Monte Carlo simulation study of exchange biased hysteresis loops in nanoparticles

We present the results of Monte Carlo simulations of the magnetic properties of a model for a single nanoparticle consisting in a ferromagnetic core surrounded by an antiferromagnetic shell. The simulations of hysteresis loops after cooling in a magnetic field display exchange bias effects. In order to understand the origin of the loop shifts, we have studied the thermal dependence of the shell and interface magnetizations under field cooling. These results, together with inspection of the snapshots of the configurations attained at low temperature, show the existence of a net magnetization at the interface which is responsible for the bias of the hysteresis loops.Comment: 9 pages, 3 figures embedded. To be published in Physica

Modelling exchange bias in core/shell nanoparticles

We present an atomistic model of a single nanoparticle with core/shell structure that takes into account its lattice strucutre and spherical geometry, and in which the values of microscopic parameters such as anisotropy and exchange constants can be tuned in the core, shell and interfacial regions. By means of Monte Carlo simulations of the hysteresis loops based on this model, we have determined the range of microscopic parameters for which loop shifts after field cooling can be observed. The study of the magnetic order of the interfacial spins for different particles sizes and values of the interfacial exchange coupling have allowed us to correlate the appearance of loop asymmetries and vertical displacements to the existence of a fraction of uncompensated spins at the shell interface that remain pinned during field cycling, offering new insight on the microscopic origin of the experimental phenomenology.Comment: 7 pages, 3 figures. Contribution presented at HMM 2007 held at Napoli 4-6 June 2007. To be published in J. Phys. Condens. Matte

Critical behavior of ferromagnetic pure and random diluted nanoparticles with competing interactions: variational and Monte Carlo approaches

The magnetic properties and critical behavior of both ferromagnetic pure and metallic nanoparticles having concurrently atomic disorder, dilution and competing interactions, are studied in the framework of an Ising model. We have used both the free energy variational principle based on the Bogoliubov inequality and Monte Carlo simulation. As a case of study for random diluted nanoparticles we have considered the Fe$_{0.5}$Mn$_{0.1}$Al$_{0.4}$ alloy characterized for exhibiting, under bulk conditions, low temperature reentrant spin glass (RSG) behavior and for which experimental and simulation results are available. Our results allow concluding that the variational model is successful in reproducing features of the particle size dependence of the Curie temperature for both pure and random diluted particles. In this last case, low temperature magnetization reduction was consistent with the same type of RSG behavior observed in bulk in accordance with the Almeida-Thouless line at low fields and a linear dependence of the freezing temperature with the reciprocal of the particle diameter was also obtained. Computation of the correlation length critical exponent yielded the values $\nu=0.926\pm 0.004$ via Bogoliubov and$\nu =0.71\pm 0.04$ via Monte Carlo. This fact indicates that even though thermodynamical models can be indeed used in the study of nanostructures and they can reproduce experimental features, special attention must be paid regarding critical behavior. From both approaches, differences in the $\nu$ exponent with respect to the pure Ising model agree with Harris and Fisher arguments.Comment: 11 pages, 11 figures. Submitted to Phys. Rev.

Change in the magnetic configurations of tubular nanostructures by tuning dipolar interactions

We have investigated the equilibrium states of ferromagnetic single wall nanotubes by means of atomistic Monte Carlo simulations of a zig-zag lattice of Heisenberg spins on the surface of a cylinder. The main focus of our study is to determine how the competition between short-range exchange (J) and long-range dipolar (D) interactions influences the low temperature magnetic order of the nanotubes as well as the thermal-driven transitions involved. Apart from the uniform and vortex states occurring for dominant J or D, we find that helical states become stable for a range of intermediate values of γ = D/J that depends on the radius and length of the nanotube. Introducing a vorticity order parameter to better characterize helical and vortex states, we find the pseudo-critical temperatures for the transitions between these states and we establish the magnetic phase diagrams of their stability regions as a function of the nanotube aspect ratio. Comparison of the energy of the states obtained by simulation with those of simpler theoretical structures that interpolate continuously between them, reveals a high degree of metastability of the helical structures that might be relevant for their reversal modes

