Order out of a Coulomb phase and Higgs transtion: frustrated transverse interactions of Nd2Zr2O7

Abstract: The pyrochlore material Nd$2$Zr$_2$O$_7$ with an "all-in-all-out" (AIAO) magnetic order shows novel quantum moment fragmentation with gapped flat dynamical spin ice modes. The parameterized spin Hamiltonian with a dominant frustrated ferromagnetic transverse term reveals a proximity to a U(1) spin liquid. Here we study magnetic excitations of Nd$_2$Zr$_2$O$_7$ above the ordering temperature ($T\text{N}$) using high-energy-resolution inelastic neutron scattering. We find strong spin ice correlations at zero energy with the disappearance of gapped magnon excitations of the AIAO order. It seems that the gap to the dynamical spin ice closes above $T_\text{N}$ and the system enters a quantum spin ice state competing with and suppressing the AIAO order. Classical Monte Carlo, molecular dynamics and quantum boson calculations support the existence of a Coulombic phase above $T_\text{N}$. Our findings relate the magnetic ordering of Nd$_2$Zr$_2$O$_7$ with the Higgs mechanism and provide explanations for several previously reported experimental features.