Hi everyone,
I've been given a copper complex to measure, which is thought to be an antiferromagnetically coupled (AFC) copper(II) with a ligand radical. Although the AFC ground state should be EPR-silent, the powder has an EPR signal. To better understand the situation, I'd like to study the signal as a function of temperature. I've seen a few papers where they can fit the integrated EPR intensity as a function of temperature to the J value. What is the best way of modelling such a system in EasySpin?
I'm reading this paper on a related AFC copper-copper system: https://doi.org/10.1039/C4DT03322A
Figure 4 shows that the EPR intensity as a function of T peaks around 35K, then declines all the way up to near-RT.
I tried to reproduce the fits they show in figure 3 using their spin-Hamiltonian parameters in pepper while varying Exp.Temperature, i.e.,
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Sys.S = [1/2, 1/2]; %two coppers
Sys.Nucs = ['Cu,Cu']; %two coppers
Sys.g = [2.068 2.091 2.165; 2.068 2.091 2.165]; %both spins with the same g-tensor
Sys.A = [0 0 0 0 0 0; 0 0 0 0 0 0]; %They didn't model any hyperfine coupling
Sys.J = 1*unitconvert(26,'cm^-1->MHz')
D = unitconvert(86E-4,'cm^-1->MHz')
E = -1*unitconvert(48E-4,'cm^-1->MHz')but I find that the intensity just increases with T, but never peaks and then decreases as in their fig. 3 and 4. So I read on, and they say "we assumed isotropic ΔH, constant at low T but increasing linearly with T above 40K", so it looks like they modelled the intensity peak by assuming that the decreasing signal after the peak is just due to isotropic line-broadening, which they claim increases linearly with T. Adding in Sys.lwpp, for example, with an increasing value as a function of T, I am able to reproduce something similar to their result in fig. 3. Is this reasonable?
From my understanding of AFC, what is going on here is that you have
Near 0K, almost all the molecules are in their EPR-silent S = 0 state
As T increases, some of the S = 1 state gets populated, and the EPR signal gains intensity. The temperature behaviour here depends on the value of J.
As T continues to increase, the occupancy of the S = 1 state continues to increase, but the parallel state of the Zeeman splitting begins to get more populated, so the signal gets weaker. I guess this is seen in the form of line-broadening.
Is this the correct interpretation?
It seems like the choice to have line-broadening increase linearly after 40K is kind of arbitrary. They also say that the EPR intensity-vs-T peak is of an "antiferromagnetically coupled binuclear copper compound" is expected to be "close in T units" to " the exchange interaction parameter J0". How can that be the case if we also have the line-broadening-vs-T issue at play? Presumably, T could increase above J, but maybe the intensity is already beginning to decrease. Is there a way to model this EPR intensity-vs-T peaking behaviour without invoking the arbitrary assumption about line-broadening? How should I know where to expect the signal maximum? Is this behaviour related to the Néel temperature, or does that not apply in strong, intramolecular exchange coupling?