Magnetic structure of the two-dimensional XY antiferromagnet ${\mathrm{Sr}}_2{\mathrm{CoSi}}_2{\mathrm{O}}_7$ studied using single-crystal neutron diffraction

We report a combined polarized and unpolarized neutron diffraction study on a multiferroic ${\mathrm{Sr}}_2{\mathrm{CoSi}}_2{\mathrm{O}}_7$ (SCSO) single crystal below and above the antiferromagnetic ordering temperature ${\mathrm{T}}_N$ = 6.5 K. Unpolarized neutron diffraction measurements at 15 K confirm the melilite-type tetragonal $P\overline{4}{2}_{1}m$ space group as the parent structure of SCSO. The low temperature study at 2.3 K, in contrast, reveals symmetry lowering with the orthorhombic $Cm{m}^{\prime }{2}^{\prime }$ and $P{2}_1{2}_1^{\prime }{2}^{\prime }$ magnetic space groups being equally possible. In these $Cm{m}^{\prime }{2}^{\prime }$ and $P{2}_1{2}_1^{\prime }{2}^{\prime }$ magnetic space groups we obtain a very similar ordered magnetic moment about 2.86 and $2.94{\mu }_B/{\mathrm{Co}}^{2+}$, respectively, which lies in the $\mathit{ab}$ plane. Our spin polarized flipping ratio measurements under an applied magnetic field of 6 T in the paramagnetic state support the results of our bulk magnetization data, indicating strong easy-plane spin anisotropy, responsible for the in-plane order below ${\mathrm{T}}_N$.

Figure 1

(a) Illustration of the refined nuclear structure of the SCSO single crystal at 15 K in the $P\overline{4}{2}_{1}m$ space group. Ellipses represent the anisotropic displacement parameters. Oxygen are named to denote angle and bond distance which are given in Table 3. (b) Temperature dependent sample rotation scans performed on (300) magnetic reflection using neutron diffraction.

Figure 2

(a), (b) Integrated intensities of reflections of purely magnetic origin (left) and both magnetic and nuclear origin (right) as function of temperature. Error bars are inside the symbols. Solid lines represents the fit to Eq. (1). The corresponding fitted critical exponents are denoted in the figure. (c)–(e) Observed and calculated structure factors are presented for both SSG representations along with corresponding reliability factors $R_F$.

Figure 3

Refined magnetic structure of SCSO at 2.3 K projected in the $\mathit{ab}$ plane with the magnetic propagation vector ${\mathbf{q}}_m$ = (000). Gray and dashed black squares correspond to the orthorhombic $P{2}_1^{\prime }{2}_1{2}^{\prime }$ and $C{m}^{\prime }m{2}^{\prime }$ unit cell, respectively. The slight canting of the magnetic moments (blue arrows) is discussed in the text.

Figure 4

(a) Low-field and (b) high-field bulk magnetization curve of SCSO obtained at various temperatures. Solid lines represent the experimental data. Solid circles (right) are calculated magnetic moments along [001] and [100] in pink and orange color, respectively, using linear spin wave theory.

Figure 5

Refined free AFM component and $R_F$ against fixed FM component. The dashed vertical line shows the value obtained from the free model. Rectangle box guides the deviation window for $R_F$.

Figure 6

Calculated and observed asymmetry ($A$) is plotted for data measured with field applied along [551] (a) and along [115] (b). The corresponding refinement quality is denoted in the figure.