Three non interacting spins simulation

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i.tlem
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Posts: 1
Joined: Mon Dec 16, 2024 7:49 am

Three non interacting spins simulation

Post by i.tlem »

Hi,

I want to simulate a spin triangle. In a first time I want to plot the energy levels of three S = 1/2 non-interacting spins.
I do not understand why instead of having a ground state corresponding to one S = 1/2, I get a completely different behavior (S = 3/2)
Am I missing an argument that can explain the observed energy levels?

clear all

% Definition of the spin system
Cu3.S = [1/2, 1/2, 1/2]; % Three spin-1/2
Cu3.g = [2.1; 2.1; 2.1]; % g-factor for all spins

% Coupling constants
J12 = 0;
J13 = 0;
J23 = 0;
% Dipolar interaction magnitude
%dm = 0.0;
% DMI vectors (in MHz)
%d12 = [dm dm 0];
%d13 = [dm dm 0];
%d23 = [dm dm 0];

Cu3.J = [J12 J13 J23] ; % Exchange coupling
%Cu3.dvec = [d12; d13; d23]; % DMI vectors

% Line broadening (Lorentzian)
Cu3.lwpp = 5;

% Experimental parameters
Exp.mwFreq = 9.5; % Microwave frequency in GHz
Exp.Range = [0 1000]; % Magnetic field range in mT
Exp.nPoints = 1024; % Number of points in the spectrum
Exp.Temperature = 5; % Temperature in Kelvin

% Define parameters for energy level calculation
FieldRange = linspace(Exp.Range(1), Exp.Range(2), 500); % Magnetic field range
Ori = 'z'; % Orientation of the magnetic field
Opt.SlopeColor = true; % Option to color the slopes of the energy levels

% Simulate the EPR spectrum
[B, spect] = pepper(Cu3, Exp);

% Create a figure with two subplots
figure;

% First subplot: EPR spectrum
subplot(2, 1, 1);
plot(B, spect, 'LineWidth', 1.5);
title('EPR Spectrum');
xlabel('Magnetic Field (mT)', 'Interpreter', 'latex');
ylabel('Absorption (a.u.)', 'Interpreter', 'latex');
grid on;
% Second subplot: Energy levels
subplot(2, 1, 2);
levelsplot(Cu3, Ori, FieldRange, Exp.mwFreq, Opt);
title('Energy Levels for Cu3 System');
xlabel('Magnetic Field (mT)', 'Interpreter', 'latex');
ylabel('Energy (MHz)', 'Interpreter', 'latex');
grid on;

Thanks

Attachments
Levels.png
Levels.png (44.67 KiB) Viewed 2134 times
Matt Krzyaniak
EasySpin Guru
Posts: 155
Joined: Tue Jul 22, 2014 11:01 am
Location: Northwestern University

Re: Three non interacting spins simulation

Post by Matt Krzyaniak »

The simple answer is that you have no coupling between the spins so at zero field the S=1/2 and S=3/2 manifolds are degenerate. So in your levelsplot, the two different manifolds overlap and it looks like you're observing just the S=3/2 manifold, when in reality you're observing both manifolds, its just that the S=-1/2 -> 1/2 levels overlap. If you were to add in some isotropic exchange coupling, you'd lift the degeneracy between S=1/2 and S=3/2 and see the differences.

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