Ruderman-Kittel-Kasuya-Yosida Exchange Research Articles

Monte Carlo study of magnetocaloric effect and magnetic properties of the nano- borophene bilayer with RKKY exchange interactions of a mixed spin 2 and 3/2

In this study, we have studied the magnetic properties and magnetocaloric effect of the nano-borophene bilayer with RKKY (Ruderman-Kittel-Kasuya-Yosida) exchange interactions of mixed spin 2 and 3/2 using Monte Carlo calculations. In the first part of this investigation, the ground state phase diagrams for zero temperature are reported and discussed. We also determined the critical temperature for varying the number of non-magnetic layers (NML) and the interacting couplings Jss. In the second part, we investigated the influence of the parameter NML, the exchange couplings Jss and Jσσ, and the crystal field on the total magnetizations and the magnetic hysteresis loop. The specific heat and magnetic entropy changes versus of the temperature under the effect of different external magnetic fields and the parameter Jss. Finally, we analyzed the relative cooling power (RCP) for distinct external magnetic field and Jss.

Oscillatory exchange bias controlled by RKKY in magnetic multilayers

Ferromagnetic/antiferromagnetic bilayers are interfaced with normal metal/ferromagnetic bilayers to form F*/AF/N/F valves. The N-spacer thickness is chosen such that it mediates strong indirect exchange [Ruderman–Kittel–Kasuya–Yosida (RKKY)] between the outer ferromagnetic layers, which varies in strength/direction depending on the N thickness and changes its direction on switching F. The system exhibits a strong modulation of the F*/AF exchange bias, oscillating in strength synchronously with the oscillation in the interlayer RKKY exchange across the normal metal spacer. The effect is explained as due to a superposition taking place within the antiferromagnetic layer of the direct-exchange proximity effect from the F*/AF interface and the indirect RKKY exchange from F penetrating AF via N. The modulation, expressed via the strength of the F*/AF bias field, reaches 400% at the first RKKY peak.

Electrical control of Ruderman–Kittel–Kasuya–Yosida exchange interaction in zigzag edge MoS2 nanoflakes

In this study, we investigate the spin–spin correlation of two magnetic impurities in zigzag edge MoS2 nanoflakes using a three-orbital tight-binding model. In particular, we consider the dependence of the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction on the local electric field strength for providing a degree of tunability in triangular and rectangular nanoflakes. Our results indicate that manipulating the local electric field at the zigzag edges could allow the control of all the different components of the RKKY interaction in MoS2 nanoflakes. Interestingly, the Dzyaloshinskii–Moriya JDM oscillates but does not decay due to strong spin–orbit coupling. Moreover, the electric field induces a sizable JDM interaction as a function of the magnetic separation along zigzag edges for various Fermi energies. Our findings provide a method for enhancing the RKKY exchange interactions with magnetic arrays in these materials.

Signatures of interfacial topological chiral modes via RKKY exchange interaction in Dirac and Weyl systems

We theoretically investigate the features of Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between two magnetic impurities, mediated by the interfacial bound states inside a domain wall (DW). The latter separates the two regions with oppositely signed inversion symmetry broken terms in graphene and Weyl semimetal. The DW is modelled by a smooth quantum well which hosts a number of discrete bound states including a pair of gapless, metallic zero-energy modes with opposite chiralities. We find clear signatures of these interfacial chiral bound states in spin response (RKKY exchange interaction) which is robust to the deformation of the quantum well.

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.

Simulating Exotic Phases of Matter with Bond-Directed Interactions with Arrays of Majorana-Cooper Pair Boxes.

It is suggested that networks of Majorana-Cooper pair boxes connected by metallic nanowires can simulate various exotic states of matter. In this simulation Majorana-Cooper boxes play the role of effective spins S=1/2 and the metallic connections generate the Kondo screening and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. Depending on what prevails-whether it is the Kondo effect or the RKKY exchange, one will have either a Kondo lattice or an effective spin model. The list of exotic states includes the famous hexagonal Kitaev model, a generalization of this model for a Kondo lattice, and various spin models with three-spin interactions. Special emphasis is made on the discussion of the Kondo lattice scenario.

