Ruderman-Kittel-Kasuya-Yosida Interaction Research Articles

Reconfigurable Chiral Spintronic THz Emitters

AbstractCollective spin arrangements manifest diverse spin textures, encompassing ferromagnetism, antiferromagnetism, and chiral vortices. However, mapping these spin textures in ultrathin magnetic multilayers has remained elusive. A reconfigurable chiral spintronic terahertz emission method is introduced through investigations on a model system of synthetic antiferromagnet and the spin information of individual ferromagnet (FM) layers is extracted. Upon femtosecond photoexcitation of the synthetic antiferromagnet (FM1/Ru/FM2), the ferromagnets generate a pair of linearly polarized ultrafast spin currents, which, after relaxation at the FM/Ru interface, emit corresponding THz pulses. The Ruderman–Kittel–Kasuya–Yosida interactions between the two FMs give rise to magnetic‐field‐controlled spin textures causing a spin relaxation imbalance at the interfaces and induce a phase shift between the orthogonal components of the emitted terahertz fields, consequently reconfiguring the polarization of the emitted terahertz field from linear to circular. This approach offers a novel means of investigating electronic and magnetic states in ultrathin spintronic heterostructures, low‐dimensional quantum materials, topological insulators, and Weyl semimetals. Furthermore, it enables the exploration of spin textures, including skyrmions, merons, and solitons.

Exchange coupling in (Co/Pt)2/Nb/(Pt/Co)2 multilayers induced by the Yu–Shiba–Rusinov bound states

The Ruderman–Kittel–Kasuya–Yosida (RKKY) theory of oscillatory exchange interaction in synthetic antiferromagnetic multilayers results in the oscillation behavior of giant magnetoresistance ratio. In addition, the formation of Yu–Shiba–Rusinov (YSR) bound states will induce an extra antiferromagnetic interaction, which is expected to mediate stronger exchange coupling than conventional RKKY interaction. However, the YSR bound states have only been studied in some superconducting hosts with magnetic impurities. The narrow range of material systems that are not compatible with the device integration architecture limits the practical application of YSR interaction. Here, we observe the RKKY interaction and provide the evidence for YSR interaction in Pt/(Co/Pt)2/Nb/(Pt/Co)2/Pt synthetic antiferromagnetic multilayers by quantitatively determining the coupling energy via ferromagnetic resonance technique.

Field-free control and switching of perpendicular magnetization by voltage induced manipulation of RKKY interaction

Voltage control of magnetization offers substantial advantages in energy efficiency for the development of spintronics technology. However, achieving a complete 180° magnetization switching remains as a challenging task since the electric field cannot provide torques to turn the magnetic moment in the ferromagnetic material. To address this challenge, we explore the utilization of synthetic antiferromagnetic (sAFM) structure coupled by Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction in the two ferromagnetic (FM) Co layers separated by a suitable thickness Ru spacer layer. One of the FM layers was prepared to be in contact with the GdOx layer, where ionic motion of oxygen can be manipulated via an application of electric field. Depending on the oxidation state at the interface with GdOx, the RKKY coupling can be adjusted and achieves reversible transitions between antiferromagnetic (AFM) and FM orders of FM layers at room temperature. The transition is mediated by the migration and redistribution of oxygen ions, transforming the Co/Gd interface into Co/GdOx and vice versa. This method suggests a stable and electrical route for magnetization reversals without an external magnetic field.

Experimental evidence of the oscillation behavior of the interlayer DMI effect

Chiral spin interactions play an important role in magnetism. Recent reports have revealed a new type of antisymmetric and indirect spin interaction, namely, the interlayer Dzyaloshinskii–Moriya interaction (DMI), which is predicted to arise from the three-site spin–orbit scattering of delocalized electrons as an additional Ruderman–Kittel–Kasuya–Yosida (RKKY) effect. Here, we investigated the interlayer DMI and RKKY interaction in the similar Pt/Co/Pt/Ru/Pt/Co/Pt structures as a function of spacer thickness. Both interactions present a synchronous damping oscillation and support the predicted relevance between them. The coupling strength of the interlayer DMI was finely engineered by tunning thickness of the nonmagnetic spacer. This work can deepen the understanding of the interlayer DMI and guide the control and use of the interlayer DMI in the field-free spin–orbit torque switching or the design of three-dimensional chiral spin textures.

