Relaxation and aging of a superferromagnetic domain state

Abstract

In agreement with recent model calculations on interacting magnetic nanoparticles the magnetic relaxation of a field-cooled superferromagnetic ͑SFM͒ granular multilayer ͓Co 80 Fe 20 (1.4 nm)/Al 2 O 3 (3 nm)͔ 10 follows a power-law decay retaining a finite asymptotic remanence. Unexpectedly, a second isothermal upward relaxation is observed after field quenching the sample. It is attributed to slow equilibration of the thermoremanent magnetization inside the SFM domains. Magnetization hole burning via aging reveals the chaotic nature of the domain state.Magnetic single-domain nanoparticles ͑''superspins''͒ and their mutual interactions are very interesting not only for potential applications but also for rich fundamental research in magnetism. It is well known that highly diluted magnetic nanoparticle systems show superparamagnetic ͑SPM͒ behavior as described by the Néel-Brown model 1 for isolated particles when the magnetic dipole interactions between particles are negligible. When interparticle interactions are involved, the system eventually shows collective behavior which overcomes the individual anisotropy properties of the particles. Superspin glass ͑SSG͒ was found at low-enough temperatures for intermediate particle densities. 2 Apart from classical dipole interaction, 3-5 exchange and other nonclassical interactions 6,7 were considered at higher particle densities. Superferromagnetic ͑SFM͒ ordering due to tunneling exchange was claimed to occur in quasi-one-dimensional Fe particle arrays 8 and probably also occurs in Co/Cu͑100͒ ultrathin films just below the percolation threshold of the Co islands. 9 However, SFM ordering may even occur in purely dipolar systems, e.g., in regular two-dimensional superspin lattices. 4,5 Recently, the concentration dependent crossover between SSG and SFM behavior has been evidenced in discontinuous magnetic metal-insulator multilayers ͑DMIM͒ ͓Co 80 Fe 20 (t n )/Al 2 O 3 (3 nm)͔ 10 . 10 These granular systems were found to possess generic spin-glass behavior for nominal CoFe thicknesses t n р1 nm, 11 while SFM behavior with domain state properties is encountered at t n у1.2 nm, 12 but below the percolation limit, t n ϭ1.8 nm, above which Ohmic conduction and ordinary ferromagnetism are encountered. 13 Three elements of randomness are involved: a finite dispersion of the superspin sizes ͓e.g. magnetic moments m Ϸ(3.0Ϯ0.3)ϫ10 3 B for t n ϭ0.9 nm, where B is Bohr's magneton 14 ͔, random anisotropy axes around a preferential in-plane direction as defined by an external magnetic field BϷ3 mT applied during the multilayer growth, 15 and a random spatial distribution with tendency towards hexagonal self-assembly within the planes and smecticlike periodicity along the film normal. 14 A similar scenario was recently chosen in Monte Carlo simulations on an ensemble of superspins with random spatial distribution, anisotropy, and spin sizes by Ulrich et al. 16 They observed a crossover between different asymptotic de-cay laws ranging from stretched exponential behavior, m TRM (t)ϭm 0 exp...

Collective magnetic states of ferromagnetic nanoparticles in the superspin limit

“…[27]. A competition between a fast relaxation of SFM domain walls towards lower total magnetization and a slow relaxation within the SFM domains towards higher local magnetization was evidenced previously [39]. In the present case, again, both domain wall relaxation on a mesoscale and droplet-like growth processes on a nanoscale are observed to compete.…”

Collective states of interacting ferromagnetic nanoparticles

“…(3) Relaxation curves, m(t), of a SFM sometimes show a peculiar behavior after rapidly FC the sample. One can observe an intermediate increase of m(t) after switching off the field [33]. In this case the relaxation is characterized by two processes.…”

Magnetic relaxation in terms of microscopic energy barriers in a model of dipolar interacting nanoparticles

“…It has also been observed experimentally in arrays of micromagnetic dots tracked by focused ion beam irradiation on a Co layer with perpendicular anisotropy, 13,14 and also in discontinuous multilayers. 43 …”