Magnetism of the geometrically frustrated spin-chain compound ${\mathrm{Sr}}_3\mathrm{Ho}\mathrm{Cr}{\mathrm{O}}_6$: Magnetic and heat capacity measurements and neutron powder diffraction

This paper reports on the complex magnetic properties of ${\mathrm{Sr}}_3\mathrm{Ho}\mathrm{Cr}{\mathrm{O}}_6$, which is a spin-chain compound subject to geometrical frustration. This experimental study is based on magnetization and heat capacity measurements, combined with neutron powder diffraction. Our investigations provide evidence of a long-range antiferromagnetic ordering, taking place at $T_N\simeq 15\mathrm{K}$. We focus on the nature of this magnetic ordering in zero field, as well as on the characteristics of the magnetization process at $T<T_N$. Particular attention is paid to the hysteresis loops recorded at $T⪡T_N$, which exhibit a peculiar succession of magnetization steps.

Figure 1

(Color online) (a) Room-temperature x-ray pattern, indexed in the $R\overline{3}c$ space group; the stars correspond to the impurity $\mathrm{Sr}{\mathrm{Ho}}_2{\mathrm{O}}_4$. Drawings of the ${\mathrm{Sr}}_3\mathrm{Ho}\mathrm{Cr}{\mathrm{O}}_6$ structure: (b) projection in the basal plane to show the hexagonal structure and (c) along the $c$ axis to evidence the 1D character of the structure. The solid lines indicate the unit cell and the dotted lines the triangular sublattice. Some interatomic distances (Cr-O, Ho-O, and intrachain Cr-Ho) are given. The $\mathrm{Ho}{\mathrm{O}}_6$ and $\mathrm{Cr}{\mathrm{O}}_6$ polyhedra are also shown. (d) corresponds roughly to (b) but details are added concerning the proposed magnetic structure.

Figure 2

dc magnetic susceptibility recorded with a magnetic field of $0.1\mathrm{T}$, in the ZFC (filled circles) and FC (open circles) modes. The inset displays the $T$ dependence of the reciprocal susceptibility (after subtraction of a constant term ${\chi }_0$) over the whole $T$ range (see text).

Figure 3

Imaginary and real parts of the ac magnetic susceptibility (main panel and inset, respectively), recorded in zero dc field at various frequencies: 10 (filled squares), ${10}^2$ (open circles), ${10}^3$ (filled triangles), and ${10}^4\mathrm{Hz}$ (open diamonds).

Figure 4

Main panel: Total heat capacity of ${\mathrm{Sr}}_3\mathrm{Ho}\mathrm{Cr}{\mathrm{O}}_6$ (filled circles) and of ${\mathrm{Sr}}_3\mathrm{Zn}\mathrm{Pt}{\mathrm{O}}_6$ (open squares). Inset: Magnetic heat capacity of ${\mathrm{Sr}}_3\mathrm{Ho}\mathrm{Cr}{\mathrm{O}}_6$, obtained after subtraction of the lattice contribution (see text).

Figure 5

(Color online) Neutron diffraction patterns, recorded from $1.5\text{to}300\mathrm{K}$ with $\lambda =0.24266\mathrm{nm}$. The gray (blue) and black colors are used for the magnetic ordered and paramagnetic states, respectively.

Figure 6

(Color online) Enlargement of a few superimposed NPD patterns to illustrate the evolution vs $T$ of the shape and intensity of the first magnetic peak (a) and corresponding integrated intensity—from 15 to 18 in $2\theta$—vs $T$ (b).

Figure 7

(Color online) (a) Neutron diffraction pattern of ${\mathrm{Sr}}_3\mathrm{Ho}\mathrm{Cr}{\mathrm{O}}_6$ at $9\mathrm{K}$. The crosses and the solid line correspond to the experimental and calculated diagrams, respectively. In the main panel, the upper Bragg ticks are for the crystalline structure, while the other sets of ticks correspond to the two magnetic contributions, which have the same magnetic structure but different coherence lengths (see text). The inset is an enlargement of the first peak showing the combination of these three contributions: crystalline contribution (●), main magnetic contribution (+), and additional magnetic contribution having a shorter coherence length (엯). The solid line is the sum of these three contributions, while the crosses are the data. (b) Enlargement of selected NPD patterns showing the evolution of the small-angle part vs temperature. For clarity the patterns have been smoothed.

Figure 8

Field dependence of magnetization curves recorded at three temperatures. The arrows indicate the direction of the field variation along the half loops.

Figure 9

Magnetization curve recorded at $5\mathrm{K}$ on a ceramic sample (open circles). The solid line is a fitting curve to the ceramic data, that is used to calculate the corresponding curve for a single crystal with $H\Vert c$ (dashed line), using our modelization (see the Appendix).

Figure 10

Reverse leg of a half loop recorded at $2\mathrm{K}$ in a partially oriented powder sample (see text). The arrows indicate changes in slope that are more clearly visible in the derivative curve shown in the inset (solid line). The inset also displays the corresponding curve obtained in a randomly oriented ceramic sample (dashed line).

Figure 11

Sketch of the vectorial projections used to calculate the contribution to the global magnetization of a grain whose $c$ axis is tilted by an angle $\theta$ from the direction of the applied magnetic field (see the Appendix).