Pierre-Michel Déjardin

Effect of a dc bias field on the dynamic hysteresis of single-domain ferromagnetic particles

Dynamic magnetic hysteresis in uniaxial superparamagnetic nanoparticles in superimposed ac and dc magnetic fields of arbitrary amplitude is considered using Brown’s model of coherent rotation of the magnetization. The dependence of the area of the dynamic hysteresis loop on the temperature, frequency, and ac and dc bias fields is analyzed. In particular, the dynamic hysteresis loop of a single-domain ferromagnetic particle is substantially altered by applying a relatively weak dc field. Furthermore, it is shown that at intermediate to low ac field amplitudes, the dc bias field permits tuning of the magnetic power absorption of the particles, while for strong ac field amplitudes the effect becomes entirely analogous to that produced by the exchange biased anisotropy. Simple analytical formulas are provided in the linear response regime for the steady-state magnetization and loop area, exhibiting perfect agreement with the numerical solution of Brown’s Fokker–Planck equation. Comparison with previous result...

Relaxation of the magnetization in uniaxial single-domain ferromagnetic particles driven by a strong ac magnetic field

The magnetization spectrum and reversal time of uniaxial single-domain ferromagnetic particles driven by an ac magnetic field of arbitrary strength applied along the easy axis are evaluated by solving the infinite hierarchy of recurrence equations for the Fourier components of the relaxation functions governing the frequency dependence of the magnetization. A simple analytic equation for the reversal time is also obtained via the mean first passage time method exhibiting pronounced nonlinear effects such as a rapid decrease in the reversal time as the strength of the ac field increases. For weak ac fields, the results agree with perturbation theory.

Magnetic relaxation of a system of superparamagnetic particles weakly coupled by dipole-dipole interactions

Long range dipole-dipole interactions in the thermal fluctuations of the magnetization of an assembly of single-domain ferromagnetic particles are considered, ignoring orientational correlations between the particles, so that the evolution of the magnetization orientations may be described by a nonlinear Fokker-Planck equation (FPE) reducing to the usual linear one in the limit of infinite dilution [W. F. Brown Jr., Phys. Rev. 130, 1677 (1963)]. The thermally activated relaxation time scale of the assembly is estimated, leading to a simple and transparent modification of the axially symmetric asymptotes for the superparamagnetic relaxation time.

Nonlinear stationary ac response of the magnetization of uniaxial superparamagnetic nanoparticles

The nonlinear stationary ac response of the magnetization of assemblies consisting of (i) noninteracting uniaxial superparamagnetic nanoparticles with aligned easy axes and (ii) randomly oriented nanoparticles subjected to superimposed ac and dc bias magnetic fields of arbitrary strength and orientation is calculated by averaging Gilbert’s equation augmented by a random field. The magnetization dynamics of uniaxial particles driven by a strong ac field applied at an angle to the easy axis of the particle (so that the axial symmetry is broken) alters drastically leading to new nonlinear effects due to coupling of the thermally activated magnetization reversal mode with the precessional modes via the driving ac field. In particular, the high frequency response reveals significant nonlinear effects in the precessional motion with significant consequences for the dynamic hysteresis and ultra-fast switching of the magnetization following an ultrafast change in the applied field.

Analytical Solutions for the Dynamic Kerr-Effect - Linear-Response of Polar and Polarizable Molecules to a Weak AC Electric-Field Superimposed on a Strong DC Bias Field

The infinite hierarchy of differential-recurrence relations for ensemble averages of the spherical harmonics pertaining to the noninertial rotational Brownian motion of an ensemble of polar and anisotropically polarizable molecules in a strong external dc electric field is derived by averaging the underlying Langevin equation. This procedure avoids recourse to the Fokker–Planck equation, the solution of which involves complicated mathematical manipulations. By calculating the Laplace transforms of the relaxation functions for the dynamic Kerr effect of symmetric top molecules, two equilibrium correlation functions are established, thus allowing one to express the corresponding birefringence ac responses by using linear response theory. Exact analytic solutions for the spectra of these correlation functions and relaxation times are first calculated for two limiting cases, namely, pure induced dipole moments and pure permanent moments, using the continued fraction method. The general case where both types o...

