Field-free switching of perpendicular magnetization by two-dimensional PtTe2/WTe2 van der Waals heterostructures with high spin Hall conductivity.

The key challenge of spin-orbit torque applications lies in exploring an excellent spin source capable of generating out-of-plane spins while exhibiting high spin Hall conductivity. Here we combine PtTe2 for high spin conductivity and WTe2 for low crystal symmetry to satisfy the above requirements. The PtTe2/WTe2 bilayers exhibit a high in-plane spin Hall conductivity σs,y ≈ 2.32 × 105 × h/2e Ω-1 m-1 and out-of-plane spin Hall conductivity σs,z ≈ 0.25 × 105 × h/2e Ω-1 m-1, where h is the reduced Planck's constant and e is the value of the elementary charge. The out-of-plane spins in PtTe2/WTe2 bilayers enable the deterministic switching of perpendicular magnetization at room temperature without magnetic fields, and the power consumption is 67 times smaller than that of the Pt control case. The high out-of-plane spin Hall conductivity is attributed to the conversion from in-plane spin to out-of-plane spin, induced by the crystal asymmetry of WTe2. Our work establishes a low-power perpendicular magnetization manipulation based on wafer-scale two-dimensional van der Waals heterostructures.

Long-Range Orbital Torque by Momentum-Space Hotspots.

While it is often assumed that the orbital response is suppressed and short ranged due to strong crystal field potential and orbital quenching, we show that the orbital response can be remarkably long ranged in ferromagnets. In a bilayer consisting of a nonmagnet and a ferromagnet, spin injection from the interface results in spin accumulation and torque in the ferromagnet, which rapidly oscillate and decay by spin dephasing. In contrast, even when an external electric field is applied only on the nonmagnet, we find substantially long-ranged induced orbital angular momentum in the ferromagnet, which can go far beyond the spin dephasing length. This unusual feature is attributed to nearly degenerate orbital characters imposed by the crystal symmetry, which form hotspots for the intrinsic orbital response. Because only the states near the hotspots contribute dominantly, the induced orbital angular momentum does not exhibit destructive interference among states with different momentum as in the case of the spin dephasing. This gives rise to a distinct type of orbital torque on the magnetization, increasing with the thickness of the ferromagnet. Such behavior may serve as critical long-sought evidence of orbital transport to be directly tested in experiments. Our findings open the possibility of using long-range orbital response in orbitronic device applications.

Orbital Dynamics in Centrosymmetric Systems.

Orbital dynamics in time-reversal-symmetric centrosymmetric systems is examined theoretically. Contrary to common belief, we demonstrate that many aspects of orbital dynamics are qualitatively different from spin dynamics because the algebraic properties of the orbital and spin angular momentum operators are different. This difference generates interesting orbital responses, which do not have spin counterparts. For instance, the orbital angular momentum expectation values may oscillate even without breaking neither the time-reversal nor the inversion symmetry. Our quantum Boltzmann approach reproduces the previous result on the orbital Hall effect and reveals additional orbital dynamics phenomena, whose detection schemes are discussed briefly. Our work will be useful for the experimental differentiation of the orbital dynamics from the spin dynamics.

Spin Swapping Effect of Band Structure Origin in Centrosymmetric Ferromagnets.

We theoretically demonstrate the spin swapping effect of band structure origin in centrosymmetric ferromagnets. It is mediated by an orbital degree of freedom but does not require inversion asymmetry or impurity spin-orbit scattering. Analytic and tight-binding models reveal that it originates mainly from k points where bands with different spins and different orbitals are nearly degenerate, and thus it has no counterpart in normal metals. First-principle calculations for centrosymmetric 3d transition-metal ferromagnets show that the spin swapping conductivity of band structure origin can be comparable in magnitude to the intrinsic spin Hall conductivity of Pt. Our theory generalizes transverse spin currents generated by ferromagnets and emphasizes the important role of the orbital degree of freedom in describing spin-orbit-coupled transport in centrosymmetric materials.

