Zero field splitting E>D/3 again

[yvesjour]

In a previous post of 18 December 2020 I pointed out that esfit resulted in values of E>D/3 which corresponds to a principal axis error of the D-tensor. Stefan Stoll told me that this was a current limitation of the program and that I could recalculate the principal values of the tensor which I did.
I have the same problem again to simulate a rhombic S=3/2 spectrum with a large value of D=9.9 cm-1 (magnetic measurements). I can only determine in this case the E/D ratio and the best fit gives E/D=0.3478. When I recalculate the D values I find D=-10.11 cm-1.If I run esfit again with this new value of D I find a ratio E/D=0.3503.
In short I am going round in circles and I would like to have a solution because I cannot publish a simulation with a value of E>D/3. If I block the E/D ratio at 0.33333 and only determine the g values, the simulation is less good

best regards

Yves

[Stefan Stoll]

I suggest to take the D and E values from the best fit and then convert them to the conventional frame using zfsframes. Let's say the fit results in D=1.2 (in some units) and E/D = 0.4. Then the principal values of the D tensor are

Code: Select all

D = 1.2;
EoD = 0.4;
Dpv = [-1/3+EoD, -1/3-EoD, 2/3]*D

Using zfsframes you can now look at the D and E values for all possible permutations of the principal axes:

Code: Select all

zfsframes(Dpv)

This gives

Code: Select all

==================================================================
D tensor in various axis system conventions
==================================================================
Principal values (PVs) of D tensor in input order:
  D1 = +0.08     D2 = -0.88     D3 = +0.8
This D tensor is traceless (sum of PVs is zero).
This D tensor is neither exactly axial nor exactly orthorhombic.
Principal axis system conventions:
  Poole 1974:    |Dz|>=|Dx|>=|Dy|    (used for organic triplets)
  Blumberg 1967: |Dz|>=|Dy|>=|Dx|    (used for transition metals)
  (for references see documentation)
Computation of D and E:
  D = 3/2*Dz      E = (Dx-Dy)/2
  Dx = -D/3+E     Dy = -D/3-E        Dz = 2/3*D
D and E in all possible principal axis systems:
  123->xyz:  D = +1.200    E = +0.480    E/D = +0.40    
  132->xyz:  D = -1.320    E = -0.360    E/D = +0.27    Blumberg 
  213->xyz:  D = +1.200    E = -0.480    E/D = -0.40    
  231->xyz:  D = +0.120    E = -0.840    E/D = -7.00    
  312->xyz:  D = -1.320    E = +0.360    E/D = -0.27    Poole 
  321->xyz:  D = +0.120    E = +0.840    E/D = +7.00    
The Blumberg convention is the recommended one.

This shows that you can get the Blumberg convention (0=<E/D=<1/3) if you swap the second and the third axis (132->xyz). You can verify this by calculating D and E from the principal values:

Code: Select all

Dpv_ = Dpv([1 3 2]);   % swap axes
D_ = 3/2*Dpv_(3)
E_ = (Dpv_(1)-Dpv_(2))/2
E_/D_

which gives

Code: Select all

D_ =
   -1.3200
E_ =
   -0.3600
ans =
    0.2727

All the above tensors are equivalent, and using any of them in a simulation will give the same spectrum. Be aware though that you might need to add DFrame if you swap axes and if there are other tensors in the system.

[yvesjour]

Hello
Thank you for these long explanations, I did not know the zfsframe function. However if the Blumberg convention gives me effectively the same spectrum with a ratio E/D <1/3 these new values of D and E do not give me a good simulation of the magnetic data. As the best fit from esfit gives a value of E/D very close to 1/3 I locked the E/D ratio at 1/3 and only optimised the values of the g tensor.
I am really grateful to you for spending so much time answering questions in the forum when you have your own research to do at the University

[Stefan Stoll]

Please post a self-contained minimal script that demonstrates the problem you are encountering, so we can look into this.