This user guide explains how to simulate rapid-scan EPR signals using EasySpin's function blochsteady. It also shows how to use rapidscan2spc to convert a rapid-scan time domain signal into its corresponding EPR spectrum.

This user guide contains the following topics:

• Time-domain cw EPR signal
• Some options
• Field sweeps
• Powder averages
• Converting rapid-scan signal to spectrum

EasySpin can calculate the periodic time-dependent response of a simple spin-1/2 to the excitation fields in a cw EPR experiment: an oscillating microwave field of amplitude B₁ perpendicular to the applied magnetic field B₀, which is modulated with peak-to-peak amplitude B_m.

The function that calculates this response is blochsteady. It is called with many input arguments.

blochsteady(g,T1,T2,deltaB0,B1,ModAmp,ModFreq)

The first three input parameters contain the essentials about the spin-1/2: its g factor in g, its longitudinal relaxation time (in μs) in T1, and its transverse relaxation time (in μs) in T2. These three spin system parameters are sufficient to calculate the response. blochsteady currently does not support any more complicated spin systems beyond a spin-1/2. Some exemplary values are:

g = 2;
T1 = 4;    % microseconds
T2 = 0.5;  % microseconds

The next four input parameters give the experimental parameters. deltaB1 is the field offset from the resonance frequency of the spin, in mT. Setting it to zero sets the field on-resonance with the spin. B1 is the microwave magnetic field amplitude at the sample, in mT. The last two parameters give the peak-to-peak modulation amplitude (ModAmp, in mT) and the modulation frequency (ModFreq, in kHz) of the applied field modulation along B₀. Again, here are some exemplary values:

B1 = 0.05;      % mT
deltaB0 = 0;    % mT
ModAmp = 0.5;   % mT
ModFreq = 100;  % kHz   

With these inputs, blochsteady calculates one period of the periodic steady-state response of the magnetic moment of the spin. You can call blochsteady without any outputs:

blochsteady(g,T1,T2,deltaB0,B1,ModAmp,ModFreq);

Then it will plot the calculated results. Or you can ask for up to four outputs, which will give the time axis and the three components of the time-dependent magnetization vector. For example, to plot the absorption (My, component of the magnetic moment out of phase with the microwave) and the dispersion (Mx, component of the magnetic moment in phase with the microwave), use

[t,Mx,My,Mz] = blochsteady(g,T1,T2,deltaB0,B1,ModAmp,ModFreq);
plot(t,My,t,Mx);

blochsteady can take one more input argument, a structure. In it, you can set the number of points you want to have in the time-domain signal:

Opt.nPoints = 1000;   % number of points
blochsteady(g,T1,T2,deltaB0,B1,ModAmp,ModFreq,Opt);

There are settings for the solving algorithm, which runs in the frequency domain: Opt.kmax can be used to manually specify the maximum Fourier order used in the calculation. Normally, there is no need to specify this, since an optimal value for this is determined automatically. Opt.Method can be used to select the method for the construction of the time-domain signal. Except for speed, this setting has no effect on the final outcome.

Opt.kmax = 200;      % the higher the better (but also slower)
Opt.Method = 'fft';  % alternative: 'td', which is slower

blochsteady does not have built-in capabilities for a field sweep. You can set one up using a for loop. Here is a brief example, using the same inputs as above:

deltaB0 = linspace(-1,1)*2;  % range of field offsets, mT
for b = 1:numel(deltaB0)
  [t,My(:,b)] = blochsteady(g,T1,T2,deltaB0(b),B1,ModAmp,ModFreq);
end

This gives a two-dimensional array My. One way of plotting it is as follows:

pcolor(deltaB0,t,My);
shading flat
xlabel('field offset (mT)');
ylabel('time (\mus)');

Let's take a nitroxide as an example. First, simulate the powder spectrum, without field modulation

Nx.g = [2.008 2.006 2.002];
Nx.Nucs = '14N';
Nx.A = [20 20 90];   % MHz
Nx.lwpp = 0.2;       % mT
Exp.mwFreq = 9.5;    % GHz
Exp.Harmonic = 0;    % no field modulation!
Exp.Range = [333 345];   % mT
[B,spc] = pepper(Nx,Exp);

Next, define the field offset range and all the other parameters needed for the rapid-scan signal.

DeltaB0 = B-mean(B); % range of field offsets, mT

T1 = 1;    % microseconds
T2 = 0.2;  % microseconds
B1 = 0.01; % microwave field amplitude, mT
Bmpp = 7;  % peak-to-peak modulation amplitude, mT
fm = 100;  % modulation frequency, kHz

Options.nPoints = 4000; % lots of points due to the large modulation amplitude

Now, loop over the field offset range, calculate the time-domain signals for each field value, and add them up using the spectral intensity as weight.

spc_rs = 0;
for k = 1:numel(spc)
  [t,td] = blochsteady(2,T1,T2,DeltaB0(k),B1,Bmpp,fm,Options);
  spc_rs = spc_rs + td*spc(k);
end

Finally, we can plot the result:

plot(t,spc_rs);
xlabel('time (\mus)');

To convert an experimental or simulated rapid-scan time domain signal to its corresponding spectrum, use the function rapidscan2spc. Here is a simple example.

Mxy = -Mx + 1i*My;     % dispersion and absorption
ModAmp = 1;            % modulation amplitude, in mT
ModFreq = 50;          % modulation frequency, in kHz
g = 2;                 % g value for frequency/field conversions
[B,spc] = rapidscan2spc(Mxy,ModAmp,ModFreq,g);
plot(B,spc);

The input time domain signal must contain both the dispersion (real part) and the absorption (imaginary part) for this to work.