Local structure and magnetism of $\mathrm{L}{\mathrm{a}}_x\mathrm{E}{\mathrm{u}}_{1-x}\mathrm{P}{\mathrm{O}}_4$ solid solutions

By combining high spinning speed (60 kHz) and low-field (4.7 T) ${}^{31}\mathrm{P}$ solid-state NMR with magnetic susceptibility measurements, we experimentally characterized a series of solid solutions belonging to the $\mathrm{L}{\mathrm{a}}_x\mathrm{E}{\mathrm{u}}_{1-x}\mathrm{P}{\mathrm{O}}_4$ ($0\le x\le 1$) series. Analyses of the magnetic susceptibility data were carried out using the free ion model and crystal field theory calculations allowing to extract the electronic structure. The paramagnetic shifts of the P sites having one $\mathrm{E}{\mathrm{u}}^{3+}$ cation in their surrounding were predicted by combining the determined crystal field and energy level values with density functional theory (DFT) calculations. For the $\mathrm{L}{\mathrm{a}}_{0.9}\mathrm{E}{\mathrm{u}}_{0.1}\mathrm{P}{\mathrm{O}}_4$ sample, these theoretical shifts gave a very good overall trend allowing the unambiguous attribution of each P site. This study paves the way for the future analysis of both magnetic susceptibility and NMR data for a broad range of materials containing paramagnetic rare-earth cations.

Figure 1

Example of the $C_s$ symmetry for the $\mathrm{LaP}{\mathrm{O}}_4$ crystalline structure represented by a 4.5-Å sphere with La as a central atom. The following color code is used: La atoms are in green, P atoms in orange, and O atoms in red. Here, the seven P sites have been differentiated to illustrate the discussion through the paper. In the insert is presented the local environment around the P atom.

Figure 2

${}^{31}\mathrm{P}$ MAS NMR spectra of (a) $\mathrm{L}{\mathrm{a}}_{0.9}\mathrm{E}{\mathrm{u}}_{0.1}\mathrm{P}{\mathrm{O}}_4$ and (b) $\mathrm{L}{\mathrm{a}}_{0.1}\mathrm{E}{\mathrm{u}}_{0.9}\mathrm{P}{\mathrm{O}}_4$ and their corresponding fits acquired at 4.7 T at a MAS rate of 60 kHz. The insert shows an enlargement of the low intensity signals of $\mathrm{L}{\mathrm{a}}_{0.9}\mathrm{E}{\mathrm{u}}_{0.1}\mathrm{P}{\mathrm{O}}_4$.

Figure 3

Field cooled magnetic susceptibility curves of (a) $\mathrm{L}{\mathrm{a}}_{0.1}\mathrm{E}{\mathrm{u}}_{0.9}\mathrm{P}{\mathrm{O}}_4$, (b) $\mathrm{L}{\mathrm{a}}_{0.5}\mathrm{E}{\mathrm{u}}_{0.5}\mathrm{P}{\mathrm{O}}_4$, and (c) $\mathrm{L}{\mathrm{a}}_{0.9}\mathrm{E}{\mathrm{u}}_{0.1}\mathrm{P}{\mathrm{O}}_4$. To fit the ${\chi }_{\mathrm{mol}.\mathrm{Eu}3+}$, we considered Model 1, Model 2, and approaches as discussed in the text. $\mathrm{L}{\mathrm{a}}_{0.1}\mathrm{E}{\mathrm{u}}_{0.9}\mathrm{P}{\mathrm{O}}_4$ calculated magnetic susceptibility based on Model 3 is included in (c).

Figure 4

Model structures used for the calculations of the isotropic hyperfine coupling constants: (a) the ${\mathrm{P}}_1\mathrm{G}{\mathrm{d}}_1\mathrm{L}{\mathrm{a}}_6{\mathrm{O}}_{25}{\mathrm{H}}_{21}$ cluster C1 (considering here P2 as the central atom) and (b) the $\mathrm{G}{\mathrm{d}}_1{\mathrm{P}}_7\mathrm{L}{\mathrm{a}}_{11}{\mathrm{O}}_{40}{\mathrm{H}}_{11}$ cluster C2. The following color code is used: La atoms are in green, P atoms in orange, Gd atoms are in pink, H atoms are in white, and O atoms in red. In the insert, the local environment around the P atom is presented.

Figure 5

Variation of the ${}^{31}\mathrm{P}{\delta }_{exp}$ obtained by Bregiroux et al. [19] at 31.25 kHz against the average electron spin polarization $\langle S_z\rangle$ determined by Golding and Halton [30] for the $\mathrm{LnP}{\mathrm{O}}_4$ ($\mathrm{Ln}=\mathrm{La}-\mathrm{Eu}$) series. The dashed line is a linear correlation with an adjusted coefficient of 0.95.

Figure 6

Comparison between the experimental [${\delta }_p$(exp)] and theoretical paramagnetic shifts (${\delta }_p$) determined using Eq. (3). The peak numbers refer to ${\delta }_p$(exp). The theoretical paramagnetic shifts are obtained by summing the pseudocontact shifts determined using the Golding and Pyykkö Approach (${\delta }_{\mathrm{PC}3}$) or the Bleaney Theory (${\delta }_{\mathrm{PC}4}$) with the Fermi contact shifts (FC) determined using cluster1 (${\delta }_{\mathrm{FC}1}$), cluster 2 (${\delta }_{\mathrm{FC}2}$), or by including the g-tensor approach (${\delta }_{\mathrm{FC}3}$). More details are given in Table 7.