Half-Magnetization Plateau Stabilized by Structural Distortion in the Antiferromagnetic Heisenberg Model on a Pyrochlore Lattice

Magnetization plateaus, visible as anomalies in magnetic susceptibility at low temperatures, are one of the hallmarks of frustrated magnetism. We show how an extremely robust half-magnetization plateau can arise from coupling between spin and lattice degrees of freedom in a pyrochlore antiferromagnet and develop a detailed symmetry of analysis of the simplest possible scenario for such a plateau state. The application of this theory to the spinel oxides ${\mathrm{C}\mathrm{d}\mathrm{C}\mathrm{r}}_2{\mathrm{O}}_4$ and ${\mathrm{H}\mathrm{g}\mathrm{C}\mathrm{r}}_2{\mathrm{O}}_4$, where a robust half-magnetization plateau has been observed, is discussed.

Figure 1

A section of the pyrochlore lattice, showing its two-sublattice tetrahedral structure. At zero magnetization, tetragonal lattice distortion favors the spin configurations of the type shown in (a), while at half magnetization trigonal lattice distortion favors the configuration (b). AF bonds are marked with solid black lines and FM bonds with dashed lines.

Figure 2

Phase diagram as a function of magnetic field $h$ and dimensionless coupling constant $b$. Solid lines denote first and dashed lines, second order transitions. Spin configurations and irrep of the order parameter in each phase is also shown.

Figure 3

Magnetization as a function of magnetic field for $b=0$ (straight line) to $b=0.24$ (robust plateau) in steps of 0.03.

Figure 4

Maximal values of the second order invariants ${\Lambda }_{\mathsf{E}}^2$ and ${\Lambda }_{{\mathsf{T}}_2}^2$ for classical spins as a function of the magnetization per site $M$. A ridge (dashed line) divides three dimensional from coplanar spin configurations. Spin ordering patterns are shown for the symmetrical cases of ${\Lambda }_{\mathsf{E}}^2=0$ and ${\Lambda }_{{\mathsf{T}}_2}^2=0$.