Spin current symmetries generated by GdFeCo ferrimagnet across its magnetisation compensation temperature

TL;DR

This work probes spin current generation in a GdFeCo ferrimagnet across its magnetisation compensation temperature using spin-torque ferromagnetic resonance to separate spin Hall effect (SHE) and spin anomalous Hall effect (SAHE) torques. By combining lineshape analysis and DC-bias measurements, it shows that SHE- and SAHE-driven torques retain their signs across compensation, with SAHE DL torque opposing SHE and dominating away from compensation. The authors attribute SHE to Gd 5d electrons and SAHE to FeCo 3d electrons, explaining the observed symmetry and sign behavior as a consequence of sublattice-specific spin transport. Near compensation, enhanced SHE DL torque suggests longer spin dephasing or slight out-of-plane canting, while the absence of sign reversals points to spin-current absorption, not sign changes, driving previous self-torque observations. Overall, the study reveals how ferrimagnetic sublattices contribute to spin current generation and how tuning across compensation can selectively access different spin-current symmetries for torquing adjacent layers or the ferrimagnet itself.

Abstract

Ferrimagnets, composed of antiferromagnetically coupled magnetic sublattices whose net magnetisation can be tuned by temperature, offer a unique platform for probing the symmetry of the spin currents they generate and for identifying the sublattice contributions to these currents. Here, we investigate the spin current symmetries produced by GdFeCo ferrimagnet at a fixed concentration and across a broad temperature range, including the magnetisation compensation point. Using complementary techniques based on spin-torque ferromagnetic resonance spectroscopy, we separate the contributions of the spin Hall effect (SHE) and the spin anomalous Hall effect (SAHE). We show that the torques arising from both mechanisms retain their sign across the magnetisation compensation temperature, and that the SAHE-driven damping-like torque has the opposite sign to the SHE-driven term. We suggest that both effects originates from distinct electronic subsystems: the SHE emerging from Gd 5d electrons, and the SAHE from FeCo 3d electrons. Consequently, the SHE sign remains insensitive to the magnetisation state, whereas the SAHE sign does not invert at compensation, reproducing our observations. Together, these insights clarify the interplay between sublattices in ferrimagnetic spin transport and highlight the potential of ferrimagnetic spin currents to generate spin torques in adjacent layers or within the ferrimagnet itself.

Figures (6)

• Figure 1: (a) Symmetry of the spin Hall effect (SHE) for the spin current $\vec{J}_s^{SHE}$ along the $\hat{z}$ axis. (b) Symmetry of the spin anomalous Hall effect (SAHE) for the spin current $\vec{J}_s^{SAHE}$ along the $\hat{z}$ axis.
• Figure 2: (a) Hall voltage $V_Y$ as a function of an out-of-plane magnetic field for different temperatures. (b) Hall voltage $V_Y$ as a function of the magnetic field applied along the current line for different temperatures. The yellow background highlights the magnetic field range provided by the ST-FMR setup. (c) Schematic of the parallel ($\parallel$) and perpendicular ($\perp$) configurations for specific temperature ranges with the associated spin current symmetries.
• Figure 3: Summary of the lineshape analysis for temperatures ranging from 15 K to 300 K and for positive external magnetic field. The blue (orange) background corresponds to the Gd- (FeCo-) dominant regime. Across all temperatures, both the symmetric and antisymmetric components remain positive, i.e. the associated torque efficiencies are positive $\xi_{DL,FL'}^{SHE} > 0$.
• Figure 4: Summary of the DC-bias analysis from 15 K to 300 K. The blue (orange) background corresponds to the Gd- (FeCo-) dominant regime. The left panel shows the linewidth modulation upon applied DC current, while the right panel shows the resonance field shift. In the perpendicular configuration ($\perp$), $\xi^{SHE}_{DL} > 0$ and $\xi^{SHE}_{FL'}>0$. In the parallel configuration ($\parallel$), $\xi^{SHE+SAHE}_{DL} < 0$ and $\xi^{SHE+SAHE}_{FL'} > 0$. The SHE and the SAHE symmetries have the same sign across the magnetisation compensation.
• Figure 5: (a) DL and (b) FL' torque efficiencies extracted by the DC-bias technique as a function of temperature. The blue (orange) background corresponds to the Gd- (FeCo-) dominant regime. The dashed parallel lines at 100 K and 175 K separate the $\parallel$ and $\perp$ magnetisation configurations.