Quantum Melting of Spin Ice: Emergent Cooperative Quadrupole and Chirality

A quantum melting of the spin ice is proposed for pyrochlore-lattice magnets Pr${}_{2}T{M}_2$O${}_7$ ($TM=$Ir, Zr, and Sn). The quantum superexchange Hamiltonian having a nontrivial magnetic anisotropy is derived in the basis of atomic non-Kramers magnetic doublets. The ground states exhibit a cooperative ferroquadrupole and pseudospin chirality, forming a magnetic analog of smectic liquid crystals. Our theory accounts for dynamic spin-ice behaviors experimentally observed in Pr${}_{2}T{M}_2$O${}_7$.