We study the exchange coupling mediated by itinerant carriers with spin-orbit interaction by both analytic and numeric approaches. The mediated exchange coupling is non-collinear and its spatial trends depend on the Fermi surface topology of the itinerant carriers. Taking Rashba interaction as an example, the exchange coupling is similar to the conventional Ruderman-Kittel-Kasuya-Yosida type in weak coupling. On the other hand, in the strong coupling, the spiral interaction dominates. In addition, inclusion of finite spin relaxation always makes the non-collinear spiral exchange interaction dominant. Potential applications of our findings are explained and discussed.
Local spin magnetization in itinerant non-collinear magnets: The local spin Berry curvature
National Institute for R&D of Isotopic and Molecular Technologies（同位素与分子技术国家研发研究所）；Laboratoire de Physique des Solides, Université Paris-Saclay, CNRS（巴黎萨克雷大学CNRS固体物理实验室）
We show that the hyperfine mediated dynamics of heavy hole states confined in neutral self- assembled quantum dots leads to a nuclear spin diffusion mechanism. It is found that the oftentimes neglected effective heavy hole hyperfine non-collinear interaction is responsible for the low degree of nuclear spin polarization in neutral quantum dots. Moreover, our results demonstrate that after pumping the nuclear spin state is left in a complex mixed state, from which it is not straightforward to deduce the sign of the Ising-like interactions.
We develop a comprehensive theory for magnetoelectricity in magnetically ordered quasi-2D systems whereby in thermal equilibrium an electric field can induce a magnetization $m$ and a magnetic field can induce a polarization. This effect requires that both space-inversion and time-reversal symmetry are broken. Antiferromagnetic (AFM) order plays a central role in this theory. We define a Néel operator $τ$ such that a nonzero expectation value $\langle τ\rangle$ signals AFM order, in the same way $m$ signals ferromagnetic (FM) order. While $m$ is even under space inversion and odd under time re…
In this letter we develop the theory of Hall effect driven by non-collinear magnetic textures (topological Hall effect - THE) in diluted magnetic semiconductors (DMS). We show that a carrier spin-orbit interaction induces a chiral magnetic ordering inside a bound magnetic polaron (BMP). The inner structure of non-collinear BMP is controlled by the type of spin-orbit coupling, allowing to create skyrmion- (Rashba) or antiskyrmion-like (Dresselhaus) configurations. The asymmetric scattering of itinerant carriers on polarons leads to the Hall signal which exists in weak external magnetic fields a…
We investigate near-Fermi-energy (EF) element-specific electronic and spin states of ferromagnetic van der Waals (vdW) metal Fe5GeTe2. The soft x-ray angle-resolved photoemission spectroscopy (SX-ARPES) measurement provides spectroscopic evidence of localized Fe 3d band. We also find prominent hybridization between the localized Fe 3d band and the delocalized Ge/Te p bands. This picture is strongly supported from direct observation of the remarkable spin polarization of the ligand p bands near EF, using x-ray magnetic circular dichroism (XMCD) measurements. The strength of XMCD signal from lig…
Intra-unit-cell resolved intertwining of multi-$Q$ charge and spin textures in an itinerant skyrmion magnet
RIKEN Center for Emergent Matter Science（理化学研究所物质结构科学研究中心）；Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), University of Tokyo（东京大学应用物理系及量子相电子研究中心）；Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）；Research Center for Advanced Science and Technology, University of Tokyo（东京大学先进科学技术研究中心）
We present a minimal one-dimensional model of collective spin excitations in itinerant ferromagnetic superlattices within the regime of parabolic spin-carrier dispersion. We discuss the cases of weakly and strongly modulated magnetic profiles finding evidences of antiferromagnetic correlations for long-wave magnons (especially significant in layered systems), with an insight into the ground state properties. In addition, the presence of local minima in the magnonic dispersion suggests the possibility of (thermal) excitation of spin waves with a relatively well controlled wave length. Some of t…
We investigate the non-collinear exchange coupling across the trilayer magnetic junction composed of an intermediate layer with Rashba interaction and two sandwiching ferromagnetic ones. To compute the mediated exchange coupling, one needs to go beyond the single-particle argument and integrate over the contributions from the whole Fermi surface. Surprisingly, we find that the topology of the Fermi surface plays a crucial role in determining whether the oscillatory RKKY or the spiral interactions would dominate. At the end, we discuss the connection of our numerical results to experiments and …
We revisit the non-collinear exchange coupling across the trilayer magnetic junction mediated by the diluted-magnetic-semiconductor thin film. By numerical approaches, we investigate the spiral angle between the ferromagnetic layers extensively in the parameter space. In contrast to previous study, we discovered the important role of spin relaxation, which tends to favor spiral exchange over the oscillatory Ruderman-Kittel-Kasuya-Yosida interaction. Finally, we discuss the physics origins of these two types of magnetic interactions.
