In a spin ice, the magnetic moments on a pyrochlore lattice obey ice rules — two spins point in, two point out at each tetrahedron. The resulting state is a Coulomb phase: a liquid with algebraic correlations, emergent gauge fields, and deconfined monopole excitations that behave like magnetic charges. The Coulomb phase is topological — it cannot be smoothly connected to a trivially ordered state.
Pandey, Kundu, and Damle (arXiv 2602.23041, February 2026) show that when the effective spin is 3/2 instead of 1/2, the pyrochlore lattice supports two topologically distinct Coulomb phases separated by a first-order confinement transition. The distinction is in what can deconfine.
In the first phase, only charges that are multiples of three can exist as free excitations. A single charge, or a charge of two, is confined — the energetic cost of separating it from its anticharge grows linearly with distance, like quarks in QCD. The system is a Zā confined Coulomb liquid: it has the algebraic correlations and emergent gauge structure of a Coulomb phase, but with a restricted excitation spectrum.
In the second phase, all integer charges deconfine. Singles, doubles, triples — all can propagate freely through the lattice. This is the conventional Coulomb phase, familiar from spin-1/2 ice.
The transition between them is first-order. The polarization field — the coarse-grained variable describing the local spin configuration — has flux quantized in units of three in the confined phase, reflecting the Zā restriction. At the transition, this quantization relaxes, and the full integer spectrum becomes available.
The mechanism is the competition between antiferromagnetic exchange and single-ion anisotropy. The anisotropy comes from crystal field effects and spin-orbit coupling, which split the spin-3/2 manifold into states with different symmetries. When the anisotropy dominates, the ground state manifold has an internal Zā structure that imposes the charge restriction. When exchange dominates, the full spin-3/2 degree of freedom participates, and all charges deconfine.
The predicted transition temperature is approximately 1.42 times the anisotropy energy scale. Materials with appropriately tuned magnetic parameters — certain rare-earth pyrochlores with effective spin-3/2 moments — could exhibit both phases.
Two liquids, same lattice, same correlations, different rules about what's allowed to be free.