I am a little confused with the origin of the hysteresis in magnetic materials. In the first link, it is annouced in the 3rd page that a heisenberg hamiltonian cannot explan the coercive field. And in the later part of the notes,one can easily get a conclusion that if the anisotropy is zero, the coercive field is zero. However, in the second link, using a ising model, the hysteresis is explained with mean field theory as a competition of different solutions, thus one can still get a hysteresis loop without anisotropy. So which one is the right mechanics in the reality? Is magnetic anisotropy necessary for hysteresis behaior of a 3D material?
http://ocw.mit.edu/courses/materials-science-and-engineering/3-024-electronic-optical-and-magnetic-properties-of-materials-spring-2013/lecture-notes/MIT3_024S13_2012lec25.pdf
http://www.physics.udel.edu/~jim/PHYS460_660_13S/statmech/Hysteresis.pdf
Hello, Pang!
Generally speaking, hysteresis phenomena is just a delayed response of the system on the external perturbation having periodic variation in time. If one integrates the system's energy variation over the period, the integral will be exact amount of the work done by the system. If no phase transition occurs over the period, this work is completely transformed into the heat. One has to introduce the dissipation function in the system to be able to convert the work into the heat. Turning back to the magnetic hysteresis, one can consider it as a time-dependent irreversible thermodynamic process. The dissipation function is mainly magnetization precession damping function. Magnetic moment can change its projection onto magnetic field (effective field, more generally) only if the damping mechanism exists in the system. Damping is also time dependent process (i.e. developing in certain time scale determined typically by certain effective damping constant). From this point one can conclude that nothing more than magnetization precession damping is necessary to observe a hysteretic responce of a magnetic system on a time-dependent periodic variation of magnetic field. Magnetic anisotropy, as well as magnetic field and thermal fluctuations, change (locally or globally) the effective field magnitude and direction (generally, the effective field is a tensor), while only the damping allows magnetic moment to be reoriented in the direction of the effective field within the finite time.
Anisotropy in the case of magnetization is minimized almost to zero super-soft magnetic materials where there is a rectangular magnetic hysteresis loop. The sum of components of different kinds of anisotropy is called the effective anisotropy. If we study the magnetization curve is an area above the curve. Just count field over the magnetization curve and you will know what is the anisotropy. So it looks like that is necessary but for the best soft magnetic materials to the smallest.
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