Effects of spin non-collinearities in magnetic nanoparticles

Abstract

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

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

“…47 Later it was shown that 49,50 in fact the effective energy of the many-spin particle is a polynomial in the components of its net magnetic moment. This polynomial can be, with a fairly good approximation, limited to a sum of a quadratic and a quartic contribution with coefficients that change in sign and magnitude with the intrinsic properties of the particle, namely its size, shape, underlying lattice structure, and physical parameters such as the exchange coupling and on-site core and surface anisotropy.…”

“…(2). This effective potential comprises a cubic anisotropy contribution, with the coefficient ζ , [47][48][49][50] that accounts for the surface anisotropy. The latter is initially modeled in the many-spin description of a nanocluster with the help of Néel's model for atomic spins.…”

“…Indeed, the condition of validity for the EOSP model [47][48][49][50] obtained for a nanocluster with an SC crystal lattice is ζ = K 4 /K 2 1/4 (ζ 0.35 for an fcc lattice). In this case, the spin noncolinearities induced by surface anisotropy are supposed to be not too strong, and thereby the anisotropy energy minima are mainly determined by the uniaxial contribution, whereas the cubic contribution only introduces saddle points.…”

“…This potential comprises contributions that stem from the core and surface anisotropies of the particle with coefficients whose sign and magnitude depend on the intrinsic features. [48][49][50] Therefore, this effective model then allows us to represent the magnetic state of a nanoparticle by a single macroscopic magnetic moment while taking into account to some extent the intrinsic properties. Consequently, a dilute assembly of the so-represented nanoparticles provides a system of weakly interacting magnetic moments each evolving in an effective potential.…”

Single-Particle Phenomena in Magnetic Nanostructures

“…Then, the correction ψψ is the solution of the Helmholtz equation with boundary conditions [66] Δ À k 2…”