Magnetization curve of spin ice in a [111] magnetic field

Spin ice in a magnetic field in the [111] direction displays two magnetization plateaus: one at saturation and an intermediate one with finite entropy. We study the crossovers between the different regimes from a point of view of (entropically) interacting defects. We develop an analytical theory for the nearest-neighbor spin ice model, which covers most of the magnetization curve. We find that the entropy is nonmonotonic, exhibiting a giant spike between the two plateaus. This regime is described by a monomer-dimer model with tunable fugacities. At low fields, we develop an RG treatment for the extended string defects, and we compare our results to extensive Monte Carlo simulations. We address the implications of our results for cooling by adiabatic (de)magnetization.

Figure 1

Properties of spin-ice as the [111] magnetic field is varied. These curves are for illustration and do not show actual numerical or experimental data. We have indicated the regions where various analytic approaches discussed in the text apply.

Figure 2

The pyrochlore lattice of corner-sharing tetrahedra.

Figure 3

(Color online) A single tetrahedron inscribed in a cube. The easy axes of the pyrochlore lattice (or $⟨111⟩$ axes), ${\widehat{\mathbf{d}}}_{\kappa }$, are indicated by the short-dashed lines.

Figure 4

The magnetization from Monte Carlo simulations.

Figure 5

The basic coarse-graining step in our RG transformation.

Figure 6

(Color online) The crossover between exponents.

Figure 7

(Color online) The magnetization (top) and the entropy (bottom) around the transition between the plateaux. The simple Bethe approximation is compared to the Monte Carlo results. The exact result for the entropy at zero monomer density and Pauling’s estimate for the entropy at zero magnetic field are shown for reference. The series expansion contains the results from Ref. 14 on the monomer-dimer model.

Figure 8

Configurations $A$ and $B$. Tetrahedra are shown on top of each other. Small arrows indicate a short sequence of a loop. Up and down spins are denoted by black and grey dots.

Figure 9

Configurations $A$ and $B^{\prime }$. Tetrahedra are shown on top of each other. Small arrows indicate a short sequence of a loop. Up and down spins are denoted by black and grey dots.