Dynamics Of Magnetic Moments Research Articles

Theoretical studies to elucidate the influence of magnetic dipolar interactions occurring in the magnetic nanoparticle systems, for biomedical applications

In recent years, the study of magnetic nanoparticles has been intensively developed not only for their fundamental theoretical interest, but also for their many technological applications, especially biomedical applications, ranging from contrast agents for magnetic resonance imaging to the deterioration of cancer cells via hyperthermia treatment. The theoretical and experimental research has shown until now that the magnetic dipolar interactions between nanoparticles can have a significant influence on the magnetic behaviour of the system. But, this influence is not well understood. It is clear that the magnetic dipolar interaction intensity is correlated with the nanoparticle concentration, volume fraction and magnetic moment orientations. In this paper, we try to understand the influence of magnetic dipolar interactions on the behaviour of magnetic nanoparticle systems, for biomedical applications. For the model, we considered spherical nanoparticles with uniaxial anisotropy and lognormal distribution of the sizes. The model involves a simulation stage of the spatial distribution and orientation of the nanoparticles and their easy axes of magnetic anisotropy, and an evaluation stage of the Néel relaxation time. To assess the Néel relaxation time, we are going to discretise and adapt, to the local magnetic field, the Coffey analytical solution for the equation Fokker-Planck describing the dynamics of magnetic moments of nanoparticles in oblique external magnetic field. There are three fundamental aspects of interest in our studies on the magnetic nanoparticles: their spatial & orientational distributions, concentrations and sizes.

Disparate ultrafast dynamics of itinerant and localized magnetic moments in gadolinium metal

The Heisenberg–Dirac intra-atomic exchange coupling is responsible for the formation of the atomic spin moment and thus the strongest interaction in magnetism. Therefore, it is generally assumed that intra-atomic exchange leads to a quasi-instantaneous aligning process in the magnetic moment dynamics of spins in separate, on-site atomic orbitals. Following ultrashort optical excitation of gadolinium metal, we concurrently record in photoemission the 4f magnetic linear dichroism and 5d exchange splitting. Their dynamics differ by one order of magnitude, with decay constants of 14 versus 0.8 ps, respectively. Spin dynamics simulations based on an orbital-resolved Heisenberg Hamiltonian combined with first-principles calculations explain the particular dynamics of 5d and 4f spin moments well, and corroborate that the 5d exchange splitting traces closely the 5d spin-moment dynamics. Thus gadolinium shows disparate dynamics of the localized 4f and the itinerant 5d spin moments, demonstrating a breakdown of their intra-atomic exchange alignment on a picosecond timescale.

Berry-phase effects and electronic dynamics in a noncollinear antiferromagnetic texture

Antiferromagnets (AFMs), in contrast to ferromagnets, show a nontrivial magnetic structure with zero net magnetization. However, they share a number of spintronic effects with ferromagnets, including spin-pumping and spin transfer torques. Both phenomena stem from the coupled dynamics of free carriers and localized magnetic moments. In the present paper I study the adiabatic dynamics of a spin-polarized electrons in a metallic AFM exhibiting a noncollinear 120$^\circ$ magnetic structure. I show that the slowly varying AFM spin texture produces a non-Abelian gauge potential related to the time/space gradients of the N\'{e}el vectors. Corresponding emergent electric and magnetic fields induce rotation of spin and influence the orbital dynamics of free electrons. I discuss both the possibility of a topological spin Hall effect in the vicinity of topological AFM solitons with nonzero curvature and rotation of the electron spin traveling through the AFM domain wall.

The glassy behaviour of poorly crystalline Fe2O3 nanorods obtained by thermal decomposition of ferrous oxalate

Nanorod ferrous oxalate dihydrate (FeC2O4 × 2H2O) which had been synthesized by the microemulsion method, was used as a precursor in the thermal decomposition process performed in air atmosphere. The formation of nanocrystalline hematite as the final product was preceded by the appearence of an intermediate product. Comprehensive study comprising several complementary techniques (x-ray diffraction, transmission electron microscopy, selected area electron diffraction, thermogravimetric/differential thermal analyses and SQUID magnetometry) confirmed that the intermediate product corresponds to the poorly crystalline Fe2O3. Due to the specific nanorod shape and poorly crystalline structure, the investigated Fe2O3 showed high coercive field value of at Special attention in this study was devoted to the peculiar magnetic properties of poorly crystalline Fe2O3, which were thoroughly investigated by employing sophisticated experimental procedures such as relaxation of thermoremanent magnetization for different cooling fields, zero field and field cooled memory effects as well as aging experiments for different waiting times. At low temperatures and weak applied magnetic fields, the investigated system behaves similarly to spin glasses, manifesting slow, collective relaxation dynamics of magnetic moments through memory, rejuvenation and aging effects.

