Field-induced magnetic transitions in the highly anisotropic ferrimagnet ${\text{ErFe}}_5{\text{Al}}_7$ studied by high-field x-ray magnetic dichroism

We present a comprehensive study of the magnetic properties of the strongly anisotropic ferrimagnet ${\mathrm{ErFe}}_5{\mathrm{Al}}_7$ in pulsed magnetic fields up to 30 T applied along the hard magnetization axis within the basal plane of the tetragonal lattice around the compensation temperature ($T_{\mathrm{comp}}$). Macroscopic measurements showed two anomalies at about 8 T and 25 T in a small temperature range around $T_{\mathrm{comp}}$. High-field x-ray magnetic circular dichroism (XMCD) data at the Er $M_5$- and the Fe $L_3$-edge resonances provide insight into the element-selective magnetization processes, revealing a coherent rotation of Er $4f$ and Fe $3d$ moments, with stepwise jumps including an unexpected one from an easy to a hard magnetization axis. XMCD at the Er $L_3$-edge resonance elucidates the role of Er $5d$ electrons in coupling the Er $4f$ and the Fe $3d$ moments. Finally, an in-plane anisotropy constant was evaluated from a simulation of the magnetization process at temperatures well below $T_{\mathrm{comp}}$ using a two-sublattice model.

Figure 1

(a) Magnetization as function of magnetic field applied along the [100], [110], and [001] axis. Data are from down field sweep. (b) Field dependence of relative length change $\mathrm{\Delta }L/L$ in magnetic fields applied along the hard axis [110] within the basal plane of the tetragonal lattice of ${\mathrm{ErFe}}_5{\mathrm{Al}}_7$. Red and blue lines are data from up and down field sweeps. (c) Color-coded plot of $d(\mathrm{\Delta }L/L)/dH$ of the up-sweep data with the compensation temperature $T_{\mathrm{comp}}$. Symbols exhibit anomalies in the field-dependent magnetization data.

Figure 2

XAS and XMCD spectra measured using circularly polarized light, ${\mu }^{+}$ and ${\mu }^{-}$, at the (a) Er $M$ and (b) Fe $L$ edges at 10 K under zero magnetic field. (c) Er $M_5$- (blue) and Fe $L_3$-edge (red) XMCD integrals as function of temperature under zero magnetic field. The signs of the integrals are reversed with respect to (a) and (b). The ferrimagnetic configuration in the red- and blue-colored area is shown schematically in the insets (see text for details). All the XMCD spectra were measured after applying a 30-T magnetic-field pulse along the [110] axis. ${\vec{H}}_{\mathrm{pre}}$ indicates the direction of the magnetic field pulse.

Figure 3

(a)–(d) Bulk magnetization and (e)–(h) Er $M_5$-edge ($3d_{5/2}\to 4f$), and (i)–(l) Fe $L_3$-edge ($2p_{3/2}\to 3d$) XMCD amplitudes as functions of magnetic fields applied along the hard axis [110] within the basal plane of the tetragonal lattice at 10 K [(a), (e), and (i)], 26 K [(b), (f), and (j)], 34 K [(c), (g), and (k)], and 50 K [(d), (h), and (l)]. Red and blue lines are data from up and down field sweeps. The red and blue arrows in (b) and (c) denote anomalies observed during the up and down sweep of the field pulse, respectively. The sign of the Er $M_5$- and Fe $L_3$-edge XMCD amplitudes are reversed with respect to those in Figs. 2 and 2. The experimental errors in panels (e)–(l) are of the order of the thickness of the solid lines. (m) Configuration of the Er $4f$ moments ($M_{\mathrm{Er}}$) and the Fe $3d$ moments ($M_{\mathrm{Fe}}$) in the (001) plane deduced from the high-field soft XMCD results in panels (e)–(l) at 26 K and 34 K at the first ($H_{c1}$) and the second ($H_{c2}$) field-induced transitions. The hard and easy axes are shown by solid (black) and dashed (gray) lines, respectively.

Figure 4

(a) Er $M_5$-edge XAS spectra at 34 K at selected magnetic fields applied along the [110] axis. The spectra were obtained by the averaged sum of right- and left-circular polarized light. (b) XAS spectra at 0 T subtracted from the XAS spectra at 12 T at 34 K. (c) Magnetic-field dependence of the Er $M_5$-edge XAS difference signals obtained by integrating the range delimited by the two dashed lines in panel (b). (d) Direction of the Er $4f$ moment at selected magnetic fields with respect to the incoming beam with the propagation vector $\mathrm{k}$ and the principal crystallographic axes within the basal plane of ${\mathrm{ErFe}}_5{\mathrm{Al}}_7$. The electric field (E) of the x-ray beam is in the (110) plane.

Figure 5

(a) Er $L_3$-edge XAS spectra at 30.3 T. (b) Er $L_3$-edge XMCD spectra at selected magnetic fields. (c) Magnetic-field dependence of the XMCD signals obtained by integrating the range delimited by the two dashed lines in panel (b), where the electric-dipole transition ($2p_{3/2}\to 5d$) is predominantly involved. The lines are guides to the eye. (d) Schematic of the electronic structure involved in the electric-dipole (ED) and electric quadrupole (EQ) transitions at the Er $L_3$ and $M_5$ edges. (e) Er $M_5$-edge XMCD spectra at selected magnetic fields. (f) Er $M_5$-edge XMCD integrals as a function of magnetic field. The sign of the integrated XMCD signal is reversed as in Figs. 3–3. The spectra in panels (b) and (e) were obtained during the down sweeps, respectively. Red and blue symbols in panels (c) and (f) are data from up and down sweep of magnetic fields. All results were measured at 34 K and for magnetic fields applied along the [110] axis.

Figure 6

(a) Field dependence of the Er ($M_{\mathrm{Er}}$), Fe ($M_{\mathrm{Fe}}$), and total magnetization ($M_{\mathrm{tot}}$) at 10 K simulated by the two-sublattice model. (b) Field-dependent angles $\alpha$ and $\beta$ defined with respect to the magnetic field (see inset). $M_{\mathrm{tot}}$ as a function of magnetic fields simulated for the selected anisotropy constants at (c) 26 K and (d) 34 K. The simulated results for different $K$ are vertically shifted for clarity.

Figure 7

Time dependence of the pulsed magnetic field used for soft (red) and hard (blue) x-ray dichroic measurements at UE46-PGM1 BESSY II and ID24 ESRF, respectively.

Figure 8

Field-dependent XMCD amplitude at 30.3 K at the (a) Er $M_5$ edge and (b) at the Fe $L_3$ edge. Numerical sum of the field-dependent XMCD amplitudes (c) at the Er $M_5$ edge at 28 and 34 K and (d) at the Fe $L_3$ edge at 26 and 34 K. Red and blue lines are data from up and down field sweeps

Figure 9

SVD analysis for the Er $L_3$-edge XMCD spectral data. (a) Contribution of components to the variance of dataset [Fig. 5]. (b) First four components.