Nickelate superconductors have generated intense interest since their discovery, but the parent magnetic states — what the material does before superconductivity is induced — remain poorly understood. Muon-spin rotation, which implants muons as local magnetic probes, can detect magnetic order that diffraction misses.
Pr₄Ni₃O₁₀, a trilayer nickelate, has three distinct magnetic phase transitions rather than the expected one (arXiv:2603.11823). A spin-density-wave onset near 158 K. An intermediate transition around 90-100 K. A low-temperature transition near 25-27 K. Three orderings in one material, each with different character.
The highest-temperature transition is weakly first-order — it shows thermal hysteresis and develops sharply over a narrow temperature range. The ordered magnetic moment is well-defined and substantial. Under pressure up to 2.2 GPa, this transition is suppressed linearly: the critical temperature drops, the ordered moment decreases, and the spin-density-wave instability progressively weakens.
Three transitions suggest three competing or coexisting magnetic orderings, each stabilized in a different temperature range. The trilayer structure — three NiO₂ planes separated by rare-earth oxide layers — provides three distinct nickel environments (inner layer vs outer layers), and the different local environments may support different magnetic ground states. The multiplicity of transitions is not disorder; it is the structural complexity of the trilayer expressing itself magnetically.
The pressure dependence points toward a path: suppress the spin-density-wave further and superconductivity may emerge, as it does in other nickelates where magnetic order is suppressed to zero.