We consider interaction effects related to a nonuniform magnetization in ferromagnetic nanowires and their possible generalization to nanorings. First we show that the electric current in a ferromagnetic nanowire with more than one domain wall induces an exchange coupling between the walls mediated by the spin-dependent interference of scattered carriers. This interaction reveals a complex behavior as a function of mutual orientations and separation of the domain walls, thus affecting the domain wall dynamics. Then we consider how the theory should be modified in the case of a magnetized quant…
A cluster composed of a few magnetic atoms assembled on the surface of a nonmagnetic substrate is one suitable realization of a bit for future concepts of spin-based information technology. The prevalent approach to achieve magnetic stability of the bit is decoupling the cluster spin from substrate conduction electrons in order to suppress spin-flips destabilizing the bit. However, this route entails less flexibility in tailoring the coupling between the bits which is ultimately needed for spin-processing. Here, we show using a spin-resolved scanning tunneling microscope, that we can write, re…
Complex magnetic order arises due to the competition of different interactions between the magnetic moments. Recently, there has been an increased interest in such states not only to unravel the fundamental physics involved, but also with regards to applications exploiting their unique interplay with moving electrons. Whereas it is the Dzyaloshinskii-Moriya interaction (DMI) that has attracted much attention because of its nature to induce non-collinear magnetic order including magnetic-field stabilized skyrmions, it is the frustration of exchange interactions that can drive magnetic order dow…
The dynamics of itinerant electrons in topological insulator (TI) thin films is investigated using a multi-band decomposition approach. We show that the electron trajectory in the 2D film is anisotropic and confined within a characteristic region. Remarkably, the confinement and anisotropy of the electron trajectory are associated with the topological phase transition of the TI system, which can be controlled by tuning the film thickness and/or applying an in-plane magnetic field. Moreover, persistent electron wavepacket oscillation can be achieved in the TI thin film system at the phase trans…
Collective ferromagnetic motion in a conducting medium is damped by the transfer of the magnetic moment and energy to the itinerant carriers. We present a calculation of the corresponding magnetization relaxation as a linear-response problem for the carrier dynamics in the effective exchange field of the ferromagnet. In electron systems with little intrinsic spin-orbit interaction, a uniform magnetization motion can be formally eliminated by going into the rotating frame of reference for the spin dynamics. The ferromagnetic damping in this case grows linearly with the spin-flip rate when the l…
We present a theory of both the itinerant carrier-mediated RKKY interaction and the virtual excitations-mediated Bloembergen-Rowland (BR) interaction between magnetic moments in graphene induced by proximity effect with a ferromagnetic film. We show that the RKKY/BR interaction consists of the Heisenberg, Ising, and Dzyaloshinskii-Moriya (DM) terms. In the case of the nearest distance, we estimate the DM term from the RKKY/BR interaction is about 0.13 meV for the graphene/Co interface, which is consistent with the experimental result of DM interaction $0.16 \pm 0.05$ meV. Our calculations indi…
We propose an RKKY-type interaction that is mediated by a spin liquid. If a spin liquid ground state exists such an interaction could leave a fingerprint by ordering underlying localized moments such as nuclear spins. This interaction has a unique phenomenology that is distinct from the RKKY interaction found in fermionic systems; most notably the lack of a Fermi surface and absence of the requirement for itinerant electrons, since most spin liquids are insulators. As a working example we investigate the two-dimensional spin-1/2 kagome antiferromagnet (KAFM), although the treatment remains gen…
