Amp in resfield

[Hui18]

Hi:

I am trying to use Amp produced by resfields function. May I know whether Amp is gamma times the square of matrix element or just the square of matrix element itself? For example, in the paper(http://e-collection.library.ethz.ch/ese ... 411-02.pdf), is Amp calculated in the same way as Equation (2.50)?

Thank you very much in advance for your help!

[Stefan Stoll]

resfields includes in the amplitudes (a) the square of the transition magnetic dipole moment, (b) the field-to-frequency conversion factor (which you call gamma), and (c) if a temperature is given, the population difference according to the Boltzmann distribution.

[hintze]

Sorry for either hijacking or necrobumping this thread, but I would have chosen the same subject title for my question.

As far as I understand from your answer, @Stefan Stoll, the weighting factor of a given orientation is not taken into account in the amplitude output by resfields, is it? That means that if I would like to reconstruct the intensities from a spectral simulation, I also have to use the weights output by sphgrid. Or do I miss something here?

[Stefan Stoll]

That is absolutely correct.

[thanasis]

I am taking my turn to resurrect this question, as the thread is the most relevant: I would like to know how we can strip the resfield calculation down only to the matrix element |<n|Sx|m>|^2, ignoring all other factors.

I would like to compare the transition probabilities calculated from ES with the ones analytically derived in different textbooks and papers for different exchange-coupled systems. For the arithmetic result to be directly comparable, should I take special care of the energy and field units?

There is also an undocumented Grad field, which (when we set Opt.Verbosity to 2) is commented as gradient. Would that be the orientational gradient of a state energy?

Thanks!

[Stefan Stoll]

Here is a simple demo script on how to reproduce the transition rates calculated by resfields. Obvioulsy, if you tilt the magnetic field relative to the g-tensor frame, then things get a bit more tedious due to the Euler angles needed to handle the tilted orientations, but the physics is exactly the same.

Code: Select all

clc, clear

Sys.S = 1/2;
Sys.g = [2 2.1 2.2];
Exp.Range = [300 400];
Exp.mwFreq = 9.5;
Exp.CrystalOrientation = [0 0 0];
Opt.Freq2Field = false;
[B,TransRate0] = resfields(Sys,Exp,Opt)


H = sham(Sys,[0 0 1]*B);
[V,E] = eig(H);
[Sx,Sy,Sz] = sop(Sys.S,'x','y','z');
u = V(:,1);
v = V(:,2);
c = bmagn*Sys.g(1)/planck/1e9;
TransRate1 = c^2 * (abs(u'*Sx*v)^2 + abs(u'*Sy*v)^2)/2

[thanasis]

Thanks Stefan!

I had been reading the sop documentation and couldn't figure out how to treat exchange-coupled systems. E.g., something like:

Code: Select all

Sys.S = [5/2 5/2 5/2];
Gx = 0; Gy = 0; Gz = 0.2;
GG = [0 Gz -Gy; -Gz 0 Gx; Gy -Gx 0];
gz = 2;
gxy = 2;
Ja = -22.6;
Jb = -19.3;
Sys1.g = [gxy gz; gxy gz; gxy gz];
Sys1.ee = (100*clight/1e6)*[-2*Ja*eye(3) - 2*GG; -2*Ja*eye(3) + 2*GG; -2*Jb*eye(3) - 2*GG];

Indeed, when I used this sample script to make the calculation for my system, sop threw an error:

Error using sop
sop: Could not determine what 'x' is for the given spin system.

Error in sop

Is there a way to get around this?

[Stefan Stoll]

For calculating the transition moments and rates, you need the sum over spins:

Code: Select all

[S1x,S1y,S1z] = sop(Sys.S,'x1','y1','z1');
[S2x,S2y,S2z] = sop(Sys.S,'x2','y2','z2');
[S3x,S3y,S3z] = sop(Sys.S,'x3','y3','z3');
Sx = S1x+S2x+S3x;
Sy = S1y+S2y+S3y;

[thanasis]

Thanks for this Stefan,

I now made the calculations as you suggested, assuming:

Code: Select all

Exp.Temperature = 4.2; Exp.mwFreq=9.801; Exp.CenterSweep=[350 700];

For the previously defined system, and for those experimental conditions, the results are:
<1|Sx|2> = <1|Sy|2> = 0.231365072811767
and since TransRate1 = c^2 * (<1|Sx|2> + <1|Sy|2>)/2 with c = bmagn*Sys.g(1)/planck/1e9 = 27.99249, I get Trans1Rate1 = 181.2929.

However the resfields result is TransRate0 = 10.1332 (with a very minor additional transition corresponding to transition 3-4). By removing the temperature from Exp, resfields calculates all possible resonances, and then indeed the 1-2 resonance is given with a TransRate0 = 181.2929 (and all others with non-realistic values for my experimental conditions). So I conclude that TransRate0 and TransRate1 coincide when we neglect thermal populations, right?

UPDATE: Subsequently, I calculated the Boltzmann populations of states 1 and 2 and multiplied with their difference:

Code: Select all

pop = exp(-Ener*1e6*planck/boltzm/Exp.Temperature);
Intensity1 = TransRate1 * (pop(1) - pop(2))

which yields 20.206058, about double the result from resfield. I suppose I need to apply the 1/g Aasa-Vanngard correction. This gives practically the resfields result if g = 2.

[Stefan Stoll]

You got it!