Ruderman-Kittel-Kasuya-Yosida Interaction Research Articles

Two-dimensional parabolic Dirac system in the presence of nonmagnetic and magnetic impurities

We theoretically investigate the effect of the nonmagnetic and magnetic impurities to the 2D parabolic Dirac system. The induced charge density by the charged impurity is obtained by the linear response theory within the random phase approximation. We also calculate in-detail, the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between two magnetic impurities placed within the 2D sheet of the Dirac materials with isotropic and anisotropic dispersion. For the anisotropic dispersion, the RKKY interaction is also anisotropic and related to the lattice parameters which can be obtained through the DFT calculation or the experiments. The features of the RKKY interaction also can be treated as a signature of the topological phase transition as well as the change of Berry curvature. Our results are also illuminating to the study of the static screening and the RKKY interaction of the isotropic or anisotropic 3D Dirac/Weyl semimetals or the 2D transition metal dichalcogenide family.

Inhomogeneous Kondo destruction by RKKY correlations

The competition between the indirect exchange interaction (IEC) of magnetic impurities in metals and the Kondo effect gives rise to a rich quantum phase diagram, the Doniach Diagram (Doniach, 1977). A Kondo screened phase is separated from a spin ordered phase when the local exchange coupling J and the concentration of magnetic moments nM are varied. In disordered metals, both the Kondo temperature and the IEC are widely distributed due to the scattering of the conduction electrons from the impurity potential. Therefore, it is a question of fundamental importance, how this Doniach diagram is modified by the disorder, and if one can still identify separate phases. Recently, Nejati et al. (2017) investigated the effect of Ruderman–Kittel–Kasuya–Yosida (RKKY) correlations on the Kondo effect of two magnetic impurities, renormalizing the Kondo interaction based on the Bethe–Salpeter equation and performing the poor men’s renormalization group (RG) analysis with the RKKY-renormalized Kondo coupling. In the present study, we extend this theoretical framework, allowing for different Kondo temperatures of two RKKY-coupled magnetic impurities due to different local exchange couplings and density of states. As a result, we find that the smaller one of the two Kondo temperatures is suppressed more strongly by the RKKY interaction, thereby enhancing their initial inequality. In order to find out if this relevance of inequalities between Kondo temperatures modifies the distribution of the Kondo temperature in a system of a finite density of randomly distributed magnetic impurities, we present an extension of the RKKY coupled Kondo RG equations. We discuss the implication of these results for the interplay between Kondo coupling and RKKY interaction in disordered electron systems and the Doniach diagram in disordered electron systems.

Screening, Friedel oscillations, RKKY interaction, and Drude transport in anisotropic two-dimensional systems

We investigate the effect of the mass anisotropy on Friedel Oscillations, Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, screening properties, and Boltzmann transport in two dimensional (2D) metallic and doped semiconductor systems. We calculate the static polarizability and the dielectric function within the random phase approximation with the mass anisotropy fully taken into account without making any effective isotropic approximation in the theory. We find that carrier screening exhibits an isotropic behavior for small momenta despite the anisotropy of the system, and becomes strongly anisotropic above a certain threshold momentum. Such an anisotropy of screening leads to anisotropic Friedel oscillations, and an anisotropic RKKY interaction characterized by a periodicity dependent on the direction between the localized magnetic moments. We also explore the disorder limited dc transport properties in the presence of mass anisotropy based on the Boltzmann transport theory. Interestingly, we find that the anisotropy ratio of the short range disorder limited resistivity along the heavy- and light-mass directions is always the same as the mass anisotropy ratio whereas for the long range disorder limited resistivity the anisotropy ratio is the same as the mass ratio only in the low density limit, and saturates to the square root of the mass ratio in the high density limit. Our theoretical work should apply to many existing and to-be-discovered anisotropic 2D systems.

RKKY interaction in spin polarized doped zigzag carbon nanotube in Holstein model

We have theoretically studied the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in zigzag gapped graphene nanotube in the presence of Holstein phonons . We investigate the effect of quantities such as the gap parameter, intensity of the electron-phonon interaction, nanotube diameter, next nearest neighbor hopping parameter, chemical potential, etc. on the spatial behavior of the RKKY interaction. Since the RKKY interaction can be obtained from the static spin susceptibility function, we first need to calculate this function. The spin susceptibility is calculated using Green's function approach via computing the correlation function of spin density operators for the Holstein model Hamiltonian. We also exploit the random phase approximation (RPA) to correct the spin susceptibility function using the self energy due to the electron-phonon interaction. The results indicate an oscillating behavior for the spatial dependence of the RKKY interaction. It is also clear that the mentioned quantities listed above affect the spatial behavior of RKKY interaction. • Using Holstein model Hamiltonian, the excitation spectrum of electrons on nanotube has been found. • To obtain RKKY interaction, the spin susceptibility has been calculated using Green's function approach in Holstein model. • We have the effects of diameter, electron-phonon coupling and electron doping on the RKKY interaction in zigzag nanotube. • Results show an oscillating behavior for spatial dependence of coupling exchange constant between two local impurities.

