Surface-induced cubic anisotropy in nanomagnets

– We investigate the effects of surface anisotropy in a spherical magnetic nanoparticle. By computing minor loops, 2D and 3D energyscape, and by investigating the behaviour of the net magnetisation, we show that the behaviour of a many-spin particle is modeled by a macro-spin effective energy containing a uniaxial and cubic anisotropy terms. Introduction. – A magnetic nanoparticle exhibits many interesting and challenging novel properties such as exponentially slow relaxation at low temperature and superparamagnetic behavior above some temperature that depends on the particle’s size and its underlying material. The magnetisation of a superparamagnetic particle shuttles in a fast motion between the various anisotropy-energy minima. The stability of the magnetisation against this thermallyactivated reversal has become a crucial issue in fundamental research as well as in technological applications. Controlling this behavior, in view of room temperature applications, requires a fair understanding of the magnetisation dynamics at the nanosecond time scale. There are two competing approaches to the study of the static and dynamic properties of a nanoparticle. i) One-spin particle (OSP): a macroscopic approach that models a nanoparticle as a single magnetic moment, assuming coherent motion of all atomic magnetic moments, and is exemplified by the Stoner-Wohlfarth model for statics and Néel-Brown model for dynamics [1]. ii) Many-spin particle (MSP): this microscopic approach involves the atomic magnetic moment with continuous degrees of freedom as its building block. It allows taking account of the local environment inside the particle, including the microscopic interactions and single-site anisotropy [2]. This approach becomes necessary when dealing with a very small nanoparticle because the spin non-collinearities induced by strong boundary effects and surface anisotropy invalidate the coherent-motion assumption. However, investigating the dynamics of an MSP is a real challenge. Indeed, within this approach one is faced with complex many-body aspects with the inherent difficulties related with analysing the energyscape (location of the minima, maxima, and saddle points of the energy potential). This analysis is unavoidable since it is a crucial step in the calculation of the relaxation time and thereby in the study of the magnetisation stability against thermally-activated reversal. One may then address the question as to whether there exist some cases in which the full-fledged theory that has been developed for the OSP approach [see [3] and references therein] can still be used to describe an MSP. However,