magnetic dipole, their manifestation in measurable physical phenomena has remained largely elusive. In this work, we investigate x-ray absorption near the Fe K-edge of hematite under an applied electric field, which explicitly breaks space-inversion symmetry. We observe an electric-field-induced x-ray nonreciprocal linear dichroism (E-induced XNLD) that reflects the time-reversal-odd nature of the magnetic order. Numerical simulations based on ab-initio density functional theory reproduce the observed spectra, including their dependence on the antiferromagnetic domain and x-ray polarization. Furthermore, a symmetry-resolved multipole analysis reveals that this response originates from the magnetic quadrupole and the magnetic toroidal octupole induced by the applied electric field. These results demonstrate that electric-field-modulated x-ray absorption provides direct access to the antiferroic order of higher-order multipoles in time-reversal-odd antiferromagnets, thereby establishing a general framework to uncover hidden symmetry properties in magnetic materials.

Figures (11)

• Figure 1: (a) Magnetic structures of hematite viewed along the $a_h$ axis (top panels) and the $c_h$ axis (bottom panels). Thick red arrows denote Fe spins, and black lines represent the rhombohedral primitive cell. The numbers next to the Fe$^{3+}$ ions denote the site numbers. Above $T_\mathrm{M}$, the Fe spins lie perpendicularly to the $c_h$ axis. The two states of $L_{\perp}+$ and $L_{\parallel}+$, with the Néel vector $\mathbf{L}$ aligned perpendicular and parallel to the $a_h$ axis, respectively, are depicted. $\mathbf{M}$ denotes net magnetization that appears due to spin canting. Below $T_\mathrm{M}$, the spins are aligned along the $c_h$ axis. (b) Schematic illustration of the experimental setup.
• Figure 2: Spectra of x-ray absorption and electric-field-induced change in x-ray transmittance. (a) X-ray absorption spectrum around the Fe K pre-edge. The inset shows the spectrum in the wide energy range including the main edge. (b) Electric-field-modulated x-ray transmittance spectrum. The AC component of the transmitted light intensity ($\Delta I$), obtained under an applied AC voltage, is normalized by the DC component ($I_{\mathrm{DC}}$). The spectra obtained with the peak amplitude of 200 V, 150 V, 100 V, and 50 V are shown. (c) Voltage dependence of $\Delta I/I_{\mathrm{DC}}$ integrated in the energy range from 7.1095 keV to 7.1110 keV [see the dashed-line region in panel (b)]. The red line shows the result of least-square fitting.
• Figure 3: Domain state dependence of electric-field–modulated x-ray transmittance. (a,b) Schematic illustration of the experimental geometry for the $L_{\perp}$ (a) and $L_{\parallel}$ (b) states. The polarization of the incident x-ray beam ($\boldsymbol{\epsilon}$) is aligned along the $x$ axis for measurements of the $L_{\perp}\pm$ states and oriented at $45^\circ$ with respect to the $x$ axis for the measurements of the $L_{\parallel}\pm$ states. (c,d) Electric-field–modulated x-ray transmittance spectrum in the $L_{\perp}$ (c) and $L_{\parallel}$ (d) states. Measurements were performed in the $L_{\perp}+$ and $L_{\parallel}+$ (red), and $L_{\perp}-$ and $L_{\parallel}-$ (blue) domains. The spectra were obtained under an applied AC voltage with a peak amplitude of 200 V. Solid curves represent the results of numerical simulations (see Sec. VB).
• Figure 4: Polarization angle dependence of electric-field–modulated x-ray transmittance. (a,b) Electric-field–modulated x-ray transmittance spectra measured for different polarization angles ($\theta$) in the $L_{\perp}+$ domain (a) and $L_{\parallel}+$ domain (b). The spectra were obtained under an applied AC voltage with a peak amplitude of 200 V. Solid curves represent the results of numerical simulations (see Sec. \ref{['sec:simulations']}). (c) Polarization angle dependence of $\Delta I/I_{\mathrm{DC}}$ integrated in the energy range from 7.1095 keV to 7.1110 keV for the $L_{\perp}+$ domain (red) and $L_{\parallel}+$ domain (blue). Solid curves represent the results of least-squares fits using a cosine function ($\propto \cos 2\theta$) for the $L_{\perp}+$ domain and a sine function ($\propto \sin 2\theta$) for the $L_{\parallel}+$ domain.
• Figure 5: (a) Multipole decomposition of the simulated electric-field-induced XNLD spectrum. The total spectrum corresponds to the simulation for the $L_{\perp}$ domain shown in Fig. \ref{['fig:XAS_Edep']}(b). The spectrum is decomposed into contributions from the magnetic toroidal octupole $I_{3,2}+I_{3,-2}$ and the magnetic quadrupole $I_{2,2}-I_{2,-2}$. The details of each multipole are discussed in the main text.