Exchange Bias in Weakly Interlayer-Coupled van der Waals Magnet Fe3GeTe2.

van der Waals (vdW) magnetic materials provide an ideal platform to study low-dimensional magnetism. However, observations of magnetic characteristics of these layered materials truly distinguishing them from conventional magnetic thin film systems have been mostly lacking. In an effort to investigate magnetic properties unique to vdW magnetic materials, we examine the exchange bias effect, a magnetic phenomenon emerging at the ferromagnetic-antiferromagnetic interface. Exchange bias is observed in the naturally oxidized vdW ferromagnet Fe3GeTe2, owing to an antiferromagnetic ordering in the surface oxide layer. Interestingly, the magnitude and thickness dependence of the effect is unlike those expected in typical thin-film systems. We propose a possible mechanism for this behavior, based on the weak interlayer magnetic coupling inherent to vdW magnets, demonstrating the distinct properties of these materials. Furthermore, the robust and sizable exchange bias for vdW magnets persisting up to relatively high temperatures presents a significant advance for realizing practical two-dimensional spintronics.

Exploitable Magnetic Anisotropy of the Two-Dimensional Magnet CrI3.

Magnetic anisotropy often plays a central role in various static and dynamic properties of magnetic materials. In particular, for two-dimensional (2D) van der Waals materials, as inferred from the Mermin-Wagner theorem, it is an essential prerequisite for stabilizing ferromagnetic order. In this work, we carry out first-principles calculations for a CrI3 monolayer and investigate how its magnetic anisotropy is interrelated to adjustable parameters governing the underlying electronic structure. We explore various routes for controlled manipulation of magnetic anisotropy: chemical adsorption, substitutional doping, optical excitation, and charge transfer through a heterostructure. In particular, the vertical stacking of CrI3 and graphene is noteworthy in regard to controlling magnetic anisotropy: the spin anisotropy axis is switchable between the out-of-plane and in-plane directions, which is accompanied by a variation in the anisotropy energy of up to 500%. Our results show the possibility that dynamic control of the anisotropy of the 2D magnet CrI3 may enable the development of an advanced spintronic device with enhanced energy efficiency and high operation speed.

Author Correction: Long-range chiral exchange interaction in synthetic antiferromagnets.

In the version of this Article originally published, the sentence 'D.-S.H. wrote the paper with K.L., J.H. and M.K.' in the author contributions was incorrect; it should have read 'D.-S.H. wrote the paper with K.L., J.H., M.-H.J. and M.K.' This has been corrected in the online versions of the Article.

Long-range chiral exchange interaction in synthetic antiferromagnets.

The exchange interaction governs static and dynamic magnetism. This fundamental interaction comes in two flavours-symmetric and antisymmetric. The symmetric interaction leads to ferro- and antiferromagnetism, and the antisymmetric interaction has attracted significant interest owing to its major role in promoting topologically non-trivial spin textures that promise fast, energy-efficient devices. So far, the antisymmetric exchange interaction has been found to be rather short ranged and limited to a single magnetic layer. Here we report a long-range antisymmetric interlayer exchange interaction in perpendicularly magnetized synthetic antiferromagnets with parallel and antiparallel magnetization alignments. Asymmetric hysteresis loops under an in-plane field reveal a unidirectional and chiral nature of this interaction, which results in canted magnetic structures. We explain our results by considering spin-orbit coupling combined with reduced symmetry in multilayers. Our discovery of a long-range chiral interaction provides an additional handle to engineer magnetic structures and could enable three-dimensional topological structures.

Generalized Spin Drift-Diffusion Formalism in the Presence of Spin-Orbit Interaction of Ferromagnets.

We generalize the spin drift-diffusion formalism by considering spin-orbit interaction of a ferromagnet, which generates transverse spin currents in the ferromagnet. We consider quantum-mechanical transport of transverse spins in a spin-orbit coupled ferromagnet and develop a generalized drift-diffusion equation and boundary condition. By combining them, we identify previously unrecognized spin transport phenomena in heterostructures including ferromagnets. As representative examples, we show self-generated spin torque and self-generated charge pumping in ferromagnet-normal metal bilayers. The former is a torque exerting on a ferromagnet, originating from a transverse spin current leaving from the ferromagnet itself, whereas the latter is the Onsager reciprocity of the former. Our work not only provides a concise formalism for the effects of nondephased transverse spins in ferromagnets but also enables to design spintronic devices without an external spin source.

Bloch Chirality Induced by an Interlayer Dzyaloshinskii-Moriya Interaction in Ferromagnetic Multilayers.

