System: S=3/2, ZFI-axial (E=0), zC _|_ H, rotation around z

[trukhan]

I try to simulate the spectra of a system (S = 3/2 and axial zero-field splitting tensor) for its different orientations with respect to a static magnetic field. In particular, I try to simulate the spectra when the axial axis z of crystal (zC) is perpendicular to the field and there is a rotation around zC. I expected that in this case, in view of axial symmetry, the spectra should not change. Indeed, it turned out that the energy of the transitions and the positions of the lines do not change. However, there is a change in the relative intensities of the lines! How is this possible? Why?

Code: Select all

clear, clf;
Sys.S = 3/2;
Sys.g = 2;
Sys.D = clight/1e4*0.2;
Sys.lwpp = 10;
Exp.mwFreq = 9.7;
Exp.Range = [0 700];

alpha=0;
beta=90;
gamma=0; d=30;
Exp.CrystalOrientation = pi/180*[alpha beta gamma]; 
[Bres1,Int1] = eigfields(Sys,Exp);
[B,S1]=pepper(Sys,Exp);

Exp.CrystalOrientation = pi/180*[alpha beta gamma+d];
[Bres2,Int2] = eigfields(Sys,Exp);
[B,S2]=pepper(Sys,Exp);

Exp.CrystalOrientation = pi/180*[alpha beta gamma+2*d];
[Bres3,Int3] = eigfields(Sys,Exp);
[B,S3]=pepper(Sys,Exp);

Exp.CrystalOrientation = pi/180*[alpha beta gamma+3*d];
[Bres4,Int4] = eigfields(Sys,Exp);
[B,S4]=pepper(Sys,Exp);
gammaSweep=[gamma gamma+d gamma+2*d gamma+3*d]

plot(B,S1,B,S2,B,S3,B,S4);

[Stefan Stoll]

In order to do the rotation you want to do, increment alpha instead of gamma.

The change in intensities you see in your current rotation is due to changes in the transition dipole moment, as the mw field (along the xL axis) is hitting the spin system from different orientations as you rotate.

[trukhan]

Thank you!
Now I understand!
I thought that Exp.CrystalOrientation describes the rotation of the crystal relative to the laboratory coordinate system. But in fact it is Euler angles for the transformation of the crystal frame to the lab frame (C → L) as stated in "documentation/frames.html".

P.S.
It seems to me that there is a typo in the "documentation/frames.html" paragraph "Crystal orientation in the spectrometer":
"In order to find the transformation that works in reverse, from the crystal to the lab frame (L → C), use the following: First, ..."
It should be
"In order to find the transformation that works in reverse, from the lab to the crystal frame (L→C), use the following: First,..."

P.P.S. (tiniest not relevant remark)
Also on the page "documentation/pepper.html" in all browsers I see an incorrect display of the letters ä and å in the surname "Vänngård".

[Stefan Stoll]

Thanks for pointing out the typos - they will be fixed in the next patch release.