  A recent experiment on the bulk compound 4Hb-TaS$_2$ reveals an unusual
time-reversal symmetry-breaking superconducting state that possesses a magnetic
memory not manifest in the normal state. Here we provide a mechanism for this
observation by studying the magnetic and electronic properties of 4Hb-TaS$_2$.
We discuss the criterion for a small magnetization in the normal state in terms
of spin and orbital magnetizations. Based on an analysis of lattice symmetry
and Fermi surface structure, we propose that 4Hb-TaS$_2$ realizes
superconductivity in the interlayer, equal-spin channel with a gap function
whose phase winds along the Fermi surface by an integer multiple of $6\pi$. The
enhancement of the magnetization in the superconducting state compared to the
normal state can be explained if the state with a gap winding of $6\pi$ is
realized, accounting for the observed magnetic memory. We discuss how this
superconducting state can be probed experimentally by spin-polarized scanning
tunneling microscopy.
