Dynamical Spin Susceptibility Research Articles

Magnetic fluctuations and resonant peak in cuprates

The theory of the dynamical spin susceptibility is developed, as relevant for the normal-state magnetic response and the resonant magnetic peak in superconducting (SC) cuprates. The analysis is based on the equations of motion for spins within the t– J model and the memory-function representation of magnetic response whereby the main damping of the spin collective mode comes from the decay into fermionic degrees of freedom. In the normal state the damping is generally large. Assuming the saturation of equal-time correlations at low T leads us to the anomalous ω/ T scaling, well known from experiments on cuprates at low doping. In the SC phase a d-wave gap leads to a sharp resonant peak with reduced intensity and downward dispersion.

Possible isotope effect on the resonance peak formation in high-Tccuprates

Within effective $t\ensuremath{-}J$ Hamiltonian we analyze the influence of electronic correlations and electron-phonon interaction on the dynamical spin susceptibility in layered cuprates. We find an isotope effect on the resonance peak in the magnetic spin susceptibility $\mathrm{Im}\mathrm{}\ensuremath{\chi}(\mathbf{q},\ensuremath{\omega}),$ seen by inelastic neutron scattering. It results from both the electron-phonon coupling and the electronic correlation effects taken into account beyond random-phase approximation scheme. We find at optimal doping the isotope coefficient ${\ensuremath{\alpha}}_{\mathrm{res}}\ensuremath{\approx}0.4$ which can be further tested experimentally.

Magnetic susceptibilities of diluted magnetic semiconductors and anomalous Hall-voltage noise

The carrier-spin and impurity-spin densities in diluted magnetic semiconductors are considered using a semiclassical approach. Equations of motions for the spin densities and the carrier-spin current density in the paramagnetic phase are derived, exhibiting their coupled diffusive dynamics. The dynamical spin susceptibilities are obtained from these equations. The theory holds for p-type and n-type semiconductors doped with magnetic ions of arbitrary spin quantum number. Spin-orbit coupling in the valence band is shown to lead to anisotropic spin diffusion and to a suppression of the Curie temperature in p-type materials. As an application we derive the Hall-voltage noise in the paramagnetic phase. This quantity is critically enhanced close to the Curie temperature due to the contribution from the anomalous Hall effect.

Anomalous dynamical spin susceptibility in theSU(N)Heisenberg spin-glass model andSrCr9xGa12−9xO19

We solve the $\mathrm{SU}(N)$ Heisenberg spin-glass model in the limit of large N focusing on the dynamical spin susceptibility. We show that the results for the model at $S=3/2,$ which is appropriate for the ${\mathrm{SrCr}}_{9x}{\mathrm{Ga}}_{12\ensuremath{-}9x}{\mathrm{O}}_{19}$ compound, have a qualitative behavior in close agreement with neutron-scattering data. Quantum fluctuations produce a significant transfer of spectral weight to higher frequencies, while thermal fluctuations are responsible for a dramatic change in the low-frequency part of the dynamical spin susceptibility where T becomes comparable to the spin-glass transition temperature.

Scaling of the magnetic response in doped antiferromagnets.

A theory of the anomalous omega/T scaling of the dynamic magnetic response in cuprates at low doping is presented. It is based on the memory function representation of the dynamical spin susceptibility in a doped antiferromagnet where the damping of the collective mode is constant and large, whereas the equal-time spin correlations saturate at low T. Exact diagonalization results within the t-J model are shown to support assumptions. Consequences, for both the scaling function and the normalization amplitude, are well in agreement with neutron scattering results.

Theory of spin dynamics in electron-doped high-Tcsuperconductors

Spin dynamics in the superconducting and the normal state of electron-doped high-${T}_{c}$ cuprates is studied based on the scenario of the Fermi surface topology. We use the slave-boson mean-field approach to the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}J$ model and include the antiferromagnetic spin fluctuations via the random-phase approximation. A detailed analysis of the momentum and energy dependences of the dynamical spin susceptibility for different dopings is performed. It is found that the spin response in the superconducting state is commensurate in the overdoped regime and above a frequency typically of $0.07J$ in the underdoped and optimally doped regime. Meanwhile, it is commensurate in the normal state. These are consistent with the recent neutron-scattering experiment. The low-energy incommensurate response shows weak frequency dependence and its incommensurability is very small. These results contrast with those in the hole-doped cuprates in which the spin response is incommensurate except when it is at the resonance frequency and shows a remarkable downward dispersion. A strong frequency dependent change in spin response when entering the superconducting state is found. The frequency dependence of the spin response shows that a spin resonance appears in the underdoped regime, but does not in the overdoped regime.

Spin dynamics from majorana fermions.