Dynamics of magnetic moments coupled to electrons and lattice oscillations

Inspired by the models of A. Rebei and G. J. Parker and A. Rebei et. al., we study a physical model which describes the behaviour of magnetic moments in a ferromagnet. The magnetic moments are associated to 3d electrons which interact with conduction band electrons and with phonons. We study each interaction separately and then collect the results assuming that the electron-phonon interaction can be neglected. For the case of the spin-phonon interaction, we study the derivation of the equations of motion for the classical spin vector and find that the correct behaviour, as given by the Brown equation for the spin vector and the Bloch equation, using the results obtained by D. A. Garanin for the average over fluctuations of the spin vector, can be obtained in the high temperature limit. At finite temperatures we show that the Markovian approximation for the fluctuations is not correct for time scales below some thermal correlation time $\tau_{Th}$. For the case of electrons we workout a perturbative expansion of the Feynman-Vernon functional. We find the expression for the random field correlation function. The composite model (as well as the individual models) is shown to satisfy a fluctuation-dissipation theorem for all temperature regimes if the behaviour of the coupling constants of the phonon-spin interaction remains unchanged with the temperature. The equations of motion are derived.

Magnetic fluctuations near the Mott transition towards a spin liquid state

Dynamics of magnetic moments near the Mott metal-insulator transition is investigated by a combined slave-rotor and dynamical mean-field theory solution of the Hubbard model with additional fully frustrated random Heisenberg couplings. In the paramagnetic Mott state, the spinon decomposition allows to generate a Sachdev-Ye spin liquid in place of the collection of independent local moments that typically occurs in the absence of magnetic correlations. Cooling down into the spin liquid phase, the onset of deviations from pure Curie behavior in the spin susceptibility is found to be correlated to the temperature scale at which the Mott transition lines experience a marked bending. We also demonstrate a weakening of the effective exchange energy upon approaching the Mott boundary from the Heisenberg limit, due to quantum fluctuations associated to zero and doubly occupied sites.

Microwave spectroscopy on heavy‐fermion systems: Probing the dynamics of charges and magnetic moments

AbstractInvestigating solids with light gives direct access to charge dynamics, electronic and magnetic excitations. For heavy fermions, one has to adjust the frequency of the probing light to the small characteristic energy scales, leading to spectroscopy with microwaves. We review general concepts of the frequency‐dependent conductivity of heavy fermions, including the slow Drude relaxation and the transition to a superconducting state, which we also demonstrate with experimental data taken on UPd2Al3. We discuss the optical response of a Fermi liquid and how it might be observed in heavy fermions. Microwave studies with focus on quantum criticality in heavy fermions concern the charge response, but also the magnetic moments can be addressed via electron spin resonance (ESR). We discuss the case of YbRh2Si2, the open questions concerning ESR of heavy fermions, and how these might be addressed in the future. This includes an overview of the presently available experimental techniques for microwave studies on heavy fermions, with a focus on broadband studies using the Corbino approach and on planar superconducting resonators.

Computational Studies for the Stochastic Landau--Lifshitz--Gilbert Equation

The stochastic Landau--Lifshitz--Gilbert equation describes the thermally induced dynamics of magnetic moments in ferromagnetic materials. Solutions of this highly nonlinear stochastic PDE are unit vector fields and satisfy an energy estimate. These are crucial properties to construct a convergent discretization in space and time. We propose a convergent finite element approximation of the problem based on the midpoint rule. The numerical scheme preserves the underlying properties of the continuous problem. Further, we construct a robust and efficient Newton-multigrid solver for the solution of the nonlinear systems associated with the discretized problems at each time level. Computational studies show the optimal convergence behavior of the scheme in the case of smooth solutions. Long-time dynamics for finite ensembles of spins evidence the ergodicity of an invariant measure of the continuum model. Numerical experiments in two dimensions demonstrate pathwise finite time blow-up behavior of the solution which goes together with a smooth evolution of expectations. Finally, thermally activated switching of spherical magnetic nanoparticles in three dimensions with space-time white noise is examined for a range of physical parameters.

