Distance between two Spins

[sg_epr]

I am trying to calculate distance between two exchanged coupled S = 1 systems using pepper. Since it is a powder sample, I am really confused about how to use exchange parameters in 2X2 matrix form to calculate the distance between the spins. Not sure about how to corelate between pepper's frame of reference and my molecule's unit cell. Would appreciate any suggestion on it. Thanks

[thanasis]

What are your assumptions? If you know/think that the interactions are dipolar in nature, then you have relations relating coupling energies with distance, since the interactions are assumed to be through space.

However, if you are considering a superexchange mechanism, then you cannot directly extract distances. You will have to go through complicated and imprecise magnetostructural correlations to maybe get an idea.

[sg_epr]

Yes, i am expecting the interaction to be dipolar in nature. Though, not sure how to use eeD matrix to determine R using number of formulas given in different references suggesting D ~ 1/R3.

[thanasis]

To get a quick and dirty estimate of the dipolar exchange interaction energy, you can use the expression Sys.ee = Jdip*[1 1 -2]. There, you can vary Jdip manually to get something close to your spectrum and then convert to cm-1 or MHz through the relations Jdip = 0.433/r^3 or 12993/r^3, respectively.

If you want to fit your Jdip, you'll have to define a Sys.Jdip = Jdip and write a custom function that calculates the interaction.

Finally, if you want more precise directional parameters, there are analytical equations of varying complexities that you can use in your custom function (e.g. see reference in post viewtopic.php?f=3&t=328&p=1010#p1010).

[sg_epr]

Dear thanasis, Thanks for your response. I went through the links you gave, but my system is a rhombic one with Jdip being a traceless matrix (eeD not of the form [1 1 -2] but [a b -a-b]). How can I use this matrix to determine the R, in the formulas given by you (Jdip = 0.433/r3)? Thanks

[thanasis]

Now I need to take a step back and understand the physics of your problem...

-Spin-spin interactions are described by 3x3 tensors. What exactly is the 2x2 traceless [a b -a -b] matrix?
-I believe (Stefan please correct me if I misunderstood) that the sys.eeD matrix is by definition traceless (http://easyspin.org/documentation/spinsystem.html). I haven't used it (I always use the full sys.ee matrix), but I believe that the [-1 -1 2] matrix is actually made up of the diagonal elements of the 3x3 dipolar tensor, assuming collinear local g1 and g2 tensors. So, I do not think you need to worry about it being traceless, it already is.
-What is the source of the rhombicity? Do the S=1 spins (Ni(II) maybe?) have inherent single-ion anisotropy? Is it due to the dipolar induced anisotropy?

[sg_epr]

Sorry, for the typo creating the confusion, eeD it is a 3X3 matrix not 2X2 matrix, with diagonal elements to be a, b and -a-b. The point I am not sure about is whether the first two elements in eeD should be equal or not. Since in literature (EasySpin documentation or otherwise) I could not find any compliance for first two elements to be equal, I decided to vary them with respect to each other (so my eeD has elements a, b and -a-b rather than a a -2a) and intuited that if indeed they should be equal, I would get roughly similar values after good fitting is achieved. I thought more so because my both S = 1 systems have unequal g values (Gxx, Gyy Gzz not same as gxx gyy gzz) due to their crystallographic in-equivalence. Now since I am getting significantly different values of a & b after fitting, I am wondering if there is any constraint over first two elements of eeD to be equal. Will appreciate any clarification on it.Thanks

[thanasis]

This is clearer... As per your model, in the case of two similar spins with collinear g tensors, a = 1, b = 1 and -a-b = -2 (spins are parallel), or a = -1, b = -1 and -a-b = 2 (spins antiparallel, e.g. when there an inversion center between them). By definition the sys.eeD tensor is traceless as you require, so no need to worry about that.

As I said, this is good for a simple case. For a more complicated situation (non-collinear g tensors, i.e. non-zero η and ξ angles), go back to the paper I cited in my other post (there are other even more precise models for non-similar spins, with more elaborate equations). You will need to make a custom function where you will reconstruct the 3x3 matrix according to the equations they mention and use that matrix as sys.ee.

[sg_epr]

Actually I am considering non-identical g tensors for two centers due to the different crystal fields at them which may arise due to crystallographically non-identical positions. This non-identical positions may be anything depending upon the crystallographic details. Now, this brings up my question, in this uncertain conditions can we be sure of eeD being [a, a, -2a] putting constraint on first two elements to be equal. Instead, can I consider eeD to be [a b -a-b] and give the system a freedom to acquire whether a and b acquire similar values or not (magnitude as well as sign) ? I went through a number of references which clearly suggest that D is a traceless symmetric tensor but nowhere I could find a reason of why / in which circumstances first two elements needs to be fixed equal to each other.
Regarding the collinearity of g tensor, I assume that if I am not mentioning any preferred coordination axes in my code, both the g tensors are represented in same reference axes and hence collinear.

[thanasis]

In that case, the "quick n dirty" approach won't do as the tensor will no longer be diagonal. For similar ions the tensor will be symmetric (Jij = Jji) and you'll have 6 independent elements, but for non-similar spins, this won't hold and you will need all its 9 elements to do a proper calculation.

In either case you will need to choose a model and provide your sys.ee with the full analytical equations for each of the elements.