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A spin-freezing perspective on cuprates

The high-temperature superconducting state in cuprates appears if charge carriers are doped into a Mott insulating parent compound. An unresolved puzzle is the unconventional nature of the normal state above the superconducting dome, and its connection to the superconducting instability. At weak hole-doping, a "pseudo-gap" metal state with signatures of time-reversal symmetry breaking is observed, which near optimal doping changes into a "strange metal" with non-Fermi liquid properties. Qualitatively similar phase diagrams are found in multi-orbital systems, such as pnictides, where the unconventional metal states arise from a Hund coupling induced spin-freezing. Here, we show that the relevant model for cuprates, the single-orbital Hubbard model on the square lattice, can be mapped onto an effective multi-orbital problem with strong ferromagnetic Hund coupling. The spin-freezing physics of this multi-orbital system explains the phenomenology of cuprates, including the pseudo-gap, the strange metal, and the d-wave superconducting instability. Our analysis suggests that spin-freezing is the universal mechanism which controls the properties of unconventional superconductors.