Indirect exchange interaction in Rashba-spin-orbit-coupled graphene nanoflakes

We study the indirect exchange interaction, named Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling, between localized magnetic impurities in graphene nanoflakes with zig-zag edges in the presence of the Rashba spin-orbit interaction (RSOI). We calculate the isotropic and anisotropic RKKY amplitudes by utilizing the tight-binding (TB) model. The RSOI, as a gate tunable variable, is responsible for changes of the RKKY amplitude. We conclude that there is not any switching of the magnetic order (from ferro- to antiferro-magnetic and vice versa) in such a system through the RSOI. The dependence of the RKKY amplitude on the positions of the magnetic impurities and the size of the system is studied. The symmetry breaking, which can occur due to the Rashba interaction, leads to spatial anisotropy in the RKKY amplitude and manifests as collinear and noncollinear terms. Our results show the possibility of control and manipulation of spin correlations in carbon spin-based nanodevices.     

Indirect magnetic interaction in the “net fractal” systems

A localized spin system of fractal symmetry with indirect exchange between them is considered. We define a specific class of fractals as the “net fractals” which display multidimensional logarithmic periodicity. Basing on this property we model the effective indirect exchange interaction by the conventional RKKY exchange with the logarithmic coordinates playing role of the real space ones. Finally, we discuss the case of non-ideal “net fractals” in which fractional dynamics of the electrons is expected. In this case we show that RKKY exchange integrals are given by the formulas derived under assumption that a system has a fractional spectral dimension.     

Transport spectroscopy of Kondo quantum dots coupled by RKKY interaction

We develop the theory of conductance of a quantum dot which carries a spin and is coupled via RKKY interaction to another spin-carrying quantum dot. The found dependence of the differential conductance on the bias and magnetic field at a fixed RKKY interaction strength may allow one to distinguish between the possible ground states of the system. Transitions between the ground states are achieved by tuning the RKKY interaction, and the nature of these transitions can be extracted from the temperature dependence of the linear conductance. The feasibility of the corresponding measurements is evidenced by recent experiments by Craig et al.     

Screening, Kohn anomaly, Friedel oscillation, and RKKY interaction in bilayer graphene

We calculate the screening function in bilayer graphene (BLG) in both the intrinsic (undoped) and the extrinsic (doped) regimes within the random phase approximation, comparing our results with the corresponding single layer graphene and the regular two-dimensional electron gas. We find that the Kohn anomaly is strongly enhanced in BLG. We also discuss the Friedel oscillation and the RKKY interaction, which are associated with the nonanalytic behavior of the screening function at q=2k(F). We find that the Kohn anomaly, the Friedel oscillation, and the RKKY interaction are all qualitatively different in the BLG compared with the single layer graphene and the two-dimensional electron gas.     

Kondo effect in the presence of magnetic impurities

We measure transport through gold grain quantum dots fabricated using electromigration, with magnetic impurities in the leads. A Kondo interaction is observed between dot and leads, but the presence of magnetic impurities results in a gate-dependent zero-bias conductance peak that is split due to a RKKY interaction between the spin of the dot and the static spins of the impurities. A magnetic field restores the single Kondo peak in the case of an antiferromagnetic RKKY interaction. This system provides a new platform to study Kondo and RKKY interactions in metals at the level of a single spin.     

Anisotropy of the oscillatory exchange coupling in magnetic multilayers

We discuss the influence of quantum-well effect on the anisotropy and oscillation period of the RKKY interaction in magnetic multilayers. Taking into account local strains we have calculated the magnetoelastic contribution to the effective coupling.     

Extended dynamical mean field theory study of the periodic Anderson model

We investigate the competition of the Kondo and the RKKY interactions in heavy fermion systems. We solve a periodic Anderson model using extended dynamical mean field theory (EDMFT) with quantum Monte Carlo method. We monitor simultaneously the evolution of the electronic and magnetic properties. As the RKKY coupling increases the heavy fermion quasiparticle unbinds and a local moment forms. At a critical RKKY coupling there is an onset of magnetic order. Within EDMFT the two transitions occur at different points and the disappearance of the magnetism is not described by a local quantum critical point.     