Coupled stochastic dynamics of magnetic moment and anisotropy axis of a magnetic nanoparticle

An algorithm is developed for numerical simulation of coupled stochastic dynamics of magnetic moment and magnetic anisotropy axis of a nanoparticle. Time-correlation functions of the magnetic moment and its components longitudinal and transverse to the magnetic anisotropy axis are calculated by averaging along the stochastic trajectory. The longitudinal and transverse relaxation times are found by fitting the time correlation functions. Existing theoretical relations derived by the effective field approach in the limit of small fields are confirmed. The time-correlation functions of magnetic moments of nanoparticles in dependence on their properties are calculated numerically for arbitrary large magnetic fields and it is shown that they may be approximated by a sum of several exponentials. These results are applied for the calculation of relaxivity parameters of nuclear magnetic resonance (NMR) imaging in dependence on the field strength.

Vortex dynamics in ferromagnetic superconductors: Vortex clusters, domain walls, and enhanced viscosity

We demonstrate that there is a long-range vortex-vortex attraction in ferromagnetic superconductors due to polarization of the magnetic moments. Vortex clusters are then stabilized in the ground state for low vortex densities. The motion of vortex clusters driven by the Lorentz force excites magnons. This regime becomes unstable at a threshold velocity above which domain walls are generated for slow relaxation of the magnetic moments and the vortex configuration becomes modulated. This dynamics of vortices and magnetic moments can be probed by transport measurements.

Significance of nutation in magnetization dynamics of nanostructures

The dynamics of magnetic moments in nanostructures is closely linked to that of gyroscopes. The Landau-Lifshitz-Gilbert equation describes precession and relaxation but does not include nutation. Both precession and relaxation have been observed in experiments, in contrast to nutation. The extension of the atomistic Landau-Lifshitz-Gilbert equation by a nutation term allows us to study the significance of nutation in magnetization dynamics of nanostructures: for a single magnetic moment, a chain of Fe atoms, and Co islands on Cu(111). We find that nutation is significant at low-coordination sites and on the time scale of about 100 fs; its observation challenges strongly today's experimental techniques.

Theoretic 3-D study of the high-frequency magnetic moment dynamics in thin ferromagnetic films with in-plane uniaxial anisotropy by considering eddy-current generation

In the present paper, theoretic investigations of polarisation vector precession trajectories represented by a macro spin in ferromagnetic films with in-plane uniaxial anisotropy were realised. For this purpose, the Landau–Lifschitz–Gilbert differential equation (LLG) in combination with the Maxwell equations were solved for three dimensions by considering a linear progression of the magnetisation or polarisation with an external field. The frequency and time dependent polarisation trajectories illustrate how a magnetic moment precesses if effective damping and eddy-currents impacts its motion. For computation, typical parameter values like the saturation polarisation Js=μ0·Ms=1.4T and in-plane uniaxial anisotropy μ0·Hu=4.5mT were employed. The main focus of simulation was on the variation of the effective damping parameter αeff between 0.01 and 0.05 and ferromagnetic film thickness tm between 200nm and 1200nm. The frequency-dependent calculations were carried out between 50MHz and 6GHz. The time-dependent simulations were done for a duration between 5 and 30ns.

Ferromagnetic resonance and bistability field in a uniaxial magnetic film

Peculiarities of ferromagnetic resonance (FMR) corresponding to bias along the “hard” magnetic axis of a film with 2D uniaxial anisotropy are studied based on numerical solution of magnetic moment dynamics equations. It is shown that an additional resonance peak is formed in the FMR spectrum in the vicinity of “bistability field” Hb. The dependence of this field on the amplitude of the microwave field and damping parameters is analyzed.

Precessional damping of Fe magnetic moments in a FeNi film

We report on the element-resolved precessional dynamics of Fe magnetic moments in a homogeneous FeNi thin film. In our pump–probe experiment the magnetic system is excited by a magnetic field pulse from a stripline. The instantaneous response to the field-pulse excitation is monitored as a function of time in a stroboscopic measurement using element-selective x-ray resonant magnetic scattering (XRMS). Our data show that Fe and Ni moments are aligned parallel to each other at all times, while they oscillate around the effective field direction given by the step field pulse and applied bias field. The field dependence of the precessional motion and damping of Fe magnetic moments is analysed and compared with time-resolved magneto-optical Kerr effect (tr-MOKE) measurement data from the literature, showing good agreement.Additional studies prove the capability of our setup to conduct temperature-dependent studies. In the case of the presented FeNi system no changes in the frequency or damping behaviour are observed within a temperature range of 150–350 K.

