Theoretical Physics Group

Hysteresis modeling

Using zero temperature Monte Carlo simulations we have studied the magnetic hysteresis in a three-dimensional Ising model with nearest neighbor exchange and dipolar interaction. The average magnetization of spins located inside a sphere on a cubic lattice is determined as a function of magnetic field varied periodically. The simulations have justified the appearance of hysteresis

Magnetic hysteresis for N=15203 lattice points and for zero exchange

and allowed us to have a deeper insight into the series of metastable configuration states developed during this process.

Configuration of spins in magnetic fields decreasing from saturation

Relevant paper was published in the

Non-reversible magnetization processes in ferromagnetic materials are represented by rather complex hysteresis curves. The phenomenological description of such curves needs the use of multi-valued, yet unambiguous, deterministic functions.

In the Preisach model of hysteresis the history dependent calculation of consecutive Everett-integrals of the two-variable Preisach-function can account for the main features of hysteresis curves. We proposed a modification of the traditional Preisach model on the basis of population dynamics considerations. Our product model is an output dependent modification of the traditional model in order to remove its non-real congruency property.

The differential susceptibility is assumed to be a product of a magnetization dependent factor and an expression containing two terms: one for the reversible process and an integral of a Preisach type distribution for the irreversible part. Thus the magnetization is an indirect function, in which the saturation is a natural property of the hysteresis model, and the reversible and irreversible parts of the magnetization are added up indirectly. The envelope function is related to the paramagnetic process and in the specific case of uni-axial anisotropy it is a hyperbolic tangent function. The measurement of the anhysteretic curve may provide the direct link to the evaluation methods of experimental data applied for traditional Preisach modeling.

This empirical model of hysteresis can easily be extended to other irreversible physical processes, such as first order phase transitions.

Relevant paper was published in

1. György Szabó and György Kádár:
   Magnetic hysteresis in an Ising-like dipole-dipole model
   Phys. Rev. B 58 (1998) 5584.
2. György Kádár:
   On the product Preisach model of hysteresis
   Physica B 275 (2000) 40.
3. György Szabó and György Kádár:
   Hysteresis in a dipolar Ising model
   Physica B 275 (2000) 187.
4. György Kádár and György Szabó:
   Hysteresis modeling
   J. Magn. Magn. Mat. 215-216 (2000) 592.