Dzyaloshinsky-Moriya Term Research Articles

Indirect exchange interaction between magnetic impurities in one-dimensional gapped helical states

We investigate theoretically indirect exchange interaction between magnetic impurities mediated by one-dimensional gapped helical states. Such states, containing massive Dirac fermions, may be realized on the edge of a two-dimensional topological insulator when time-reversal symmetry is weakly broken. We find that the indirect exchange interaction consists of Heisenberg, Dzyaloshinsky–Moriya, in-plane and out-of-plane Ising terms. These terms decay exponentially when the Fermi level lies inside the bandgap whereas the Dzyaloshinsky–Moriya term has smallest amplitude. Outside the bandgap, the massive helical states modify oscillatory behaviors of the range functions so that the period of oscillations decreases near the edge of band in terms of energy gap or Fermi energy. In addition, the out-of-plane Ising term vanishes in the case of zero-gap structure. Also, the oscillation amplitude of out-of-plane Ising term increases versus energy gap but it decreases as a function of Fermi energy. While the oscillation amplitudes of other components remain constant as functions of energy gap and Fermi energy. Analytical results are also obtained for subgap and over gap regimes. Furthermore, the effects of electron–electron interactions are analyzed.

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.

RKKY interaction of magnetic impurities in Dirac and Weyl semimetals

We theoretically study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities in both Dirac and Weyl semimetals (SMs). We find that the internode process, as well as the unique three-dimensional spin-momentum locking, has significant influences on the RKKY interaction, resulting in both a Heisenberg and an Ising term, and an additional Dzyaloshinsky-Moriya term if the inversion symmetry is absent. These interactions can lead to rich spin textures and possible ferromagnetism in Dirac and time-reversal symmetry-invariant Weyl SMs. The effect of anisotropic Dirac and Weyl nodes on the RKKY interaction is also discussed. Our results provide an alternative scheme to engineer topological SMs and shed new light on the application of Dirac and Weyl SMs in spintronics.

Enhancement of the Kondo Effect through Rashba Spin-Orbit Interactions

We study a one-orbital Anderson impurity in a two-dimensional electron bath with Rashba spin-orbit interactions in the Kondo regime. The spin SU(2) symmetry-breaking term couples the impurity to a two-band electron gas. A Schrieffer-Wolff transformation shows the existence of the Dzyaloshinsky-Moriya interaction away from the particle-hole symmetric impurity state. A renormalization group analysis reveals a two-channel Kondo model with ferro- and antiferromagnetic couplings. The parity-breaking Dzyaloshinsky-Moriya term renormalizes the antiferromagnetic Kondo coupling with an exponential enhancement of the Kondo temperature.

The entanglement dynamics of interacting qubits embedded in a spin environment with Dzyaloshinsky-Moriya term

We investigate the entanglement dynamics of two interacting qubits in a spin environment, which is described by an XY model with Dzyaloshinsky-Moriya (DM) interaction. The competing effects of environmental noise and interqubit coupling on entanglement generation for various system parameters are studied. We find that the entanglement generation is suppressed remarkably in weak-coupling region at quantum critical point (QCP). However, the suppression of the entanglement generation at QCP can be compensated both by increasing the DM interaction and by decreasing the anisotropy of the spin chain. Beyond the weak-coupling region, there exist resonance peaks of concurrence when the system-bath coupling equals to external magnetic field. We attribute the presence of resonance peaks to the flat band of the self-Hamiltonian. These peaks are highly sensitive to anisotropy parameter and DM interaction.

Magnetic order in the frustrated Heisenberg model for the fcc type-I configuration

The Heisenberg model for the fcc type-I configuration with various types of interactions is studied with use of the noninteracting spin-wave theory. It is shown that local anisotropy, four-spin exchange interactions, and biquadratic interactions can lift the continuous degeneracy of the ground state through the stabilization of a noncollinear magnetic state. Moreover, in the particular case of a pyrite structure, a Dzyaloshinsky-Moriya term or a symmetric anisotropic exchange stabilizes the double-$\mathbf{k}$ configuration. The single-$\mathbf{k}$ state is also discussed. We prove, in particular, that quantum fluctuations favor such a case. Consequences for the magnetic moment reduction and for the spin-wave spectra of the presence of such stabilizing terms are calculated and compared with data. Experiments seem to indicate that the minimal model built from the nearest-neighbor Heisenberg interaction and a stabilizing term is not satisfactory.

