Honeycombs of triangles and magnetic frustration in $\mathrm{Sr}{L}_2{\mathrm{O}}_4$ ($L=\mathrm{Gd}$, Dy, Ho, Er, Tm, and Yb)

The crystal structures, magnetic order, and susceptibility have been investigated for magnetically frustrated ${\mathrm{SrDy}}_2{\mathrm{O}}_4$, ${\mathrm{SrHo}}_2{\mathrm{O}}_4$, ${\mathrm{SrEr}}_2{\mathrm{O}}_4$, ${\mathrm{SrTm}}_2{\mathrm{O}}_4$, and ${\mathrm{SrYb}}_2{\mathrm{O}}_4$. Powder neutron-diffraction structural refinements reveal columns of $L{\mathrm{O}}_6$ octahedra that run along one crystallographic direction, with Sr-O polyhedra in the interstices. The lanthanide sublattice displays multiple triangular interconnections: one-dimensional strings form the backbones of four types of chains of lanthanide triangles sharing edges arranged in a honeycomb pattern. This crystal structure produces strong geometric frustration for the magnetic system that is evidenced in both magnetic susceptibility and neutron-scattering data at low temperatures. The susceptibility measurements for the series, including ${\mathrm{SrGd}}_2{\mathrm{O}}_4$ for which data are also reported, lack the sharp features characteristic of three-dimensional long-range magnetic ordering. Metamagnetic behavior is observed in the magnetization vs applied field data at 1.8 K for the cases of $L=\mathrm{Dy}$, Er, and Ho. Magnetic neutron-scattering studies for the Dy and Er materials show only very broad magnetic scattering at low temperatures, while the Ho system exhibits long-range two-dimensional order. Any magnetic scattering in the Tm and Yb compounds, if present, was too weak to be detected in these measurements.

Figure 1

Neutron powder-diffraction pattern of ${\mathrm{SrYb}}_2{\mathrm{O}}_4$ at ambient temperature. Upper curve: data and fit, short vertical lines, calculated peak positions. Lower curve: difference between observed and calculated pattern.

Figure 2

(Color online) (a) The crystal structure of ${\mathrm{SrDy}}_2{\mathrm{O}}_4$ shown as an arrangement of $L{\mathrm{O}}_6$ octahedra and isolated Sr atoms in channels, viewed down the crystallographic $c$ axis. (b) The arrangement of $L{\mathrm{O}}_6$ octahedra perpendicular to $c$ showing both the double-row columns of octahedra, and the manner in which those columns share corner oxygens with each other.

Figure 3

(Color online) The geometries of the $L{\mathrm{O}}_6$ octahedra in the double-row columns, for (a) $L\left(1\right)$, and (b) $L\left(2\right)$. The lanthanide-oxygen distances are shown for the case of ${\mathrm{SrDy}}_2{\mathrm{O}}_4$. $L\left(1\right)$ shown as larger dark circles, $L\left(2\right)$ shown as larger lighter circles, oxygen as small black circles.

Figure 4

Detailed view of the magnetic atom sublattice in the “honeycomb” direction in ${\mathrm{SrDy}}_2{\mathrm{O}}_4$, showing the four lanthanide chains running perpendicular to the honeycomb net. Lines connect near neighbor lanthanides. $L\left(1\right)$ shown as dark circles, $L\left(2\right)$ shown as lighter circles.

Figure 5

Side view of the lanthanide chains, running parallel to the crystallographic $c$ axis. $L\left(1\right)$ shown as dark circles, $L\left(2\right)$ shown as lighter circles. Lines connect lanthanide near neighbors. Interlanthanide distances are shown for the case of Dy. The primary chains, CH1 and CH2, have shorter $L\text{−}L$ separations, and the secondary, or connecting chains, CH3 and CH4, have longer $L\text{−}L$ distances. The shorter $L\text{−}L$ distances along the spines of the chains are also seen.

Figure 6

The temperature dependence of the inverse magnetic susceptibility for ${\mathrm{SrGd}}_2{\mathrm{O}}_4$ between 320 and 2 K. Data taken on cooling in an applied field of 500 Oe. Inset: detail of the inverse susceptibility in the low-temperature region.

Figure 7

The temperature dependence of the inverse magnetic susceptibility for ${\mathrm{SrDy}}_2{\mathrm{O}}_4$ between 320 and 2 K. Data taken on cooling in an applied field of 50 Oe. Inset: detail of the inverse susceptibility in the low-temperature region.

Figure 8

The temperature dependence of the inverse magnetic susceptibility for ${\mathrm{SrHo}}_2{\mathrm{O}}_4$ between 320 and 2 K. Data taken on cooling in an applied field of 50 Oe. Inset: detail of the inverse susceptibility in the low-temperature region.

Figure 9

The temperature dependence of the inverse magnetic susceptibility for ${\mathrm{SrEr}}_2{\mathrm{O}}_4$ between 320 and 2 K. Data taken on cooling in an applied field of 50 Oe. Inset: detail of the inverse susceptibility in the low-temperature region.

Figure 10

The temperature dependence of the inverse magnetic susceptibility for ${\mathrm{SrTm}}_2{\mathrm{O}}_4$ between 320 and 2 K. Data taken on cooling in an applied field of 50 Oe. Inset: detail of the inverse susceptibility in the low-temperature region.

Figure 11

The temperature dependence of the inverse magnetic susceptibility for ${\mathrm{SrYb}}_2{\mathrm{O}}_4$ between 320 and 2 K. Data taken on cooling in an applied field of 100 Oe. Inset: detail of the inverse susceptibility in the low-temperature region.

Figure 12

The magnetization for ${\mathrm{SrLn}}_2{\mathrm{O}}_4$ materials as a function of applied field at 1.8 K. Zero-field cooling.

Figure 13

The derivatives, $dM∕dH$ of the magnetization data in Fig. 12, as a function of applied field.

Figure 14

A broad magnetic peak is observed below $\sim 5\mathrm{K}$ in ${\mathrm{SrDy}}_2{\mathrm{O}}_4$ (inset), indicating that short-range magnetic order develops at low temperatures in this system.

Figure 15

(a) A very broad peak showing the short-range magnetic order develops below $\sim 20\mathrm{K}$ in ${\mathrm{SrEr}}_2{\mathrm{O}}_4$; (b) integrated intensity, full width at half maximum (FWHM), and position of the broad peak as a function of temperature.

Figure 16

(Color online) (a) Broad distribution of magnetic scattering at intermediate temperatures, indicating the development of short-range correlations in ${\mathrm{SrHo}}_2{\mathrm{O}}_4$. This scattering begins to develop below $\sim 40\mathrm{K}$. (b) The magnetic scattering at low temperatures, indicating the development of two-dimensional long-range magnetic order. The solid curve is a fit assuming long-range order within the ab plane, and no correlations between planes.

Figure 17

(a) Plots of the integrated intensity, position, and FWHM as a function of temperature for the short-range order correlations in ${\mathrm{SrHo}}_2{\mathrm{O}}_4$. (b) Intensity vs temperature at the 2D (02) peak position. The change in slope around 4 K indicates a crossover from short-range magnetic correlations to 2D long-range order.