Cs₂RuO₄

Chemical formula:

Cs₂RuO₄

Lattice type:

Orthorhombic, space group Pnma

How to grow:

Self-flux method

Magnetic model:

S = 1 Heisenberg antiferromagnet with orthogonal sets of single-ion easy-plane anisotropies

Why is it cool:

A unique example of a continuous spin-flop transition

Spin-flop transitions are notoriously first order: when the field along the easy axis reaches a critical value, the staggered magnetization of an antiferromagnet abruptly jumps into the perpendicular plane. Cs₂RuO₄ is the rare exception where this reorientation is continuous, a genuine quantum critical point hidden inside the ordered phase [1]. The crystal structure is the same as in Cs₂CoBr₄, but the interaction hierarchy is entirely different: the S = 1 moments of Ru⁶⁺ are coupled into a genuinely three-dimensional network, as our neutron spectroscopy directly shows. The key ingredient is single-ion anisotropy. The strongest interactions connect ions whose local easy planes are nearly orthogonal to one another, so no spin arrangement can satisfy the anisotropy on all sites at once. When the field is applied along the one direction shared by the alternating easy planes, this built-in frustration converts the usual first-order flop into a continuous transition, as simulations of a minimal chain model with orthogonal anisotropy planes confirm [1].

Left: representative inelastic neutron scattering spectra of Cs₂RuO₄. Right: simulated magnetization (top) and staggered magnetization (bottom) for a minimal chain model connecting near-orthogonal single-ion anisotropy planes; the order parameter vanishes continuously at the spin-flop field.

• [1] S. D. Nabi, M. Zhu, K. Yu. Povarov, D. G. Mazzone, J. Lass, Y. Wu, Z. Yan, S. Gvasaliya, A. Zheludev, Spin-flop-like transition as quantum critical point in Cs₂RuO₄ , Phys. Rev. B 112, 134436 (2025); arXiv:2507.19853.