Impurity Spin States Research Articles

Quantum dynamics of impurities coupled to a Fermi sea

We consider the dynamics of an impurity atom immersed in an ideal Fermi gas at zero temperature. We focus on the coherent quantum evolution of the impurity following a quench to strong impurity-fermion interactions, where the interactions are assumed to be short range like in cold-atom experiments. To approximately model the many-body time evolution, we use a truncated basis method, where at most two particle-hole excitations of the Fermi sea are included. When the system is initially non-interacting, we show that our method exactly captures the short-time dynamics following the quench, and we find that the overlap between initial and final states displays a universal non-analytic dependence on time in this limit. We further demonstrate how our method can be used to compute the impurity spectral function, as well as describe many-body phenomena involving coupled impurity spin states, such as Rabi oscillations in a medium or highly engineered quantum quenches.

Inelastic magnetic scattering effect on local density of states of topological insulators

Magnetic ions such as Fe, Mn and Co with localized spins may be adsorbed on the surface of topological insulators like \Bi. They form scattering centers for the helical surface states which have a Dirac cone dispersion as long as the local spins are disordered. However, the local density of states (LDOS) may be severely modified by the formation of bound states. Commonly only elastic scattering due to normal and exchange potentials of the adatom is assumed. Magnetization measurements show, however, that considerable magnetic single ion anisotropies exist which lead to a splitting of the local impurity spin states resulting in a singlet ground state. Therefore inelastic scattering processes of helical Dirac electrons become possible as described by a dynamical local self energy of second order in the exchange interaction. The self energy influences bound state formation and leads to significant new anomalies in the LDOS at low energies and low temperatures which we calculate within T-matrix approach. We propose that they may be used for spectroscopy of local impurity spin states by appropriate tuning of chemical potential and magnetic field.

Friedel-oscillations-induced surface magnetic anisotropy

We present detailed numerical studies of the magnetic anisotropy energy of a magnetic impurity near the surface of metallic hosts (Au and Cu) that we describe in terms of the tight-binding surface Green's-function technique. We study the case when spin-orbit coupling originates from the $d$ band of the host material and we also investigate the case of a strong local spin-orbit coupling on the impurity itself. The splitting of the impurity's spin states is calculated to leading order in the exchange interaction between the impurity and the host atoms using the diagrammatic Green's-function technique. The magnetic anisotropy constant is an oscillating function of the separation $d$ from the surface. It asymptotically decays as $\ensuremath{\sim}1/{d}^{2}$ and its oscillation period is determined by the extremal vectors of the host's Fermi surface. Our results clearly show that the host-induced magnetic anisotropy energy is by several orders of magnitude smaller than the anisotropy induced by the local mechanism, which provides sufficiently large anisotropy values to explain the size dependence of the Kondo resistance observed experimentally.

Surface-Induced Magnetic Anisotropy of Impurities

We present theoretical and numerical studies of the magnetic anisotropy energy of an atomic-like impurity near the surface of a metallic host (Au). The valence band of the host metal is described in terms of a realistic tight-binding surface Green's function technique. We compare two models: (i) when spin-orbit coupling is taken into account in the d-band of the host and (ii) when the impurity's d-level experiences strong spin-orbit splitting. The level splitting of the impurity's spin-states is calculated in leading (first or second) order of the exchange interaction between the impurity and the host atoms. It is shown that the magnetic anisotropy constant is an oscillating function of the distance d of the impurity from the surface. For large distances, an asymptotic analysis implies that the period of these oscillations is determined by the extremal vectors of the host's Fermi Surface and the amplitude decays as 1/d2. Our numerical results clearly suggest that the host-induced magnetic anisotropy energy is by several orders smaller in magnitude than the one originating from a strong local spin-orbit coupling.

