MAE term in Tc

[Suman Mishra]

Hi everyone,

I have one question regarding MAE term in Tc calculation.

As I know about mean field approximation for Curie temperature calculation it includes only exchange energy contribution given by Jij = 3KbTc/ez  . There is no contribution from anisotropy here but in the input files and in mentioned Hamiltonian of vampire manual we can add the anisotropy term. where does this term get added and will it affect the Curie temperature?

Thanks in advance

Suman

[gabo...@gmail.com]

If you are referring to H = Hexc + Hani + Happ of equation (1) in [1] or the equation on slide 14 in [2], then as an example look at the uniaxial anisotropy Hani of equation (5) in [1] and the material:uniaxial-anisotropy-constant on page 47 (pdf page 49) of the VAMPIRE 5.0 manual [3].

A way to change the Hani term should be to use materials having a different anisotropy energy, k, value.  For example, see TABLE II in [1].  Also, the document at [4] does have materials (Fe, Co, Ni, Gd) having different M vs T curves.

So based on that I would expect k having some affect on the Curie temperature,Tc, but how much of an affect I'm not sure.  However, there is the Tc workshop example at [5].  In the Ni.mat file you should see the line:

material[1]:uniaxial-anisotropy-constant=k

So to get a better answer to your question, what you could to is run different VAMPIRE simulations using the workshop example with different values such as the following.

Calculation 1 - material[1]:uniaxial-anisotropy-constant=4e-26

Calculation 2 - material[1]:uniaxial-anisotropy-constant=5e-26

Calculation 3 - material[1]:uniaxial-anisotropy-constant=6e-26

That way you could compare resulting M vs T results for the varying k values to see how much of an affect it has.  Although, it is noted that not all materials have uniaxial anisotropy.  In [1], you can see there is equation (6) for Hani if the material happens to have cubic anisotropy.

And as you have already mentioned, Jij is part of the Hexc term [6,7].

[1] https://arxiv.org/pdf/1310.6143.pdf

[2] https://raw.githubusercontent.com/richard-evans/vampire-workshop/master/pdf-slides/1_intro/Introduction.pdf

[3] https://vampire.york.ac.uk/resources/vampire-manual.pdf

[4] https://www.researchgate.net/profile/Oreci-Da-Silva/project/Micromagnetic-and-Atomistic-Spin-Simulation-With-Mumax-3-and-Vampire-4/attachment/5ab600fd4cde266d58937587/AS:606511990599681@1521615135886/download/Micromagnetic+Simulation+of+Curie+Temperature+with+Vampire+4+Mat%3DFe.+Co%2C+Ni+and+Gd.pdf

[5] https://github.com/richard-evans/vampire-workshop/tree/master/input-files/1_intro/1b_Curie_temp

[6] https://vampire.york.ac.uk/tutorials/simulation/curie-temperature/

[7] https://vampire.york.ac.uk/tutorials/system-generation/crystal-structure/

Kind Regards,

Gavin

VAMPIRE user

[Suman Mishra]

---------- Forwarded message ---------
From: Suman Mishra <mishras...@gmail.com>
Date: Mon, Jul 25, 2022 at 7:09 PM
Subject: Re: MAE term in Tc
To: gabo...@gmail.com <gabo...@gmail.com>

Hi Gavin,

Thank you for your reply. The Hamiltonian which is given in reference [6] for curie temperature calculation the anisotropy term has not been included. So according to that there should be no effect of anisotropy in the Tc with monte-carlo simulation. However with constrained monte-carlo simulation we can add the effect of anisotropy in the Tc or magnetization. That's what I understood. Correct me if I'm wrong.

Thanks

Suman

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[gabo...@gmail.com]

That looks correct.  Also, on the webpage of reference [6], you can see that the unixaxial anistropy has been set to zero:

material[1]:uniaxial-anisotropy-constant=0.0

Also, in the VAMPIRE manual, you should see that if there is no "uniaxial-anisotropy-constant" line in the .mat file then it will default that to being zero:

material:uniaxial-anisotropy-constant = float [default 0.0 J/atom]

Kind Regards,

Gavin

VAMPIRE user