The induction of unconventional superconductivity by twisting two layers of graphene a small angle was groundbreaking1, and since then has attracted widespread attention to novel phenomena caused by lattice or angle mismatch between two-dimensional (2D) materials2. While many studies address the influence of angle mismatch between layered 2D materials3-5 , the impact of the absorption alignment on the physical properties of planar molecules on 2D substrates has not been studied in detail. Using scanning probe microscopy (SPM) we show that individual cobalt phthalocyanine (CoPc) molecules adsor…
Cavity spintronics explores light matter interactions at the interface between spintronic and quantum phenomena. Until now, studies have focused on the hybridization between ferromagnets and cavity photons.In this article, we realize antiferromagnetic cavity-magnon polaritons. The collective spin motion in single hematite crystals (α-Fe2O3) hybridizes with 18 - 45 GHz microwave cavity photons with required specific symmetries. We show theoretically and experimentally that the photon-magnon coupling in the collinear phase is mediated by the dynamical Neel vector and the weak magnetic moment in …
Collinear antiferromagnets (AFs) support two degenerate magnon excitations carrying opposite spin polarizations, by which magnons can function as electrons in various spin-related phenomena. In an insulating ferromagnet(F)/AF/F trilayer, we explore the magnon-mediated interlayer coupling by calculating the magnon thermal energy in the AF as a function of the orientations of the Fs. The effect manifests as an interlayer exchange interaction and a perpendicular magnetic anisotropy; they both depend on temperature and the AF thickness. In particular, the exchange interaction turns out to be antif…
We calculate the electron-mediated exchange interaction between two domain walls in magnetic wires. This corresponds to the equilibrium regime and, therefore, the interaction can be additionally controlled by an electric current. The exchange interaction is long ranged and oscillates as a function of the distance between the walls. It also depends oscillatory on the polarization angle of the walls, having the maximum value for collinear polarization.
We present a microscopic calculation of magnetization damping for a magnetic "toy model." The magnetic system consists of itinerant carriers coupled antiferromagnetically to a dispersionless band of localized spins, and the magnetization damping is due to coupling of the itinerant carriers to a phonon bath in the presence of spin-orbit coupling. Using a mean-field approximation for the kinetic exchange model and assuming the spin-orbit coupling to be of the Rashba form, we derive Boltzmann scattering integrals for the distributions and spin coherences in the case of an antiferromagnetic exchan…
Time-reversal (T) symmetry breaking is a fundamental physics concept underpinning a broad science and technology area, including topological magnets, axion physics, dissipationless Hall currents, or spintronic memories. A best known conventional model of macroscopic T-symmetry breaking is a ferromagnetic order of itinerant Bloch electrons with an isotropic spin interaction in momentum space. Anisotropic electron interactions, on the other hand, have been a domain of correlated quantum phases, such as the T-invariant nematics or unconventional superconductors. Here we report discovery of a brok…
There is accelerating interest in developing memory devices using antiferromagnetic (AFM) materials, motivated by the possibility for electrically controlling AFM order via spin-orbit torques, and its read-out via magnetoresistive effects. Recent studies have shown, however, that high current densities create non-magnetic contributions to resistive switching signals in AFM/heavy metal (AFM/HM) bilayers, complicating their interpretation. Here we introduce an experimental protocol to unambiguously distinguish current-induced magnetic and nonmagnetic switching signals in AFM/HM structures, and d…
Kitaev spin liquids (KSLs) contain both itinerant Majorana fermions and localized $Z_2$ flux excitations. The mobile fermions transport energy, while the fluxes hinder heat flow. By controlling the flux configuration, one can separate a KSL into different domains via $Z_2$ flux walls. We show that at low temperatures, the wall significantly suppresses the Majorana-mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and blocks the heat transfer between domains.