Hole‐Mediated RKKY Interaction in 2D Ferromagnetic CrTe2 Ultra‐Thin Films

AbstractThe rapid development of 2D magnetic materials has opened new possibilities in the field of spintronics. CrTe2, a 2D material with perpendicular magnetic anisotropy (PMA) and ferromagnetic transient temperature near room temperature, holds promise for various applications. However, the underlying mechanism responsible for its global magnetism remains unclear. This work focuses on investigating the magneto‐transport properties of ultra‐thin CrTe2 Field Effect Transistor (FET) under the influence of top gate biases. The application of gate voltage ranging from 25 to −15 V tunes its coercivity (HC) and Curie temperature (TC) (from 152 to 191 K). Notably, a linear correlation is observed between the TC and the hole concentration () in the CrTe2 film, indicating the involvement of the Ruderman–Kittel–Kasuya–Yosida interaction. This experimental analysis sheds light on the mechanism of the CrTe2’s ferromagnetism and paves the way for future advancements and applications in this material.

Vanishing RKKY interactions in Ce-based cage compounds

We report the results of thermodynamic measurements in external magnetic field of the cubic Ce-based cage compounds CeT 2Cd20 (T = Ni,Pd). Our analysis of the heat-capacity data shows that the Γ7 doublet is the ground state multiplet of the Ce3+ ions. Consequently, for the Γ7 doublet it can be theoretically shown that the Ruderman–Kittel–Kasuya–Yosida interaction between the localized Ce moments mediated by the conduction electrons, must vanish at temperatures much lower than the energy separating the ground state doublet from the first excited Γ8 quartet. Our findings provide an insight as to why no long range order has been observed in these compounds down to temperatures in the milliKelvin range.

The Study of Transport Properties of (III−Mn) V Diluted Magnetic Semiconductors

We investigated the transport properties of diluted magnetic semiconductors (DMSs) theoretically by using the Heisenberg and Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange interaction models by considering both spin and charge disorder. The formalism is applied to the specific case of Ga 1 − x Mn x As . Using the Heisenberg model and the Green function formalism the total thermal excitation of the magnon is calculated. The magnetization and Curie temperature of Mn -doped GaAs is calculated. The theoretical calculation of T C of Ga 1 − x Mn x As at x = 0.08 has a good agreement with the experimental calculation at x = 0.08 (i.e., 162 k). The exchange interaction constant and spin-dependent relaxation time is calculated by using RKKY interaction. The electrical conductivity and hole mobility are calculated by using the Boltzmann transport equation and the spin-dependent relaxation time. The electrical conductivity of Mn -doped III–V DMS is exponentially increased with temperature and magnetic impurity concentration. Hole mobility of Mn -doped III–V diluted magnetic semiconductor is increased with the magnetic impurity concentration.

Effective Hamiltonian of magnetic moments in proximity with an s-wave superconductor

In this paper, we consider two magnetic moments in proximity with an s-wave superconductor, where each magnetic moment has an internal energy level. The effective Hamiltonian of the two magnetic moments is derived in this paper by the method of path integral in the weak coupling limit. Interestingly, there are four new terms by the proximity effect, including the Ruderman–Kittel–Kasuya–Yosida interaction, the hopping term, the cross and on-site superconducting pairing potentials. Additionally, since the parity of electrons is conserved, the Hilbert space is split into two subspaces of even and odd parities, respectively. We also investigate the consequences of the effective Hamiltonian in the Coulomb blockade regime by varying the distance between the two magnetic moments. We found that a quantum phase transition happens whenever there is a level crossing for the ground states. The degeneracy of the ground states is also changed after the quantum phase transition, and the electron occupations for the magnetic moments with both singlet and triplet states are discontinuous at the level crossing, since the electronic states are always entangled with the spin states of the two magnetic moments.

Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund's Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory.

We apply a generalized Schrieffer-Wolff transformation to the extended Anderson-like topological heavy fermion (THF) model for the magic-angle (θ=1.05°) twisted bilayer graphene (MATBLG) [Phys. Rev. Lett. 129, 047601 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.047601], to obtain its Kondo lattice limit. In this limit localized f electrons on a triangular lattice interact with topological conduction c electrons. By solving the exact limit of the THF model, we show that the integer fillings ν=0,±1,±2 are controlled by the heavy f electrons, while ν=±3 is at the border of a phase transition between two f-electron fillings. For ν=0,±1,±2, we then calculate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between the f moments in the full model and analytically prove the SU(4) Hund's rule for the ground state which maintains that two f electrons fill the same valley-spin flavor. Our (ferromagnetic interactions in the) spin model dramatically differ from the usual Heisenberg antiferromagnetic interactions expected at strong coupling. We show the ground state in some limits can be found exactly by employing a positive semidefinite "bond-operators" method. We then compute the excitation spectrum of the f moments in the ordered ground state, prove the stability of the ground state favored by RKKY interactions, and discuss the properties of the Goldstone modes, the (reason for the accidental) degeneracy of (some of) the excitation modes, and the physics of their phase stiffness. We develop a low-energy effective theory for the f moments and obtain analytic expressions for the dispersion of the collective modes. We discuss the relevance of our results to the spin-entropy experiments in TBG.

Superconductivity in Ce-based cage compounds

Cerium-based ternary compounds CeNi2Cd20 and CePd2Cd20 do not exhibit long-range order down to millikelvin temperature range. Given the large separation between Ce ions which significantly reduces the super-exchange interactions and vanishingly small Ruderman–Kittel–Kasuya–Yosida interaction, here we show that nodal superconductivity mediated by the valence fluctuations must be a ground state in these materials. We propose that the critical temperature for the superconducting transition can be significantly increased by applying hydrostatic pressure. We employ an extended periodic Anderson lattice model which includes the long-range Coulomb interactions between the itinerant electrons as well as the local Coulomb interaction between the predominantly localized and itinerant electrons to compute a critical temperature of the superconducting transition. Using the slave-boson approach we show that fluctuations mediated by the repulsive electron–electron interactions lead to the emergence of d-wave superconductivity.

Anomalous Spin Textures in a 2D Topological Superconductor Induced by Point Impurities

AbstractTopological superconductors are foreseen as good candidates for the search of Majorana zero modes, where they appear as edge states and can be used for quantum computation. In this context, it becomes necessary to study the robustness and behavior of electron states in topological superconductors when a magnetic or non‐magnetic impurity is present. The focus is on scattering resonances in the bands and on spin texture to know what the spin behavior of the electrons in the system will be. It is found that the scattering resonances appear outside the superconducting gap, thus providing evidence of topological robustness. Non‐trivial and anisotropic spin textures related to the Dzyaloshinskii–Moriya interaction are also found. The spin textures show a Ruderman–Kittel–Kasuya–Yosida interaction governed by Friedel oscillations. It is believed that the results are useful for further studies which consider many‐point‐impurity scattering or a more structured impurity potential with a finite range.

Accurate finite-difference micromagnetics of magnets including RKKY interaction: Analytical solution and comparison to standard micromagnetic codes

Within this paper we show the importance of accurate implementations of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions for antiferromagnetically coupled ferromagnetic layers with thicknesses exceeding the exchange length. In order to evaluate the performance of different implementations of RKKY interaction, we develop a benchmark problem by deriving the analytical formula for the saturation field of two infinitely thick magnetic layers that are antiparallelly coupled. This benchmark problem shows that state of the art implementations in commonly used finite-difference codes lead to errors of the saturation field that amount to more than 20% for mesh sizes of 2 nm which is well below the exchange length of the material. In order to improve the accuracy, we develop higher order cell-based and nodal-based finite-difference codes that significantly reduce the error compared to state of the art implementations. For the second order cell-based approach and first order nodal-based approach the error of the saturation field is reduced by about a factor of 10 (2% error) for the same mesh size of 2 nm.

