Crystal field Hamiltonian (for orbital angular momenta)

H = ham_cf(Sys)
H = ham_cf(Sys,OAMs)
H = ham_cf(Sys,OAMs,'sparse')

This function computes the Hamiltonian, in MHz, for the crystal-field interactions of the orbital angular momenta (OAMs) in the spin system described by the structure Sys.

If the vector OAMs is given, the crystal field Hamiltonian of only the specified orbital angular momenta is returned (1 is the first OAM, 2 the second, etc.). Otherwise, all OAMs are included.

The crystal field is assumed to be expanded in terms of extended Stevens operators, with the linear-combination parameters in the spin system fields Sys.CF1, Sys.CF2, etc. Each of these fields must have 2k+1 elements for each OAM (with index q going from +k to -k), e.g. Sys.CF1 should have 3 elements. Alternatively, only one element can be given, which then corresponds to the q=0 element, all others being zero.

If 'sparse' is given as third argument, the Hamiltonian matrix is returned in sparse format instead of full format.

Here is a very simple example.

clear, clc
Sys.S = 1/2;    % spin-1/2
Sys.L = 1;      % and orbital angular momentum 1
Sys.soc = 20;   % spin-orbit coupling, MHz
Sys.CF1 = 100;  % rank-1 crystal field parameter, (k,q)=(1,0), in MHz

H = ham_cf(Sys)

H =
  100.0000         0         0         0         0         0
         0         0         0         0         0         0
         0         0 -100.0000         0         0         0
         0         0         0  100.0000         0         0
         0         0         0         0         0         0
         0         0         0         0         0 -100.0000

ham, ham_ee, ham_ez, ham_ezho, ham_hf, ham_nn, ham_nq, ham_nz, ham_oz, ham_so, ham_zf, zfsframes