Fitting 3 e-spins with common hyperfines, Jiso and AE

[thanasis]

I am trying to fit my EPR data to a model that considers:
-Three S=1/2 spins
-Three nuclear spins, each coupled to its own atom's electron spin through an axial hyperfine interaction
-Three equal isotropic J couplings between the e-spins
-Three equal antisymmetric exchange couplings between the e-spins
-Common gxy and gz parameters for each e-spin

So far, I have compiled the following script:

Code: Select all

cm=100*clight/1e6; % Conversion constant from cm-1 to MHz
gxy = 2.05; gz = 2.2;
J = -100; % in cm-1
w1=5; w2=5;
ACuxy=50; ACuz=200; %Aperp and Apar for Cu in MHz
d = 2;
Gx=0; Gy=0; Gz=cm*d; %Convert Gz from cm-1 to MHz
%--------------------------------------------------------------------------
Sys1.S = [1/2 1/2 1/2];
Sys1.g = [gxy gz; gxy gz; gxy gz];
ee12 = [J Gz -Gy; -Gz J Gx; Gy -Gx J];
ee13 = [J Gz -Gy; -Gz J Gx; Gy -Gx J];
ee23 = [J -Gz Gy; Gz J -Gx; -Gy Gx J];  % The Gx,y,z signs have been reversed because d13(S1xS3)=-d13(S3xS1)
Sys1.ee = [ee12;ee13;ee23];
Sys1.lwpp=[w1 w2];
Sys1.Nucs='Cu,Cu,Cu';
Sys1.A = [ACuxy ACuz 0 0 0 0; 0 0 ACuxy ACuz 0 0; 0 0 0 0 ACuxy ACuz];
%--------------------------------------------------------------------------
Exp.Temperature = 4.1; Exp.mwFreq=9.423781; Exp.CenterSweep=[400.0 300.0]; Exp.nPoints=2048;
Vary1.g = [0.05 0.05];
Vary1.ee = cm*[10 1 0; 1 10 0; 0 0 10]; % Vary J by 10 & Gz by 1. Fix Gx, Gy (to zero)
Vary1.lwpp = [5 5];
Vary1.A = [10 50];
esfit('constrain',spc,Sys1,Vary1,Exp,[],FitOpt);

The constrain function is:

Code: Select all

function y = constrain(Sys1,Exp,Opt);
fullSys = Sys1;
fullSys.g = [Sys1.g];
fullSys.A = [Sys1.A];
fullSys.Nucs = 'Cu,Cu,Cu';
fullSys.ee = [Sys1.ee];
[x,y] = pepper(fullSys,Exp,Opt);
return

I am 99% sure that I get the gxy, gz, Axy and Az constraints right, but I can't seem to get the J and d (= |Gz|) constraints from the ee matrix correctly. In particular, I get three occurrences of J (probably the principal values Jijx, Jijy and Jijz) and two occurrences of d of opposite signs. How should I correctly define fullSys.ee in my constrain function?

Thanks in advance!

[Stefan Stoll]

Please see my answer to your other post with a similar question.