arXiv subjects

H. Kachkachi

Publications and source records attributed to H. Kachkachi.

At least 37 records · Page 2Linked to original sources

arXiv2013

Microwave-assisted switching of a nanomagnet: analytical determination of the optimal microwave field

We analytically determine the optimal microwave field that allows for the magnetization reversal of a nanomagnet modeled as a macrospin. This is done by minimizing the total injected energy. The results are in good agreement with the fields obtained numerically using the optimal control theory. For typical values of the damping parameter, a weak microwave field is sufficient to induce switching through a resonant process. The optimal field is orthogonal to the magnetization direction at any time and modulated both in amplitude and frequency. The dependence of the pulse shape on the applied field and damping parameter is interpreted. The total injected energy is found to be proportionnal to the energy barrier between the initial state and the saddle point and to the damping parameter. This result may be used as a means for probing the damping parameter in real nanoparticles.

cond-mat.mes-hall↗

arXiv2012

Comment on "Thermal fluctuations of magnetic nanoparticles" [arXiv:1209.0298]

We comment on some misleading and biased statements appearing in the manuscript arXiv:1209.0298 ("Thermal fluctuations of magnetic nanoparticles") about the use of the damped Landau-Lifshitz equation and the kinetic Langer theory for the calculation of the relaxation rate of magnetic nanoclusters. We reiterate simple scientific arguments, part of which is well known to the whole community, demonstrating that the authors' criticisms are unfounded and that they overstate the issue of damping in the Landau-Lifshitz equation with no unanimous experimental evidence.

cond-mat.mes-hall↗

arXiv2012

Unified decoupling scheme for exchange and anisotropy contributions and temperature-dependent spectral properties of anisotropic spin systems

We compute the temperature-dependent spin-wave spectrum and the magnetization for a spin system using the unified decoupling procedure for the high-order Green's functions for the exchange coupling and anisotropy, both in the classical and quantum case. Our approach allows us to establish a clear crossover between quantum-mechanical and classical methods by developing the classical analog of the quantum Green's function technique. The results are compared with the classical spectral density method and numerical modeling based on the stochastic Landau-Lifshitz equation and the Monte Carlo technique. As far as the critical temperature is concerned, there is a full agreement between the classical Green's functions technique and the classical spectral density method. However, the former method turns out to be more straightforward and more convenient than the latter because it avoids any \emph{a priori} assumptions about the system's spectral density. The temperature-dependent exchange stiffness as a function of magnetization is investigated within different approaches.

cond-mat.mtrl-sci↗

arXiv2011

Dynamics of a magnetic dimer with exchange, dipolar and Dzyalozhinski-Moriya interaction

We investigate the dynamics of a magnetic system consisting of two magnetic moments coupled by either exchange, dipole-dipole, or Dzyalozhinski-Moriya interaction. We compare the switching mechanisms and switching rates as induced by the three couplings. For each coupling and each configuration of the two anisotropy axes, we describe the switching modes and, using the kinetic theory of Langer, we provide (semi-)analytical expressions for the switching rate. We then compare the three interactions with regard to their efficiency in the reversal of the net magnetic moment of the dimer. We also investigate how the energy barriers vary with the coupling. For the dipole-dipole interaction we find that the energy barrier may either increase or decrease with the coupling depending on whether the latter is weak or strong. Finally, upon comparing the various switching rates, we find that the dipole-dipole coupling leads to the slowest magnetic dimer, as far as the switching of its net magnetic moment is concerned.

cond-mat.mtrl-sci↗

arXiv2010

Optimal switching of a nanomagnet assisted by microwaves

We develop an efficient and general method for optimizing the microwave field that achieves magnetization switching with a smaller static field. This method is based on optimal control and renders an exact solution for the 3D microwave field that triggers the switching of a nanomagnet with a given anisotropy and in an oblique static field. Applying this technique to the particular case of uniaxial anisotropy, we show that the optimal microwave field, that achieves switching with minimal absorbed energy, is modulated both in frequency and in magnitude. Its role is to drive the magnetization from the metastable equilibrium position towards the saddle point and then damping induces the relaxation to the stable equilibrium position. For the pumping to be efficient, the microwave field frequency must match at the early stage of the switching process the proper precession frequency of the magnetization, which depends on the magnitude and direction of the static field. We investigate the effect of the static field (in amplitude and direction) and of damping on the characteristics of the microwave field. We have computed the switching curves in the presence of the optimal microwave field. The results are in qualitative agreement with micro-SQUID experiments on isolated nanoclusters. The strong dependence of the microwave field and that of the switching curve on the damping parameter may be useful in probing damping in various nanoclusters.

cond-mat.mtrl-sci↗

arXiv2010

Spin configurations in hard-soft coupled bilayer systems: from rigid magnet to exchange spring transitions

