Spin ice, monopoles and quantum spin ice

5 problems

• Does classical spin ice $\mathrm{Dy_2Ti_2O_7}$ order or keep its Pauling entropy?

  Contested

  Ice-rule states are so numerous that spin ice keeps a leftover entropy at low temperature, as water ice does. Long-range dipolar forces predict an ordered state below about 0.2 K, but experiments struggle to reach equilibrium there.

• Has emergent quantum electrodynamics been observed in a quantum spin ice?

  Partially resolved

  Quantum spin ice should host three kinds of emergent particles: photons, electric-like spinons and magnetic monopoles. Cerium pyrochlores such as $\mathrm{Ce_2Zr_2O_7}$ show signs of these, but alternative explanations are not fully excluded.

• Origin of anomalous magnetic noise from monopoles in $\mathrm{Dy_2Ti_2O_7}$

  Partially resolved

  Magnetization noise in spin ice, produced by moving monopoles, does not follow a simple random-walk picture. Its spectrum and slow relaxation point to constrained monopole motion, but a full quantitative account is lacking.

• Measure the emergent-photon $T^3$ heat capacity and speed in quantum spin ice

  Open

  Emergent photons should add a heat capacity growing as the cube of temperature, like lattice vibrations, with a size fixed by the photon speed. Measuring it and matching the speed predicted from the measured interactions would be a sharp test.

• Zero-flux or pi-flux quantum spin ice in cerium pyrochlores?

  Contested

  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.