Spin-Hall Topological Hall Effect in Highly Tunable Pt/Ferrimagnetic-Insulator Bilayers

Tailoring Dzyaloshinskii-Moriya Interaction and Spin-Hall Topological Hall Effect in Insulating Magnetic Oxides by Interface Engineering

Chiral spin textures, as exotic phases in magnetic materials, hold immense promise for revolutionizing logic, and memory applications. Recently, chiral spin textures have been observed in centrosymmetric magnetic insulators (FMI), due to an interfacial Dzyaloshinskii-Moriya interaction (iDMI). However, the source and origin of this iDMI remain enigmatic in magnetic insulator systems. Here, the source and origin of the iDMI in Pt/Y3Fe5O12 (YIG)/substrate structures are deeply delved by examining the spin-Hall topological Hall effect (SH-THE), an indication of chiral spin textures formed due to an iDMI. Through carefully modifying the interfacial chemical composition of Pt/YIG/substrate with a nonmagnetic Al3+ doping, the obvious dependence of SH-THE on the interfacial chemical composition for both the heavy metal (HM)/FMI and FMI/substrate interfaces is observed. The results reveal that both interfaces contribute to the strength of the iDMI, and the iDMI arises due to strong spin-orbit coupling and inversion symmetry breaking at both interfaces in HM/FMI/substrate. Importantly, it is shown that nonmagnetic substitution and interface engineering can significantly tune the SH-THE and iDMI in ferrimagnetic iron garnets. The approach offers a viable route to tailor the iDMI and associated chiral spin textures in low-damping insulating magnetic oxides, thus advancing the field of spintronics.

Topological Spin Textures: Basic Physics and Devices

In the face of escalating modern data storage demands and the constraints of Moore's Law, exploring spintronic solutions, particularly the devices based on magnetic skyrmions, has emerged as a promising frontier in scientific research. Since the first experimental observation of skyrmions, topological spin textures have been extensively studied for their great potential as efficient information carriers in spintronic devices. However, significant challenges have emerged alongside this progress. This review aims to synthesize recent advances in skyrmion research while addressing the major issues encountered in the field. Additionally, current research on promising topological spin structures in addition to skyrmions is summarized. Beyond 2D structures, exploration also extends to 1D magnetic solitons and 3D spin textures. In addition, a diverse array of emerging magnetic materials is introduced, including antiferromagnets and 2D van der Waals magnets, broadening the scope of potential materials hosting topological spin textures. Through a systematic examination of magnetic principles, topological categorization, and the dynamics of spin textures, a comprehensive overview of experimental and theoretical advances in the research of topological magnetism is provided. Finally, both conventional and unconventional applications are summarized based on spin textures proposed thus far. This review provides an outlook on future development in applied spintronics.

Observation of Topological Hall Effect in a Chemically Complex Alloy

The topological Hall effect (THE) is the transport response of chiral spin textures and thus can serve as a powerful probe for detecting and understanding these unconventional magnetic orders. So far, the THE is only observed in either noncentrosymmetric systems where spin chirality is stabilized by Dzyaloshinskii-Moriya interactions, or triangular-lattice magnets with Ruderman-Kittel-Kasuya-Yosida-type interactions. Here, a pronounced THE is observed in a Fe-Co-Ni-Mn chemically complex alloy with a simple face-centered cubic (fcc) structure across a wide range of temperatures and magnetic fields. The alloy is shown to have a strong magnetic frustration owing to the random occupation of magnetic atoms on the close-packed fcc lattice and the direct Heisenberg exchange interaction among atoms, as evidenced by the appearance of a reentrant spin glass state in the low-temperature regime and the first principles calculations. Consequently, THE is attributed to the nonvanishing spin chirality created by strong spin frustration under the external magnetic field, which is distinct from the mechanism responsible for the skyrmion systems, as well as geometrically frustrated magnets.

Tuning Rashba-Dresselhaus effect with ferroelectric polarization at asymmetric heterostructural interface

The spin-orbit interaction (SOI) plays an essential role in materials properties, and controlling its intensity has great potential in the design of materials. In this work, asymmetric [(La0.7Sr0.3MnO3)8/(BaTiO3)t/(SrTiO3)2]8 superlattices were fabricated on (001) SrTiO3 substrate with SrO or TiO2 termination, labelled as SrO-SL and TiO2-SL, respectively. The in-plane angular magnetoresistance of the superlattices shows a combination of two- and four-fold symmetry components. The coefficient of two-fold symmetry component has opposite sign with current I along [100] and [110] directions for TiO2-SL, while it has the same sign for SrO-SL. Detailed study shows that the asymmetric cation inter-mixing and ferroelectricity-modulated electronic charge transfer induce asymmetric electronic potential for SrO-SL with dominating Rashba SOI, and symmetric electronic potential for TiO2-SL with dominating Dresselhaus SOI induced by BaTiO3. This work shows that the Rashba and Dresselhaus SOIs are sensitive to the ferroelectric polarization in the asymmetric structure.