Influence of the single-ion anisotropy field and the Dzyaloshinsky–Moriya term on bulk spin fluctuations dynamics. Application to the frustrated weak ferromagnet FeF 3

We have theoretically investigated the influence of the anisotropy field and the Dzyaloshinsky–Moriya type coupling on the bulk magnetic excitations in a noncolinear frustrated structure. Application to the cubic frustrated weak ferromagnet FeF 3 is presented. Using a Green function formalism and matching technique procedure, the dispersion curves of the bulk magnons are obtained within a single framework by matching the evanescent and travelling solutions, respectively, of the secular equation, satisfying surface boundary conditions. The calculation concerns, in particular, the spin fluctuation dynamics in the bulk of an antiferromagnetic lattice, the spin order being in the direction normal to the surface boundary. The competing nearest J 1 AB and next nearest neighbours exchange interactions ( J 2 AA(BB)) are considered. The theoretical approach determines the evanescent spin fluctuation field in the two-dimensional plane parallel to the surface. It is shown that the propagating and evanescent spin-waves from a surface are strongly dependent on the values of ratio ε= J 1 AB/ J 2 AA(BB). The presence of anisotropy field and antisymmetric exchange term induces an energy gap on the bulk spin-wave continuum which involves a new ground state of spin quantum.

Proton NMR in a TDAE-C60 single crystal.

The temperature dependence of the methyl proton NMR shift of a TDAE-${\mathrm{C}}_{60}$ single crystal follows a Curie-Weiss law above ${T}_{C}$ with a positive Curie temperature ${T}_{C}\ensuremath{\approx}12$ K as expected for the case of a ferro-magnetic transition. Below ${T}_{C}$ the shifts are proportional to the magnetization and saturate below 10 K. The internal field at the TDAE protons amounts at 6 K to 600 G and exceeds by an order of magnitude the internal field determined by electron-spin resonance at the ${\mathrm{C}}_{60}^{\ensuremath{-}}$ ions. The result shows that in addition to the direct ${\mathrm{C}}_{60}^{\ensuremath{-}}$-${\mathrm{C}}_{60}^{\ensuremath{-}}$ interactions which seem to be of antiferromagnetic nature, a part of the exchange coupling between the ${\mathrm{C}}_{60}^{\ensuremath{-}}$ ions is mediated by the TDA${\mathrm{E}}^{+}$ groups. It is this indirect coupling which might give rise to the Dzyaloshinsky-Moriya term in the spin Hamiltonian which is responsible for weak ferromagnetism in this system.

Heisenberg ferromagnet with Dzyaloshinsky-Moriya interactions: A real space renormalization group approach

We study the anisotropic Heisenberg ferromagnet with anti-symmetric Dzyaloshinsky-Moriya (DM) interactions for arbitrary dimensions. We use a real space renormalization group approach of the Migdal-Kadanoff type in order to obtain the phase diagrams and critical exponents. The effect of the Dzyaloshinsky-Moriya term in the global phase diagram is worked out in detail. Our results suggest that in all dimensions the effect of the DM interaction is to renormalize the parameters of the anisotropic exchange Hamiltonian. Finally we discuss the modification of hyperscaling associated with the zero temperature Heisenberg-like fixed point.

Anisotropy in Two-Center Exchange Interactions

The exchange interaction between electrons on two different centers is developed in a bipolar series of angular momentum operators. In contrast to the isotropic Hamiltonian commonly used to represent this interaction, we find that all forms of anisotropic terms are needed, antisymmetric as well as symmetric ones. The degrees of the anisotropy assume all values commensurate with the angular momenta of the electrons. Beside the Dzyaloshinsky-Moriya term ${\mathrm{S}}_{1}$\ifmmode\times\else\texttimes\fi{}${\mathrm{S}}_{2}$, two-center exchange interactions contain antisymmetric anisotropies of higher degrees. For ions with strong orbital contributions to their magnetic moments, anisotropic exchange does not enter merely as a perturbation, and we find that the magnitudes of the symmetric and antisymmetric anisotropies are as large as the isotropic part of the exchange interaction. Explicit expressions containing radial integrals are derived for the coefficients representing the anisotropy in the exchange interaction. These anisotropy coefficients are related to the more conventional exchange constants; we also find the number of independent parameters needed to describe two-center exchange interactions for various situations. The coefficients of anisotropy representing the exchange interaction between ions with $N$ equivalent electrons are related to the coefficients for the interaction between ions with one electron. Although anisotropic superexchange is not considered in detail, both the form of the Hamiltonian representing this interaction, and also the number of independent parameters in the Hamiltonian, immediately follow from the Hamiltonian for the two-center exchange interaction.