resfields_eig

Exact resonance fields (eigenfields) of a spin system.

Syntax
B = resfields_eig(Sys,Par)
B = resfields_eig(sys,Par,Opt)
[B,Int] = resfields_eig(...)
Description

Given a spin system Sys and a set of orientations Par.SampleFrame, resfields_eig computes exact resonance fields (so called eigenfields) for a cw EPR experiment.

Sys is a spin system structure.

Par is a structure containing fields for the experimental parameters.

mwFreq
Required parameter giving the spectrometer frequency in GHz.
SampleFrame

An Nx3 array that specifies the sample orientations for which the EPR spectrum should be computed. Each row of SampleFrame contains the three Euler rotation angles that transform the lab frame to the sample/crystal frame.

Exp.SampleFrame = [0 0 0];                   % sample/crystal frame aligned with lab frame
Exp.SampleFrame = [0 pi/2 0];                % sample/crystal frame tilted relative to lab frame
Exp.SampleFrame = [0 pi/2 pi/4];             % sample/crystal frame tilted relative to lab frame
Exp.SampleFrame = [0 0 0; 0 pi/2 pi/4];      % two samples/crystals
mwMode

Specifies the microwave excitation mode. Possible settings are

Exp.mwMode = 'perpendicular';  % default
Exp.mwMode = 'parallel';
Exp.mwMode = {k pol};

Resonator experiments:
For conventional experiments with linearly polarized microwave in a resonator, use 'perpendicular' (default) or 'parallel'. In the perpendicular mode, the microwave magnetic field B1 is oscillating along the laboratory x axis (xL), perpendicular to the external static magnetic field B0. In the parallel mode, it is oscillating along the laboratory z axis (zL), parallel to B0. The perpendicular mode is by far the most common.

Beam experiments:
For experiments with a microwave (or THz) beam, use Exp.mwMode = {k pol}. k specifies the propagation direction, in one of three possible ways: (i) a letter code for the direction, e.g. 'y', 'z', 'xy'; (ii) a 3-element cartesian vector, e.g. [0;1;0] specifies the lab y axis; (iii) two polar angles [phi_k theta_k] that specify the orientation. theta_k is the angle between the microwave propagation direction and the lab z axis, and phi_k is the angle between the lab x axis and the projection of the propagation vector onto the lab xy plane. For example, [pi/2 pi/2] gives the lab y axis.

For linearly polarized mw irradiation, additionally provide pol, the polarization angle of the radiation, in radians. To calculate the microwave propagation direction nk and the B1 direction nB1 from k and pol, use

k = 'y';   % propagation along y lab axis
pol = -pi/2; % B1 along x lab axis
[phi,theta] = vec2ang(k);  % convert to angles
[nB1,~,nk]  = erot([phi,theta,pol],'rows')

For unpolarized excitation, set pol='unpolarized'. For circularly polarized radiation, set pol='circular+' or pol='circular-', depending on the sense of rotation.

Range
2-element vector [Bmin Bmax]
If set, resfields_eig will only return eigenfields falling between Bmin and Bmax (both in mT).

The structure Opt contains computational options.

Freq2Field, 1 (default) or 0
Determines whether the frequency-to-field conversion factor is included in the line intensities of field-swept spectra. 1 indicates yes, 0 indicates no. The factor is the generalized 1/g Aasa-Vänngård factor. This setting is ignored for frequency-swept spectra.
Threshold
Relative threshold for eigenfields. Only eigenfields with a relative transition intensity above the threshold are returned. The relative intensity of the strongest transition is 1. The default value is 1e-4.

resfields_eig returns the resonance fields (mT) in B and, optionally, transition intensities (MHz^2/mT^2) in Int. The intensities returned are integrated over the plane normal to the external magnetic field direction if only two of the three Euler angles are specified in Ori (see above).

Examples

The resonance fields of an S=3/2 system with orthorhombic zero-field splitting for an arbitrary orientation are

B =
   59.5729
  123.0851
  148.9710
  253.3805
  387.0805
  512.8191

These values are exact within the numerical accuracy of MATLAB's generalised eigenproblem solver eig(A,B).

Algorithm

resfields_eig solves a generalised eigenproblem in Liouville space describing the fixed-frequency swept-field situation in cw EPR experiments. This approach was first described in R.L. Belford et al., J.Magn.Reson. 11, 251-265 (1973).

See also

pepper, resfields, resfields_perturb