Nonlinear electro-optical response. I. Steady state Kerr effect relaxation arising from a weak ac electric field superimposed on a strong dc bias field

The dynamic Kerr effect (excluding inertial effects) of an assembly of both polar and anisotropically polarizable molecules acted on by a strong external dc electric field superimposed on a weak ac electric field is evaluated by starting from the Smoluchowski equation valid in the noninertial limit. The calculation proceeds by expanding the expectation value of the second Legendre polynomial which describes the Kerr effect relaxation, as a power series up to the second order in the small ac field strength, so that frequency components in ω and 2ω exist. This is accomplished using the matrix continued fraction method which allows one to express exactly the solution of the infinite hierarchy of differential-recurrence relations for the first and second order ac responses of ensemble averages of the Legendre polynomials (relaxation functions). In order to illustrate these results, diagrams showing the behavior of the real and imaginary parts of the complex birefringence functions are presented. In particular...

Thermal and surface anisotropy effects on the magnetization reversal of a nanocluster

The relaxation rate and temperature-dependent switching field (SF) curve of a spherical magnetic nanocluster are calculated by including the effect of surface anisotropy (SA) via an effective anisotropy model. In particular, it is shown that SA may change the thermally activated magnetization reversal by more than an order of magnitude, and that temperature-dependent SF curves noticeably deviate from the Stoner–Wohlfarth astroid. With recent and future μ-SQUID measurements in mind, we indicate how comparison of our results with experimental data on isolated clusters may allow one to obtain valuable information on SA.

Nonlinear electro-optical response. II. Steady state dielectric relaxation in coupled fields

Nonlinear dielectric response of polar and polarizable molecules dissolved in a nonpolar solvent arising from a weak ac field superimposed on a strong dc bias field are established. The general case when both permanent and induced dipole moments are taken into account is considered. By expanding the expectation value of the first Legendre polynomial as a power series in the ac field strength up to the second order, we find two distinct components in ω and 2ω. Matrix continued fraction methods are used in order to express exactly the solution of the infinite hierarchy of the five-term differential recurrence relations for the ensemble averages of the Legendre polynomials (relaxation functions). The spectra of the real and imaginary parts of the first and second order complex dielectric response functions are presented in figures in order to show the essential differences between the linear and the nonlinear dielectric responses. The analytical expressions so obtained can be checked in so far as each compon...

Application of free rotational models of molecular reorientation to the explanation of high frequency effects in dielectric relaxation

Exact solutions obtained by Gross [J. Chem. Phys. 23, 1415 (1955)] and Sack [Proc. Phys. Soc. London, Sect. B 70, 402 (1957)] for the complex polarizability of assemblies of nonelectrically interacting rotators subjected to a variety of collisions and various approximations to that quantity, specifically the Rocard equation are reappraised in view of recent attempts to use a variety of forms of that equation for the interpretation of far infrared resonance absorption spectra. It is shown that for small values of the inertial parameter (heavy damping) the Rocard equation yields a really good approximation for the complex polarizability only for the small collision model considered by Gross and Sack. In the case of large inertial parameter values it is emphasized by means of plots of the complex polarizability that such an approximation always exhibits behavior characteristic of a sharply resonant system, i.e., a pronounced absorption peak well in excess of the Debye peak and a strongly negative real part, ...

Extended rotational diffusion and orientational relaxation of symmetric top molecules in a strong dc electric field: Second-rank orientational correlation functions

Second-rank orientational correlation functions (pertaining to Kerr effect relaxation and Raman scattering) are obtained using the extended rotational diffusion (J-diffusion) model of symmetric top polar molecules in a strong constant external field. It is shown that the shape of the molecule noticeably affects all second-rank correlation functions and relaxation times in the rare collision limit. In the opposite limit of frequent collisions, the quantities of interest are shown to be shape independent as a consequence of vanishingly small inertial effects. An interpolation formula for the orientation relaxation times in the intermediate regime between the rare and frequent collision limits is also given.