Computer simulation of magnetization relaxation in amorphous magnetics with random anisotropy

On the basis of Heisenberg model, the magnetic properties of amorphous terbium were studied by the Monte Carlo method. The temperature dependences of spontaneous magnetization and magnetic susceptibility were plotted as functions of the fraction of the constant of anisotropy to the exchange constant D/J ₀. The behavior of magnetization in an external magnetic field was studied, and the dependence of a coercive field and residual magnetization on the value D/J ₀ was found. The relaxation of magnetization was investigated after the external magnetic field was switched off.     

Magnetic relaxation in a random system of interacting rodlike nanoparticles

It is shown in the framework of the generalized mean-field approximation taking into account spatial fluctuations of the local magnetic field that the collective effect of dipole interaction in a random 3D system of identical (rodlike) magnetic nanoparticles with parallel easy magnetization axes shifts the relaxation magnetization curves towards shorter times (i.e., accelerates the relaxation process). In addition, the course of this process depends (via the demagnetizing field) on the sample shape. The interaction between nanograins affects the magnetization relaxation of a random 2D system only when the magnetic moments of the grains are perpendicular to the plane of the system.     

The influence of measurement and relaxation time on flux jumps in high temperature superconductors

The influence of the magnetization and relaxation time on flux jumps in high temperature superconductors (HTSC) under varying magnetic field is studied using the fundamental electromagnetic field equations and the thermal diffusion equation; temperature variety corresponding to flux jump is also discussed. We find that for a low sweep rate of the applied magnetic field, the measurement and relaxation times can reduce flux jump and to constrain the number of flux jumps, even stabilizing the HTSC, since much heat produced by the motion of magnetic flux can transfer into coolant during the measurement and relaxation times. As high temperature superconductors are subjected to a high sweep rate or a strong pulsed magnetic field, magnetization undergoes from stability or oscillation to jump for different pause times. And the period of temperature oscillation is equal to the measurement and relaxation time.     

Dynamics of paramagnetic agents by off-resonance rotating frame technique

Off-resonance rotating frame technique offers a novel tool to explore the dynamics of paramagnetic agents at high magnetic fields (B0 > 3T). Based on the effect of paramagnetic relaxation enhancement in the off-resonance rotating frame, a new method is described here for determining the dynamics of paramagnetic ion chelates from the residual z-magnetizations of water protons. In this method, the dynamics of the chelates are identified by the difference magnetization profiles, which are the subtraction of the residual z-magnetization as a function of frequency offset obtained at two sets of RF amplitude omega(1) and pulse duration tau. The choices of omega(1) and tau are guided by a 2-D magnetization map that is created numerically by plotting the residual z-magnetization as a function of effective field angle theta and off-resonance pulse duration tau. From the region of magnetization map that is the most sensitive to the alteration of the paramagnetic relaxation enhancement efficiency R(1rho)/R1, the ratio of the off-resonance rotating frame relaxation rate constant R(1rho) verse the laboratory frame relaxation rate constant R(1), three types of difference magnetization profiles can be generated. The magnetization map and the difference magnetization profiles are correlated with the rotational correlation time tauR of Gd-DTPA through numerical simulations, and further validated by the experimental data for a series of macromolecule conjugated Gd-DTPA in aqueous solutions. Effects of hydration water number q, diffusion coefficient D, magnetic field strength B0 and multiple rotational correlation times are explored with the simulations of the magnetization map. This method not only provides a simple and reliable approach to determine the dynamics of paramagnetic labeling of molecular/cellular events at high magnetic fields, but also a new strategy for spectral editing in NMR/MRI based on the dynamics of paramagnetic labeling in vivo.     

Relaxation properties in classical diamagnetism

It is an old result of Bohr that, according to classical statistical mechanics, at equilibrium a system of electrons in a static magnetic field presents no magnetization. Thus a magnetization can occur only in an out of equilibrium state, such as that produced through the Foucault currents when a magnetic field is switched on. It was suggested by Bohr that, after the establishment of such a nonequilibrium state, the system of electrons would quickly relax back to equilibrium. In the present paper, we study numerically the relaxation to equilibrium in a modified Bohr model, which is mathematically equivalent to a billiard with obstacles, immersed in a magnetic field that is adiabatically switched on. We show that it is not guaranteed that equilibrium is attained within the typical time scales of microscopic dynamics. Depending on the values of the parameters, one has a relaxation either to equilibrium or to a diamagnetic (presumably metastable) state. The analogy with the relaxation properties in the Fermi Pasta Ulam problem is also pointed out.     

Measurement of the relaxation rate of the magnetization in Mn12O12-acetate using proton NMR echo

We present a novel method to measure the relaxation rate W of the magnetization of Mn 12O (12)-acetate (Mn12) magnetic molecular cluster in its S = 10 ground state at low T. It is based on the observation of an exponential growth in time of the proton NMR signal during the thermal equilibration of the magnetization of the molecules. We can explain the novel effect with a simple model which relates the intensity of the proton echo signal to the microscopic reversal of the magnetization of each individual Mn12 molecule during the equilibration process. The method should find wide application in the study of magnetic molecular clusters in off-equilibrium conditions.     

