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The search for quantum spin liquids—topological magnets with fractionalized excitations—has been a central theme in condensed matter and materials physics. Despite numerous theoretical proposals, connecting experiment with detailed theory exhibiting a robust quantum spin liquid has remained a central challenge. Here, focusing on the strongly spin-orbit coupled effectiveS = 1/2 pyrochlore magnet Ce₂Zr₂O₇, we analyze recent thermodynamic and neutron-scattering experiments, to identify a microscopic effective Hamiltonian through a combination of finite temperature Lanczos, Monte Carlo, and analytical spin dynamics calculations. Its parameter values suggest the existence of an exotic phase, aπ-flux U(1) quantum spin liquid. Intriguingly, the octupolar nature of the moments makes them less prone to be affected by magnetic disorder, while also hiding some otherwise characteristic signatures from neutrons, making this spin liquid arguably more stable than its more conventional counterparts.

The single-ion anisotropy and magnetic interactions in spin-ice systems give rise to unusual non-collinear spin textures, such as Pauling states and magnetic monopoles. The effective spin correlation strength (J_eff) determines the relative energies of the different spin-ice states. With this work, we display the capability of capacitive torque magnetometry in characterizing the magneto-chemical potential associated with monopole formation. We build a magnetic phase diagram of Ho₂Ti₂O₇, and show that the magneto-chemical potential depends on the spin sublattice (αorβ), i.e., the Pauling state, involved in the transition. Monte Carlo simulations using the dipolar-spin-ice Hamiltonian support our findings of a sublattice-dependent magneto-chemical potential, but the model underestimates theJ_efffor theβ-sublattice. Additional simulations, including next-nearest neighbor interactions (J₂), show that long-range exchange terms in the Hamiltonian are needed to describe the measurements. This demonstrates that torque magnetometry provides a sensitive test forJ_effand the spin-spin interactions that contribute to it.