Dear Mohammad,

The Jiles-Atherton never gives you information of the magnetic interaction between magnetic nanoparticles or multilayers. This (simple) model only information on the magnetic energy in a hysteresis loop, i.e. the part of the magnetization associated to a lossless energy and the one with losses. In the static part can work quite well but when there are AC fields the things are much more complex, for instance, appear new losses of energy by eddy currents. If you have multilayers these can be considered not very important for many cases and it can work, allowing you to distinguish the reversible and no reversible energies employed in the hysteresis loop.

The most physical model, although not so simple, is the Preisach model. Two good references for following both models are

1.I. D. Mayergoyz, Mathematical Models of Hysteresis ,Springer-Verlag, New York, (1991).

2. D. C. Jiles and D. L. Atherton, J. Magn. Magn. Mater. 61, 48 (1986).

Dear Daniel,

I really appreciate your comprehensive answer.

I will go through the references, then I will get back to you if I had questions.

Best,

Reza.

Dear Mohammad,

I may suggest the Limiting loop proximity hysteresis model. “With only four parameters, it has low computational cost and reduced mathematical complexity, thus permitting a fast numerical implementation and simple parameter estimation procedure.” Here it follows simple MATLAB scrip for implementation. It is also available embedded in the HysterSoft (Department of Electrical and Computer Engineering Florida State University and Florida A&M University).

[1]de Almeida, Luiz Alberto Luz, et al. "Limiting loop proximity hysteresis model." IEEE transactions on magnetics 39.1 (2003): 523-528.

[2]Dimian, M., and P. Andrei. "Scalar and vector hysteresis simulations using HysterSoft." Journal of Physics: Conference Series. Vol. 585. No. 1. IOP Publishing, 2015.

https://www.researchgate.net/profile/Luiz_Luz_De_Almeida/publication/3109929_Limiting_loop_proximity_hysteresis_model/links/5899f7684585158bf6f8a5f6/Limiting-loop-proximity-hysteresis-model.pdf

Script

% Parameters

Ms=1;

h0=0.3;

Hc=0.35;

zeta=1;

% example of input H

t=0:0.01:30; % cria vetor de tempo

H=1*(-0.1*t+1).*sin(0.85*t); % cria entrada

M=zeros(size(t)); % inicializa vetor M

deltaAnterior=1;

Hr=H(1); % inicializa Hr ponto de reversão

Mr=M(1); % inicializa Mr ponto de reversão

for n=2:length(H)

if (H(n)-H(n-1))>0 deltaAtual=1;

else deltaAtual=-1; end

if ne(deltaAtual,deltaAnterior) % é ponto de reversão?

Hr=H(n-1); % Atualiza Hr apenas no ponto de reversão

Mr=M(n-1); % Atualiza Mr apenas no ponto de reversão

deltaAnterior=deltaAtual; % atualiza delta para próxima iteração

end

Hpr=h0*tan(pi*Mr/(2*Ms))+deltaAtual*Hc-Hr;

x=(H(n)-Hr)/Hpr;

M(n)=(2*Ms/pi)*atan((Hpr*ProFunc(x,zeta)+H(n)-deltaAtual*Hc)/h0);

end

plot(H,M)

% function file

function y = ProFunc(x,zeta)

%ProFunc Proximity Function P(x).

y=(zeta*x < pi/2).*(1-sin(zeta*x))+(zeta*x >= pi/2).*0;

Dear Alberto,

Thanks for sharing the manuscript and the script for calculation. This model seems very interesting, very fast, simple with good accuracy.

Best,

Reza.