RKKY interaction and local density of states for a triangular triple quantum dot system

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

Screened spin−1 and −1/2 Kondo effect in a triangular quantum dot system with interdot Coulomb repulsion

A microscopic model for the CuO2 lattice which takes into account two orbitals of copper (3d, 3d and three orbitals of oxygen (2px, y, z) is considered. Applying the canonical transformation to eliminate the d–p hybridizations, the effective spin‐dependent Hamiltonian is derived describing superexchange interaction (SX) and Ruderman‐Kittel‐Kasuya‐Yosida (RKKY)‐type interaction. The possible role of apical oxygen degrees of freedom (β (2pz − 2px(y) hopping integral), Δ (2pz − 3d hybridization), and ε (apical oxygen energy)) for antiferromagnetic frustration effects in the CuO2 plane due to SX is investigated. The presence of an apical orbital coupled to the in‐plane copper and oxygen orbitals can effectively enhance these effects. Therefore, both these interactions (SX and RKKY) can cooperate in destroying the antiferromagnetic order in the sublattice of copper spins upon doping. It is shown that the increase of the frustration due to doping favours the formation of the superconducting state. The RKKY interaction is of ferromagnetic character. For small hole concentrations SX and RKKY integrals are of the same order of magnitude but different in sign.

The Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction has been extensively explored in isotropic Dirac systems with linear dispersion, which typically follows an exponent decaying rate with the impurity distance R, i.e., J ∝ 1/R d (1/R 2d−1) in d-dimensional systems at finite (zero) Fermi energy. This fast decay makes it rather difficult to be detected and limits its application in spintronics. Here, we theoretically investigate the influence of anisotropic dispersion on the RKKY interaction, and find that the introduction of non-relativistic dispersion in semi-Dirac semimetals (S-DSMs) can significantly prolong the decay of the RKKY interaction and can remarkably enhance the Dzyaloshinskii–Moriya interaction around the relativistic direction. The underlying physics is attributed to the highly increased density of states in the linear-momentum direction as a result of the interplay of relativistic and non-relativistic electrons. Furthermore, we propose a general formula to determine the decaying rate of the RKKY interaction, extending the typical formula for isotropic DSMs. Our results suggest that the S-DSM materials are a powerful platform to detect and control the magnetic exchange interaction, superior to extensively adopted isotropic Dirac systems.

The heavy rare earth metals were obtained in pure form and as single crystals about ten years ago. This made a detailed experimental investigation possible. Neutron scattering in particular has been an important tool. As a result we have, by now, obtained a very complete knowledge about the magnetic interactions. The experimental facts, which are reviewed in [1], revealed that the magnetic properties are determined by an intricate interplay of forces of similar magnitude. The dominant is the indirect Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction, which we shall attempt to calculate from first principles, here. Of importance also is the crystal field anisotropy and magnetoelastic effects. The anisotropy of this origin is of a single ion type. Recent neutron scattering measurements [2] have shown also that two-ion anisotropy maybe of importance. There are numerous possibilities for anisotropy of the interaction between the moments at different sites. As we shall see, the RKKY interaction, which is mediated by the conduction electrons, is anisotropic in the magnetically ordered phase. The two-ion interaction, which is mediated by phonons, is strongly anisotropic. The magnitude of the interaction between the spin system and the lattice is determined by the coupling between the spin- and orbital-momentum of the electrons. If the spin-orbit coupling and the orbital momentum is large we must therefore expect large anisotropies both of single-ion and two-ion nature. Also the RKKY interaction becomes anisotropic, as discussed by Kaplan and Lyons [3].KeywordsExchange InteractionConduction ElectronAugmented Plane WaveSpiral PhaseRKKY InteractionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

For a system of two magnetic adatoms on a metal surface at finite temperatures, we calculate the spectral density at adatom sites. At sufficiently low temperatures, the peak structure at the Fermi level, which originates from the coupling between the local moments of adatoms and conduction electrons, corresponds to the Yosida–Kondo resonance. In addition, we also consider the indirect Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between the adatoms, which is mediated by the conduction electrons of the metal surface, and depends strongly on the adatom separation. Under strong ferromagnetic (FM) RKKY interaction, the peak structure disappears, while under antiferromagnetic (AF) RKKY interaction, the width of the peak structure increases in comparison to that of the single adatom case. Our conclusion of the spectral density variation in the two dimensional system can be confirmed by experiments on the surface, for example by the scanning tunneling spectroscopy.

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.

We have systematically investigated the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between two magnetic impurities in Weyl semimetals with arbitrary monopole charge Q. We find that the RKKY interaction becomes intrinsically anisotropic for , and its dependence on Fermi energy and impurity separation is directly controlled by the monopole charge. With the increase of Q, the RKKY interaction becomes more long-ranged and more anisotropic, which makes interesting magnetic orders easier to form and thus may have important applications in spintronics.

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction has been extended to the case when an external magnetic field is taken into account. It has been shown that the RKKY Hamiltonian should contain the Zeeman-like term in which the effective gyromagnetic factor occurs. This effective gyromagnetic factor contains a correction term which is linearly dependent on the contact potential between the localized spins and conduction electrons. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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.

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)].

We propose versatile materials based on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in a zigzag silicene nanoribbon (ZSNR) on half filling in the presence of an out-of-plane electric field. We show that the topological phase transition in the band dispersion of ZSNR can be probed by using the RKKY interaction. We find that, due to the zero-energy edge states of the ZSNR, the exchange coupling is significantly enhanced when the impurities are located on the zigzag edges, and also explore that the strength of the interaction in the topological insulator phase is much greater than that when the system is in the band insulator region. We present a model to investigate the phase of a system of two magnetic impurities located on the edge of the ZSNR and find that three different magnetic phases, spiral, ferromagnetic, and anti-ferromagnetic, are possible for different values of the electric field. This electrical tunability of the magnetic phases in silicene can be explored by using current experimental techniques and can be of interest in the field of spintronics.

The Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction is an essential long-range magnetic interaction between magnetic impurities or magnetic layered structures, the magnitude of which oscillates with the distance between them. We investigated the RKKY interaction between two magnetic impurities in both time-reversal and inversion symmetry-broken Weyl semimetals (WSMs) where the energy dispersion is tilted in momentum space and the momentum of the conduction electrons is locked with the pseudo-spin. Two important features are revealed: firstly, at the small tilt limit, the RKKY coupling varies quadratically with the tilt parameter and strikingly, at large separation distances , decays as compared to the conventional dependence exhibited by WSMs with non-tilted dispersion. The slower decay by two orders (i.e. as opposed to ) of the RKKY coupling is significant for maintaining a long-range RKKY coupling. Secondly, the RKKY coupling exhibits an anisotropy with respect to the angle between the tilt direction (w) and the separation direction R, unlike the case of non-tilted WSMs, which exhibits isotropic RKKY coupling. Consequently, the RKKY coupling in tilted WSMs alternately favors ferromagnetic and anti-ferromagnetic orders and vice-versa with the change of the angle. Our results are derived analytically and verified by numerical calculations based on realistic parameter values.

STM/STS measurements of quasi two-dimensional electronic states near artificially created defects in magnetic fields

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.