Compact spin qubits using the common gate structure of fin field-effect transistors

The sizes of commercial transistors are of nanometer order, and there have already been many proposals of spin qubits using conventional complementary metal–oxide–semiconductor transistors. However, most of the previously proposed spin qubits require many wires to control a small number of qubits. This causes a significant “jungle of wires” problem when the qubits are integrated into a chip. Herein, to reduce the complicated wiring, we theoretically consider spin qubits embedded into fin field-effect transistor (FinFET) devices such that the spin qubits share the common gate electrode of the FinFET. The interactions between qubits occur via the Ruderman–Kittel–Kasuya–Yosida interaction via the channel of the FinFET. The possibility of a quantum annealing machine is discussed in addition to the quantum computers of the current proposals.

Spin-Torque Memristors Based on Perpendicular Magnetic Tunnel Junctions for Neuromorphic Computing.

Spin‐torque memristors are proposed in 2009, and can provide fast, low‐power, and infinite memristive behavior for neuromorphic computing and large‐density non‐volatile memory. However, the strict requirements of combining high magnetoresistance, stable domain wall pinning and current‐induced switching in a single device pose difficulties in physical implementation. Here, a nanoscale spin‐torque memristor based on a perpendicular‐anisotropy magnetic tunnel junction with a CoFeB/W/CoFeB composite free layer structure is experimentally demonstrated. Its tunneling magnetoresistance is higher than 200%, and memristive behavior can be realized by spin‐transfer torque switching. Memristive states are retained by strong domain wall pinning effects in the free layer. Experiments and simulations suggest that nanoscale vertical chiral spin textures can form around clusters of W atoms under the combined effect of opposite Dzyaloshinskii–Moriya interactions and the Ruderman–Kittel–Kasuya–Yosida interaction between the two CoFeB free layers. Energy fluctuation caused by these textures may be the main reason for the strong pinning effect. With the experimentally demonstrated memristive behavior and spike‐timing‐dependent plasticity, a spiking neural network to perform handwritten pattern recognition in an unsupervised manner is simulated. Due to advantages such as long endurance and high speed, the spin‐torque memristors are competitive in the future applications for neuromorphic computing.

Ultralow-current magnetization switching in nearly compensated synthetic antiferromagnetic frames using sandwiched spin sources

Spin–orbit torque (SOT)-induced magnetization switching via electric currents in large spin–orbit-coupled heavy metal (HM)/ferromagnetic (FM) frames is one of the most reliable approaches to achieve increased performances in various spintronic applications. However, its widespread utilization is still challenging owing to the inherent requirement of a high electric current density for efficient magnetization switching. In this paper, we introduce a sandwiched synthetic antiferromagnetic (S-SyAF) frame, comprising CoFeB (FM)/W (HM)/CoFeB (FM) stacks, whose operation is mediated by the Ruderman–Kittel–Kasuya–Yosida interaction. The middle HM layer serves as a spin current source for the top and bottom FM layers simultaneously. In addition, the S-SyAF frame contributes to a substantial reduction in the net magnetization, which ensures a considerably increased SOT switching efficiency; further, the switching current was almost 10 times smaller than that in a conventional HM/FM frame. Thus, we believe that these experimental findings will provide a new avenue for designing future spintronic devices.

Distribution of RKKY coupling value in 1D crystal with disorder. Specific heat in XY model

The presence of disorder in one-dimensional crystals leads to the localization of all charge carriers and the calculation of the indirect exchange interaction (Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction) cannot be performed perturbatively on disorder. In two and three-dimensional systems it makes sense to calculate the magnitude of RKKY interaction perturbatively treating nearly free carriers scattering on the random potential, and this approach results in a rather high magnitude of the exchange interaction due to interference effects similar to weak localization. We show that in one-dimensional systems the indirect exchange interaction should be described as a random value with heavy-tail distribution function, which is calculated in this work, on scales of carriers localization length. We also demonstrate that heavy tails and the absence of a characteristic value of RKKY interaction magnitude leads to a significant change in observables for these systems. We calculate a specific heat for the one-dimensional XY model taking into account the effect of disorder and assuming that typical distance between impurities exceeds the localization length. In contrast to an ideal system, where specific heat temperature dependence has a peak at a certain temperature proportional to exchange constant describing characteristic energy scale, disorder eliminates the peak as soon as there is no characteristic excitation energy in this case anymore.

