Resonances from local tensor rotations in a spin triangle

[thanasis]

Hello,

I have been trying to simulate the effect of the local g-tensor orientations of an exchange coupled triangle on the gpar and gperp positions.

I assume that I have Cu(II) ions with local (g0) tensor elements g0|| = 2.25 and g0_|_ = 2.05, and by rotating my molecule I am looking at the effective geff|| (rot = 0) and geff_|_ (rot = 90).

The problem is that for geff_|_ (rot = 90) there seems to be an extra resonance I cannot account for. In the following script, I plot the calculated single-crystal spectrum along with the Zeeman diagram zoomed at the different multiplets (with levelsplot) to try to find which orientation I am seeing. By playing around, the two lower doublets can account for the same resonance (with Ori = 'x' and Ori = 'y'), but I cannot account for the higher-field resonance.

Also, when I calculate the resonance fields with resfields, I get five very closely spaced resonances, but with very different intensities. To what do they correspond?

Most importantly: is there an error somewhere?

Thanks in advance!

Code: Select all

clear all; close all;
cm=100*clight/1e6; % Conversion constant from cm-1 to MHz

Ja = -100;
Jb = -100;
Jc = -90;
Si = 1/2;

Gx = 0; Gy = 0; Gz = 0;
GG = [0 Gz -Gy; -Gz 0 Gx; Gy -Gx 0];
gxy = 2.05;
gz = 2.25;
n = 45; % How many plots?

% Rotation angles
rot = 90; % The rotation angle of the crystal
tilt = 0; % molecular axis tilt from the bc (horizontal) plane (in degrees)

%The spin system
Sys1.S=[Si Si Si];
Sys1.lwpp = [0 1];
Sys1.g = [gxy gz; gxy gz; gxy gz];
Sys1.ee = [-2*Ja*eye(3) - 2*GG; -2*Jb*eye(3) + 2*GG; -2*Jc*eye(3) - 2*GG]*cm;

for i=1:n
% Euler angles for the g-frames. Each angle refers to an atom
euler_tilt_angle(i) = 4*(i-1); % The tilt angle
euler1 = [0 0 0]; euler2 = [60 0 0]; euler3 = [-60 0 0]; % Cu(II) ions with Jahn-Teller axis parallel to molecular z-axis (at zero tilt angle)
euler_tilt = [0 euler_tilt_angle(i) 0]; % Create an Euler rotation for that angle
euler1 = euler1 + euler_tilt;
euler2 = euler2 + euler_tilt;
euler3 = euler3 + euler_tilt;
Sys1.gFrame = [euler1; euler2; euler3]*pi/180;

%Experimental conditions for simulations
%--------------------------------------------------------------------------
Exp.Temperature = 2; Exp.mwFreq=9.4;   Exp.CenterSweep = [planck*Exp.mwFreq*1e12/(bmagn*0.5*(gz+gxy)) 60*sqrt(Exp.mwFreq/9.4)]; Exp.nPoints=500;
 
% FOR SINGLE-CRYSTALS
Exp.CrystalSymmetry = 146;        % space group R3
Exp.MolFrame = [0 tilt 0]*pi/180;  % molecular frame tilted towards the bc plane
cori0 = [0 0 0]*pi/180;              % initial crystal orientation in lab frame
nRot_L = [1;0;0];               % rotation axis = x axis of lab frame i.e. EPR tube axis based on frame definitions
rho = rot*pi/180;               % rotation angle
cori = rotatecrystal(cori0,nRot_L,rho);   % rotate crystal by rho around nRot
Exp.CrystalOrientation = cori;
tic
[B,spc] = pepper(Sys1,Exp);
toc
spc = spc/max(spc);

figure(1)
subplot(4,1,1)
plot(B,spc)
axis tight

subplot(4,1,2)
Ori = 'y'; FieldRange = [min(B) max(B);]; Freq = Exp.mwFreq; Par.Units = 'cm^-1';
levelsplot(Sys1,Ori,FieldRange,Freq,Par);
ylim([144 146])

subplot(4,1,3)
Ori = 'x'; FieldRange = [min(B) max(B);]; Freq = Exp.mwFreq; Par.Units = 'cm^-1';
levelsplot(Sys1,Ori,FieldRange,Freq,Par);
ylim([-135.5 -134.5])

subplot(4,1,4)
Ori = 'y'; FieldRange = [min(B) max(B);]; Freq = Exp.mwFreq; Par.Units = 'cm^-1';
levelsplot(Sys1,Ori,FieldRange,Freq,Par);
ylim([-155.5 -154.5])

% Arguments for eigfields
Par.mwFreq = Exp.mwFreq;
Par.CrystalOrientation = Exp.CrystalOrientation;
Par.CenterSweep = Exp.CenterSweep;
[Bres,int] = resfields(Sys1,Par); % The resonance field
Breson1(i) = Bres(1);
Breson2(i) = Bres(2);
Breson3(i) = Bres(3);
Breson4(i) = Bres(4);
Breson5(i) = Bres(5);
end

greson1 = (planck*Exp.mwFreq*1e12/bmagn)./Breson1;
greson2 = (planck*Exp.mwFreq*1e12/bmagn)./Breson2;
greson3 = (planck*Exp.mwFreq*1e12/bmagn)./Breson3;
greson4 = (planck*Exp.mwFreq*1e12/bmagn)./Breson4;
greson5 = (planck*Exp.mwFreq*1e12/bmagn)./Breson5;

figure(2)
plot(euler_tilt_angle,greson1);
axis tight
legend show
legend('boxoff')
hold on
plot(euler_tilt_angle,greson2)
plot(euler_tilt_angle,greson3)
plot(euler_tilt_angle,greson4)
plot(euler_tilt_angle,greson5)
set(gca,'FontName','Times','Fontsize',6,'XColor','k','YColor','k')

[Stefan Stoll]

I don't see a problem right away, but the script is a bit too long to digest. Can you simplify it by just plotting spectrum and energy level diagram for a single tilt?

Something to remember is that when you tilt the g tensor, the features in the EPR spectrum will occur at tilted orientations, not along x, y, and z. So it could be that your Ori='x' etc. input to levelsplot needs to be changed.

[thanasis]

I think this little video illustrates the situation.
Tensor rotation = 0 means that the local g|| is normal to the triangle plane.
Tensor rotation = 90 means that the local g|| is in the triangle plane.

For the level plots orientation = x (Ori = 'x'), so we are at g_|_. This g_|_ resonance of the triangle should go from 2.05 (local g_|_) to 2.25 (local g||) . One does, but there's another one that doesn't move along with it.

The low-lying doublets and the quartet are zoomed in at the subplots.

Change the extension from "zip" to "mp4" to view the video.