Magnetization amplification in interlayer superconductivity*

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 [1]. Here we provide a possible mechanism for this observation by studying the magnetic and electronic properties of 4Hb-TaS$_2$. We discuss the criterion for a vanishingly small magnetization in the normal state in terms of the spin and orbital magnetizations. Based on 4Hb-TaS$_2$'s centrosymmetry and Fermi surface structure, we propose a simple mechanism that gives rise to the experimentally observed magnetic memory in the 4Hb-TaS$_2$ superconducting state: ferromagnetism mediated interlayer superconductivity that leads to amplified magnetization in the superconducting state. We discuss how this superconducting state can be probed experimentally in terms of spin polarized superconducting vortices.