Exchange interaction for non parallel spin

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Exchange interaction for non parallel spin

Postby Qing Zhang » Wed Dec 06, 2017 7:04 am

Hello,

My name is Qing Zhang from Prof. Myriam P. Sarachik's group. Could you please help me about the question of the Dy3 paper (Phys. Rev. Lett. 100, 247205):

I am interested in anisotropic exchange in molecular magnets. I am able to rotate the local tensor frame for anisotropic g and zero field splitting terms. However I do not know how to tilt tensors associated with anisotropic exchange. An important example would be the ising model applied for the interpretation single crystal of magnetization of Dy3 (Phys. Rev. Lett. 100, 247205). I make an attempt to reproduce the characteristic Zeeman splitting diagram (fig 3)

% code before exchange:
Sys.S = [1/2 1/2 1/2];
Sys.g = [0 0 1; 0 0 1; 0 0 1]; % anisotropic g tensors
Sys.gFrame = [0 0 0; 0 120 0; 0 240 0]*pi/180;
Sys.ee = [0;0;0]*(-1e5); % coupling, in MHz

% code after adding exchange:
Sys.ee = [0 0 1;0 0 1;0 0 1]*(-1e5); % coupling, in MHz
Sys.eeFrame = [0 0 0; 0 120 0; 0 240 0]*pi/180;

Could you please give me any suggestion about how to write the code about the exchange or how to calculate the Zeeman splitting diagram? Thank you very much!


Best regards,

Qing Zhang
Attachments
image.png
Zeeman energy of Dy3 molecule
image.png (134.81 KiB) Viewed 72 times
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Re: Exchange interaction for non parallel spin

Postby katarkon » Wed Dec 06, 2017 9:40 am

Use function levelsplot.
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Re: Exchange interaction for non parallel spin

Postby Qing Zhang » Thu Dec 07, 2017 10:23 pm

Thank you for your comment. I am familiar with levelsplot. I should be clearer in my question; the code does not match the desired field dependence (i.e. a double degenerate singlet ground state at low field, like a) of the attached figure). This is most likely due to the required rotation of the anisotropic exchange. Could you please tell me how to show the following expression by the easyspin spin system: j_zz * S_zi * S_zk (the S_zi is equal 1/2, but S_zi is not parallel with S_zk)? Thank you.
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Re: Exchange interaction for non parallel spin

Postby Matt Krzyaniak » Fri Dec 08, 2017 11:36 am

Here's a little snippet of code that might help you in thinking about how the rotations work and how things sum together to generate the effective interactions(you can do the same with the exchange coupling)

Code: Select all
Sys.g = [0 0 1; 0 0 1; 0 0 1];
Sys.gFrame = [0 0 0; 0 120 0; 0 240 0]*pi/180;

g = diag(Sys.g(1,:));
R_m2g = erot(Sys.gFrame(1,:)); % mol frame -> g frame
R_g2m = R_m2g.'; % g frame -> mol frame
g1 = diag(R_g2m*g*R_g2m.')

g = diag(Sys.g(2,:));
R_m2g = erot(Sys.gFrame(2,:)); % mol frame -> g frame
R_g2m = R_m2g.'; % g frame -> mol frame
g2 = diag(R_g2m*g*R_g2m.')

g = diag(Sys.g(3,:));
R_m2g = erot(Sys.gFrame(3,:)); % mol frame -> g frame
R_g2m = R_m2g.'; % g frame -> mol frame
g3 = diag(R_g2m*g*R_g2m.')


gavg=(g1+g2+g3)/3
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