Two-Dimensional Kagome Correlations and Field Induced Order in the Ferromagnetic $XY$ Pyrochlore ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathbf{O}}_7$

Neutron scattering measurements show the ferromagnetic $XY$ pyrochlore ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ to display strong quasi-two-dimensional (2D) spin correlations at low temperature, which give way to long range order (LRO) under the application of modest magnetic fields. Rods of scattering along $⟨111⟩$ directions due to these 2D spin correlations imply a magnetic decomposition of the cubic pyrochlore system into decoupled kagome planes. A magnetic field of $\sim 0.5\mathrm{T}$ applied along the $[1\overline{1}0]$ direction induces a transition to a 3D LRO state characterized by long-lived, dispersive spin waves. Our measurements map out a complex low temperature-field phase diagram for this exotic pyrochlore magnet.

Figure 1

Left: The cubic pyrochlore lattice, showing the positions of magnetic ${\mathrm{Yb}}^{3+}$ ions. This structure can be decomposed into alternating triangular (blue or dark atoms) and kagome planes (gold or light atoms), along the $⟨111⟩$ directions. The bonds within the kagome planes are shown in red (dark) lines. Right: a view along $[111]$ shows the structure of the kagome planes.

Figure 2

(a) Color contour maps of elastic neutron scattering in the HHL plane. In zero applied field, diffuse rods of scattering that extend along the [111] direction are visible at 800 mK and below. The diffuse scattering in applied field (30 mK, 2 T) is similar to the disordered state (4 K, 0 T). (b) Cuts of the scattering along the rod direction show the evolution of this 2D scattering with temperature and field. (c) Cuts perpendicular to the rod direction at 500 mK, 0 T, and within the field induced LRO state at 30 mK, 2 T.

Figure 3

Color contour maps of the inelastic neutron scattering along the [HHH] direction. The data is binned in [H,H,-2H] over the range [$-0.1$, 0.1]. Panel (a) is a schematic of the nuclear zones in the HHL plane, and the blue line shows the direction of the cut in the inelastic panels. Panels (b)–(d) show the absence of well defined spin excitations in low field, even at 30mK [panels (c) and (d)]. Resolution-limited spin waves appear at all wave vectors upon application of a magnetic field greater than $\sim 0.5\mathrm{T}$ [panels (e)–(h)], indicating a LRO state.

Figure 4

(a) Phase diagram for ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. At 30 mK, the transition to LRO is indicated near 0.5 T (inset), which is evinced by inelastic neutron data at points III and IV [shown in Figs. 3c, 3e]. (b) Changes in elastic Bragg scattering as a function of field at 30 mK. (c) and (d) Inelastic neutron scattering data at points I and II confirm the phase boundary, which is measured from magnetization data [panel (e)] above $T=2\mathrm{K}$.