Influence of the demagnetizing factor on the magnetization of an ensemble of Stoner-Wohlfarth particles

The influence of the demagnetizing factor on the coercivity of a sample of oriented uniaxial Stoner-Wohlfarth particles is investigated in the approximation of a relaxation model with a self-consistent determination of the demagnetization field. The demagnetizing field is shown to change the particle magnetization reversal conditions and to reduce the blocking temperature and coercivity, for which, despite allowance for the demagnetizing field, the Neel-Brown relation holds. It is also shown that under the demagnetizing field, the internal magnetic field in which the particles are located is not stationary but varies with time concordantly with the time sweep of the temperature during magnetization in a constant external field after zero-field cooling (ZFC). Nonstationarity of the internal field in the ZFC regime causes the interval of transition temperatures of the ensemble particles from a blocked state to a state with equilibrium magnetization to increase.     

铁磁/反铁磁双层膜中的磁锻炼效应

采用Monte Carlo 方法,研究铁磁/反铁磁双层膜中的磁锻炼效应.结果表明,反铁磁层中冷场诱发的界面净磁化(钉扎效应)的磁弛豫可导致系统中的交换偏置场的磁锻炼效应.进一步研究表明,反铁磁层中掺杂可调控交换偏置场的磁锻炼效应,原因在于反铁磁层中掺杂能有效地改变冷场诱发的净磁化的磁弛豫过程.     

Rotational Brownian dynamics simulations of non-interacting magnetized ellipsoidal particles in d.c. and a.c. magnetic fields

The rotational Brownian motion of magnetized tri-axial ellipsoidal particles (orthotropic particles) suspended in a Newtonian fluid, in the dilute suspension limit, under applied d.c. and a.c. magnetic fields was studied using rotational Brownian dynamics simulations. The algorithm describing the change in the suspension magnetization was obtained from the stochastic angular momentum equation using the fluctuation-dissipation theorem and a quaternion formulation of orientation space. Simulation results are in agreement with the Langevin function for equilibrium magnetization and with single-exponential relaxation from equilibrium at small fields using Perrin's effective relaxation time. Dynamic susceptibilities for ellipsoidal particles of different aspect ratios were obtained from the response to oscillating magnetic fields of different frequencies and described by Debye's model for the complex susceptibility using Perrin's effective relaxation time. Simulations at high equilibrium and probe fields indicate that Perrin's effective relaxation time continues to describe relaxation from equilibrium and response to oscillating fields even beyond the small field limit.     

Time development of magnetization

A simple model of Bloch wall motion is described for materials in which there exists a magnetic diffusion after-effect. The model is applied to the statistical system of independent Bloch walls. A qualitative explanation of the time development of magnetization in the d.c. magnetic field, based on this model, is given.     

Magnetic viscosity in Nd60Fe30Al10 amorphous alloys

Ferromagnetic amorphous Nd₆₀Fe₃₀Al₁₀ alloys melt spun at wheel speeds between 5 and 20 m/s exhibit hard magnetic properties, which are found to be very sensitive to the cooling conditions. The magnetization reversion mechanisms leading to the rather high coercive forces found are investigated by thermally activated magnetic relaxation experiments; the mean fluctuation field and the activation volume are measured—in specimens cooled at different rates—at the critical field for extensive magnetization reversion. These preliminary results show a qualitative agreement with the predictions of a ferromagnetic cluster model.     

Magnetic relaxation in a suspension of antiferromagnetic nanoparticles

A kinetic model is proposed to describe the low-frequency magnetodynamics of antiferromagnetic nanoparticles suspended in a fluid. Because of their small size, apart from an anisotropic magnetic susceptibility typical of antiferromagnets, these particles also have a constant magnetic moment caused by sublattice decompensation. An orientational crossover takes place in such a nanosuspension (colloid) when magnetized by a constant field: the axes of easy particle magnetization that were initially aligned along the field become oriented perpendicularly. This effect changes significantly the characteristics of the system’s magnetic response: the dynamic susceptibility spectrum and the relaxation time in a pulsed field.     

Nonlinear response of superparamagnetic particles with cubic anisotropy to a sudden change in the applied strong static magnetic field

The nonlinear response of superparamagnetic particles with cubic anisotropy to a sudden change in an applied strong static magnetic field is analyzed. The relaxation function spectrum and the relaxation time of the magnetization are calculated for typical values of the anisotropy and dissipation parameters.     

On the shape of the gamma resonance spectra of slowly relaxing nanoparticles in a magnetic field

A nonstandard shape of the gamma resonance spectra of nanoparticles in the form of inverted five-step pedestal has been predicted, observed, and analytically described. This shape corresponds to the limit of high temperatures and slow relaxation of the homogeneous magnetization of single-domain particles with axial magnetic anisotropy. To describe the Mössbauer spectra of the ensemble of chaotically oriented nanoparticles in a magnetic field, a continual magnetic-dynamics model has been developed in the limit of slow relaxation. This model adequately describes the polarization effects observed in the experimental absorption spectra. The revealed features significantly expand the methodical capabilities of Mössbauer spectroscopy for the diagnostics of magnetic nanomaterials.     

