  The interplay of quantum spin liquids with itinerant conduction electrons is
of crucial interest for understanding layered structures composed of frustrated
magnet and metal monolayers. Using parton-mean-field theory, we here
demonstrate that a type-II heavy Fermi liquid, which is characterized by a
vortex lattice in the slave boson condensate, can occur in the vicinity of the
quantum phase transition separating fractionalized and heavy Fermi liquid
phases. The magnetic flux threading each such vortex is about $ v_f/ 137 c$
times smaller than the magnetic flux threading vortices in type-II
superconductors, where $v_f$ is the speed of magnetic excitations and $c$ the
speed of light. This makes a magnetic observation of this effect challenging.
We propose scanning tunneling spectroscopy instead and investigate its
signatures. If a type-II heavy Fermi liquid is cooled into a type-II
superconductor, vortices in the slave boson condensate and in the
superconducting condensate mutually attract. We argue that the type-II heavy
Fermi liquid thereby provides a compelling explanation for the magnetic memory
observed recently [Persky \textit{et al.}, Nature \textbf{609}, 692 (2022)] in
thermal cycles of 4Hb-TaS$_2$.
