Element- and orbital-selective magnetic coherent rotation at the first-order phase transition of a hard uniaxial ferrimagnet

$3d\text{−}4f$ intermetalic compounds with heavy rare-earth elements show first-order phase transitions in high magnetic fields due to the competition between the exchange interaction and the magnetocrystalline anisotropy. However, the microscopic picture of the field-induced noncollinear magnetic structures remains elusive. Here we report the direct experimental observation of the coherent stepwise rotation of the $3d$ and $4f$ magnetic moments of the uniaxial hard ferrimagnet ${\mathrm{TmFe}}_5{\mathrm{Al}}_7$ by using soft x-ray magnetic circular dichroism in pulsed magnetic fields up to 25 T. The element- and shell-selective moments show a transition from the collinear ferrimagnet toward the forced ferromagnetic state via a canted phase, which is explained by a two-sublattice model.

Figure 1

X-ray absorption spectra (XAS) for a ${\mathrm{TmFe}}_5{\mathrm{Al}}_7$ single crystal at the (a) Tm $M_{4,5}$ and (b) the Fe $L_{2,3}$ edges in zero field at 12 K. The spectra were normalized to the absorption intensity at (a) 1462.3 and (b) 707.5 eV, respectively.

Figure 2

X-ray magnetic circular dichroism (XMCD) spectra during the down sweep at the (a) Tm $M_{4,5}$ and (b) Fe $L_{2,3}$ edges in pulsed magnetic fields up to 24 T. The inset of (a) shows an enlarged view at the $M_4$ edge. All spectra are normalized to the (a) $M_5$ and (b) $L_3$ XAS peak intensity at each field.

Figure 3

(a) Bulk magnetization for field aligned along the [001] direction (left scale) and the field derivative (right scale) at 12 K. The solid (dashed) line corresponds to the up-sweep (down-sweep) result. Spin (circle) and orbital (triangle) magnetic moments projected along the [001] direction for the (b) Tm $4f$ and (c) Fe $3d$ electrons as a function of magnetic field. Filled (open) symbols were extracted from the spectra obtained during the up (down) sweep.

Figure 4

Field dependence of the (a) Tm (solid line) and Fe (dashed line) sublattice magnetization and (b) the canting angle of the Tm (solid line) and Fe (dashed line) sublattice magnetization away from the [001] axis as shown in the inset simulated by the two-sublattice model. Field dependence of the (c) Tm (Fe) magnetic moment for the $4f$ ($3d$) electrons and (d) the canting angles extracted from (c). (e) A schematic diagram of the field-induced coherent rotation of the Tm $4f$ and the Fe $3d$ moments estimated from the data in (c) during the down sweep. The arrow lengths are scaled to the magnitude of the magnetic moment at 0 T.