eigfields
Introduced in 1.3
Synopsis

Exact resonance fields (eigenfields) of a spin system.

B = eigfields(Sys,Par,Ori)
B = eigfields(sys,Par,Ori,Opt)
[B,Int] = eigfields(...)
Description

Given a spin system Sys and a set of orientations Ori, eigfields 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.
Detection 'perpendicular' (default) or 'parallel'
Determines the cw EPR detection mode. In the perpendicular mode, the excitation and detection mw fields are along the laboratory x axis, in the parallel mode they are along the z axis, parallel to the external static field. The perpendicular detection mode is the most common, and it is the default here.
Range 2-element vector [Bmin Bmax]
If set, eigfields will only return eigenfields falling between Bmin and Bmax (both in mT).

Ori gives a list of orientations for which resonance fields should be computed. It can be either a 2xn or a 3xn array, giving either two (φ θ) or three (φ θ, χ) Euler angles in radians to describe each orientation.

φ, in the first row, is the angle between the x axis and the xy plan projection of the orientation of the external field in the molecular frame of the spin system. θ, in the second row, is the angle at which the external field is off the z axis of the molecular frame. The optional χ, in the third row, specifies the third Euler angle and fixes the x axis of the laboratory in the molecular frame.

Altogether, these three angles define the relative orientation between the molecular frame and the laboratory frame. The external field is along the lab z axis, and the excitation/detection field is along the lab x axis. Resonance fields depend only on the first two angles, intensities also on the third.

If the third angle is not given, intensities are integrated over all possible values of χ.

The structure Opt contains computational options.

[eqn]
Threshold Relative threshold for eigenfields. Only eigenfields with a relative transition intensity above the threshold are returned. Works only if transition intensities are computed, i.e. if two output arguments are requested. The relative intensity of the strongest transition is 1.

eigfields 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

eigfields 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