Using the Majorana fermion representation of spin-1/2 local moments, we show how the dynamic spin correlation and susceptibility are obtained directly from the one-particle Majorana propagator. We illustrate our method by applying it to the spin dynamics of a nonequilibrium quantum dot, computing the voltage-dependent spin relaxation rate and showing that, at weak coupling, the fluctuation-dissipation relation for the spin of a quantum dot is voltage dependent. We confirm the voltage-dependent Curie susceptibility recently found by Parcollet and Hooley [Phys. Rev. B 66, 085315 (2002)]].

Local fluctuations in quantum critical metals

We show that spatially local, yet low-energy, fluctuations can play an essential role in the physics of strongly correlated electron systems tuned to a quantum critical point. A detailed microscopic analysis of the Kondo lattice model is carried out within an extended dynamical mean-field approach. The correlation functions for the lattice model are calculated through a self-consistent Bose-Fermi Kondo problem, in which a local moment is coupled both to a fermionic bath and to a bosonic bath (a fluctuating magnetic field). A renormalization-group treatment of this impurity problem--perturbative in $\epsilon=1-\gamma$, where $\gamma$ is an exponent characterizing the spectrum of the bosonic bath--shows that competition between the two couplings can drive the local-moment fluctuations critical. As a result, two distinct types of quantum critical point emerge in the Kondo lattice, one being of the usual spin-density-wave type, the other ``locally critical.'' Near the locally critical point, the dynamical spin susceptibility exhibits $\omega/T$ scaling with a fractional exponent. While the spin-density-wave critical point is Gaussian, the locally critical point is an interacting fixed point at which long-wavelength and spatially local critical modes coexist. A Ginzburg-Landau description for the locally critical point is discussed. It is argued that these results are robust, that local criticality provides a natural description of the quantum critical behavior seen in a number of heavy-fermion metals, and that this picture may also be relevant to other strongly correlated metals.

Magnetic fluctuations and resonant peak in cuprates: Towards a microscopic theory

The theory for the dynamical spin susceptibility within the t-J model is developed, as relevant for the resonant magnetic peak and normal-state magnetic response in superconducting (SC) cuprates. The analysis is based on the equations of motion for spins and the memory-function presentation of magnetic response where the main damping of the low-energy spin collective mode comes from the decay into fermionic degrees of freedom. It is shown that the damping function at low doping is closely related to the c-axis optical conductivity. The analysis reproduces doping-dependent features of the resonant magnetic scattering.

Magnetic properties in the high-temperature cuprate superconductors with nonmagnetic impurities

We study the effects of nonmagnetic impurities on the magnetic properties of the ${\mathrm{CuO}}_{2}$ planes in high-temperature cuprate superconductors, on the basis of the d-p model, within the fluctuation exchange approximation and the coherent potential approximation. The spin correlations between electrons in the neighborhood of the impurity are decreased, due to electron repulsion by the impurity. The antiferromagnetic contribution to the dynamical spin susceptibility decreases due to the nonmagnetic impurities, and the calculated superconducting temperature correspondingly decreases.

Locally critical point in an anisotropic Kondo lattice.

We report the first numerical identification of a locally quantum critical point at which the criticality of the local Kondo physics is embedded in that associated with a magnetic ordering. We are able to numerically access the quantum critical behavior by focusing on a Kondo-lattice model with Ising anisotropy. We also establish that the critical exponent for the q-dependent dynamical spin susceptibility is fractional and compares well with the experimental value for heavy fermions.

Understanding the origin of non-Fermi liquid behaviour in doped Kondoinsulators

We have made inelastic neutron scattering measurements on the doped Kondo insulators Ce(Rh0.8Pd0.2)Sband (Ce0.7Th0.3)RhSb.Previous bulk property measurements showed non-Fermi liquid (NFL) behaviour forboth compositions. In our inelastic neutron scattering data these two compounds alsoshow E/Tscaling behaviour in the dynamical spin susceptibility with different exponents,which is considered a characteristic feature of NFL systems. We discuss howthese two different exponents might be related to different microscopicmechanisms of the NFL behaviour in the bulk properties as well as theE/Tscaling behaviour seen in the dynamical susceptibility.

Theory of superconductivity coexisting with the antiferromagnetic state in UPd2Al3

We investigate the superconductivity (SC) coexisting withthe antiferromagnetic (AF) state observed in UPd2Al3.Referring to the band calculation, we consider the band structure with adual nature, that is, localized electrons, which mainly construct the AFstate, and itinerant electrons, which form the heavy fermion state andthe unconventional SC at lower temperatures. Within the random-phaseapproximation (RPA), we estimate the AF transition temperature TN, andcalculate the dynamical spin susceptibility. It possesses a collective spin wave around Q = (0, 0, 0.5) belowTN.In this situation, we evaluate the Eliashberg equation for the remaining itinerant band withinthe RPA. The most favourable even-parity pairing symmetry is cos(kx + 2ky) − cos(kx − 2ky) modulated by acos(kz)-like function. Thisis the symmetry dxywhich, in addition, possesses a tiny gap around the AF zone boundary.