Probing divacancy defects in a zigzag graphene nanoribbon through an RKKY exchange interaction

We investigate the effects of vacancy defects on the electronic and magnetic properties of zigzag graphene nanoribbons (zGNRs) by making use of the Green’s function formalism in combination with a tight-binding Hamiltonian. We explain the evolution of indirect exchange coupling, known as the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction, including single, double, and multiple 5-8-5 divacancy (DV) defects. Our numerical calculations show that changes in the electronic structure and exchange coupling of zGNRs depend to a significant degree on the location of DV defects with respect to the ribbon edges and the number of DV defects. In the case where both impurities are located on the edge, the magnitude of the exchange coupling is several orders of magnitude higher than when they are placed on the interior of the nanoribbon. Furthermore, a periodic DV causes a dramatic change in the magnetic ground state of the ribbon. In the limit of a high vacancy potential, the strength of the RKKY interaction is approximately independent of the Fermi energy. We demonstrate that, on the one hand, the defect engineering of atomic vacancies is a promising way to modify the magnetic properties of graphene nanoribbons, and, on the other hand, unusual RKKY oscillations around the DVs are a new technique for directly probing the local vacancies in a zGNR through the RKKY exchange interaction.

Ultralow-Current Magnetization Switching in Nearly Compensated Synthetic Antiferromagnetic Frames Using Sandwiched Spin Sources

Spin–orbit torque (SOT)-induced magnetization switching via electric currents in large spin–orbit-coupled heavy metal (HM)/ferromagnetic (FM) frames is one of the most reliable approaches to achieve increased performances in various spintronic applications. However, its widespread utilization is still challenging owing to the inherent requirement of a high electric current density for efficient magnetization switching. In this paper, we introduce a sandwiched synthetic antiferromagnetic (S-SyAF) frame, comprising CoFeB (FM)/W (HM)/CoFeB (FM) stacks, whose operation is mediated by the Ruderman–Kittel–Kasuya–Yosida interaction. The middle HM layer serves as a spin current source for the top and bottom FM layers simultaneously. In addition, the S-SyAF frame contributes to a substantial reduction in the net magnetization, which ensures a considerably increased SOT switching efficiency; further, the switching current was almost 10 times smaller than that in a conventional HM/FM frame. Thus, we believe that these experimental findings will provide a new avenue for designing future spintronic devices.

Anisotropic RKKY interactions in nodal-line semimetals

Nodal-line semimetals (NLSMs) are typically characterized by a nodal ring, a closed line of Dirac points in the Brillouin zone, which features a torus-shaped Fermi surface, as well as a quantized Berry phase $\ensuremath{\pi}$. By investigating the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in NLSMs, a close relationship between the magnetic interaction and the radius ${k}_{0}$ of the nodal ring is revealed. For impurities deposited in the direction normal to the nodal-ring plane, when the long-range interaction at half-band filling follows the decaying law ${R}^{\ensuremath{-}3}$ with impurity distance, which is a result of anisotropic dispersion of semi-Dirac semimetal, the decaying rate for the relatively short-range impurity distance would be prolonged by nodal-ring radius ${k}_{0}$, which is prominent for the intermediate radius. This phenomenon originates from the competition between the contribution from the electron states inside and outside the nodal ring. In contrast, for impurities distributed in the nodal-ring plane, the RKKY interaction $J\ensuremath{\propto}{k}_{0}^{2}\mathrm{cos}(2{k}_{0}R){R}^{\ensuremath{-}4}$ shows an oscillation, from whose period one can easily determine the parameter ${k}_{0}$ of the nodal ring. Furthermore, at finite Fermi energy, we find a distinct signature of the RKKY interaction to characterize the topological trivial and topological nontrivial phases in NLSMs.

