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Condens. Matter 2019, 4, 86 9 of 15 from its original direction along [010], and in the fit we can consider just one Fe site where its MM is slightly deviated from [010], while Beff possesses a broad distribution. Figure 7. The 57Fe Mössbauer spectrum of LiFePO4 at temperature T = 4.2 K and external magnetic field Bext = 6 T. The inset displays the distribution of Beff at the 57Fe nuclei. 3.3. Theoretical Exploration of Magnetism and Hyperfine Interactions The magnetic structure of LFP was deduced to be antiferromagnetic (AF)—as also confirmed here for the sample studied—with the easy magnetization axis along the [010] direction, based on neutron scattering experiments [9,10]. Other experiments [11–13] confirmed this finding, except small deviations from this direction due to anisotropic exchange, which is not taken into account in the following considerations. In addition to the easy magnetization direction, another question arises. Namely, what is the arrangement of the magnetic moments in the LiFePO4 unit cell? There are three possible MM orders which result in an AF order. These are: Fe1 and Fe2 MMs are parallel (↑↑) being antiparallel (↑↓) to ↓↓ Fe3 and Fe4 (AF1), (Fe1 ↑↑ Fe3) ↑↓ (Fe2 ↓↓ Fe4) (AF2), and (Fe1 ↑↑ Fe4) ↑↓ (Fe2 ↓↓ Fe3) (AF3). Our DFT PBE spin-polarized calculations (without SOC) show that the AF2 order exhibits the lowest energy, followed by AF1 and the highest energy occurs for AF3. In all calculations the lattice parameters from Reference [3], i.e., a = 10.332 Å, b = 6.010 Å and c = 4.692 Å, were employed. Table 2 collects results of these calculations (see the second column). The AF2 order is observed in reality (see, e.g., Reference [10]) and was also confirmed in other computations [8,18]. Table 2. Results of density functional theory (DFT) calculations for the three antiferromagnetic (AF) configurations. The first column indicates the AF configuration. ∆EAF is the unit cell total energy relative to the lowest energy configuration. Bhf covers the contact (isotropic) interaction only. Order AF1 AF2 AF3 ∆EAF (meV) 35.9 00.0 65.1 Vzz (1021 V/m2) η 14.2 0.61 14.1 0.63 13.1 0.55 Bhf (T) 32.7 32.8 31.4PDF Image | Mossbauer Spectroscopy of Triphylite (LiFePO4) at Low Temperatures
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