Gilbert damping in magnetic multilayers

We study the enhancement of the ferromagnetic relaxation rate in thin films due to the adjacent normal metal layers. Using linear response theory, we derive the dissipative torque produced by the s-d exchange interaction at the ferromagnet-normal metal interface. For a slow precession, the enhancement of Gilbert damping constant is proportional to the square of the s-d exchange constant times the zero-frequency limit of the frequency derivative of the local dynamic spin susceptibility of the normal metal at the interface. Electron-electron interactions increase the relaxation rate by the Stoner factor squared. We attribute the large anisotropic enhancements of the relaxation rate observed recently in multilayers containing palladium to this mechanism. For free electrons, the present theory compares favorably with recent spin-pumping result of Tserkovnyak et al. [Phys. Rev. Lett. \textbf{88},117601 (2002)].

Quantum criticality in the SO(5) theory of antiferromagnetism and superconductivity

The quantum critical point scenario is studied within the unified theory of superconductivity and antiferromagentism based on the SO(5) symmetry. The quantum-critical scaling function for the dynamic spin susceptibility is obtained from the lattice SO(5) quantum nonlinear σ-model in three dimensions, revealing that in the quantum-critical region the frequency scale for spin excitations is simply set by the absolute temperature. Implications for the non-Fermi liquid behavior of the normal-state resistivity due to spin fluctuations in the quantum-critical region are also noted.

Coherence peak in the spin susceptibility from nesting in spin-triplet superconductors: A probe for line nodes inSr2RuO4

We study the dynamical spin susceptibility $\chi ({\bf q},\omega)$ for spin-triplet superconductivity. We show that a large peak at $\omega = 2 \Delta$ appears in $\textrm{Im} \chi_{zz}({\mathbf{Q}}, \omega)$, where $z$ is the direction of the $\mathbf{d}$ vector for triplet pairing, if Fermi surface has a nested part with the nesting vector $\mathbf{Q}$ and the order parameter is $+\Delta$ and $-\Delta$ in this part of the Fermi surface. If there are line nodes in the nested part of the Fermi surface, a peak appears in either $\textrm{Im} \chi_{zz}(\mathbf{Q}, \omega)$ or $\textrm{Im} \chi_{+-}(\mathbf{Q}, \omega)$, or both, depending on the perpendicular component of the nesting vector. The comparison with inelastic neutron scattering experiments can determine the position of the line nodes in triplet superconductor Sr$_2$RuO$_4$.

Dynamical Spin Susceptibility in the t – J Model in the Superconducting Phase

Dynamical spin susceptibility is calculated for the t–J model in the superconducting phase using the memory function method in terms of the Hubbard operators. The self-consistent system of equations for the memory function is obtained within the mode-coupling approximation. Both itinerant hole excitations and localized spin fluctuations contribute to the memory function. Moreover, the itinerant contribution itself consists of two parts, i.e., the contribution of Bogoliubov quasiparticles and that of Cooper pairs. The spin dynamics is diffusive in the hydrodynamic limit, but the itinerant part does not contribute to the spin diffusion. In the high frequency region, spin–wave-like excitations continue to exist. We discuss our analytic results in the light of neutron scattering experiments performed on the cuprate superconductors.

Spin dynamics in a structurally ordered non-Fermi-liquid compound: YbRh 2Si 2

Muon spin relaxation (μSR) experiments have been carried out at low temperatures in the non-Fermi-liquid heavy-fermion compound YbRh 2Si 2. The longitudinal-field μSR relaxation function is exponential, indicative that the dynamic spin fluctuations are homogeneous. The relaxation rate 1/ T 1 varies with applied field as H −y, y=1.0±0.1 , which implies a scaling law of the form χ″(ω)∝ω −yf(ω/T), lim x→0 f(x)=x for the dynamic spin susceptibility.

LONGITUDINAL DYNAMICAL SPIN SUSCEPTIBILITY IN HEISENBERG FERROMAGNETS

We study the longitudinal dynamical spin susceptibility [Formula: see text] within the framework of Heisenberg model in the ferromagnetic phase, where no external field exists. On the basis of memory function formalism within the framework of the irreducible Green's functions we obtained the self-consistent equations for [Formula: see text] in mode coupling approximation. The expression for the longitudinal spin susceptibility is valid in the whole range of system frequencies. Its validity in the range of low and high frequencies was discussed in particular for the magnetic systems in ferromagnetic phase.

Dynamical Properties of One-Dimensional Multicomponent Quantum Liquids in Metallic Phase

We investigate low-energy dynamical properties of one-dimensional multicomponent quantum liquids with the short-range interaction as well as the $1/x$-type long-range interaction. By calculating the single-particle spectrum and the dynamical spin susceptibility by means of the bosonization method, we discuss how the orbital degeneracy and the band splitting affect the dynamical response functions. The effect of the long-range interaction is also addressed. Although the long-range interaction suppresses charge fluctuations, it effectively enhances spin fluctuations via the formation of the Wigner crystal.