  We theoretically investigate the magnetic properties and nonequilibrium
dynamics of two interacting ultracold polar and paramagnetic molecules in a
one-dimensional harmonic trap in external electric and magnetic fields. The
molecules interact via a multichannel two-body contact potential, incorporating
the short-range anisotropy of intermolecular interactions. We show that various
magnetization states arise from the interplay of the molecular interactions,
electronic spins, dipole moments, rotational structures, external fields, and
spin-rotation coupling. The rich magnetization diagrams depend primarily on the
anisotropy of the intermolecular interaction and the spin-rotation coupling.
These specific molecular properties are challenging to calculate or measure.
Therefore, we propose the quench dynamics experiments for extracting them from
observing the time evolution of the analyzed system. Our results indicate the
possibility of controlling the molecular few-body magnetization with the
external electric field and pave the way towards studying the magnetization of
ultracold molecules trapped in optical tweezers or optical lattices and their
application in quantum simulation of molecular multichannel many-body
Hamiltonians and quantum information storing.
