Neutron diffraction is a powerful technique for determining the magnetic structure of antiferromagnetic materials. However, for some of these, determining the detailed magnetic structure remains a challenge. In goethite ($\alpha$-FeOOH) the antiferromagnetic unit cell coincides with the chemical unit cell and, consequently, nuclear and magnetic diffraction peaks occur at the same positions. Analysis of diffraction data from goethite is further complicated by finite-size peak broadening, resulting from goethite commonly occurring in nanocrystalline form. For these reasons, determining the magnetic structure of goethite has been challenging, and few detailed studies have been published. Even today, not all aspects of the magnetic structure are well established. Here, we investigate the magnetic structure of three samples of goethite nanoparticles with polarized neutron powder diffraction (xyz-polarization analysis). Two samples consist of acicular goethite particles that are approximately 40 nm long and with different thicknesses, and one sample consists of pseudo-spherical particles with a diameter of approximately 5 nm. The larger particles consist of several crystallites whereas the 5-nm particles are mostly single crystalline. The polarization analysis enables us to separate magnetic scattering from nuclear and spin-incoherent scattering, resulting in data that can readily be analyzed. For the two samples with the larger particle size, we find nuclear correlation lengths in the [100] direction that are approximately 3 nm longer than the magnetic correlation lengths, indicating a magnetically disordered layer perpendicular to the antiferromagnetic modulation direction. We find no evidence of a magnetically disordered surface layer in the 5-nm particles. We find the magnetic structure to be antiferromagnetic but, in contrast to most previous studies, we find the spin orientation in all three samples to make an angle of 28-${30}^{\circ }$ with respect to the crystallographic $b$ axis.

中文翻译：

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针铁矿纳米粒子的轴外旋转取向

中子衍射是一种确定反铁磁材料磁性结构的强大技术。然而，对于其中一些，确定详细的磁性结构仍然是一个挑战。在针铁矿（$\alpha$-FeOOH），反铁磁晶胞与化学晶胞重合，因此，核和磁衍射峰出现在相同位置。来自针铁矿的衍射数据的分析由于有限尺寸的峰展宽而进一步复杂化，这是由于针铁矿通常以纳米晶形式出现。由于这些原因，确定针铁矿的磁性结构具有挑战性，很少有详细的研究发表。直到今天，磁性结构的所有方面都还没有被很好地确立。在这里，我们用极化中子粉末衍射（xyz极化分析）研究了三个针铁矿纳米颗粒样品的磁性结构。两个样品由大约40 nm长且厚度不同的针状针铁矿颗粒组成，一个样品由直径约5 nm的假球形颗粒组成。较大的颗粒由数个微晶组成，而5 nm的颗粒大多为单晶。极化分析使我们能够将磁散射与核散射和自旋非相干散射分开，从而可以轻松分析数据。对于具有较大粒径的两个样品，我们发现在[100]方向上的核相关长度比在磁相关长度上长约3 nm，表明垂直于反铁磁调制方向的磁无序层。我们没有发现在5 nm颗粒中存在磁混乱表面层的证据。我们发现磁性结构是反铁磁性的，但与大多数以前的研究相比，${30}^{\circ }$ 关于晶体学 $b$ 轴。