Local magnetic anisotropy by polarized neutron powder diffraction: Application of magnetically induced preferred crystallite orientation

Polarized neutron diffraction allows one to determine the local susceptibility tensor on the magnetic site both in single crystals and powders. It is widely used in the studies of single crystals, but it is still hardly applicable to a number of highly interesting powder materials, such as molecular magnets or nanoscale systems because of the low luminosity of existing instruments and the absence of appropriate data analysis software. We show that these difficulties can be overcome by using a large area detector in combination with the two-dimensional Rietveld method and powder samples with a magnetically induced preferred crystallite orientation. This is demonstrated by revisiting two test powder compounds, namely, the low anisotropy (soft) ferrimagnetic compound ${\mathrm{Fe}}_3{\mathrm{O}}_4$ and the spin-ice compound ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ with high local anisotropy. The values of the magnetic moments in ${\mathrm{Fe}}_3{\mathrm{O}}_4$ and the susceptibility tensors of ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ at various temperatures and fields were found in perfect agreement with these found earlier in single-crystal experiments. The magnetically induced preferred crystallite orientation was used to study the local susceptibility of a single-molecule magnet $\mathrm{Co}{\left({\left[{\left({\mathrm{CH}}_3\right)}_2\mathrm{N}\right]}_2\mathrm{CS}\right)}_2{\mathrm{Cl}}_2$. Hence, the studies of local magnetic anisotropy in powder systems might now become accessible.

Figure 1

The principal scheme of the scattering at the polycrystalline sample. A notation is explained in the text.

Figure 2

Flipping sum diffraction patterns collected on ${\mathrm{Fe}}_3{\mathrm{O}}_4$ at $T=150$ K, $H=0$ T. The measured 2D pattern is shown on the top, the calculated is shown on the bottom (a), and chi squares normalized per number of points is 5.87. Diffraction profile estimated near the equatorial plane (b). $\gamma$ is the azimuthal angle and $\nu$ is the elevation angle in the laboratory coordinate system $\left(xyz\right)$, where $\vec{x}\left|\right|{\vec{k}}_i, \vec{z}\left|\right|\vec{H}$.

Figure 3

The distribution of $H_{pV}$ and the sum of the integrated intensities for the reflection (111) measured with a magnetic field 6 T (triangles) and without it (circles) at the diffractometer 5C1 at 150 K over the Debye cone ($\varphi =0{}^{\circ }$ correspond to the scattering in the equatorial plane). The model values after 2D Rietveld refinement are given by the dotted lines.

Figure 4

Flipping sum and difference diffraction patterns collected on ${\mathrm{Fe}}_3{\mathrm{O}}_4$ at $T=150$ K, 6 T. The measured 2D pattern is shown on the top, the calculated one is shown on the bottom (a), and chi squares normalized per number of points is 3.93. Diffraction profiles estimated near the equatorial plane (b). The position of reflections is marked by “$|$.” Black lines show the differences between experimental points (blue) and model line (orange).

Figure 5

The measured and calculated flipping sum (top) and difference (bottom) diffraction patterns collected on ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ at diffractometer 5C1, $T=5$ K, $H=1$ T for (a) 2D and (b) 1D diffraction profiles. Chi squares normalized per number of points is 0.57 for 2D diffraction patterns.

Figure 6

Temperature dependence of the susceptibility components ${\chi }_{\parallel }$ (circles) and ${\chi }_{\perp }$ (triangles) for single (open symbols, taken from Ref. [6]) and powder (solid symbols) ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ at 1 T. The inset shows Ho magnetization ellipsoids at 50 K.

Figure 7

The measured and calculated flipping sum (top) and difference (bottom) diffraction patterns collected on $\mathrm{Co}{\left({\mathrm{L}}_1\right)}_2{\mathrm{Cl}}_2$ at diffractometer 6T2, $T=2$ K, $H=5$ T. Chi squares normalized per number of points is 6.71. The inset shows Co magnetization ellipsoids surrounded by S (yellow) and Cl (green).