RKKY interaction at helical edges of topological superconductors

We study spin configurations of magnetic impurities placed close to the edge of a two-dimensional topological superconductor both analytically and numerically. First, we demonstrate that the spin of a single magnetic impurity close to the edge of a topological superconductor tends to align along the edge. The strong easy-axis spin anisotropy behind this effect originates from the interaction between the impurity and the gapless helical Majorana edge states. We then compute the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities placed close to the edge. We show that, in the limit of large interimpurity distances, the RKKY interaction between the two impurities is mainly mediated by the Majorana edge states and leads to a ferromagnetic alignment of both spins along the edge. This effect can be used to detect helical Majorana edge states.

Spin torque oscillator and magnetization switching in double-barrier Rashba Zeeman magnetic tunnel junction

In this work, we have studied the spin torque based magnetization oscillations and switching in presence of Rashba–Zeeman (RZ), Ruderman–Kittel–Kasuya–Yosida (RKKY) and Dzyaloshinskii–Moriya (DM) interactions in a double-barrier RZ|Heavy Metal (HM)|RZ magnetic tunnel junction (MTJ). The system has stable magnetization oscillations and can work as an oscillator or a switcher for a significant difference in the strength of RKKY and DM interaction under suitable spin transfer torque (STT). For the proposed system with same order of RKKY and DM interaction, a nonlinear characteristic of the magnetization oscillation is observed. However, this nonlinearity of oscillations can be reduced by an external magnetic field or considering a material with suitable RZ interaction. In addition to this, our study reveals the magnetization switching can be tuned by using suitable STT. A dependence of switching time on layer thickness is also observed. Also, the switching speed increases with the thickness for systems having either same order of RKKY and DM interaction or dominated by RKKY interaction. An opposite characteristic is seen when DM interaction dominates over RKKY interaction.

Noncollinear twisted RKKY interaction on the optically driven SnTe(001) surface

The nontrivial spin texture on the (001) surface of topological crystalline insulator SnTe hosts exotic scientific importance and spintronic applications. Here, we study the effects of weak Floquet optical driving on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities on a doped SnTe(001) surface. Due to peculiar spin-orbit hybridization, we find a noncollinear twisted RKKY interaction with XYZ-Heisenberg, symmetric in-plane, and asymmetric Dzyaloshinskii-Moriya (DM) terms. We see that contributions from the $z$ $(x)$ component of the XYZ-Heisenberg (DM) interaction are dominant for most parameters. The interactions, including DM terms that are responsible for interesting spin textures, require doping in most cases. We propose to modify the interactions in situ via optical control of band structure, and thereby doping. A notable aspect of this control protocol is breaking of electron-hole symmetry, which stems from the DM interaction.

Spintronic leaky-integrate-fire spiking neurons with self-reset and winner-takes-all for neuromorphic computing

Neuromorphic computing using nonvolatile memories is expected to tackle the memory wall and energy efficiency bottleneck in the von Neumann system and to mitigate the stagnation of Moore’s law. However, an ideal artificial neuron possessing bio-inspired behaviors as exemplified by the requisite leaky-integrate-fire and self-reset (LIFT) functionalities within a single device is still lacking. Here, we report a new type of spiking neuron with LIFT characteristics by manipulating the magnetic domain wall motion in a synthetic antiferromagnetic (SAF) heterostructure. We validate the mechanism of Joule heating modulated competition between the Ruderman–Kittel–Kasuya–Yosida interaction and the built-in field in the SAF device, enabling it with a firing rate up to 17 MHz and energy consumption of 486 fJ/spike. A spiking neuron circuit is implemented with a latency of 170 ps and power consumption of 90.99 μW. Moreover, the winner-takes-all is executed with a current ratio >104 between activated and inhibited neurons. We further establish a two-layer spiking neural network based on the developed spintronic LIFT neurons. The architecture achieves 88.5% accuracy on the handwritten digit database benchmark. Our studies corroborate the circuit compatibility of the spintronic neurons and their great potential in the field of intelligent devices and neuromorphic computing.

