X-ray study of ferroic octupole order producing anomalous Hall effect

Abstract

Recently found anomalous Hall, Nernst, magnetooptical Kerr, and spin Hall effects in the antiferromagnets Mn₃X (X = Sn, Ge) are attracting much attention for spintronics and energy harvesting. Since these materials are antiferromagnets, the origin of these functionalities is expected to be different from that of conventional ferromagnets. Here, we report the observation of ferroic order of magnetic octupole in Mn₃Sn by X-ray magnetic circular dichroism, which is only predicted theoretically so far. The observed signals are clearly decoupled with the behaviors of uniform magnetization, indicating that the present X-ray magnetic circular dichroism is not arising from the conventional magnetization. We have found that the appearance of this anomalous signal coincides with the time reversal symmetry broken cluster magnetic octupole order. Our study demonstrates that the exotic material functionalities are closely related to the multipole order, which can produce unconventional cross correlation functionalities.

Fig. 1. Experimental setup, principles for XMCD measurement, and typical XMCD spectrum in Mn₃Sn.

a Schematic of the magnetic structure of Mn₃Sn and experimental setup. A circularly polarized X-ray beam was irradiated on the cleaved (0001) plane. θ_in (θ_B) is an angle between (0001) plane and X-ray beam (magnetic field) within a plane containing [2–1–10] and [0001]. The angle between X-ray and magnetic field (θ_in − θ_B) is 10 degrees for samples #1 and #2, and θ_in − θ_B = 0 for sample #3. b Principle of XMCD. L₃ (L₂) edge corresponds to the excitation between 2p_3/2 (2p_1/2) core level and unoccupied d states. c Typical XMCD spectrum (left axis) and XAS (right axis) of Mn₃Sn obtained for B = 1 T. The XMCD intensity is normalized by the peak intensity of XAS.

Fig. 2. Field orientation and strength dependences of XMCD signals.

a Field-orientation dependence of XMCD spectrum for B = 1 T (red and blue curve), and XMCD for θ_B = 90° and B = 0 T (dashed sky-blue). For θ_B = 15° (θ_in = 25°), the spectral shape is almost field independent, and the residual XMCD signal is still observed at 0 T as shown in the inset. To measure the XMCD signal at 0 T, 0.1 T is firstly applied, and the field is reduced to be 0 T. b θ_in dependence of XMCD peak intensity for L₃ edge (≡ L₃ I_XMCD) and B = 0.1 T and 1 T. Corresponding field angle θ_B is also presented in the upper horizontal axis. The dashed line represents a fit proportional to cosθ_in for the data. c Field-swept XMCD at constant photon energies of 638.8 eV and 640.0 eV for θ_B = 15° (θ_in = 25°, red and magenta curves) and θ_B = 90° (θ_in = 100°, blue and sky-blue curves), respectively. The photon energy for each field direction corresponds to the maximum XMCD intensity at the L₃ edge as indicated by red and blue solid arrows in a, respectively. Red (blue) and magenta (sky-blue) curves correspond to reducing and increasing field sweep processes, respectively. Field sweep directions are also shown by arrows with the same colors. A large ferroic response with a small switching field of ~0.01 T (see inset) is observed for θ_B = 15° (θ_in = 25°), whereas a slight negative slope is observed for θ_B = 90° (B||[0001] and θ_in = 100°).

Fig. 3. XMCD sum rule analysis and temperature dependence of XMCD spectra.

a Magnetic moments in Mn₃Sn obtained from sum rule analyses for θ_B = 15° (solid symbols) and B||[0001] (open symbols), respectively. Circles and diamonds correspond to the magnetic moments of $m_{S_{\mathrm{eff}}}$ and $m_L$, respectively. Relatively large errors in $m_{S_{\mathrm{eff}}}$ for θ_B = 15° are determined from the uncertainty of XMCD integration by the oscillating behavior above ~655 eV, which is observed only for θ_B = 15°. b XMCD spectra for T = 300 K and 200 K. The XCMD intensity of Fig. 3b (sample #3) is almost 1.5–1.7 times smaller than that of Fig. 2a (sample #1). Although the origin of intensity variation is not clear, might be arising from extrinsic difference of sample conditions including surface contaminations and/or distinct sample batch.

Fig. 4. Calculated XMCD spectra and density of states.

a–c The XMCD and XAS spectra were obtained by the model calculation for different magnetic structures and X-ray configurations shown in the insets. For Mn₃Sn, x²–y² type orbit is predicted to be the ground state for minority spins from our first-principles calculation as shown in the insets. The orbital arrangement obtained from the first-principles calculation is used in the atomic model calculation for XAS and XMCD. The individual XMCD response from each sublattice A, B, and C is indicated by magenta, dashed light green, and blue curves, respectively. The total sum of the XMCD spectrum is shown by the bold orange line. In a, the magnetic moments are completely canceled, while the magnetic moments on sublattice B and C in b are slightly tilted toward the X-ray direction to reproduce the situation with in-plane external field of ~1 T (the tilted angles are exaggeratingly illustrated in the inset). In c, the X-ray direction is perpendicular to the plane, and magnetic moments are also slightly tilted to the out-of-plane direction (the corresponding perpendicular applied field is ~1.6 T). d–f Projected components of DOSs for T moment (D^T), S (D^S), and L (D^L) (left to right) were obtained from the first-principle calculations. In e, the value of D^S is 50 times magnified. The magnitude of D^T_x is much larger than those of D^S_x and D^L_x.