High-field soft-x-ray dichroism of a hard ferrimagnet with easy-plane anisotropy

Sh. Yamamoto, D. I. Gorbunov, I. F. Diaz-Ortega, A. Miyata, T. Kihara, Y. Kotani, T. Nakamura, N. V. Mushnikov, A. V. Andreev, H. Nojiri, and J. Wosnitza

Phys. Rev. B 104, 064405 – Published 4 August 2021

Abstract

We performed soft x-ray spectroscopic studies of the ferrimagnet ${TbFe}_{5} {Al}_{7}$ with strong easy-plane anisotropy in pulsed magnetic fields up to 29 T along with bulk magnetization and magnetostriction measurements. We observed pronounced amplitude changes of x-ray magnetic circular dichroism and x-ray absorption spectra at the field-induced magnetic transition. This microscopically evidences the simultaneous rotation of the Tb $4 f$ and Fe $3 d$ magnetic moments from a collinear ferrimagnetic order along the [100] axis to a state with the moments close to [010], the other easy-axis direction of the tetragonal lattice in magnetic fields applied along the [100] axis. We determined the magnetic-anisotropy constant of ${TbFe}_{5} {Al}_{7}$ by simulating the high-field macro- and microscopic magnetization process using a two-sublattice model.

Received 4 February 2021
Revised 5 July 2021
Accepted 21 July 2021

DOI:https://doi.org/10.1103/PhysRevB.104.064405

Physics Subject Headings (PhySH)

Ferrimagnetism Magnetic anisotropy Magnetic phase transitions

Ferrimagnets Intermetallic compounds

Magnetization measurements X-ray magnetic circular dichroism X-ray magnetic linear dichroism

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Sh. Yamamoto ^1,*, D. I. Gorbunov¹, I. F. Diaz-Ortega ², A. Miyata¹, T. Kihara², Y. Kotani³, T. Nakamura ^2,3, N. V. Mushnikov⁴, A. V. Andreev⁵, H. Nojiri ², and J. Wosnitza^1,6

¹Hochfeld-Magnetlabor Dresden (HLD-EMFL) and Würzburg-Dresden Cluster of Excellence ct.qmat, Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany
²Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
³Japan Synchrotron Radiation Research Institute, SPring-8, Sayo, Hyogo 679-5198, Japan
⁴Institute of Metal Physics, Ural Branch of the Russian Academy of Sciences, Kovalevskaya 18, 620990 Ekaterinburg, Russia
⁵FZU Institute of Physics, Czech Academy of Sciences, 18221 Prague, Czech Republic
⁶Institut für Festkörper- und Materialphysik, TU Dresden, 01062 Dresden, Germany

^*s.yamamoto@hzdr.de

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Vol. 104, Iss. 6 — 1 August 2021

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Images

Figure 1
XMCD spectra at the (a) Tb $M_{5}$ and (b) Fe $L_{3}$ edge. These spectra were obtained in zero field at 20 K after a field pulse of 10 T was applied along the [100] axis. The vertical dashed lines represent the photon energies at which magnetic-field-dependent XMCD data of (c) Tb and (d) Fe at 20 and 10.5 K were recorded. The spectra are normalized to the XAS intensity at each energy and temperature. The sign of the XMCD in (c) and (d) is reversed with respect to those in (a) and (b). The positive (negative) values of the reversed Tb $M_{5}$ - and Fe $L_{3}$ -edge XMCD signals correspond to the moment direction (anti)parallel to the field direction.
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Figure 2
(a) Time dependence of remnant magnetization (symbols) at selected temperatures after removing the cooling magnetic field of 14 T. The solid line is the fit of the double exponential function to the time evolution of magnetization at 40 K. (b) Relative amplitude of each exponential component, defined by Eq. (1), as a function of temperature.
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Figure 3
(a) Magnetization and (b) longitudinal magnetostriction $Δ L / L$ (left scale) and its field derivative (right scale) at 50 K as function of magnetic field applied along the [100] axis. (c) $H - T$ phase diagram of ${TbFe}_{5} {Al}_{7}$ with magnetic field applied along the [100] axis determined by peak positions in $d M / d H$ and $d (Δ L / L) / d H$ data taken during field upsweep. The gray solid line is a guide for the eyes. Soft x-ray spectra in pulsed magnetic fields, shown in Figs. 4, 5, 6, were measured along the dashed vertical line. The antiparallel arrows sketch the collinear ferrimagnetic structure below $T_{comp}$ .
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Figure 4
(a) Tb $M$ -edge and (b) Fe $L$ -edge XMCD spectra at selected magnetic fields during the up sweep in pulsed magnetic fields at 50 K. All spectra are normalized to the (a) $M$ -edge and (b) $L$ -edge XAS integral at each field.
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Figure 5
(a) Averaged Tb $M$ -edge XAS spectra at 10 T (red) and 28 T (blue) compared with Tb $M_{5}$ -edge XAS spectra measured by using linear polarization perpendicular (red) and close to parallel (blue) to the Tb moments of ${Tb}_{x} {Fe}_{1 - x}$ [34]. The inset shows the Tb $4 f$ -moment direction in the (001) plane, $M_{Tb}$ , at 10 T (red arrow) and 28 T (blue arrow) with respect to the beam propagation direction, $k$ (see text for details). (b) XAS spectra at 0 T [XAS(0T)] subtracted from the XAS spectra at selected magnetic fields [XAS(H)] obtained during field upsweep.
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Figure 6
Field dependence of (a) the integrated Tb $M_{5}$ -edge (left) and Fe $L_{3}$ -edge (right) XMCD signal and (b) the integrated Tb $M_{5}$ -edge XAS difference at 50 K. The sign of the integrated XMCD signal in panel (a) is reversed as in Figs. 1 and 1. (c) Tb $4 f$ ( $M_{Tb}$ ) and Fe $3 d$ ( $M_{Fe}$ ) moment as function of magnetic field simulated by the two-sublattice model. The inset shows the canting angles used in the simulation (see text for details). (d) Schematic diagram of the sublattice-moment rotation in magnetic field estimated from the data in (a) and (b) during the field upsweep. The black arrows show the rotation direction on increasing magnetic fields.
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