RKKY interaction in metallic overlayers of fractional dimensionality

Within an analytical approach we study the RKKY interaction mediated by the electron gas, which shows fractional spectral dimensionality. We derive formula for the RKKY exchange integral in a system of nonintegral dimensionality. Also the modifications of magnetic interaction and magnetic moments in metallic overlayers due to the surface/interface effects are considered. Presented at the VIII-th Symposium on Surface Physics, Třešt’ Castle, Czech Republic, June 28 – July 2, 1999.     

SPECIAL FEATURES OF 1-DIMENSIONAL DILUTE MAGNETIC ALLOYS

The susceptibility, range function and RKKY interaction of 1-di-mensional dilute magnetic alloys are given. The special features are: there is only ferromagnetic phase transition for small values of 2K_F(R_j-R_i); 1-dimensional range function and RKKY interaction are alonger distance interaction than the 3-dimensional case. Comparisons between our theory and others' are made.     

Ruderman-Kittel-Kasuya-Yosida and magnetic-field interactions in coupled Kondo quantum dots

We investigate theoretically the transport properties of two independent artificial Kondo impurities. They are coupled together via a tunable Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. For strong enough antiferromagnetic RKKY interaction, the impurity density of states increases with the applied in-plane magnetic-field. This effect can be used to distinguish between antiferromagnetic and ferromagnetic RKKY interactions. These results may be relevant to explain some features of recent experiments by Craig et al. [Science 304, 565 (2004)].     

From bubble to Skyrmion: Dynamic transformation mediated by a strong magnetic tip

Skyrmions in thin metallic ferromagnetic films are stable due to competition between the RKKY interaction and uniaxial magnetic anisotropy. We study static nonlinear excitations in magnetic film in the presence of strong cylindrical magnetic tip of nanometer size. We mimic the RKKY interaction by the next-nearest-neighbors ferromagnetic and antiferromagnetic exchange interactions. We demonstrate analytically and numerically dissipative transformation of a bubble created by a strong magnetic tip into a stable Skyrmion.     

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.     

Indirect RKKY interaction in doped armchair nanotube due to electron phonon interaction effects

We study the Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction in doped armchair nanotube in the presence of gap parameter. The effects of both next nearest neighbor hopping parameter and electron-Holstein phonon on RKKY interaction have been addressed. RKKY interaction as a function of distance between localized moments have been analyzed. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain the transverse static spin susceptibility of armchair graphene nanoribbon in the presence of electron-phonon coupling and gap parameter. The spin susceptibility components are calculated using Green’s function approach for Holstein model Hamiltonian. The effects of electron doping on dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of next nearest neighbor hopping parameter on the spatial behavior of RKKY interactions are different in the presence of electron phonon coupling.     

Influence of Randomness and Localization on RKKY Interactions in Diluted Magnetic Semiconductors

We show that the spatially random distribution of magnetic moments of dopants in diluted magnetic semiconductors can partially localize the itinerant carriers and change the carrier-mediated indirect RKKY interaction. From numerical calculations of the electron states taking into account the interaction with magnetic impurities which are random both in spatial positions and in orientations of magnetic moments, we obtain the electron states and the RKKY interaction as a function of the distance between magnetic dopants L and of the sp - d exchange integral J. With the increase of disorder, the localization of itinerant electrons become stronger and the long-range regular oscillatory behaviour of the RKKY interaction gradually disappears and is replaced by severe fluctuations. The randomness and localization may enhance the RKKY interaction between dopants with short and middle distances and in favour of the ferromagnetism.     

The effects of electron–phonon interaction on anisotropic RKKY interaction in graphene nanoribbon

We study the Ruderman–Kittle–Kasuya–Yosida (RKKY) interaction in doped armchair graphene nanoribbon. The effects of both external magnetic field and electron-Holstein phonon on RKKY interaction have been addressed. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a magnetic field along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain both transverse and longitudinal static spin susceptibilities of armchair graphene nanoribbon in the presence of electron-phonon coupling and magnetic field. The spin susceptibility components are calculated using the spin dependent Green’s function approach for Holstein model Hamiltonian. The effects of spin polarization on the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of magnetic field on the spatial behavior of in-plane and longitudinal RKKY interactions are different in the presence of magnetic field.     

