“Color-Tripole Ice” as a Conceptual Generalization of “Spin Ice”

“Spin Ice” is an exotic type of frustrated magnet realized in “pyrochlore” materials Ho2Ti2O7, Dy2Ti2O7, Ho2Sn2O7, and so forth, in which magnetic atoms (spins) reside on a sublattice made of the vertices of corner-sharing tetrahedra. Each spin is Ising-like with respect to a local axis which connects the centers of two tetrahedra sharing the vertex occupied by the spin. The macroscopically degenerate ground states of these magnets obey the “two-in two-out” “ice rule” within each tetrahedron. Magnetic monopoles and antimonopoles emerge as elementary excitations, “fractionalizing” the constituent magnetic dipoles. This system is also a novel type of statistical mechanical system. Here we introduce a conceptual generalization of “spin ice” to what we shall call “color-tripole ice,” in which three types of “color charges” can emerge as elementary excitations, which are Abelian approximations of the color charges introduced in high energy physics. Two two-dimensional (2D) models are introduced first, where the color charges are found to be 1D and constrained 2D, respectively. Generalizations of these two models to 3D are then briefly discussed. In the second one the color charges are likely 3D. Pauling-type estimates of the “residual (or zero-point) entropy” are also made for these models.