Single domain magnetic arrays: role of disorder and interactions

Composition dependent magnetic properties of iron oxide-polyaniline nanoclusters

“…The last term is the energy of the particles due to an externally applied magnetic field H. For the purpose of simulation we assume that the exchange interaction has a site independent constant value J ef f = J. Magnetization studies ( FC-ZFC) show that the blocking temperatures are very high, which is evident even in the hysteresis measurements. Our earlier simulations [16] suggests that the shape of the hysteresis curve (Fig.3 ) is typical of a system in which both exchange and dipolar interactions play a role. It is not possible to derive the value of either K or J from any of our experimental results.…”

“…Our earlier investigations on the γ − F e 2 O 3 polypyrrole nanocomposites reveal that superparamagnetic thresholds as evidenced by the presence of blocking are very high even for fairly small particles. Our numerical simulations based on the random anisotropy, interacting model for single domain magnetic particle arrays also show that for a system with exchange interactions, as possible in a nanocomposite, has fairly high blocking even for particles sizes ∼ 10 − 15 nm [16].…”

“…The dipolar interaction energy is calculated by summing over periodic repeats of the basic simulation cell by the method of Lekner summation [19]. The simulation of the hysteresis is performed at a temperature of 300 K by the Monte Carlo method using the standard Metropolis algorithm [16,20,21]. The simulation is started at a very low field along the z-axis of the simulation cube, using an ensemble of magnetization vectors for the array, which gives a net magnetization of zero along the z -direction.…”

Dipolar interaction energy for a system of magnetic nanoparticles

“…In a typical simulation [21] on an array of nanomagnetic particles, one works with a a system of 0 N single domain magnetic particles placed randomly in a cube of side L . The easy axes ( i n ) and the magnetic moments ( i m ) of the single domain magnetic particles are directed randomly and have a unit magnitude.…”

“…The calculations are fast and accurate and in obvious contrast to the Ewald summation methods where one needs to evaluate at least 100 -200 terms, involving error func- tions etc., the calculations are also simpler. In particular, if one is doing Monte Carlo simulations for a magnetic array the positions of the particles remain fixed for the entire simulation and only the directions of the magnetic moment vector changes in each step of the simulation [21]. In that case the space summations A, B, C, D, E, F and G involved in the dipole interaction energy between each pair of particles i and j in the array can be stored and recalled in each MC step.…”