Insights on improved room temperature ferromagnetism in chemically co-precipitated Ru-doped ZnS nanopowders

In this paper, we have reported the room temperature weak ferromagnetism in Ruthenium (Ru)-doped ZnS nanopowders (Zn1-xRuxS; x = 0.00, 0.02, 0.04 and 0.06) prepared using chemical co-precipitation route. Powder x-ray diffraction (XRD) divulges that pure as well as Ru-doped ZnS (Zn1-xRuxS) nanopowders exhibit cubic structure. Photoluminescence (PL) measurements depict the presence of defects in chemically co-precipitated Zn1-xRuxS nanopowders. Replacement of host Zn atoms with Ru is confirmed by X-ray absorption spectroscopy (XAS). Ru L3-edge XANES spectral changes clearly depict the charge transfer from S 2p state to Ru 4d state. Weak ferromagnetism is shown by pure ZnS nanopowders at room temperature. Ru doping in ZnS enhances the weak ferromagnetic ordering with magnetic moment nearly three times in comparison to pure ZnS at room temperature. Ru doping leads to metallic nature which further favors RKKY (Ruderman–Kittel–Kasuya–Yosida) exchange interaction for ferromagnetism.

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.

Manipulation of the RKKY exchange by voltages

In the last years, electric fields have been used to control the magnetic exchange interactions and anisotropies in nanometric devices. In this paper, we study the spin-spin exchange interaction between two magnetic impurities embedded in a three-dimensional nonrelativistic electron gas, namely the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. The gas is confined in an insulating structure, and an applied voltage produces local changes in the electron density, which modulates the Fermi level of the system. Using a simple model, we demonstrate that this voltage modifies the strength and wavelength of the coupling between the impurities. Depending on the voltage, the effective RKKY exchange can change from a ferro- to an antiferromagnetic coupling, and vice versa. The spin-spin coupling can also be switched on and off by the voltage.

Fingerprints of tilted Dirac cones on the RKKY exchange interaction in 8- Pmmn borophene

We theoretically investigate the indirect signatures of the tilted anisotropic Dirac cones on Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction in a two dimensional polymorph of boron atoms. Unlike the case of isotropic non-tilted Dirac material-graphene, here we observe that the tilting of the Dirac cones exhibits a significant impact on the RKKY exchange interaction in terms of the suppression of oscillation frequency. The reason can be attributed to the behavior of the Fermi level and the corresponding density of states with respect to the tilting parameter. The direct measurement of the period of the RKKY interaction can thus be a possible probe of the tilt parameter associated with the tilted Dirac cones. We also obtain the direction dependent analytical expressions of the RKKY exchange interaction, in terms of Meijer G-function. However, the effects due to tilting of the Dirac cones on the RKKY interaction depend on the spatial alignments of the two magnetic impurities with respect to the direction of tilting.

Critical phenomena in kagomé multilayer with RKKY-like interaction: A Monte Carlo study

The sandwiches of magnetic/nonmagnetic/magnetic (M/NM/M) materials have been investigated combined with Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange interactions with mixed apins-2 and 3/2 using Ising model using Monte Carlo simulations. The RKKY value is obtained for different distance between the different magnetic and non magnetic multilayer. The RKKY exchange interactions as a function of distance between the magnetic multilayer have been given. The magnetizations and magnetic susceptibilities of each magnetic bloc are obtained. The reduced critical temperatures of each bloc and the system are obtained. The reduced critical temperature is obtained for a fixed size. The theoretical calculations showed an oscillating behavior of the magnetic parameters with increasing the nonmagnetic layers. The total magnetization versus the exchange interactions and crystal field in each bloc is established. The magnetic hysteresis cycles are established for a fixed magnetic parameters.

Giant magnetocaloric effect driven by indirect exchange in magnetic multilayers

Indirect exchange coupling in magnetic multilayers, also known as the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, is known to be highly effective in controlling the interlayer alignment of the magnetization. This coupling is typically fixed at the stage of the multilayer fabrication and does not allow ex-situ control needed for device applications. It is highly desirable, in addition to the orientational control, to also control the magnitude of the intralayer magnetization, ideally switch it on/off by switching the relevant RKKY coupling. Here we demonstrate a magnetic multilayer material, incorporating thermally -- as well as field-controlled RKKY exchange, focused on to a dilute ferromagnetic alloy layer and driving it though it's Curie transition. Such on/off magnetization switching of a thin ferromagnet, performed repeatably and fully reproducibly within a low-field sweep, results in a giant magnetocaloric effect, with the estimated isothermal entropy change of -10 mJ/K cm^3 under an external field of ~10 mT, which greatly exceeds the performance of the best rare-earth based materials used in the adiabatic-demagnetization refrigeration systems.

Probing decoupled edge states in a zigzag phosphorene nanoribbon via RKKY exchange interaction

Phosphorene is an anisotropic puckered two-dimensional ($2$D) hexagonal lattice of phosphorus atoms. The edge modes in a zigzag phosphorene nanoribbon (ZPNR) are quasi-flat in nature and fully isolated from the bulk states, which are unique in comparison to the other hexagonal lattices like graphene, silicene etc. We theoretically investigate the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between two magnetic impurities placed on the nanoribbon, and extract the signatures of the flat edge states via the behavior of it. Due to the complete separation of the edge states from the bulk, we can isolate the edge mode contribution via the RKKY interaction from that of the bulk by tuning the external gate potential when both the impurities are placed at the same edge. The bulk induced RKKY interaction exhibits very smooth oscillation with the distance between the two impurities, whereas for edge modes it fluctuates very rapidly. We also explore the effect of tensile strain both in absence and presence of gate voltage and reveal that the RKKY interaction strength can be boosted under suitable doping, when both the impurities are within the bulk.