Compensation Temperature Behavior in a Nanotube Core-Shell Structure with RKKY Interactions: Monte Carlo Simulations

In this paper, we have studied the magnetic properties of the nanotube core-shell structure with RKKY (Ruderman-Kittel-Kasuya-Yosida) interactions, using Monte Carlo simulations (MCS). The system consists of hexagonal core-shell nanotube structure with mixed spins σ = ± 3/2, ± 1/2 (of the core) and S = ±1, 0 (of the shell), separated by non-magnetic nanotubes. Initially, we start this study by discussing for zero temperature, the ground-state phase diagrams in different planes. Moreover, we investigate for the positive temperature values, the effect of the RKKY interactions on the thermal magnetization and magnetic susceptibility of the system. Additionally, we study the effects of the exchange coupling interactions of the core and of the shell on the compensation and transition temperatures. Finally, we explore the behavior of the magnetic hysteresis cycles as a function of the non-magnetic nanotubes number, the temperature, and the exchange coupling parameters.

Magnetoresistance effects in a spin-fermion model for multilayers

We consider a spin-fermion model consisting of free electrons coupled to classical spins, where the latter are embedded in a quasi one-dimensional superlattice structure consisting of spin blocks separated by spinless buffers. Using a spiral ansatz for the spins, we study the effect of the electron mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction on the $T=0$ ground state of the system. We find that the RKKY interaction can lead to ferromagnetic, antiferromagnetic, or intermediate spiral phases for different system parameters. When the width is much larger than the length of the individual blocks, the spiral phases are suppressed, and the ground state oscillates between ferromagnetic and antiferromagnetic order as the size of the buffer regions is varied. This is accompanied by a corresponding oscillation in the Drude weight reflecting an increased conductivity in the ferromagnetic state compared to the antiferromagnetic one. These results are reminiscent of classic giant magnetoresistance phenomena observed in a similar geometry of thin, sandwiched magnetic and non-magnetic layers. Our analysis provides a robust framework for understanding the role of the RKKY interaction on the ground state order and corresponding transport properties of such systems, extending beyond the conventional perturbative regime.

Signature of gate-controlled magnetism and localization effects at Bi2Se3/EuS interface

Proximity of a topological insulator (TI) surface with a magnetic insulator (MI) can open an exchange gap at the Dirac point leading to exploration of surface quantum anomalous Hall effect. An important requirement to observe the above effect is to prevent the topological breakdown of the surface states (SSs) due to various interface coupling effects and to tune the Fermi level at the interface near the Dirac point. In this work, we demonstrate the growth of high-quality c-axis oriented strain-free layered films of TI, Bi2Se3, on amorphous SiO2 substrate in proximity to an MI, europium sulfide (EuS), that show stronger weak anti-localization response from the surface than previous studies with epitaxially interfaced heterostructures. Importantly, we find gate and magnetic field cooling modulated localization effects in the SSs, attributed to the position of interface Fermi level within the band gap that is also corroborated from our positron annihilation spectroscopy measurements. Furthermore, our experiments provide a direct evidence of gate-controlled enhanced interface magnetism in EuS arising from the carrier mediated Ruderman–Kittel–Kasuya–Yosida interactions across the Bi2Se3/EuS interface. These findings demonstrate the existence of complex interfacial phenomena affecting the localization response of the SSs that might be important in proximity engineering of the TI surface to observe surface quantum Hall effects.

Nonequilibrium RKKY interaction in irradiated graphene

We demonstrate that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in graphene can be strongly modified by a time-periodic driving field even in the weak drive regime. This effect is due to the opening of a dynamical band gap at the Dirac points when graphene is exposed to circularly polarized light. Using Keldysh-Floquet Green's functions, we develop a theoretical framework to calculate the time-averaged RKKY coupling under weak periodic drives and show that its magnitude in undoped graphene can be decreased controllably by increasing the driving strength, while mostly maintaining its ferromagnetic or antiferromagnetic character. In doped graphene, we find RKKY oscillations with a period that is tunable by the driving field. When a sufficiently strong drive is turned on that brings the Fermi level completely within the dynamically opened gap, the behavior of the RKKY coupling changes qualitatively from that of doped to undoped irradiated graphene.