Unified theory of the anomalous and topological Hall effects with phase-space Berry curvatures

Spontaneously broken time-reversal symmetry in magnetic materials leads to a Hall response, with a nonzero voltage transverse to an applied current, even in the absence of external magnetic fields. It is common to analyze the Hall resistivity of chiral magnets as the sum of two terms: an anomalous Hall effect arising from spin-orbit coupling and a topological Hall signal coming from skyrmions, which are topologically nontrivial spin textures. The theoretical justification for such a decomposition has long remained an open problem. Using a controlled semiclassical approach that includes all phase-space Berry curvatures, we show that the solution of the Boltzmann equation leads to a Hall resistivity that is just the sum of an anomalous term arising from momentum-space curvature and a topological term related to the real-space curvature. We also present numerically exact results from a Kubo formalism that complement the semiclassical approach.

A comparative study of the domain wall motion in ferrimagnets (Fe,Co)1-x(Gd,Tb)x

Magnetic domain walls (DWs) in rare-earth-transition-metal (RE-TM) ferrimagnetic alloys can be used as information carriers in nonvolatile spintronic devices. Due to the rich combinations of RE-TM elements (such as CoGd, FeGd, CoTb, and FeTb in our case), it is intriguing to reveal the characteristics of DW dynamics in these wide choices of RE-TM compounds. Through a systematic study of the DW motion in thin films with different compositions of stacking order Pt(3 nm)/(Fe,Co)_1-x(Gd,Tb)_x(∼8 nm)/Ta(3 nm), we show that the partially compensated ferrimagnets CoGd and FeGd can exhibit a faster DW motion under various (in-plane and out-of-plane) magnetic fields driven by current-induced spin-orbit torques. In stark contrast with the fast motion of domain walls in Gd-based ferrimagnets, we find that the CoTb system exhibits much slower DW dynamics, and the FeTb system shows no motion, but evolved into a multi-domain state upon applying current pulses. Our results demonstrate that ferrimagnets CoGd and FeGd are more suitable candidates for achieving ultrafast DW motion, which could be useful for developing spintronic memory and logic devices.

Current-driven dynamics and ratchet effect of skyrmion bubbles in a ferrimagnetic insulator

Magnetic skyrmions are compact chiral spin textures that exhibit a rich variety of topological phenomena and hold potential for the development of high-density memory devices and novel computing schemes driven by spin currents. Here, we demonstrate the room-temperature interfacial stabilization and current-driven control of skyrmion bubbles in the ferrimagnetic insulator Tm₃Fe₅O₁₂ coupled to Pt, showing the current-induced motion of individual skyrmion bubbles. The ferrimagnetic order of the crystal together with the interplay of spin-orbit torques and pinning determine the skyrmion dynamics in Tm₃Fe₅O₁₂ and result in a strong skyrmion Hall effect characterized by a negative deflection angle and hopping motion. Further, we show that the velocity and depinning threshold of the skyrmion bubbles can be modified by exchange coupling Tm₃Fe₅O₁₂ to an in-plane magnetized Y₃Fe₅O₁₂ layer, which distorts the spin texture of the skyrmions and leads to directional-dependent rectification of their dynamics. This effect, which is equivalent to a magnetic ratchet, is exploited to control the skyrmion flow in a racetrack-like device.

Strain-Tunable Interfacial Dzyaloshinskii-Moriya Interaction and Spin-Hall Topological Hall Effect in Pt/Tm3Fe5O12 Heterostructures

The interfacial Dzyaloshinskii-Moriya interaction (DMI) in heavy-metal/ferromagnet heterostructures enables to stabilize and manipulate novel topological spin textures, such as skyrmions, which arise as potential logic and memory devices for future information technology. Along these lines, we study in this work the topological spin textures in the films of magnetic insulators by detecting the spin-Hall topological Hall effect (SH-THE). The SH-THE presents obvious dependence of epitaxial strain in Pt/Tm₃Fe₅O₁₂ (TmIG) bilayers deposited on a series of (111)-oriented garnet substrates, indicating that the topological spin textures can be tuned by epitaxial strain in this system. It is interesting to note that the room-temperature and low-field peak of SH-THE is also recorded within the Pt/TmIG bilayer configuration. We have also examined the interfacial DMI in the Pt/TmIG bilayers by an extended droplet model. The results indicate that the epitaxial strain can effectively change the interfacial DMI in this system, suggesting that the strain-induced modification of the interfacial DMI is the driving force for the SH-THE and topological spin textures in the Pt/TmIG bilayers. Our outcomes open new exciting avenues and opportunities in engineering chiral magnetism and examining the future skyrmion technology in magnetic insulators through the application of epitaxial strain.

