# Spin-polarized systems

EasySpin can simulate some spin-polarized systems such as triplets. Depending on the mechanism of spin polarization, you need to use different approaches.

Although the first two sections focus on triplets, the methods can easily be extended to spin-polarized states of spins with higher multiplicity.

Inter-system crossing (ISC) triplets

To simulate the EPR spectrum of a triplet generated by inter-system crossing from a singlet state, EasySpin needs information about how ISC populated the zero-field triplet states. You can provide this information in the field `Exp.Temperature`.

`Exp.Temperature` should contain a list of populations, one entry for each state. The populations apply to the zero-field states in increasing energy order. For example, `Exp.Temperature = [0.1, 1, 0.2]` indicates a population of 0.1 of the lowest zero-field state, a population of 1 of the middle-energy zero-field state, and a population of 0.2 of the highest-energy zero-field state. The populations do not have to add up to 1.

The zero-field states in a triplet are usually denoted Tx, Ty, Tz. Their energy order depends on the signs of the zero-field splitting parameters D and E. Be careful in determining their order correctly when using `Exp.Temperature` to simulate spectra from the literature, or when interpreting results from least-squares fitting.

Here is a full example of a triplet generated by ISC from a singlet

```clear

T.S = 1;
T.D = [500 100];   % MHz
T.lwpp = 1;
Exp.mwFreq = 9.5;
Exp.Range = [310 370];
Exp.Harmonic = 0;     % no field modulation
Exp.Temperature = [0.1 1 0.2]; % zero-field populations

pepper(T,Exp);
```

The shape of the EPR spectrum only depends on the polarizations of the transitions, i.e. only on the differences of the populations in `Exp.Temperature`. Adding any constant to all three numbers will not affect the shape of spectrum. It will, however, affect the overall intensity of the simulated spectrum, since EasySpin scales the spectrum to the total population (sum over all numbers in `Exp.Temperature`).

EasySpin can handle ISC-polarized spins of higher multiplicity as well. For example,to simulate spectra from an ISC-generated quartet state, provide 4 numbers in `Exp.Temperature`.

Recombination triplets

To simulate the spin-polarized EPR spectrum of a triplet generated by recombination of two radicals, use the following two-step procedure. First, simulate the spectrum of the unpolarized triplet and ask EasySpin to return the two transitions separately. Second, combine the transitions using weighing factors corresponding to the polarizations of the transitions.

Here is an example. First, we set up the triplet and simulate its spectrum, without any spin polarization. With `Opt.Output`, request that `pepper` returns the transitions separately.

```clear
T.S = 1;
T.D = 500;   % MHz
T.lwpp = 1;
Exp.mwFreq = 9.5;
Exp.Range = [310 370];
Exp.Harmonic = 0;                % no field modulation
Opt.Output = 'separate';         % separate transitions!
[B,spcsep,tr] = pepper(T,Exp,Opt);
```

`tr` contains the list of transitions, with one row for each transition. `spc` contains the spectra of the two transitions separately, again one per row. Next, combine these two subspectra using differences in populations:

```Popul = [0 1 0];                                 % vector of populations
Pola = [Popul(2)-Popul(1), Popul(3)-Popul(2)];   % polarizations
spc = Pola(1)*spcsep(1,:) + Pola(2)*spcsep(2,:); % polarized spectrum
plot(B,spc)
```