Effective low-energy RKKY interaction in doped topological crystalline insulators

We study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities resided on the (001) plane of topological crystalline insulator (TCI) SnTe associated with four anisotropic Dirac cones protected by the mirror symmetry. The lattice Green's functions governing the correlation of both the sublattices and spins are deduced by developing a two-band effective model. We explore the RKKY Heisenberg interaction of the system established by the interference between four Dirac cones. Our key finding is that, independent of the position of magnetic impurities on the same sublattices or different ones, multiple wave vectors with different orders describe the RKKY coupling physics in TCIs. Further, both the undoped and doped spin susceptibility give rise to the same decay rates like graphene. Magnetic impurities on the same and different sublattices propose the ferromagnetic and antiferromagnetic base phase of the undoped system, respectively. Here we demonstrate that RKKY exchange in TCIs, undergoes a ferromagnetic-to-antiferromagnetic transition and vice versa in response to switching on/off the electron and hole doping. Analytic expressions of doped TCIs are obtained to draw the magnetic phase diagram of the distance between two magnetic impurities and the doping concentration, clarifying the contributions of short and long distances as well as low and high concentrations to the RKKY coupling. Our results may tailor the magnetic features of TCIs for further research and application.

X-ray detection of ultrashort spin current pulses in synthetic antiferromagnets

We explore the ultrafast generation of spin currents in magnetic multilayer samples by applying fs laser pulses to one layer and measuring the magnetic response in the other layer by element-resolved x-ray spectroscopy. In Ni(5 nm)/Ru(2 nm)/Fe(4 nm), the Ni and Fe magnetization directions couple antiferromagnetically due to the Ruderman–Kittel–Kasuya–Yosida interaction but may be oriented parallel through an applied magnetic field. After exciting the top Ni layer with a fs laser pulse, we also find that the Fe layer underneath demagnetizes, with a 4.1±1.9% amplitude difference between parallel and antiparallel orientation of the Ni and Fe magnetizations. We attribute this difference to the influence of a spin current generated by the fs laser pulse that transfers angular momentum from the Ni into the Fe layer. Our results confirm that superdiffusive spin transport plays a role in determining the sub-ps demagnetization dynamics of synthetic antiferromagnetic layers, but also evidence large depolarization effects due to hot electron dynamics, which are independent of the relative alignment of the magnetization in Ni and Fe.

Resistivity minimum in diluted metallic magnets

Resistivity minima are commonly seen in itinerant magnets and they are often attributed to the Kondo effect. However, recent experiments are revealing an increasing number of materials showing resistivity minima in the absence of indications of Kondo singlet formation. In a previous work [Z. Wang, K. Barros, G.-W. Chern, D. L. Maslov, and C. D. Batista, Phys. Rev. Lett. 117, 206601 (2016)], we demonstrated that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction can produce a classical spin liquid state at finite temperature, whose resistivity increases with decreasing temperature. The classical spin liquid exists over a relatively large temperature window because of the frustrated nature of the RKKY interaction produced by a 2D electron gas. In this work, we investigate the robustness of the RKKY-induced resistivity upturn against site dilution, which provides an alternative, and more robust, way of stabilizing the classical spin liquid state down to $T=0$. By using series expansions and stochastic Landau-Lifshitz dynamics simulation, we show that site dilution competes with thermal fluctuations and further stabilizes the resistivity upturn, which is accompanied by a negative magnetoresistivity due to suppression of the electron-spin scattering.

Long-range and tunable RKKY interaction in the topological channel of gated bilayer graphene

Two separate gate electrodes with opposite gate voltages can drive an AB-stacked bilayer graphene (BLG) under them into different quantum valley Hall states. And between the two topological domains there appears a one-dimensional boundary, dubbed the topological channel (TC). By means of the Lanczos method, we theoretically study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities in such a TC of BLG. We find that the RKKY interaction is long-range with an ${R}^{\ensuremath{-}1}$ decay rate as the distance $R$ between two magnetic impurities increases, whereas the slowest decay rate in any graphene structure is ${R}^{\ensuremath{-}2}$ according to previous literature. Moreover, we also find that the strength and sign of the RKKY interaction in the TC can be readily controlled by altering the gate voltage or carrier doping. Such a tunable and ${R}^{\ensuremath{-}1}$ decaying RKKY interaction implies the possibility of establishing and controlling a long-range magnetic ordering state in a dilute magnetic impurity-doped BLG.

RKKY interaction in three-dimensional tilted Dirac and Weyl semimetals

We theoretically investigate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities of the tilted Dirac and Weyl semimetals in three dimensions. In accordance with the untilted scenario, the RKKY interaction contains three terms, namely the Heisenberg term, the Ising term, and the Dzyaloshinsky-Moriya term. The main influence of tilt on the RKKY Hamiltonian is a modulation to the oscillation frequencies of range functions. Our results enrich the knowledge of the magnetic properties of materials with tilted Dirac cones and may see an important application in spintronics.