Tailoring dual reversal modes by helicity control in ferromagnetic nanotubes

We investigate the effects of the competition between exchange (J) and dipolar (D) interactions on the magnetization reversal mechanisms of ferromagnetic nanotubes. Using first atomistic Monte Carlo simulations for a model with Heisenberg spins on a cylindrical surface, we compute hysteresis loops for a wide range of the γ=D/J parameter, characterizing the reversal behavior in terms of the cylindrical magnetization components along the tube length. For γ's close to the value for which helical (H) states are energetically favorable at zero applied field, we show that the hysteresis loops can occur in four different classes that are combinations of two reversal modes with well-differentiated coercivities with probabilities that depend on the tube length and radius. This variety in the reversal modes is found to be linked to the metastability of the H states during the reversal that induces different paths followed along the energy landscape as the field is changed. We further demonstrate that reversal by either of the two modes can be induced by tailoring the nanotube initial state so circular states with equal or contrary chirality are formed at the ends, thus achieving low or high coercive fields at will without changing γ. Finally, the results of additional micromagnetic simulations performed on tubes with a similar aspect ratio show that dual switching modes and its tailoring can also be observed in tubes of microscopic dimensions

Interplay between surface anisotropy and dipolar interactions in an assembly of nanomagnets

We study the interplay between the effects of surface anisotropy and dipolar interactions in monodisperse assemblies of nanomagnets with oriented anisotropy. We derive asymptotic formulas for the assembly magnetization, taking into account temperature, applied field, core and surface anisotropy, and dipolar interparticle interactions. We find that the interplay between surface anisotropy and dipolar interactions is well described by the analytical expression of the assembly magnetization derived here: the overall sign of the product of the two parameters governing the surface and the dipolar contributions determines whether intrinsic and collective terms compete or have synergistic effects on the magnetization. This is illustrated by the magnetization curves of γ-Fe2O3 nanoparticle assemblies in the low concentration limit

Probing core and shell contributions to exchange bias in Co/Co3O4 nanoparticles of controlled size

Coupling at the interface of core/shell magnetic nanoparticles is known to be responsible for exchange bias (EB) and the relative sizes of core and shell components are supposed to influence the associated phenomenology. In this work, we have prepared core/shell structured nanoparticles with a total average diameter around ∼27 nm and a wide range of shell thicknesses through the controlled oxidation of Co nanoparticles well dispersed in an amorphous silica host. Structural characterizations give compelling evidence of the formation of Co3O4 crystallite phase at the shells surrounding the Co core. Field cooled hysteresis loops display nonmonotonous dependence of the exchange bias HE and coercive HC fields, that become maximum for a sample with an intermediate shell thickness, at which lattice strain is also maximum for both phases. The EB effects persist up to temperatures above the ordering temperature of the oxide shell. Results of our atomistic Monte Carlo simulations of particles with the same size and composition as in experiments are in agreement with the experimental observations and have allowed us to identify a change in the contribution of the interfacial surface spins to the magnetization reversal, giving rise to the observed maximum in HE and HC

Equilibrium and dynamic behaviour of (weakly) interacting assemblies of magnetic nanoparticles

A still open issue related with the study of assemblies of magnetic nanoparticles, deposited on a substrate or embedded in a matrix, is that of the interplay between intrinsic features of the nanoparticles pertaining to their finite-size and boundary effects, and the collective effects entailed by their mutual interactions and their interactions with the hosting matrix or substrate. In this work we develop a semi-analytical approach that allows us to derive expressions for the magnetization and the susceptibility of interacting assemblies of single-domain ferromagnetic nanoparticles. We find that upon tuning the physical parameters pertaining to each nanoparticle or the shape of the assembly and its spatial arrangement, surface and inter-particle interactions may be set up to play additive or competitive roles leading to assemblies with optimal magnetic properties