Magnetic properties of the bond and crystal field dilution Blume-Emery-Griffiths model in the presence of magnetic field

The magnetic properties of the spin-1 bond and crystal field dilution Blume-Emery-Griffiths (BEG) model in the presence of magnetic field are investigated on a simple cubic lattice by using effective field theory (EFT). In the M-H plane, the common action of bond and crystal field dilution leads to the exhibition of an irregular initial magnetization curve and slows down the magnetization process. The peak of the susceptibility curve has an explicit decline and shows a distinct shift toward the direction of increase of magnetic field. On the other hand, in the M-T plane, the magnetization curves show a discontinuity and a vertical leap in the small range of magnetic field when the negative crystal field is larger and the ratio of biquadratic and exchange interaction is positive (α>0). These results have not been revealed in previous works.     

Magnetic moments and adiabatic magnetization of free cobalt clusters

Magnetizations and magnetic moments of free cobalt clusters Co(N) (12 < N < 200) in a cryogenic (25 K < or = T < or = 100 K) molecular beam were determined from Stern-Gerlach deflections. All clusters preferentially deflect in the direction of the increasing field and the average magnetization resembles the Langevin function for all cluster sizes even at low temperatures. We demonstrate in the avoided crossing model that the average magnetization may result from adiabatic processes of rotating and vibrating clusters in the magnetic field and that spin relaxation is not involved. This resolves a long-standing problem in the interpretation of cluster beam deflection experiments with implications for nanomagnetic systems in general.     

Effect of a dc magnetic field on the magnetization relaxation of uniaxial single-domain ferromagnetic particles driven by a strong ac magnetic field

The nonlinear ac stationary response of the magnetization of noninteracting uniaxial single-domain ferromagnetic particles acted on by superimposed dc and ac magnetic fields applied along the anisotropy axis is evaluated from the Fokker-Planck equation, expressed as an infinite hierarchy of recurrence equations for Fourier components of the relaxation functions governing longitudinal relaxation of the magnetization. The exact solution of this hierarchy comprises a matrix continued fraction, allowing one to evaluate the ac nonlinear response and reversal time of the magnetization. For weak ac fields, the results agree with perturbation theory. It is shown that the dc bias field changes substantially the magnetization dynamics leading to new nonlinear effects. In particular, it is demonstrated that for a nonzero bias field as the magnitude of the ac field increases the reversal time first increases and having attained its maximum at some critical value of the ac field, decreases exponentially.     

Wigner liquid conductivity in a parallel magnetic field

It is assumed that comparatively low-mobility objects (clusters of a small number of electrons) can appear in a two-dimensional strongly correlated electronic system (Wigner liquid) against the background of mobile Fermi-type carriers. These formations can get “pinned” to inhomogeneities and play the role of additional scatterers. Clusters of two and three electrons are discussed (for a short-range order in the arrangement of electrons, as in a triangular lattice). The number of these clusters depends on both temperature and the parallel magnetic field. This results in the temperature and field dependences of the resistance and magnetization of the system. According to a simple model, resistance increases and the metal-dielectric transition occurs as the parallel magnetic field grows stronger. The model predicts a nonlinear magnetic field dependence of magnetization.     

Exchange bias with Fe substitution in LaMnO<Subscript>3</Subscript>

We observe the negative shift of the magnetic hysteresis loop at 5 K, while the sample is cooled in external magnetic field in case of 30% of Fe substitution in LaMnO₃. The negative shift and training effect of the hysteresis loops indicate the phenomenon of exchange bias. The cooling field dependence of the negative shift increases with the cooling field below 7.0 kOe and then, decreases with further increase of cooling field. The temperature dependence of the negative shift of the hysteresis loops exhibits that the negative shift decreases sharply with increasing temperature and vanishes above 20 K. Temperature dependence of dc magnetization and ac susceptibility measurements show a sharp peak (T_p) at 51 K and a shoulder (T_f) around 20 K. The relaxation of magnetization shows the ferromagnetic and glassy magnetic components in the relaxation process, which is in consistent with the cluster-glass compound.     

Quantitative model of large magnetostrain effect in ferromagnetic shapell memory alloys

A quantitative model describing the large magnetostrain effect observed in several ferromagnetic shape memory alloys such as Ni₂MnGa is briefly reported.The paper contains an exact thermodynamic consideration of the mechanical and magnetic properties of similar types of materials. As a result, the basic mechanical state equation including magnetic field effect is directly derived from a general Maxwell relation. It is shown that the magnetic field induced deformation effect is directly connected with the strain dependence of magnetization. A simple model of magnetization and its dependence on the strain is considered and applied to explain the results of experimental study of large magnetostrain effects in Ni₂MnGa. Received 29 September 1999