  Time crystal is defined as a phase of matter spontaneously exhibiting a
periodicity in time. Previous studies focused on discrete quantum time crystals
under periodic drive. Here, we propose a time crystal model based on a
levitated charged nanoparticle in a static magnetic field without drive. Both
the classical time crystal in thermal equilibrium and the quantum time crystal
in the ground state can emerge in the spin rotational mode, under the strong
magnetic field or the large charge-to-mass ratio limit. Besides, for the first
time, the \emph{time polycrystal} is defined and naturally appears in this
model. Our model paves a way for realizing time crystals in thermal
equilibrium.