Structure-property relationship of reversible magnetic chirality tuning

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction mediates collinear magnetic interactions via the conduction electrons of a nonmagnetic spacer, resulting in a ferro- or antiferromagnetic magnetization in magnetic multilayers. Recently it has been discovered that heavy nonmagnetic spacers are able to mediate an indirect magnetic coupling that is noncollinear and chiral. This Dzyaloshinskii-Moriya-enhanced RKKY interaction causes the emergence of a variety of interesting magnetic structures, such as skyrmions and spin spirals. Here, we show by spin-polarized scanning tunneling microscopy that the interchain coupling between manganese oxide chains on Ir(001) can reproducibly be switched from chiral to collinear antiferromagnetic by increasing the oxidation state of ${\mathrm{MnO}}_{2}$, while the reverse process can be induced by thermal reduction. The underlying structure--property relationship is revealed by low-energy electron diffraction intensity analysis. Density functional theory calculations suggest that the magnetic transition may be caused by a significant increase of the Heisenberg exchange which overrides the Dzyaloshinskii-Moriya interaction upon oxidation.

Voltage control of magnetic order in RKKY coupled multilayers.

In the field of antiferromagnetic (AFM) spintronics, there is a substantial effort present to make AFMs viable active components for efficient and fast devices. Typically, this is done by manipulating the AFM Néel vector. Here, we establish a method of enabling AFM active components by directly controlling the magnetic order. We show that magneto-ionic gating of hydrogen enables dynamic control of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in solid-state synthetic AFM multilayer devices. Using a gate voltage, we tune the RKKY interaction to drive continuous transitions from AFM to FM and vice versa. The switching is submillisecond at room temperature and fully reversible. We validate the utility of this method by demonstrating that magneto-ionic gating of the RKKY interaction allows for 180° field-free deterministic switching. This dynamic method of controlling a fundamental exchange interaction can engender the manipulation of a broader array of spin textures, e.g., chiral domain walls and skyrmions.

The Routes to Magnetic Graphene, from Decorations with Nanoparticles to the Broken Symmetry of its Honeycomb Lattice Bonds

Pristine graphene is nonmagnetic because the outer electrons in the rings of its honeycomb lattice are merged into sigma- and pi- bonds. To have magnetic graphene, methods have been proposed to break the bond symmetry to obtain unpaired electrons and spins, so that their interaction can turn on the graphene magnetism. These methods are therefore based on the intrinsic nature of graphene. Other methods are based on the extrinsic decoration of graphene layers with magnetic nanoparticles. Here, we discuss the routes to have graphene magnetized in intrinsic and extrinsic manners, and some of its applications. In particular, the nitrogen-doped graphene is considered. The Ruderman–Kittel–Kasuya–Yosida interaction is also proposed in a very concise manner. Short discussion about graphene substitution with nitrogen-doped biochar and iron-decorated biochar is proposed too.

Анизотропия парамагнитной восприимчивости дираковского полуметалла Cd-=SUB=-3-=/SUB=-As-=SUB=-2-=/SUB=-, обусловленная примесью хрома: ЭПР на ионах Cr-=SUP=-3+-=/SUP=-

In the literature devoted to magnetic impurities in Dirac semimetals, the appearance of anisotropic and long-range non-oscillating contributions to the Ruderman–Kittel–Kasuya–Yosida interaction is predicted. These contributions are due to the hybridization of the wave functions of magnetic impurities with the wave functions of Dirac electrons, which have a linear dispersion law. We have studied electron paramagnetic resonance (EPR) in powder samples of topological 3D Dirac semimetal Cd3As2 with an admixture of chromium ions. Anisotropy of the magnetic susceptibility in the paramagnetic state was found from the behavior of the resonance field. The appearance of magnetic anisotropy in the paramagnetic state is associated with an increase in the contribution of the orbital moments of chromium ions Cr2+ and Cr3+ due to their interaction with the orbital moments of donor Dirac electrons, which have anomalously large values of g factors.