  We perform a comparative study for the magnetization dynamics within linear
response theory of one and two dimensional massive Dirac electrons, after
switching on either a real (hermitian) or an imaginary (non-hermitian) magnetic
field. While hermitian dc magnetic fields polarize the spins in the direction
of the external magnetic field, non-hermitian magnetic fields induce only off
diagonal response. An imaginary dc magnetic field perpendicular to the mass
term induces finite magnetization in the third direction only according to the
right hand rule. This can be understood by analyzing the non-hermitian equation
of motion of the spin, which becomes analogous to a classical particle in
crossed electric and magnetic fields. Therein, the spin expectation value, the
mass term and imaginary magnetic field play the role of the classical momentum,
magnetic and electric field, respectively. The latter two create a drift
velocity perpendicular to them, which gives rise to the off-diagonal component
of the dc spin susceptibility, similarly to how the Hall effect develops in the
classical description.
