Effect of J and eeD on the powder spectrum with S=1/2

[jmonroe]

Hello All!

I'm working on simulating powder spectra of low dimensional copper(II) lattices and I have a couple general questions I'm hoping you can answer.
The general code scheme I've been using is very simple with some number of S=1/2 ions with axial or rhombic gs thus:
Sys.S=[1/2 1/2 1/2....] I have tried 2-16 spins
Sys.g=[g1 g2 g3; G1, G2, G3,....] I have tried with all g=2; with g2=g3 and in all cases g1=G1, g2=G2, and g3=G3(all the spins are identical in all of my simulations).
Sys.J=[J12 J13 J14....] and for instance in the event I am attempting to simulate a chain of interacting copper(II) ions only nearest neighbors are interacting and thus J12 is nonzero J13 is 0....J23 is non zero J24 is 0..... etc.
I need to add also Sys.lwpp=1 but this brings me to my issue.
So heres the issue...
With all J=0 I get a very messy spectrum for 2 and 4 spins which doesnt really make sense to me. Shouldn't it look very similar to the one spin system if the g's are identical?
Upon changing J at all I am left with the same exact spectrum as when I am simulating a system with only one spin, no matter the size of J.
So, my question is regarding what J and, for instance, eeD, actually do to the spin system and thus to the spectrum. I see literature precedence for extracting J values from powder spectra,(only a few at X band which is what I am doing) however I havent been convinced it actually works.
Of course, in terms of single crystal studies J and eeD (superexchange and dipolar interactions) can be studied in terms of broadening or narrowing of the spectrum, however I don't see any effect like this on the simulated powder spectra.
Thank you for reading and Please approach me with suggestions or questions (about my parameters if I haven't been clear enough) if you can help, I really appreciate it!

Jeff

[Stefan Stoll]

Please post an example script that shows these effects (maybe just two spins).

[jmonroe]

Hey Dr. Stoll! My name is Jeff Monroe I work at Clark University for Dr. Mark Turnbull and I am very grateful that you've replied to my post. I love EasySpin, it's so cool thank you! I'm relatively new to EPR, EasySpin and coding so if I've made unforgivable mistakes I apologize in advance. Our group is just starting to do in depth EPR experiments and so I am unfortunately largely self taught.

Here is an example of the effects I am seeing. The code gives three different systems Sys1 is 2 spins with J=0, Sys2 is 2 spins with J=10 and Sys3 is 2 spins with J=1000. You can see that with J=0 the spectrum has a bunch of wiggles while J=10 and J=1000 are identical.
Perhaps I need to add in hyperfine interactions to see the effect of J, however the issue there is that my compounds are interacting via superexchange strongly enough(5-10K) that the hyperfine is washed out, and I can't estimate the hyperfine coupling from solution spectra because these are extended lattices which are either insoluble or the bonds to the copper are significantly different if they do dissolve. Of course I could try to dope them into a zinc lattice but I haven't started that process yet. Furthermore I have observed in some of my complexes very broad signals likely due to dipolar coupling, and thus the interplay between these interactions is what I am really interested in, but I was starting simple here, perhaps at my own peril.

Also, just so you know, I can easily simulate these spectra with g-strain and no interactions, however I am curious to see if I can fit with J and compare the results to our SQUID measurements, if not at X-band and room temperature at lower temperatures or at Q-band. Perhaps I need to be working at a much higher frequency for this to work, in any case, I really appreciate your interest in my issues and I hope to hear from you soon!

P.S. I am collecting single crystal data on these complexes currently, I didn't necessarily expect to be able to get all this info from powder spectra but I figured it would be worth giving it a shot. I don't have the ability to go much lower than 100K for the single crystal data collection but I can get to 77K for the powder data collection and I can do Q-band at room temperature.

Code: Select all

Sys.S=[1/2 1/2];
Sys.g=[2.05,2.1,2.2;2.05,2.1,2.2];
Sys.lw=1;
Sys.J=0;
Sys1.S=[1/2 1/2];
Sys1.g=[2.05,2.1,2.2;2.05,2.1,2.2];
Sys1.lw=1;
Sys1.J=10;
Exp.mwFreq=9.79;
Exp.CenterSweep=[350, 100];
Sys2.S=[1/2 1/2];
Sys2.g=[2.05,2.1,2.2;2.05,2.1,2.2];
Sys2.lw=1;
Sys2.J=1000;
Sys3.S=1/2;
Sys3.g=[2,2.2];
[x,y]=pepper(Sys, Exp);
[x1,y1]=pepper(Sys1, Exp);
[x2,y2]=pepper(Sys2,Exp);
plot(x,y,x1,y1,x2,y2);

[jmonroe]

Oops I have Sys3 as being axial, here is the rhombic equivalent

Code: Select all

Sys.S=[1/2 1/2];
Sys.g=[2.05,2.1,2.2;2.05,2.1,2.2];
Sys.lw=1;
Sys.J=0;
Sys1.S=[1/2 1/2];
Sys1.g=[2.05,2.1,2.2;2.05,2.1,2.2];
Sys1.lw=1;
Sys1.J=10;
Exp.mwFreq=9.79;
Exp.CenterSweep=[350, 100];
Sys2.S=[1/2 1/2];
Sys2.g=[2.05,2.1,2.2;2.05,2.1,2.2];
Sys2.lw=1;
Sys2.J=1000;
Sys3.S=1/2;
Sys3.g=[2.05,2.1,2.2;2.05,2.1,2.2];
[x,y]=pepper(Sys, Exp);
[x1,y1]=pepper(Sys1, Exp);
[x2,y2]=pepper(Sys2,Exp);
plot(x,y,x1,y1,x2,y2);

[Stefan Stoll]

There are two different things going on:

1. The fact that you see oscillatory behavior when J = 0 is indicative of EasySpin's trouble to deal with spin systems where the spins are actually not coupled. Set J to a small value (like 1e-3), and the spectrum will look correct.

2. Your expectation to see splittings is not correct. When the two spins are identical and isotropically coupled, then they behave as a perfect triplet and singlet, no matter how strong or weak J is. The singlet is EPR silent, and there are two degenerate transitions within the triplet, resulting in an EPR spectrum with a single line. You will get splittings as soon as you make the two spins non-equivalent. In that case, the most intuitive regime is the weak-coupling regime, where the J coupling between the spins is significantly smaller than the resonance frequency difference between the two spins. Then the splittings correspond to J.