Exact resonance fields (eigenfields) of a spin system.
B = resfields_eig(Sys,Par) B = resfields_eig(sys,Par,Opt) [B,Int] = resfields_eig(...)
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
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
[Bmin Bmax]
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
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
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).
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)
.
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).
pepper, resfields, resfields_perturb