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

Abstract

The magnetic relaxation and hysteresis of a system of single domain particles with dipolar interactions are studied by Monte Carlo simulations. We model the system by a chain of Heisenberg classical spins with randomly oriented easy-axis and log-normal distribution of anisotropy constants interacting through dipoledipole interactions. Extending the so-called T ln͑t / 0 ͒ method to interacting systems, we show how to relate the simulated relaxation curves to the effective energy barrier distributions responsible for the long-time relaxation. We find that the relaxation law changes from quasilogarithmic to power-law when increasing the interaction strength. This fact is shown to be due to the appearance of an increasing number of small energy barriers caused by the reduction of the anisotropy energy barriers as the local dipolar fields increase.

1H-NMR study of the spin dynamics of fine superparamagnetic nanoparticles

“…This shoulder can be tentatively attributed to an enhancement due to the aforementioned increased contribution to the barriers distribution at nearly zero energy values originating from dipolar couplings between particles 26 and the application of a magnetic field. As already mentioned in Sec.…”

“…26 An estimate of the Zeeman energy E Z at 174426-3 3.4 and 14.4 kOe yields values of the order of 10 2 -10 3 erg while the particle magnetic anisotropy energy E A as calculated from the bulk magnetocrystalline anisotropy constant K bulk = 4.7 × 10 4 erg/cm 3 is only of the order of 10-10 2 erg. However, it is quite common to witness a difference of two orders of magnitude 16,27,28 between the bulk anisotropy energy density and the effective anisotropy energy density in a nanoparticle with size d 5 nm, because additional sources of anisotropy come into play (i.e., shape, surface, magnetostriction contributions, and the dipolar interaction contribution).…”

Consistent energy barrier distributions in magnetic particle chains

“…This allowed to show that increasing the chain length can lead to acceleration or deceleration of thermal relaxation depending on the initialisation. The effect of initialisation on relaxation processes has been rarely addressed and cannot be explained based solely on the knowledge of g e (δe), as suggested also earlier [8].…”

Using Monte Carlo Method to Study Magnetic Properties of Frozen Ferrofluid

“…It is very difficult to build a numerical model that finds the barrier distribution. However, we recognize that the energy difference ∆E in the translation probability is always equal to one of the actual energy barriers of the system (Iglesias & Labarta, 2004). Therefore, we can extract the barrier distribution by using the Monte Carlo method to sample the individual energy barriers of all the particles.…”

“…At the same time, MC method was used to seek the spin-glass (SG) like behavior of interacting systems at the low temperature. While almost results show the SG like behavior (for example, Anderson et al, 1997;Ulrich et al, 2003;Iglesias and Labarta, 2004;Fernadez and Aloso, 2009; …), a few other results opposed the presence of SG like behavior (Garcia-Otero et al, 2000;Porto, 2005). Recent results based on the combination between the magnetic force microscopy and the MC simulation proved the existence of the short-range magnetic order deduced by dipolar interaction at the high temperature (Georgescu et al, 2006(Georgescu et al, , 2008.…”