Fragmented Spin Liquid and Shadow Pinch Points in Dipole-Octupole Pyrochlore Spin Systems

Abstract: We study the classical dipole-octupole pyrochlore spin systems in an external magnetic field along the $[111]$ direction. We identify an intermediate fragmented spin liquid phase that precedes full spin saturation, characterized by the coexistence of three phenomena: U(1) spin liquid on the Kagome planes, spontaneous $\mathbb{Z}_2$ symmetry breaking, and partial spin polarization from explicit symmetry breaking. We show that even without dipolar interactions, the dipolar components can form a spin liquid driven by the octupolar spin liquid. The physics manifests itself experimentally as shadow pinch points: low-intensity pinch points underlying the strong Bragg peaks. We discuss how these discoveries are directly relevant to various experiments on dipole-octupole pyrochlore materials, including neutron scattering, magnetization, and magnetostriction.