Normalized magnetization

[tom.chau...@gmail.com]

Hello, 

I would like to represent the normalized magnetization (m/ms) as shown in [1] for magnetite. What is the output necessary to get such a curve ?

I tried the curie-temperature simulation as shown in the tutorial on Vampire's website, which outputs the mean-magnetisation-length. I get a curve between 0 and 0.28, as magnetite is ferrimagnetic, when the temperature range is between 0K and 1000K. 

I then tried the field-cooling simulation without any applied field with outputs : mean-magnetisation-length and magnetisation-length. However, I get similar results this time with the curie-temperature simulation with the magnetisation-length output, rather than the mean-magnetisation-length. Is there any explanation to that ?

Also, once you can get the normalized magnetization curve (m/ms), is there a way to know the value of ms ?

Thanks in advance for any response, 

[gabo...@gmail.com]

I would like to represent the normalized magnetization (m/ms) as shown in [1] for magnetite. What is the output necessary to get such a curve ?

I tried the curie-temperature simulation as shown in the tutorial on Vampire's website, which outputs the mean-magnetisation-length. I get a curve between 0 and 0.28, as magnetite is ferrimagnetic, when the temperature range is between 0K and 1000K. 

When I tried reproducing the Ni Curie temperature curve similar to that in FIG. 1 c in [1], it was the mean-magnetisation-length that was used.  See [2].

[2] https://groups.google.com/g/vampire-users/c/LS51ZlvZeyw/m/3gljoW54AwAJ

 

I then tried the field-cooling simulation without any applied field with outputs : mean-magnetisation-length and magnetisation-length.

A field cooled calculation is different from that of a Curie temperature calculation.  The field cooled uses a continuous process [3].

[3] https://groups.google.com/g/vampire-users/c/4fOcmN7F6Mc/m/UtquHVaQBgAJ

 

However, I get similar results this time with the curie-temperature simulation with the magnetisation-length output, rather than the mean-magnetisation-length. Is there any explanation to that ?

I currently don't have an explanation for that.

It is noted, though, that the magnetisation-length is the length |m|, while the mean-magnetisation-length is also the length but it's time averaged <|m|> [4].

[4] https://groups.google.com/g/vampire-users/c/ANjHmqhCXZk/m/6_86KD2ZBAAJ

 

Also, once you can get the normalized magnetization curve (m/ms), is there a way to know the value of ms ?

 

I don't think Ms is an output of VAMPIRE.  It actually seems to be an input for VAMPIRE.  In the VAMPIRE article at [5], you might recall seeing before the equation (8) in it of:

μ_s = Ms*a^3/n_at

For example, the article [6] has that Ni has a Ms of around 522 emu/cm^3.

A fcc unit cell has 4 atoms [7].

A Bohr magneton is 9.274 x 10^-21 emu [8].

The article at [5] in Table 2 has a unit cell size of 3.524 Å.

In Ni.mat at [9], you see for μ_s:

material[1]:atomic-spin-moment=0.606 !muB

Using equation (8), you can backward calculate the saturation magnetization:

Ms = μ_s*n_at/a^3 = (0.606 * 9.274 x 10^-21 emu) * 4/(3.524 x 10^-8 cm)^3 = 514 emu/cm^3

Often times, Ms is obtained experimentally by vibrating sample magnetometer (VSM) measurements [10].

[5] https://dx.doi.org/10.1088/0953-8984/26/10/103202

[6] https://doi.org/10.3390/magnetochemistry7100139

[7] https://www.quora.com/How-many-atoms-are-there-in-an-FCC-unit-cell

[8] https://en.wikipedia.org/wiki/Bohr_magneton

[9] https://github.com/richard-evans/vampire-workshop/blob/master/input-files/1_intro/1a_Ni/Ni.mat

[10] https://groups.google.com/g/vampire-users/c/dLof6AYihQE/m/o5J4IrTnAAAJ

Kind Regards,

Gavin

VAMPIRE user

[tom.chau...@gmail.com]

Hi Gavin, 

Thank you for your answer ! 

As for the Ms value of saturation magnetization at 0K, can I sum the saturation magnetizations of each element composing my material ? For magnetite Fe3O4 made of 56 atoms in the unit cell and equivalent to 3 materials in my file : Fe(2+)Fe(3+)_2 O_4, is it good to compute

Ms = 8*mu_1/a^3 + 16*mu_2/a^3 + 32*mu_3/a^3 ? 

Do you happen to know as well why when putting sim:applied-field-unit-vector = 1,0,0 with intensity 50mT in the input file, I don't necessarily get the spins aligned in this direction at 0K. For instance I get 

0.587278 0.164013 0.792593

-0.587269 -0.164039 -0.792595

...

in the .data file at 0K. I would ultimately like to compute the number of spins aligned in each direction over temperature. 

Thank you, 

Tom 

[gabo...@gmail.com]

I don't have an answer for your first question.

Regarding the 2nd question, three possibilities that I can think of are:

a) Sometimes a very small angle is needed on the field so that the spins don't get stuck.  

There are two different ways for setting that.  One is using an angle [1]:

sim:applied-field-angle-phi = 0.1

Or the second is using a vector [2,3]:

sim:applied-field-unit-vector=0.00001,0,0.99999

b) The sim:maximum-applied-field-strength might be too small making the field not strong enough to overcome the corecivity [4] (e.g., shape anisotropy, crystalline anisotropy, ...).

c) Could be caused by something else I've not thought of.

[1] https://groups.google.com/g/vampire-users/c/YqrCbmkfPXY/m/6utppW8AAwAJ

[2] https://groups.google.com/g/vampire-users/c/faPqxkUKOuw/m/t2kIrgIQBv8J

[3] https://groups.google.com/g/vampire-users/c/twoHAuMFcGQ/m/BsMqJt3JAQAJ

[4] https://groups.google.com/g/vampire-users/c/PHXwoBXTK2o/m/vF7hqZEFAQAJ

Kind Regards,

Gavin

VAMPIRE user