  A two-dimensional Pauli Hamiltonian describing the interaction of a neutral
spin-1/2 particle with a magnetic field having axial and second order
symmetries, is considered. After separation of variables, the one-dimensional
matrix Hamiltonian is analyzed from the point of view of supersymmetric quantum
mechanics. Attention is paid to the discrete symmetries of the Hamiltonian and
also to the Hamiltonian hierarchies generated by intertwining operators. The
spectrum is studied by means of the associated matrix shape-invariance. The
relation between the intertwining operators and the second order symmetries is
established and the full set of ladder operators that complete the dynamical
algebra is constructed.
