Magnetic correlations in HoxTb2−xTi2O7

Abstract

Polycrystalline samples of ${\mathrm{Ho}}_{\mathrm{x}}{\mathrm{Tb}}_{2\ensuremath{-}\mathrm{x}}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ (0 $x$ 2) have been prepared and characterized for their structural and magnetic properties. The parent compounds of this solid solution are the spin ice ${\mathrm{Ho}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ and the spin liquid ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$. Specific-heat measurements on ${\mathrm{HoTbTi}}_{2}{\mathrm{O}}_{7}$ ($x$ $=$ 1.0) reveal the absence of a long-range order state above 0.5 K. The integrated entropies of all ${\mathrm{Ho}}_{\mathrm{x}}{\mathrm{Tb}}_{2\ensuremath{-}\mathrm{x}}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ specimens up to 30 K scale well with the ratio of spin ice and spin liquid in the composition. The neutron diffraction spectrum of ${\mathrm{HoTbTi}}_{2}{\mathrm{O}}_{7}$ exhibits a dipolar spin-ice pattern and can be well described by mean-field theory for $\ensuremath{\langle}111\ensuremath{\rangle}$ Ising spins, nearest-neighbor exchange, and dipolar interactions. Inelastic neutron scattering on ${\mathrm{HoTbTi}}_{2}{\mathrm{O}}_{7}$ reveals two dispersionless excitations, one of \ensuremath{\sim}2.5 meV out of the ground state, and a 4-meV transition out of an excited state. We argue that these data suggest that the very strong single-ion effects of ${\mathrm{Ho}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ and ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ persist in the ${\mathrm{Ho}}_{\mathrm{x}}{\mathrm{Tb}}_{2\ensuremath{-}\mathrm{x}}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}(0\mathrm{ }\mathrm{ }\mathrm{x}\mathrm{ }\mathrm{ }2)$ solid solution, whereas the Tb-Ho correlations are weak, resulting in small shifts in the energy scales but with no dramatic effect on the bulk properties.