Stabilization of magnetic skyrmions by RKKY interactions

We study the stabilization of an isolated magnetic skyrmion in a magnetic monolayer on a nonmagnetic conducting substrate via the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction. Two different types of the substrate are considered, usual normal metal and single-layer graphene. While the full stability analysis for skyrmions in the presence of the RKKY coupling requires a separate effort that is outside the scope of this work, we are able to study the radial stability (stability of a skyrmion against collapse) using variational energy estimates obtained within first-order perturbation theory, with the unperturbed Hamiltonian describing the isotropic Heisenberg magnet, and the two perturbations being the RKKY exchange and the easy-axis anisotropy. We show that a proper treatment of the long-range nature of the RKKY interaction leads to a qualitatively different stabilization scenario compared to previous studies, where solitons were stabilized by the frustrated exchange coupling (leading to terms with the fourth power of the magnetization gradients) or by the Dzyaloshinskii-Moriya interaction (described by terms linear in the magnetization gradients). In the case of a metallic substrate, the skyrmion stabilization is possible under restrictive conditions on the Fermi surface parameters, while in the case of a graphene substrate the stabilization is naturally achieved in several geometries with a lattice-matching of graphene and magnetic layer.

Modeling and calculation of RKKY exchange coupling to explain Ti-vacancy-induced ferromagnetism in Ta-doped TiO2

We present a theoretical study on Ti-vacancy-induced ferromagnetism in anatase TiO2. A recent experimental study has revealed room temperature ferromagnetism in Ta-doped anatase TiO2thin films (Rusydi et al., 2012) [7]. Ta doping assists the formation of Ti vacancies which then induce the formation of localized magnetic moments around the Ti vacancies. As neighboring Ti vacancies are a few unit cells apart, the ferromagnetic order is suspected to be mediated by itinerant electrons. We propose that such an electron-mediated ferromagnetism is driven by Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange interaction. To examine our hypothesis, we construct a tight-binding based model Hamiltonian for the anatase TiO2 system. We calculate the RKKY exchange coupling constant of TiO2 as a function of distance between local magnetic moments at various temperatures. We model the system by taking only the layer containing a unit of TiO2, at which the Ti vacancy is believed to form, as our effective two-dimensional unit cell. Our model incorporates the Hubbard repulsive interactions between electrons occupying Ti d orbitals treated within mean-field approximation. The density of states profile resulting from the model captures the relevant electronic properties of TiO2, such as the energy gap of ~3.4eV and the n-type character, which may be a measure of the adequacy of the model. The calculated RKKY coupling constant shows that the ferromagnetic coupling extends up to 3–4 unit cells and enhances slightly as temperature is increased from 0 to 400K. These results support our hypothesis that the ferromagnetism of this system is driven by RKKY mechanism.

Semi-Empirical Study of the Indirect Exchange Interaction in the Rem – Al System

The Ruderman–Kittel–Kasuya–Yosida exchange interaction (RKKY) is semi-empirically studied for the first time in compounds of binary REM – Al systems (REM – rare-earth metals: Gd, Dy, Ho, Er) using experimental values of paramagnetic Curie point (θр) of these compounds. Prediction of the RKKY theory was confirmed, i.e. there is a direct proportional dependence of θр value on de Gennes factor for equiatomic compounds of heavy REM with aluminum, just as in the case of pure REM. Values of the indirect exchange interaction parameter were semi-empirically estimated for the studied compounds. In general, it was established that RKKY-type exchange interaction is typical for REM compounds with aluminum, just as for pure REM.

Asymptotic discontinuities in the RKKY interaction in the graphene Bernal bilayer

