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 N\'eel-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 N\'eel), 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.Comment: 6 pages, 6 figs, Invited Paper at III Joint European Magnetic Symposia (JEMS), San Sebastian (Spain), 26-30 June 0

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.Comment: 21 pages, 5 eps figure

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.Comment: 7 pages, 3 figure

Generalized Ginzburg-Landau theory for non-uniform FFLO superconductors

We derive a generalized Ginzburg-Landau (GL) functional near the tricritical point in the (T,H)-phase diagram for the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state, in 1,2, and 3 dimensions. We find that the transition from the normal to the FFLO state is of second order in 1 and 2 dimensions, and the order parameter with one-coordinate sine modulation corresponds to the lowest energy near the transition line. We also describe in the one-dimensional case the transformation of the sine modulation into the soliton-lattice state as the magnetic field decreases. In 3 dimensions however, we find that the transition into an FFLO state is of first order, and it is impossible to obtain an analytic expression for the critical temperature. In this case the generalized GL functional proposed here provides a suitable basis for a numerical study of the properties of the FFLO state, and in particular for computing the critical temperature, and for describing the transition into a uniform state.Comment: 9 pages of RevTex, 3 figures available upon request at [email protected]

Spin-wave theory for finite classical magnets and superparamagnetic relation

Analytical calculations based on finite-size spin-wave theory and Monte Carlo (MC) simulations are performed to investigate the validity of the well-known relation m(H,T)=M(H,T)B_D[M(H,T)NH/T] between the induced magnetization m of the magnetic particle and its intrinsic magnetization M for the Ising and isotropic classical models [B_D(x) is the Langevin function, D is the number of spin components, N is the number of atoms in the particle]. It follows from general arguments and from our analytical results for the Heisenberg model at T << T_c that this relation is not exact for any finite D and nonzero temperature. Nevertheless, corrections to this formula remain very small practically in the whole range T> 1, as confirmed by our Monte Carlo calculations. At T <~ T_c/4 there is a good agreement between the MC and finite-size spin-wave calculations for the field dependence of m and M for the Heisenberg model with free boundary conditions.Comment: 8 pages, 6 fig

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.Comment: 9 pages, 8 figure

Hysteretic properties of a magnetic particle with strong surface anisotropy

We study the influence of surface anisotropy on the zero-temperature hysteretic properties of a small single-domain magnetic particle, and give an estimation of the anisotropy constant for which deviations from the Stoner-Wohlfarth model are observed due to non-uniform reversal of the particle's magnetisation. For this purpose, we consider a spherical particle with simple cubic crystalline structure, a uniaxial anisotropy for core spins and radial anisotropy on the surface. The hysteresis loop is obtained by solving the local (coupled) Landau-Lifschitz equations for classical spin vectors. We find that when the surface anisotropy constant is at least of the order of the exchange coupling, large deviations are observed with respect to the Stoner-Wohlfarth model in the hysteresis loop and thereby the limit-of-metastability curve, since in this case the magnetisation reverses its direction in a non-uniform manner via a progressive switching of spin clusters. In this case the critical field, as a function of the particle's size, behaves as observed in experiments.Comment: 12 pages, 15 eps figure