Emergence of a spin Hall topological Hall effect in the non-collinear phase of the ferrimagnetic insulator terbium-iron garnet

Magnetic compensation in rare-earth iron garnets (REIGs) offers a unique setting for which competing sublattice moments can give rise to non-collinear (canted) magnetic configurations, in which the sublattice magnetizations are not aligned with each other or with the external magnetic field. We show that this compensation regime can also host non-trivial magnetic textures. To explore this behavior, we investigated (111)-oriented epitaxial Tb$_3$Fe$5$O${12}$/Pt heterostructures across the compensation temperature region using combined transverse magneto-transport and polar Kerr microscopy. Notably, we observe a topological Hall-like signal in the vicinity of the compensation temperature, a feature often interpreted as evidence for skyrmions in the absence of direct imaging. Here, in contrast, complementary Kerr microscopy reveals instead a non-collinear multidomain state which collapses outside the compensation regime, correlating directly with the appearance and disappearance of the spin Hall topological Hall effect (SH-THE) signal. These observations cannot be accounted for by a simple multi-anomalous-Hall-effect model, ruling out common artifacts as the origin, but indicate the presence of a topologically non-trivial contribution to the Hall response. These results establish strained REIG films as a tunable platform for exploring topological responses arising from compensation-driven non-collinear ferrimagnetic phases.

💡 Research Summary

In this work the authors investigate the emergence of a spin‑Hall‑mediated topological Hall effect (SH‑THE) in epitaxial Tb₃Fe₅O₁₂ (TbIG) thin films capped with a 2 nm Pt layer, focusing on the magnetic compensation regime where the net magnetization of the ferrimagnet vanishes. TbIG is a three‑sublattice ferrimagnet (two antiferromagnetically coupled Fe sublattices and a rare‑earth Tb sublattice) that exhibits a compensation temperature (T_comp) at which the moments of the Fe and Tb sublattices cancel. By growing ~9 nm TbIG on (111) Gd₃Ga₅O₁₂ substrates via pulsed laser deposition under controlled oxygen pressure, the authors induce a tensile strain that shifts T_comp up to ≈302 K, i.e., close to room temperature. A Pt overlayer is deposited in‑situ to enable transverse magneto‑transport measurements that exploit the spin‑Hall magnetoresistance (SMR) and the spin‑Hall anomalous Hall effect (SH‑AHE).

Hall measurements performed in a van‑der‑Pauw geometry reveal the expected SH‑AHE sign reversal across T_comp, confirming that the dominant magnetic sublattice switches from Tb‑dominated (below T_comp) to Fe‑dominated (above T_comp). However, in a narrow temperature window (≈298–320 K) an additional non‑monotonic hump appears in the Hall loops. By fitting the high‑field linear background (ordinary Hall effect) and subtracting the SH‑AHE contribution, the authors isolate a distinct SH‑THE component that peaks sharply at T_comp, diminishes at lower and higher temperatures, and shifts toward zero magnetic field as temperature rises above T_comp. The amplitude of this SH‑THE is comparable to the SH‑AHE, yet its field dependence cannot be reproduced by a simple two‑anomalous‑Hall‑effect (2‑AHE) model, which would predict extrema at finite switching fields set by sublattice reversal.

To identify the magnetic texture responsible for the SH‑THE, the authors perform polar Kerr microscopy under out‑of‑plane magnetic fields up to ±896 mT. The images show that, precisely in the same temperature range where SH‑THE is observed, the film cannot be fully saturated; instead, a multidomain state with irregular shapes and multiple contrast levels persists. These domains are not the circular skyrmion or bubble textures commonly associated with topological Hall signals; rather, they reflect a non‑collinear, canted configuration of the three sublattices. The persistence of a non‑collinear background over a broad field range, together with the incomplete recovery of the SH‑AHE when the SH‑THE component is added back, indicates that a finite scalar spin chirality ⟨S_i·(S_j × S_k)⟩ is present. This chirality generates an emergent magnetic field in real space, which couples to the spin‑Hall current in Pt and produces the observed SH‑THE.

The authors therefore conclude that the SH‑THE in TbIG/Pt heterostructures originates from a compensation‑driven non‑collinear ferrimagnetic phase rather than from conventional skyrmions or from a superposition of anomalous Hall contributions. The strain‑engineered shift of T_comp to near‑room temperature, combined with the ability to detect the emergent field electrically via the spin Hall effect, establishes strained rare‑earth iron garnet films as a versatile platform for exploring topological transport phenomena in insulating ferrimagnets. This work highlights the necessity of correlating transport signatures with direct magnetic imaging to avoid misinterpretation of Hall anomalies and opens pathways for spin‑orbit‑torque manipulation of complex magnetic textures in oxide heterostructures.