Chiral spin textures stabilized by the interfacial Dzyaloshinkii-Moriya interaction, such as skyrmions and homochiral domain walls, have been shown to exhibit qualities that make them attractive for their incorporation in a variety of spintronic devices. However, for thicker multilayer films, mixed textures occur in which an achiral Bloch component coexists with a chiral Néel component of the domain wall to reduce the demagnetization field at the film surface. We show that an interlayer Dzyaloshinkii-Moriya interaction can break the degeneracy between Bloch chiralities. We further find large population asymmetries and chiral branching in the Bloch component of the domain walls in well-ordered Co/Pd multilayers. This asymmetry is a result of the combined effect of the demagnetization field and an interlayer Dzyaloshinkii-Moriya interaction, and is strongly related to film thickness and structural ordering. This work paves the way toward the utilization of this effect toward controlling Bloch chirality in magnetic multilayers.

Topological Characterization of Classical Waves: The Topological Origin of Magnetostatic Surface Spin Waves.

We propose a topological characterization of Hamiltonians describing classical waves. Applying it to the magnetostatic surface spin waves that are important in spintronics applications, we settle the speculation over their topological origin. For a class of classical systems that includes spin waves driven by dipole-dipole interactions, we show that the topology is characterized by vortex lines in the Brillouin zone in such a way that the symplectic structure of Hamiltonian mechanics plays an essential role. We define winding numbers around these vortex lines and identify them to be the bulk topological invariants for a class of semimetals. Exploiting the bulk-edge correspondence appropriately reformulated for these classical waves, we predict that surface modes appear but not in a gap of the bulk frequency spectrum. This feature, consistent with the magnetostatic surface spin waves, indicates a broader realm of topological phases of matter beyond spectrally gapped ones.

Unidirectional Magnon-Driven Domain Wall Motion Due to the Interfacial Dzyaloshinskii-Moriya Interaction.

We demonstrate a unidirectional motion of a quasiparticle without explicit symmetry breaking along the space-time coordinate of the particle motion. This counterintuitive behavior originates from a combined action of two intrinsic asymmetries in the other two directions. We realize this idea with the magnon-driven motion of a magnetic domain wall in thin films with interfacial asymmetry. Contrary to previous studies, the domain wall moves along the same direction regardless of the magnon-flow direction. Our general symmetry analysis and numerical simulation reveal that the odd order contributions from the interfacial asymmetry is unidirectional, which is dominant over bidirectional contributions in the realistic regime. We develop a simple analytic theory on the unidirectional motion, which provides an insightful description of this counterintuitive phenomenon.

Understanding the Giant Enhancement of Exchange Interaction in Bi_{2}Se_{3}-EuS Heterostructures.

A recent experiment indicated that a ferromagnetic EuS film in contact with a topological insulator Bi_{2}Se_{3} might show a largely enhanced Curie temperature and perpendicular magnetic anisotropy [F. Katmis et al., Nature (London) 533, 513 (2016).NATUAS0028-083610.1038/nature17635]. Through systematic density functional calculations, we demonstrate that in addition to the factor that Bi_{2}Se_{3} has a strong spin orbit coupling, the topological surface states are crucial to make these unusual behaviors robust as they hybridize with EuS states and extend rather far into the magnetic layers. The magnetic moments of Eu atoms are nevertheless not much enhanced, unlike what was reported in the experiment. Our results and model analyses provide useful insights for how these quantities are linked, and pave a way for the control of properties of magnetic films via contact with topological insulators.

Additive roles of antiferromagnetically coupled elements in the magnetic proximity effect in the GdFeCo/Pt system.

Interfacial magnetic interactions between different elements are the origin of various spin-transport phenomena in multi-elemental magnetic systems. We investigate the coupling between the magnetic moments of the rare-earth, transition-metal, and heavy-metal elements across the interface in a GdFeCo/Pt thin film, an archetype system to investigate ferrimagnetic spintronics. The Pt magnetic moments induced by the antiferromagnetically aligned FeCo and Gd moments are measured using element-resolved x-ray measurements. It is revealed that the proximity-induced Pt magnetic moments are always aligned parallel to the FeCo magnetic moments, even below the ferrimagnetic compensation temperature where FeCo has a smaller moment than Gd. This is understood by a theoretical model showing distinct effects of the rare-earth Gd 4f and transition-metal FeCo 3d magnetic moments on the Pt electronic states. In particular, the Gd and FeCo work in-phase to align the Pt moment in the same direction, despite their antiferromagnetic configuration. The unexpected additive roles of the two antiferromagnetically coupled elements exemplify the importance of detailed interactions among the constituent elements in understanding magnetic and spintronic properties of thin film systems.