Intermediate coupling fixed point study in the overscreened regime of generalized multichannelSU(N)Kondo models

We study a generalized multichannel single-impurity Kondo model, in which the impurity spin is described by a representation of the $\mathrm{SU}(N)$ group that combines bosonic and fermionic degrees of freedom. The impurity spin states are described by Abrikosov pseudofermions, and we make use of a method initiated by Popov and Fedotov that allows a proper handling of the fermionic constraint. The partition function is derived within a path integral approach. We use renormalization group techniques to calculate the $\ensuremath{\beta}$ scaling function perturbatively in powers of the Kondo coupling constant, which is justified in the weak coupling limit. The truncated expansion is valid in the overscreened (Nozi\`eres-Blandin) regime, for an arbitrary $\mathrm{SU}(N)$ group and any value of the parameters characterizing the impurity spin representation. The intermediate coupling fixed point is identified. We derive the temperature dependence of various physical quantities at low $T$, controlled by a unique critical exponent, and show that the physics of the system in the overscreened regime governed by the intermediate coupling fixed point is characterized by a non-Fermi liquid behavior. Our results are in accordance with those obtained by other methods, as Bethe ansatz and boundary conformal field theory, in the case of various impurity spin symmetries. We establish in a unified way that the Kondo models in which the impurity spin is described successively by a fundamental, symmetric, antisymmetric, and mixed symmetry representation yield all the same low-energy physics in the overscreened regime. Possible generalizations of the analysis we present to the case of arbitrary impurity spin representations of $\mathrm{SU}(N)$ are also discussed.

Electron energy and phase relaxation on magnetic impurities

We discuss the effect of magnetic impurities on the inelastic scattering and dephasing of electrons. Magnetic impurities mediate the energy exchange between electrons. This mechanism is especially effective at small energy transfers E in the absence of Zeeman splitting, when the two-particle collision integral in the electron kinetic equation has a kernel K∝1/ E 2 in a broad energy range. In a magnetic field, this mechanism is suppressed at E below the Zeeman energy. Simultaneously, the Zeeman splitting of the impurity spin states reduces the electron dephasing rate, thus enhancing the effect of electron interference on conduction. We find the weak localization correction to the conductivity and the magnitude of the conductance fluctuations in the presence of magnetic field of arbitrary strength. Our results can be compared quantitatively with the experiments on energy relaxation in short metallic wires and on Aharonov–Bohm conductance oscillations in wire rings.

On the effects of spin-orbit coupling on impurity atoms in cubic ferromagnetic alloys

Recent studies on heavy transition metal impurities embedded in cubic ferromagnetic hosts have suggested the existence of a certain amount of unquenched orbital angular momentum on the impurity site. The effects of spin-orbit coupling on the electron states around heavy impurities in band ferromagnets are examined using an extension of the Wolff-Clogston (1962) approach. Model calculations are performed for cases determined by the relative sizes of the impurity spin-orbit coupling parameter lambda , the crystal field splitting, and the exchange splitting of the impurity spin states which gives rise to the local moment. The results are compared with hyperfine anomaly and Mossbauer data on Au and Ir impurities in ferromagnetic Fe, Co and Ni.

Two‐electron theory of non‐interacting surface and impurity states

AbstractSome earlier results in the Davison‐Cheng two‐electron theory of surface and impurity states are corrected. Although the surface spin state findings are only slightly modified, it is found that the inner and outer impurity spin states no longer always occur separately, but can in fact co‐exist. After discussing the connection between the two‐electron theory of monatomic crystals and the one‐electron theory of diatomic crystals, the paper concludes by briefly outlining the recent developments in the one‐electron theory of surface and impurity state interaction.

Impurity spin states in the paramagnetic phase of ferromagnets

AbstractA theory has been developed for impurity spins in a Heisenberg ferromagnet in the temperature range above Tc for which numerical calculations have been performed using as a simple model a simple cubic crystal with nearest‐neighbour exchange constant and a defect spin with different spin and nearest‐neighbour exchange values. The calculations show that there exist in certain cases resonances and localized spin states for the impurity spin the intensity of which goes to zero with increasing temperature. Since no coupling between the normal modes of the spin system has been included, the width of those states is nearly unchanged with temperature.

Determination of the Localized Impurity Spin States in FeCl2

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