Giant Topological Hall Effect in van der Waals Heterostructures of CrTe2/Bi2Te3

Discoveries of the interfacial topological Hall effect (THE) provide an ideal platform for exploring the physics arising from the interplay between topology and magnetism. The interfacial topological Hall effect is closely related to the Dzyaloshinskii-Moriya interaction (DMI) at an interface and topological spin textures. However, it is difficult to achieve a sizable THE in heterostructures due to the stringent constraints on the constituents of THE heterostructures, such as strong spin-orbit coupling (SOC). Here, we report the observation of a giant THE signal of 1.39 μΩ·cm in the van der Waals heterostructures of CrTe₂/Bi₂Te₃ fabricated by molecular beam epitaxy, a prototype of two-dimensional (2D) ferromagnet (FM)/topological insulator (TI). This large magnitude of THE is attributed to an optimized combination of 2D ferromagnetism in CrTe₂, strong SOC in Bi₂Te₃, and an atomically sharp interface. Our work reveals CrTe₂/Bi₂Te₃ as a convenient platform for achieving large interfacial THE in hybrid systems, which could be utilized to develop quantum science and high-density information storage devices.

Topological Hall Effect in a Topological Insulator Interfaced with a Magnetic Insulator

A topological insulator (TI) interfaced with a magnetic insulator (MI) may host an anomalous Hall effect (AHE), a quantum AHE, and a topological Hall effect (THE). Recent studies, however, suggest that coexisting magnetic phases in TI/MI heterostructures may result in an AHE-associated response that resembles a THE but in fact is not. This Letter reports a genuine THE in a TI/MI structure that has only one magnetic phase. The structure shows a THE in the temperature range of T = 2-3 K and an AHE at T = 80-300 K. Over T = 3-80 K, the two effects coexist but show opposite temperature dependencies. Control measurements, calculations, and simulations together suggest that the observed THE originates from skyrmions, rather than the coexistence of two AHE responses. The skyrmions are formed due to a Dzyaloshinskii-Moriya interaction (DMI) at the interface; the DMI strength estimated is substantially higher than that in heavy metal-based systems.

Interfacial Rashba-Effect-Induced Anisotropy in Nonmagnetic-Material-Ferrimagnetic-Insulator Bilayers

Interfacial magnetic anisotropy in magnetic insulators has been largely unexplored. Recently, interface-induced skyrmions and electrical control of magnetization have been discovered in insulator-based heterostructures, which demand a thorough understanding of interfacial interactions in these materials. We observe a substantial, tunable interfacial magnetic anisotropy between Tm_{3}Fe_{5}O_{12} epitaxial thin films and fifteen nonmagnetic materials spanning a significant portion of the periodic table, which we attribute to Rashba spin-orbit coupling. Our results show a clear distinction between nonmagnetic capping layers from the d block and the p block. This work offers a new path for controlling magnetic phases in magnetic insulators for low-loss spintronic applications.

Investigation of the Role of Rare-Earth Elements in Spin-Hall Topological Hall Effect in Pt/Ferrimagnetic-Garnet Bilayers

Topological magnetic textures such as skyrmions are being extensively studied for their potential application in spintronic devices. Recently, low-damping ferrimagnetic insulators (FMI) such as Tm₃Fe₅O₁₂ have attracted significant interest as potential candidates for hosting skyrmions. Here, we report the detection of the spin-Hall topological Hall effect (SH-THE) in Pt/Tm₃Fe₅O₁₂ and Pt/Y₃Fe₅O₁₂ bilayers grown on various orientations of Gd₃Ga₅O₁₂ substrates as well as on epitaxial buffer layers of Y₃Sc₂Al₃O₁₂, which separates the FMI from the substrate without sacrificing the crystal quality. The presence of SH-THE in all of the bilayers and trilayers provides evidence that rare-earth ions in either the FMI or substrate may not be critical for inducing an interfacial Dzyaloshinskii-Moriya interaction that is necessary to stabilize magnetic textures. Additionally, the use of substrates with various crystal orientations alters the magnetic anisotropy, which shifts the temperatures and strength of the SH-THE.