Carrier-mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction plays an important role in itinerant magnetism. There have been intense interest on its general trend on bipartite lattice with particle-hole symmetry. In particular, recently fabricated graphene is well described by the honeycomb lattice within tight-binding approximation. We use SUSY quantum mechanics to study the RKKY interaction on bipartite lattices. The SUSY structure naturally differentiate the zero modes and those paired states at finite energies. The significant role of zero modes is largely ignored in previous literatu…
Carrier-mediated exchange coupling, known as Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, plays a fundamental role in itinerant ferromagnetism and has great application potentials in spintronics. A recent theorem based on the imaginary-time method shows that the oscillatory RKKY interaction becomes commensurate on bipartite lattice and predicts that the effective exchange coupling is always ferromagnetic for the same sublattice but antiferromagnetic for opposite sublattices. We revisit this important problem by real- and imaginary-time methods and find the theorem misses important contrib…
During the past years there has been renewed interest in the wide-bandgap II-VI semiconductor ZnO, triggered by promising prospects for spintronic applications. First, ferromagnetism was predicted for dilute magnetic doping. In comprehensive investigation of ZnO:Co thin films based on the combined measurement of macroscopic and microscopic properties, we find no evidence for carrier-mediated itinerant ferromagnetism. Phase-pure, crystallographically excellent ZnO:Co is uniformly paramagnetic. Superparamagnetism arises when phase separation or defect formation occurs, due to nanometer-sized met…
We calculate the temperature dependent long-range magnetic coupling in the presence of dilute concentrations of random magnetic impurities in chiral multilayer two-dimensional semimetals, i.e., undoped intrinsic multilayer graphene. Assuming a carrier-mediated indirect RKKY exchange interaction among the well-separated magnetic impurities with the itinerant carriers mediating the magnetic interaction between the impurities, we investigate the magnetic properties of intrinsic multilayer graphene using an effective chiral Hamiltonian model. We find that due to the enhanced density of states in t…
Ferromagnetic heterostructures provide an ideal platform to explore the nature of spin-orbit torques arising from the interplay mediated by itinerant electrons between a Rashba-type spin-orbit coupling and a ferromagnetic exchange interaction. For such a prototypic system, we develop a set of coupled diffusion equations to describe the diffusive spin dynamics and spin-orbit torques. We characterize the spin torque and its two prominent--out-of-plane and in-plane--components for a wide range of relative strength between the Rashba coupling and ferromagnetic exchange. The symmetry and angular de…
We demonstrate that 2D Fermi liquids can support peculiar excitations that are not subject to Landau's $T^2$ dissipation. The long-lived excitations relax through correlated angular dynamics involving "lock-step" angular displacements along the Fermi surface occurring in collinear two-particle collisions, a surprising behavior that is unique to 2D systems. We develop a microscopic picture of the non-Brownian random walk, describing the angular dynamics as anomalous diffusion ("superdiffusion") on the Fermi surface. Strongly-correlated dynamics with directional memory, mediated by novel undampe…
Motivated by the discovery of the quantum anomalous Hall effect in Cr-doped \ce{(Bi,Sb)2Te3} thin films, we study the generic states for magnetic topological insulators and explore the physical properties for both magnetism and itinerant electrons. First-principles calculations are exploited to investigate the magnetic interactions between magnetic Co atoms adsorbed on the \ce{Bi2Se3} (111) surface. Due to the absence of inversion symmetry on the surface, there are Dzyaloshinskii-Moriya-like twisted spin interactions between the local moments of Co ions. These nonferromagnetic interactions twi…