Dynamical current–current correlation in two-dimensional parabolic Dirac systems

We theoretically investigate the current–current correlation of the two-dimensional (2D) parabolic Dirac system in hexogonal lattice. The analytical expressions of the random phase approximation (RPA) susceptibility, Ruderman–Kittel–Kasuya–Yosida (RKKY) Hamiltonian, and the diamagnetic orbital susceptibility in noninteracting case base on the density–density or current–current correlation function are derived and quantitatively analyzed. In noninteracting case, the dynamical polarization within RPA, and spin transverse susceptibility as well as the RKKY interaction (when close to the half-filling) are related to the current–current response in the 2D parabolic Dirac systems. Both the cases of anisotropic dispersion and isotropic dispersion are discussed.     

Direct experimental evidence for the Ruderman-Kittel-Kasuya-Yosida interaction in rare-earth metals

We show that the ferromagnetic heavy rare-earth (RE) metals show a transport spin polarization at the Fermi level in the majority spin, whereas in ferromagnetic light rare earths it is in the minority spin. The sign of the polarization is in agreement with what is expected due to the Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling formalism. We show that magnetotransport measurements on magnetic multilayer samples containing magnetic REs provide a unique opportunity to verify the RKKY coupling scheme in pure rare-earth metals, allowing us to probe both the sign and temperature dependence of the spin-density oscillation.     

Kondo quantum dots and the novel Kondo-doublet interaction

We analyze the interactions between two Kondo quantum dots connected to a Rashba-active quantum wire. We find that the Kondo-doublet interaction, at an interdot distance of the order of the wire Fermi length, is over an order of magnitude greater than the RKKY interaction. The effects induced on the Kondo-doublet interaction by the wire spin-orbit coupling can be used to control the quantum dots spin-spin correlation. These results imply that the widely used assumption that the RKKY is the dominant interaction between Anderson impurities must be revised.     

Competition between Kondo and RKKY correlations in the presence of strong randomness

We propose that competition between Kondo and magnetic correlations results in a novel universality class for heavy fermion quantum criticality in the presence of strong randomness. Starting from an Anderson lattice model with disorder, we derive an effective local field theory in the dynamical mean-field theory approximation, where randomness is introduced into both hybridization and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. Performing the saddle-point analysis in the U(1) slave-boson representation, we reveal its phase diagram which shows a quantum phase transition from a spin liquid state to a local Fermi liquid phase. In contrast with the clean limit case of the Anderson lattice model, the effective hybridization given by holon condensation turns out to vanish, resulting from the zero mean value of the hybridization coupling constant. However, we show that the holon density becomes finite when the variance of the hybridization is sufficiently larger than that of the RKKY coupling, giving rise to the Kondo effect. On the other hand, when the variance of the hybridization becomes smaller than that of the RKKY coupling, the Kondo effect disappears, resulting in a fully symmetric paramagnetic state, adiabatically connected to the spin liquid state of the disordered Heisenberg model. We investigate the quantum critical point beyond the mean-field approximation. Introducing quantum corrections fully self-consistently in the non-crossing approximation, we prove that the local charge susceptibility has exactly the same critical exponent as the local spin susceptibility, suggesting an enhanced symmetry at the local quantum critical point. This leads us to propose novel duality between the Kondo singlet phase and the critical local moment state beyond the Landau-Ginzburg-Wilson paradigm. The Landau-Ginzburg-Wilson forbidden duality serves the mechanism of electron fractionalization in critical impurity dynamics, where such fractionalized excitations are identified with topological excitations.     

Magnetic properties of bilayer nano-stanene-like structure with Ruderman–Kittel–Kasuya–Yoshida coupling

A bilayer nano-stanene-like structure with Ruderman–Kittel–Kasuya–Yoshida (RKKY) coupling described by the Ising model is proposed. The magnetic and thermodynamic properties are studied using the effective-field theory with correlations. The exchange coupling, longitudinal magnetic field, number of non-magnetic layers, and anisotropies had major influences on the magnetization, specific heat, and internal energy. Different saturation magnetizations are observed on the magnetization curve. The variation in the system blocking temperature is studied. The results provide theoretical guidance for the magnetic investigation of nanomaterials with RKKY coupling.