Chirality from interfacial spin-orbit coupling effects in magnetic bilayers.

As nanomagnetic devices scale to smaller sizes, spin-orbit coupling due to the broken structural inversion symmetry at interfaces becomes increasingly important. Here, we study interfacial spin-orbit coupling effects in magnetic bilayers using a simple Rashba model. The spin-orbit coupling introduces chirality into the behavior of the electrons and through them into the energetics of the magnetization. In the derived form of the magnetization dynamics, all of the contributions that are linear in the spin-orbit coupling follow from this chirality, considerably simplifying the analysis. For these systems, an important consequence is a correlation between the Dzyaloshinskii-Moriya interaction and the spin-orbit torque. We use this correlation to analyze recent experiments.

Optoelectronic Manifestation of Orbital Angular Momentum Driven by Chiral Hopping in Helical Se Chains.

Chiral materials have garnered significant attention in the field of condensed matter physics. Nevertheless, the magnetic moment induced by the chiral spatial motion of electrons in helical materials, such as elemental Te and Se, remains inadequately understood. In this work, we investigate the development of quantum angular momentum enforced by chirality by using static and time-dependent density functional theory calculations for an elemental Se chain. Our findings reveal the emergence of an unconventional orbital texture driven by the chiral geometry, giving rise to a nonvanishing current-induced orbital moment. By incorporating spin-orbit coupling, we demonstrate that current-induced spin accumulation arises in the chiral chain, which fundamentally differs from the conventional Edelstein effect. Furthermore, we demonstrate optoelectronic detection of the orbital angular momentum in the chiral Se chain, providing an alternative to the interband Berry curvature, which is ill-defined in low dimensions.

Enhanced spin Seebeck effect via oxygen manipulation.

Spin Seebeck effect (SSE) refers to the generation of an electric voltage transverse to a temperature gradient via a magnon current. SSE offers the potential for efficient thermoelectric devices because the transverse geometry of SSE enables to utilize waste heat from a large-area source by greatly simplifying the device structure. However, SSE suffers from a low thermoelectric conversion efficiency that must be improved for widespread application. Here we show that the SSE substantially enhances by oxidizing a ferromagnet in normal metal/ferromagnet/oxide structures. In W/CoFeB/AlOx structures, voltage-induced interfacial oxidation of CoFeB modifies the SSE, resulting in the enhancement of thermoelectric signal by an order of magnitude. We describe a mechanism for the enhancement that results from a reduced exchange interaction of the oxidized region of ferromagnet, which in turn increases a temperature difference between magnons in the ferromagnet and electrons in the normal metal and/or a gradient of magnon chemical potential in the ferromagnet. Our result will invigorate research for thermoelectric conversion by suggesting a promising way of improving the SSE efficiency.

Bulk Rashba-Type Spin Splitting in Non-Centrosymmetric Artificial Superlattices.

Spin current, converted from charge current via spin Hall or Rashba effects, can transfer its angular momentum to local moments in a ferromagnetic layer. In this regard, the high charge-to-spin conversion efficiency is required for magnetization manipulation for developing future memory or logic devices including magnetic random-access memory. Here, the bulk Rashba-type charge-to-spin conversion is demonstrated in an artificial superlattice without centrosymmetry. The charge-to-spin conversion in [Pt/Co/W] superlattice with sub-nm scale thickness shows strong W thickness dependence. When the W thickness becomes 0.6 nm, the observed field-like torque efficiency is about 0.6, which is an order larger than other metallic heterostructures. First-principles calculation suggests that such large field-like torque arises from bulk-type Rashba effect due to the vertically broken inversion symmetry inherent from W layers. The result implies that the spin splitting in a band of such an ABC-type artificial SL can be an additional degree of freedom for the large charge-to-spin conversion.

Prediction of giant spin motive force due to Rashba spin-orbit coupling.

Magnetization dynamics in a ferromagnet can induce a spin-dependent electric field through a spin motive force. Spin current generated by the spin-dependent electric field can in turn modify the magnetization dynamics through spin-transfer torque. While this feedback effect is usually weak and thus ignored, we predict that in Rashba spin-orbit coupling systems with a large Rashba parameter α(R), the coupling generates the spin-dependent electric field [±(α(R)m(e)/eh)(z[over ^]×∂m/∂t)], which can be large enough to modify the magnetization dynamics significantly. This effect should be relevant for device applications based on ultrathin magnetic layers with strong Rashba spin-orbit coupling.