We investigate equilibrium properties of an exchange-spring magnetic system constituted of a soft layer (e.g. Fe) of a given thickness on top of a hard magnetic layer (e.g. FePt). The magnetization profile M(z) as a function of the atomic position ranging from the bottom of the hard layer to the top of the soft layer is obtained in two cases with regard to the hard layer: i) in the case of a rigid interface (the FePt layer is a single layer), the profile is obtained analytically as the exact solution of a sine-Gordon equation with Cauchy's boundary conditions. Additional numerical simulations also confirm this result. Asymptotic expressions of M(z) show a linear behavior near the bottom and the top of the soft layer. In addition, a critical value of the number of atomic planes in the soft layer, that is necessary for the onset of spin deviations, is obtained in terms of the anisotropy and exchange coupling between the adjacent plane in the soft layer. ii) in the case of a relaxed interface (the FePt layer is a multilayer), the magnetization profile is obtained numerically for various Fe and FePt films thicknesses and applied field.

cond-mat.mtrl-sci↗

arXiv2009

Magnetization reversal via internal spin waves in magnetic nanoparticles

By numerically solving the equations of motion for atomic spins we show that internal spin-wave processes in large enough magnetic particles, initially in unstable states, lead to complete magnetization reversal and thermalization. The particle's magnetization strongly decreases in the middle of reversal and then recovers. We identify two main scenarios, exponential and linear spin-wave instabilities. For the latter, the longitudinal and transverse relaxation rates have been obtained analytically. Orientation dependence of these rates leads to a nonexponential relaxation of the particle's magnetization at long times.

cond-mat.other↗

arXiv2008

Magnetization reversal and nonexponential relaxation via instabilities of internal spin waves in nanomagnets

A magnetic particle with atomic spins ordered in an unstable direction is an example of a false vacuum that decays via excitation of internal spin waves. Coupled evolution of the particle's magnetization (or the vacuum state) and spin waves, considered in the time-dependent vacuum frame, leads to a peculiar relaxation that is very fast at the beginning but slows down to a nonexponential long tail at the end. The two main scenarios are linear and exponential spin-wave instabilities. For the former, the longitudinal and transverse relaxation rates have been obtained analytically. Numerical simulations show that the particle's magnetization strongly decreases in the middle of reversal and then recovers.

cond-mat.stat-mech↗

arXiv2008

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

The relaxation rate and temperature-dependent switching field curve of a spherical magnetic nanocluster are calculated by taking into account the effect of surface anisotropy via an effective anisotropy model. In particular, it is shown that surface anisotropy may change the thermally activated magnetization reversal by more than an order of magnitude, and that temperature-dependent switching field 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 surface anisotropy.

cond-mat.mtrl-sci↗

arXiv2007

Effective anisotropies and energy barriers of magnetic nanoparticles with Neel surface anisotropy

Magnetic nanoparticles with Neel surface anisotropy, different internal structures, surface arrangements and elongation are modelled as many-spin systems. The results suggest that the energy of many-spin nanoparticles cut from cubic lattices can be represented by an effective one-spin potential containing uniaxial and cubic anisotropies. It is shown that the values and signs of the corresponding constants depend strongly on the particle's surface arrangement, internal structure and elongation. Particles cut from a simple cubic lattice have the opposite sign of the effective cubic term, as compared to particles cut from the face-centered cubic lattice. Furthermore, other remarkable phenomena are observed in nanoparticles with relatively strong surface effects: (i) In elongated particles surface effects can change the sign of the uniaxial anisotropy. (ii) In symmetric particles (spherical and truncated octahedral) with cubic core anisotropy surface effects can change its sign. We also show that the competition between the core and surface anisotropies leads to a new energy that contributes to both the 2nd- and 4th-order effective anisotropies.

cond-mat.stat-mech↗

arXiv2007

Effects of dipolar interactions on the zero-field-cooled magnetization of a nanoparticle assembly

We investigate the effect of (weak) dipolar interactions on the field behavior of the temperature at the maximum of the zero-field-cooled magnetization of a polydisperse assembly of nanoparticles. For this purpose, we extend the Gittleman-Abeles-Bozowski model for the zero-field-cooled magnetization by computing the contribution of dipolar interactions to the longitudinal relaxation time. We show, in good qualitative agreement with many experimental observations, that the temperature at the maximum of the zero-field-cooled magnetization as a function of the applied field changes from a bell-like to a monotonically decreasing curve when the intensity of the dipolar interactions, or equivalently the sample concentration, increases.

cond-mat.stat-mech↗

arXiv2007

Ferromagnetic resonance in systems with competing uniaxial and cubic anisotropies

We develop a model for ferromagnetic resonance in systems with competing uniaxial and cubic anisotropies. This model applies to (i) magnetic materials with both uniaxial and cubic anisotropies, and (ii) magnetic nanoparticles with effective core and surface anisotropies; We numerically compute the resonance frequency as a function of the field and the resonance field as a function of the direction of the applied field for an arbitrary ratio of cubic-to-uniaxial anisotropy. We also provide some approximate analytical expressions in the case of weak cubic anisotropy. We propose a method that uses these expressions for estimating the uniaxial and cubic anisotropy constants, and for determining the relative orientation of the cubic anisotropy axes with respect to the crystal principle axes. This method is applicable to the analysis of experimental data of resonance type measurements for which we give a worked example of an iron thin film with mixed anisotropy.

