Spin currents and spin-torques generated by spin-orbit coupling (SOC) are exploited in spintronics to meet the high data demand in information technology. Nowadays, the large SOC of 5d non-magnetic heavy metals (HMs) is required to generate a pure spin current by the spin Hall effect (SHE). In turn, the pure spin current generates a spin-orbit torque (SOT) on an attached magnetic layer 1.

It is generally accepted that in magnetic materials, the spin polarization of the generated spin current is aligned with the direction of the magnetization due to the exchange interaction. The generation of such spin current is referred to as the Spin Anomalous Hall Effect (SAHE) 2. More recent theoretical works 3,4 have shown that the latter description is incomplete for magnetic materials with large spin-orbit coupling. In this case, the spin polarization can be preserved from alignment with the magnetization, as demonstrated in ferrimagnets 5. The total spin current is therefore the sum of SAHE-like and SHE-like spin currents 2-4 as depicted in Fig 1. The SAHE-like spin current cannot induce a torque on the magnetization because the spin polarization is aligned with the magnetization. However, the SHE-like symmetry can generate a torque if the spin current is absorbed outside the layer. We refer this torque as self-torque because the material is the source of the torque on its magnetization.

In this talk, we present the study of a ferrimagnet with strong spin-orbit coupling: GdFeCo. The SAHE and SHE spin current contributions are studied by complementary Spin Torque Ferromagnetic Resonance (ST-FMR) techniques and self-torque characterization were performed by means of harmonic Hall voltage measurements. We show in GdFeCo/Cu/NiFe trilayer that the ST-FMR voltage at NiFe resonance that is sensitive to GdFeCo SHE-like symmetry does not change sign across the magnetic compensation temperature 6. The addition of a dc current to ST-FMR experiments allows to quantify the total contribution 6,7. Additionally, we show in GdFeCo/Cu that the effective fields associated to the self-torques are amplified in the vicinity of the magnetic compensation temperature of the ferrimagnet and reverse their sign across it 7 (see Fig 2). Finally, we present more experimental results with signatures that highlight the difference between external SOT and self-torque taking advantage of characteristics temperatures in ferrimagnets. This study paves the way for further research into the generation of spin currents in ferrimagnets and the exploitation of self-torque generated in single magnetic layer for spintronic devices.

This work was supported partially from Agence Nationale de la Recherche (France) under contract N° ANR-18-CE24-0008 (MISSION), ANR-19-CE24-0016-01 (TOPTRONICS) and ANR-17-CE24-0025 (TOPSKY), from the French PIA project “Lorraine Universite d’Excellence”, reference ANR-15IDEX-04-LUE. This study is partially funded by MSCA-RISE 2020-Project N°101007825 - ULTIMATE-I. D. C.-B., A.Y.A.C and H. D, acknowledge SPIN IJL team for their internship fellow 2018, 2019 and 2020, respectively. DCB also thanks “LUE Graduated” program internship 2019 from “Lorraine Université d’Excellence”.
References
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6 H. Damas, et al., p. 2200035, PSS RLL (2022).
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