High-temperature dynamics of surface magnetism in iron thin films

Finite-temperature magnetic properties of iron thin films are investigated by computer simulation over a broad range of temperatures up to the point of the ferromagnetic–paramagnetic phase transition. The coupled dynamics of atoms and magnetic moments is treated using the large-scale spin–lattice dynamics (SLD) algorithm. We investigate surface and bulk magnetic properties of iron, and how these properties vary as a function of temperature, film thickness and surface crystallography. We find that magnetization at surfaces is enhanced at low temperatures and suppressed at higher temperatures, in agreement with experimental observations. The effective Curie temperature of a film decreases as a function of thickness. Short-range magnetic order and non-vanishing spin–spin spatial correlations are found above the Curie temperature. The spin autocorrelation functions exhibit slower oscillations with longer decoherence times near the surface. We also find that the directional spin disorder has a significant effect on the surface strain.

Control of chaotic and deterministic magnetization dynamics regimes by means of sample shape varying

Effect of demagnetization field on chaotic and deterministic nonlinear magnetization dynamics regimes formation in the presence of oscillating and constant external magnetic fields is studied using the Landau–Lifshitz–Gilbert approach. The uniformly magnetized sample is considered to be an axially symmetric particle described by demagnetization factors and to have uniaxial crystallographic anisotropy formed some angle with an applied field direction. The equations of magnetic moment motion are considered to be the synergetic equations and the system behavior is examined on the phase plane. It is investigated as to how the change in particle shape and its orientation with respect to the external field (system’s configuration) can cause the transition between chaos and regular magnetization dynamics. Moreover, the way to completely suppress chaotic dynamics of magnetic moments in such sample is proposed. To produce a regular study, all results are presented in the form of bifurcation diagrams for all sufficient dynamics regimes of the considered system. Our results suggest that varying the particle’s shape and fields’ geometry may provide a useful way of magnetization dynamics control in complex magnetic systems.

Chaotic dynamics of magnetic moments in metallic superlattices with an antiferromagnetic interaction

Chaotic oscillatory regimes of magnetic moments of an exchange-coupled multilayer structure excited by a longitudinal magnetic field have been investigated in the case of narrow loops of orientational hysteresis. The spectrum of Lyapunov exponents has been calculated using a simplified model; it is shown that their sum remains unchanged upon transitions between the regimes, but the attractors of chaotic oscillations differ strongly in fractal dimensionality and shape. It has been revealed upon the examination of the time sections of phase trajectories that the attractors of chaotic regimes do not possess the property of complete mixing. Bifurcation and parametric diagrams have been built.

Effect of sample shape on nonlinear magnetization dynamics under an external magnetic field

Effect of sample shape on the nonlinear collective dynamics of magnetic moments in the presence of oscillating and constant external magnetic fields is studied using the Landau–Lifshitz–Gilbert (LLG) approach. The uniformly magnetized sample is considered to be an ellipsoidal axially symmetric particle described by demagnetization factors and uniaxial crystallographic anisotropy formed some angle with an applied field direction. It is investigated as to how the change in particle shape affects its nonlinear magnetization dynamics. To produce a regular study, all results are presented in the form of bifurcation diagrams for all sufficient dynamics regimes of the considered system. In this paper, we show that the sample's (particle's) shape and its orientation with respect to the external field (system configuration) determine the character of magnetization dynamics: deterministic behavior and appearance of chaotic states. A simple change in the system's configuration or in the shapes of its parts can transfer it from chaotic to periodic or even static regime and back. Moreover, the effect of magnetization precession stall and magnetic moments alignment parallel or antiparallel to the external oscillating field is revealed and the way of control of such “polarized” states is found. Our results suggest that varying the particle's shape and fields’ geometry may provide a useful way of magnetization dynamics control in complex magnetic systems.

An optimal analytical expression for the superparamagnetic relaxation rate under conditions of a stochastic resonance for the model of bistable systems

An analytical expression for the superparamagnetic relaxation rate of uniaxial particles modulated by a radio-frequency field is chosen that describes adequately the magnetic moment dynamics under conditions of a stochastic resonance in the approximation of discrete orientations. The complex magnetic susceptibility components are calculated for a weak external variable field. A comparison is made with the results of numerical modeling based on a solution of the Fokker-Planck equation with a periodic drift term.

Modelling of magnetic hyperfine field in nanoparticles

In order to obtain the information on the dynamics of magnetic moments from Mssbauer spectra of nanostructured mag- netic materials one should perform a complicated description of the spectra. The possibilities of a many-state relaxation model for the description of Mssbauer spectra are studied. The many-state relaxation model is applied to explain the dependence of spectra of nanoparticles in ferrouids on temperature. For the complicated Mssbauer spectra which can have many static subspectra, the simulation of the average hyperne eld is used. For the description of dependence of the hyperne eld on temperature the many-state model can be used to obtain the temperature dependence of magnetic anisotropy or other parameters that affect the rate of relaxation.