Probing the Source of the Interfacial Dzyaloshinskii-Moriya Interaction Responsible for the Topological Hall Effect in Metal/Tm_{3}Fe_{5}O_{12} Systems

The interfacial Dzyaloshinskii-Moriya interaction (DMI) is responsible for the emergence of topological spin textures such as skyrmions in layered structures based on metallic and insulating ferromagnetic films. However, there is active debate on where the interfacial DMI resides in magnetic insulator systems. We investigate the topological Hall effect, which is an indication of spin textures, in Tm_{3}Fe_{5}O_{12} films capped with various metals. The results reveal that Pt, W, and Au induce strong interfacial DMI and topological Hall effect, while Ta and Ti cannot. This study also provides insights into the mechanism of electrical detection of spin textures in magnetic insulator heterostructures.

Chiral Hall Effect in Noncollinear Magnets from a Cyclic Cohomology Approach

We demonstrate the emergence of an anomalous Hall effect in chiral magnetic textures which is neither proportional to the net magnetization nor to the well-known emergent magnetic field that is responsible for the topological Hall effect. Instead, it appears already at linear order in the gradients of the magnetization texture and exists for one-dimensional magnetic textures such as domain walls and spin spirals. It receives a natural interpretation in the language of Alain Connes' noncommutative geometry. We show that this chiral Hall effect resembles the familiar topological Hall effect in essential properties while its phenomenology is distinctly different. Our findings make the reinterpretation of experimental data necessary, and offer an exciting twist in engineering the electrical transport through magnetic skyrmions.

Interfacial Dzyaloshinskii-Moriya interaction arising from rare-earth orbital magnetism in insulating magnetic oxides

The Dzyaloshinskii-Moriya interaction (DMI) is responsible for exotic chiral and topological magnetic states such as spin spirals and skyrmions. DMI manifests at metallic ferromagnet/heavy-metal interfaces, owing to inversion symmetry breaking and spin-orbit coupling by a heavy metal such as Pt. Moreover, in centrosymmetric magnetic oxides interfaced by Pt, DMI-driven topological spin textures and fast current-driven dynamics have been reported, though the origin of this DMI is unclear. While in metallic systems, spin-orbit coupling arises from a proximate heavy metal, we show that in perpendicularly-magnetized iron garnets, rare-earth orbital magnetism gives rise to an intrinsic spin-orbit coupling generating interfacial DMI at mirror symmetry-breaking interfaces. We show that rare-earth ion substitution and strain engineering can significantly alter the DMI. These results provide critical insights into the origins of chiral magnetism in low-damping magnetic oxides and identify paths toward engineering chiral and topological states in centrosymmetric oxides through rare-earth ion substitution.

The origin of interfacial Dzyaloshinskii-Moriya interaction (iDMI) in insulating magnetic oxides remains unclear. Here, Caretta et al. find that an intrinsic spin-orbit coupling due to rare-earth orbital magnetism generates iDMI at mirror symmetry-breaking interfaces of magnetized iron garnets Tm₃Fe₅O₁₂.

Evidence of the Topological Hall Effect in Pt/Antiferromagnetic Insulator Bilayers

The topological Hall effect has been a primary indicator of nontrivial spin textures in magnetic materials. We observe the evidence of the topological Hall effect in Pt/Cr_{2}O_{3} bilayers grown on Al_{2}O_{3}(0001) and Al_{2}O_{3}(112[over ¯]0), where the Cr_{2}O_{3} epitaxial film is an antiferromagnetic insulator. The Pt/Cr_{2}O_{3} bilayers exhibit topological Hall resistivity for Cr_{2}O_{3} thicknesses below 6 nm near and above room temperature, which is above the Néel temperature of Cr_{2}O_{3}, revealing the key role of thermal fluctuations in the formation of spin textures. The similarity of topological Hall signals in (0001)- and (112[over ¯]0)-oriented Cr_{2}O_{3} films indicates that the emergence of spin textures is insensitive to crystalline orientation.

Strain-induced perpendicular magnetic anisotropy and Gilbert damping of Tm3Fe5O12 thin films

In the attempt of implementing iron garnets with perpendicular magnetic anisotropy (PMA) in spintronics, the attention turned towards strain-grown iron garnets. One candidate is Tm₃Fe₅O₁₂ (TmIG) which possesses an out-of-plane magnetic easy axis when grown under tensile strain. In this study, the effect of film thickness on the structural and magnetic properties of TmIG films including magnetic anisotropy, saturation magnetization, and Gilbert damping is investigated. TmIG films with thicknesses between 20 and 300 nm are epitaxially grown by pulsed laser deposition on substituted-Gd₃Ga₅O₁₂(111) substrates. Structural characterization shows that films thinner than 200 nm show in-plane tensile strain, thus exhibiting PMA due to strain-induced magnetoelastic anisotropy. However, with increasing film thickness a relaxation of the unit cell is observed resulting in the rotation of the magnetic easy axis towards the sample plane due to the dominant shape anisotropy. Furthermore, the Gilbert damping parameter is found to be in the range of 0.02 ± 0.005.