Evidence for ${\mathrm{SrHo}}_2{\mathrm{O}}_4$ and ${\mathrm{SrDy}}_2{\mathrm{O}}_4$ as model $J_1$-$J_2$ zigzag chain materials

Neutron diffraction and inelastic spectroscopy is used to characterize the magnetic Hamiltonian of ${\mathrm{SrHo}}_2{\mathrm{O}}_4$ and ${\mathrm{SrDy}}_2{\mathrm{O}}_4$. Through a detailed computation of the crystal-field levels we find site-dependent anisotropic single-ion magnetism in both materials, and diffraction measurements show the presence of strong one-dimensional spin correlations. Our measurements indicate that competing interactions of the zigzag chain, combined with frustrated interchain interactions, play a crucial role in stabilizing spin-liquid type correlations in this series.

Figure 1

The structure of ${\mathrm{SrDy}}_2{\mathrm{O}}_4$. The $4c_1$ and $4c_2$ sites are dark and light blue and oxygen is shown in red, respectively, with (a) showing the hexagonal arrangement of the atoms in the $ab$ plane, and (b) the Dy${}_{4c1}$ ladder structure with the $J_1$-$J_2$ exchange pathways [3].

Figure 2

Inelastic neutron powder data for ${\mathrm{SrDy}}_2{\mathrm{O}}_4$ (blue, left) and ${\mathrm{SrHo}}_2{\mathrm{O}}_4$ (red, right) measured on HET. The calculated fits for the individual sites are shown with thin solid lines and their average, convoluted with the instrument resolution is shown in thick gray [22]. An instrumental background was added to the Dy data.

Figure 3

The level scheme of ${\mathrm{SrDy}}_2{\mathrm{O}}_4$ (blue, left) and ${\mathrm{SrHo}}_2{\mathrm{O}}_4$ (red, right). The thick lines indicate a doublet state. The ground state of Ho${}_2$ is a pseudodoublet.

Figure 4

Refined magnetic structure of ${\mathrm{SrHo}}_2{\mathrm{O}}_4$. The moments on the Ho${}_{c_1}$ sites are aligned with the $c$ axis and are ferromagnetic along the rungs and antiferromagnetic between the rungs. The moments on the Ho${}_{c_2}$ sites lie along the $b$ axis, and form an up-up-down-down structure along the chains.

Figure 5

Diffuse neutron scattering observed in ${\mathrm{SrHo}}_2{\mathrm{O}}_4$ and ${\mathrm{SrDy}}_2{\mathrm{O}}_4$ at 0.8 and 0.05 K, respectively. The sharp features are best fitted by a model of 1D scattering. The low temperature diffuse scattering in ${\mathrm{SrDy}}_2{\mathrm{O}}_4$ has an intensity reduced by approximately a factor of 10 due to the strong absorption of the sample; the first maximum in both materials is sharp and is found at $\mathbf{Q}=[00n+0.5]$.