We derive the asymptotics of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities in the graphene Bernal bilayer using a four-band model of the bilayer spectrum. We find three distinct regimes depending on the position of the Fermi energy in the bilayer spectrum: in the bonding-antibonding gap, at the gap edge, and outside the gap. In particular, for impurities on the bilayer bonding sublattice (the ``$A$'' sublattice) and Fermi energies close to the bonding-antibonding gap edge ${E}_{g}$, we identify a (integrable) logarithmic divergence of the integrand of the RKKY exchange integral. This divergence drives a number of novel RKKY effects for impurities on the $A$ sublattice: (i) an asymptotic ${R}^{\ensuremath{-}5/2}$ term at the gap edge and (ii) a derivative discontinuity in RKKY interaction as a function of the Fermi energy at the gap edge. In the case of intercalated impurities (impurities between the two layers of the bilayer), we find a remarkable discontinuity in the period of the RKKY oscillation at the gap edge. The period of the oscillation limits to $\ensuremath{\lambda}=\sqrt{2}\ensuremath{\pi}\ensuremath{\hbar}{v}_{F}/{t}_{\ensuremath{\perp}}$ as ${E}_{F}\ensuremath{\rightarrow}{E}_{g}$ from below the gap edge, while it limits to $\ensuremath{\lambda}\ensuremath{\rightarrow}\ensuremath{\infty}$ if ${E}_{F}\ensuremath{\rightarrow}{E}_{g}$ from above the gap edge $({t}_{\ensuremath{\perp}}$ is the interlayer coupling, ${v}_{F}$ the Fermi velocity of graphene). The origin of this discontinuity we attribute to (i) the $A$ sublattice divergence and (ii) interference effects driven by the intrinsic valley degree of freedom of graphene. On this basis, we predict that the magnetic response of intercalated bilayer graphene will show a profound sensitivity to doping for Fermi energies near the bonding-antibonding gap edge.

NMR response of nuclear-spin helix in quantum wires with hyperfine and spin-orbit interaction

We calculate the nuclear magnetic resonance (NMR) response of a quantum wire where at low temperature a self-sustained electron-nuclear spin order is created. Our model includes the electron mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange, electron spin-orbit interactions, nuclear dipolar interactions, and the static and oscillating NMR fields, all of which play an essential role. The paramagnet to helimagnet transition in the nuclear system is reflected in an unusual response: it absorbs at a frequency given by the internal RKKY exchange field, rather than the external static field, whereas the latter leads to a splitting of the resonance peak.

Interlayer coupling inNi80Fe20/Ru/Ni80Fe20multilayer films: Ferromagnetic resonance experiments and theory

We present a systematic study of the static and dynamic magnetization behavior of interlayer-coupled ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$(200 \AA{})/Ru(${t}_{\mathrm{Ru}}$)/${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$(100 \AA{}) trilayers as a function of the Ru spacer layer thickness ${t}_{\mathrm{Ru}}$. As ${t}_{\mathrm{Ru}}$ was varied in the range from 0 to 15.8 \AA{}, we observe a strong antiferromagnetic (AFM) exchange coupling between the two ferromagnetic (FM) layers for ${t}_{\mathrm{Ru}}$ = 5 \AA{}, which becomes weak for ${t}_{\mathrm{Ru}}$ = 10 \AA{}. For ${t}_{\mathrm{Ru}}$ = 14.1 \AA{}, the coupled magnetic system changes from AFM to FM ordering. Using broadband ferromagnetic resonance spectroscopy, we have probed the effects of the different coupling mechanisms on both the acoustic and optic magnetic modes. We found that the biquadratic exchange coupling has a negligible effect compared to Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange coupling, while the uniaxial anisotropy at the ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$/Ru interfaces also plays an important role in determining the behaviors of the modes. A mode anticrossing phenomenon is observed when the RKKY exchange interaction term is above a critical value. A theoretical framework developed is in very good agreement with our experimental results.

RKKY Interaction in Coupled Quantum Dots

In artificial nanostructures the control of localized, single spin is of great technological importance for nanospintronic applications. In that respect quantum dots (QD), as the building blocks of nanodevices, seem to be most perspective. Quantum dots are electronic systems which confine a well-defined number of electrons. The total spin of a dot can be integer or half-integer (the latter stands for odd number of confined electrons). Typical nanodevices are composed of a few QD interconnected by leads. Electrons (from a lead or metallic substrate) scattered off QD spins induce an effective spin exchange interaction, the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction [1]. Magnetic correlations of QDs spins arising from the RKKY interaction are very important as they affect conductivity, an effect of primary importance for spintronics. Magnetic moments of QDs are Kondo (partially) screened, so the strength of the RKKY coupling depends both on the QDs separation and the Kondo screening. The Kondo screening can be tuned by the gate voltage; this effect offers an opportunity to control the strength of the effective RKKY exchange. Such a tuned RKKY interaction between QD moments is deemed as a possible way to couple QD based qubits in construction of universal quantum logic gates. We focus our attention on the study of pure RKKY coupling between two dots joined by a lead, leaving the Kondo contribution aside. Two distinct configurations of interacting QDs are considered; the interaction via electrons of a substrate and the other one via electrons of metallic lead which joins adjacent dots. The problem of formation of long-range magnetic order within a quasi-1D ferromagnetic lead is discussed independently.