A. Lyberatos

The fluctuation field of ferromagnetic materials

Starting from the basic constitutive equation that describes the magnetic viscosity of a ferromagnetic material, under the single assumption of a constant external field H, a connection is shown between the different expressions used to determine experimentally the fluctuation field . The simplest method uses the relation . If is invariant during the viscous decay of the magnetization, the relation may also be employed. The relaxation curves obtained at different fields, in this case, superimpose onto a single curve on renormalizing the time. An alternative treatment that considers explicitly the demagnetizing field is also presented. The theory is then applied to magneto-optic thin films, where two activation mechanisms are involved, assuming the absence of dispersion in the energy barriers, and also to the common case of relaxation by a single activation mechanism in the presence of a dispersion of the energy barriers. In both situations, it is shown that the fluctuation field may vary in strength during magnetic reversal. A method of classification of the hard ferromagnetic materials, through experimental means, is suggested.

Thermal fluctuations in a pair of magnetostatically coupled particles

The influence of the thermal agitation on the switching dynamics for a pair of identical uniaxially anisotropic dipoles is studied for the case of the applied field parallel to the bond direction and the common anisotropy axis. A set of Langevin equations was derived from the micromagnetic energy expression and solved numerically. The switching behavior resembles a random walk over the energy barrier arising from the anisotropy of the system. The relaxation time is computed as a function of temperature, applied field, and coupling strength. The temperature dependence of the maximum energy of the fluctuations provides a method of evaluating the energy barrier of reversal. The thermal agitation is shown to reduce the symmetry of the ‘‘fanning’’ reversal mode.

Simulated annealing: An application in fine particle magnetism

Using a model of a system of interacting fine ferromagnetic particles, a computer simulation of the dynamical approach to local or global minima of the system is developed for two different schedules of the application of ac and dc magnetic fields. The process of optimization, i.e., the achievement of a global minimum, depends on the rate of reduction of the ac field and on the symmetry of the ac field cycles, The calculations carried out to illustrate these effects include remanence curves and the zero field remanence for both schedules under different conditions. The growth of the magnetization during these processes was studied, and the interaction energy was calculated to best illustrate the optimization.

Thermally induced error: Density limit for magnetic data storage

Magnetic data storage is pervasive in the preservation of digital information, and the rapid pace of computer development requires ever more capacity. Increasing the storage density for magnetic hard disk drives requires a reduced bit size, previously thought to be limited by the thermal stability of the constituent magnetic grains. The limiting storage density in magnetic recording is investigated treating the writing of bits as a thermodynamic process. A “thermal writability” factor is introduced and it is shown that storage densities will be limited to 15 to 20 TBit/in2 unless technology can move beyond the currently available write field magnitudes.

The thermodynamic limits of magnetic recording

Thermal stability of the recorded information is generally thought to set the limit of the maximum possible density in magnetic recording. It is shown that basic thermodynamics always cause the probability of success of the write process to be less than 100%. This leads to a thermally induced error rate, which eventually limits the maximum possible density beyond that given by the traditional thermal stability limit. While the thermally induced error rate is negligible for recording of simple single domain particles, it rapidly increases in the presence of a write assist, in particular if the write assist is accomplished by an increased recording temperature. For the ultimate recording system that combines thermally assisted writing with a recording scheme that uses one grain per bit, the upper bound for the maximum achievable density is 20 Tbit/inch2 for a bit error rate target of 10−2.

A method for the numerical simulation of the thermal magnetization fluctuations in micromagnetics

A new method for the numerical modelling of the thermal fluctuations in micromagnetic systems is presented. The approach is based on the set of stochastic Langevin equations, which are derived from the energy expression for the system studied. The correlation matrix of the corresponding random forces required to perform numerical simulations is evaluated using the fluctuation-dissipation theorem following a transformation to the normal coordinates. The method is tested for the finite 1D chain of classical magnetic moments. The temperature dependence of the average magnetization deviation Delta M/M(O) exhibits good agreement with analytical theory.

Magnetic viscosity in perpendicular media

The remanent magnetization of fine particle media of perpendicular anisotropy is known to exhibit a time decay of pseudologarithmic form. The viscous properties are to a large extent determined by the magnetostatic particle interaction and the particle size. A meanfield model of a perfectly aligned ensemble of Stoner-Wohlfarth particles is presented that gives a qualitative description of the hysteretic and time-dependent properties of particulate perpendicular media. The time decay of the remanent magnetization of Alumite media after initial magnetic saturation was measured. The decay was found to be logarithmic within the measuring period, and a coefficient of magnetic viscosity was obtained. Although the reversal mechanism for the particles in Alumite media is known to be incoherent, a good qualitative agreement between the theoretical model and the measurements was found by introducing a reduced effective volume acting as a scaling factor that accounts for the discrepancy in reversal mechanisms.

Review Article: FePt heat assisted magnetic recording media

Heat-assisted magnetic recording (HAMR) media status, requirements, and challenges to extend the areal density (AD) of magnetic hard disk drives beyond current records of around 1.4 Tb/in.2 are updated. The structural properties of granular high anisotropy chemically ordered L10 FePtX-Y HAMR media by now are similar to perpendicular CoCrPt-based magnetic recording media. Reasonable average grain diameter ⟨D⟩ = 8–10 nm and distributions σD/D ∼ 18% are possible despite elevated growth temperatures TG = 650–670 °C. A 2× reduction of ⟨D⟩ down to 4–5 nm and lowering σD/D < 10%–15% are ongoing efforts to increase AD to ∼4 Tb/in.2. X = Cu ∼ 10 at. % reduces the Curie temperature TC by ∼100 K below TC,bulk = 750 K, thereby lowering the write head heat energy requirement. Multiple FePtX-Y granular layers with Y = 30–35 vol. % grain-to-grain segregants like carbides, oxides, and/or nitrides are used to fully exchange decouple the grains and achieve cylindrical shape. FePt is typically grown on fcc MgO (100) seedlay...

High speed switching in magnetic recording media

The theoretical formalism behind the introduction of thermal activation into the micromagnetic approach is reviewed. The theory is introduced via an application to a single spin which shows a rapid increase of coercivity at short timescales of the order of nanoseconds. Interaction effects are shown to increase relaxation times. A model of thermally activated spin-waves is presented.

A monte carlo simulation of the dependence of the coercive force of a fine particle assembly on the volume packing factor

Abstract A computer simulation has been reported of the effect of dipole interactions on the hysteresis loops and coercive forces of fine ferromagnetic particles. An earlier conjecture was thus verified that the coercive force increases or decreases with the volume packing factor p depending on whether the effective interaction field is predominantly positive or negative. For larger values of p a pronounced shearing of the loops was also obtained.