cond-mat.other↗

arXiv2006

Intrinsic and collective effects in assemblies of nanomagnets

In this paper we review some results of our works on the magnetization processes in: i) Isolated nanomagnets, both in the one-spin approximation and as many-spin systems. Here, we focus on the intrinsic properties, e.g., those induced by finite-size, boundary and surface effects. We also investigate the crossover between the two regimes. ii) Assemblies of nanomagnets, also in the two situations. We focus on their behavior mainly due to dipole-dipole interactions. Then, we will comment on the interplay between these intrinsic and collective effects.

cond-mat.stat-mech↗

arXiv2006

Effects of spin non-collinearities in magnetic nanoparticles

In a many-spin approach that takes account of the internal structure, microscopic interactions and single-site anisotropies, we investigate the effect of spin non-collinearities induced by the boundary and surface anisotropy on the behaviour of individual magnetic nanoparticles. Through analytical and numerical calculations, we show that there are mainly two regimes separated by some critical value of the surface anisotropy constant $K_s$ which controls the intensity of spin non-collinearities: i) the so called Stoner-Wohlfarth or Néel-Brown regime of a macrospin undergoing a coherent switching, ii) the many-spin regime where the strong spin non-collinearities invalidate the coherent mechanism, and where the particle's magnetic state and switching mechanisms can no longer be modeled by a macrospin. For small-to-intermediate values of $K_s$, and within two models of surface anisotropy (transverse and Néel), the behaviour of the nanoparticle can be modeled by that of a macrospin with an effective potential energy containing a uniaxial and cubic anisotropy terms. This effective spin model provides a crossover between the two regimes.

cond-mat.stat-mech↗

arXiv2006

Surface-induced cubic anisotropy in nanomagnets

We investigate the effect of surface anisotropy in a spherical many-spin magnetic nanoparticle. By computing minor loops, two-dimensional (2D) and 3D energyscape, and by investigating the behavior of the net magnetization, we show that in the case of not too strong surface anisotropy the behavior of the many-spin particle may be modeled by that of a macrospin with an effective energy containing uniaxial and cubic anisotropy terms. This holds for both the transverse and Néel's surface anisotropy models.

cond-mat.stat-mech↗

arXiv2005

Magnetization dynamics of two interacting spins in an external magnetic field

The longitudinal relaxation time of the magnetization of a system of two exchange coupled spins subjected to a strong magnetic field is calculated exactly by averaging the stochastic Gilbert-Landau-Lifshitz equation for the magnetization, i.e., the Langevin equation of the process, over its realizations so reducing the problem to a system of linear differential-recurrence relations for the statistical moments (averaged spherical harmonics). The system is solved in the frequency domain by matrix continued fractions yielding the complete solution of the two-spin problem in external fields for all values of the damping and barrier height parameters. The magnetization relaxation time extracted from the exact solution is compared with the inverse relaxation rate from Langer's theory of the decay of metastable states, which yields in the high barrier and intermediate-to-high damping limits the asymptotic behaviour of the greatest relaxation time.

cond-mat.stat-mech↗

arXiv2005

Magnetization of nanomagnet assemblies: Effects of anisotropy and dipolar interactions

We investigate the effect of anisotropy and weak dipolar interactions on the magnetization of an assembly of nanoparticles with distributed magnetic moments, i.e., assembly of magnetic nanoparticles in the one-spin approximation, with textured or random anisotropy. The magnetization of a free particle is obtained either by a numerical calculation of the partition function or analytically in the low and high field regimes, using perturbation theory and the steepest-descent approximation, respectively. The magnetization of an interacting assembly is computed analytically in the range of low and high field, and numerically using the Monte Carlo technique. Approximate analytical expressions for the assembly magnetization are provided which take account of the dipolar interactions, temperature, magnetic field, and anisotropy. The effect of anisotropy and dipolar interactions are discussed and the deviations from the Langevin law they entail are investigated, and illustrated for realistic assemblies with the lognormal moment distribution.

cond-mat.stat-mech↗

arXiv2004

Surface anisotropy in nanomagnets: transverse or Néel ?

Through the hysteresis loop and magnetization spatial distribution we study and compare two models for surface anisotropy in nanomagnets: a model with transverse anisotropy axes and Néel's model. While surface anisotropy in the transverse model induces several jumps in the hysteresis loop because of the cluster-wise switching of spins, in the Néel model the jumps correspond to successive {\it coherent partial rotations} of the whole bunch of spins. These calculations together with experimental results suggest that Néel's model for surface anisotropy is more appropriate.

cond-mat.mtrl-sci↗