Zero-flux or pi-flux quantum spin ice in cerium pyrochlores?
In plain words
Quantum spin ice comes in two versions, labeled zero-flux and pi-flux, that differ in how emergent charges feel the internal magnetic field. Which version each cerium compound realizes depends on the signs of its exchange couplings, which are still debated.
Precise statement
For $\mathrm{Ce_2Zr_2O_7}$, $\mathrm{Ce_2Sn_2O_7}$ and $\mathrm{Ce_2Hf_2O_7}$ described by the dipolar-octupolar Hamiltonian H = sum_<ij> [J_x tau^x_i tau^x_j + J_y tau^y_i tau^y_j + J_z tau^z_i tau^z_j + J_xz (tau^x_i tau^z_j + tau^z_i tau^x_j)], determine the exchange parameters and the sign of the dominant transverse coupling that fixes the zero-flux or $\pi$-flux $U(1)$ phase, and confirm it by the predicted spinon-continuum structure. An answer is the classification per compound with fitted parameters.
What would settle it
Global fits of neutron spectra, heat capacity and magnetization in field to the XYZ model, compared with the distinct spinon spectra of each flux phase.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Gao et al. (2025) classify $\mathrm{Ce_2Zr_2O_7}$ as $\pi$-flux; parameter fits differ across groups and compounds.
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