Neutron diffraction study of spin and charge ordering in SrFeO${}_{3-\delta }$

We report a comprehensive neutron diffraction study of the crystal structure and magnetic order in a series of single-crystal and powder samples of SrFeO${}_{3-\delta }$ in the vacancy range 0 ≤ δ ≤ 0.23. The data provide detailed insights into the interplay between the oxygen vacancy order and the magnetic structure of this system. In particular, a crystallographic analysis of data on Sr${}_8$Fe${}_8$O${}_{23}$ revealed a structural transition between the high-temperature tetragonal and a low-temperature monoclinic phase with a critical temperature $T$ $=$ 75 K, which originates from charge ordering on the Fe sublattice and is associated with a metal-insulator transition. Our experiments also revealed a total of seven different magnetic structures of SrFeO${}_{3-\delta }$ in this range of δ, only two of which (namely an incommensurate helix state in SrFeO${}_3$ and a commensurate, collinear antiferromagnetic state in Sr${}_4$Fe${}_4$O${}_{11}$) had been identified previously. We present a detailed refinement of some of the magnetic ordering patterns and discuss the relationship between the magnetotransport properties of SrFeO${}_{3-\delta }$ samples and their phase composition and magnetic microstructure.

Figure 1

Crystal structures of vacancy-ordered ferrates in the system SrFeO${}_{3-x}$. For a clearer presentation, the Sr${}^{2+}$ ions are not shown. The network of cubic SrFeO${}_3$ is formed by undistorted corner-sharing FeO${}_6$ octahedra. In tetragonal ($I$-centered) Sr${}_8$Fe${}_8$O${}_{23}$, every second O position along [1,0,0] and [0,1,0] (starting from the origin and the lattice point $\frac{1}{2}$,$\frac{1}{2}$,$\frac{1}{2}$) is unoccupied, so that sequences of alternating FeO${}_6$ octahedra and FeO${}_5$ square pyramids are generated. (Fe atoms are marked in red and green). A further oxygen deficiency within these chains is found in orthorhombic Sr${}_4$Fe${}_4$O${}_{11}$, where one finds only corner-shared dimers of FeO${}_5$ square pyramids along [001].

Figure 2

Neutron diffraction data on the single crystals of composition SrFeO${}_{3.00}$ and SrFeO${}_{2.87}$ measured at various temperatures. The scans were performed along the [1,1,1] direction around the structural Bragg reflection (0, 0, 1)${}_{\mathrm{cub}}$. With decreasing temperature magnetic reflections of phase I appeared in both samples. In the oxygen-deficient crystal SrFeO${}_{2.87}$ an additional set of magnetic reflection of phase II could be observed.

Figure 3

Temperature dependence of the intensity, incommensurability, and magnetic correlation length of the helical magnetic Bragg reflections of the magnetic phase I in the single crystal SrFeO${}_{3.00}$ (left) and the magnetic phases I and II in SrFeO${}_{2.87}$ (right). For the sample SrFeO${}_{3.00}$ very weak intensity was found on the position (0, 0, $\frac{3}{4}$)${}_{\mathrm{cub}}$ indicating the presence of an additional magnetic phase (denoted as phase IV in the text) for temperatures below 65(4) K. The solid lines in the upper panels are the results of power-law fits to the measured intensity. It is interesting to note that the incommensurability is temperature dependent close to the magnetic phase transition.

Figure 4

Temperature dependence of the strong nuclear reflection (200)${}_{\mathrm{cub}}$ of SrFeO${}_{3-\delta }$ and the magnetic reflection (0.13, 0.87, 0.87)${}_{\mathrm{cub}}$ of the cubic phase SrFeO${}_3$ (denoted as phase I). For the samples with lower oxygen content, the reflection (2, 0, 0)${}_{\mathrm{cub}}$ [(4, 4, 0)${}_{\mathrm{tetr}}$ /(0, 0, 4)${}_{\mathrm{tetr}}$] shows a strong change of intensity at $T_{\mathrm{S}}$ $=$ 75(2) K indicating the presence of a structural phase transition. This transition is more pronounced in the sample SrFeO${}_{2.87}$, suggesting that this transition occurs in the tetragonal phase Sr${}_8$Fe${}_8$O${}_{23}$.

Figure 5

Temperature dependence of the reflections (2, 0, 0)${}_{\mathrm{cub}}$, (0, 0, $\frac{3}{4}$)${}_{\mathrm{cub}}$, (1, 0, $\frac{3}{4}$)${}_{\mathrm{cub}}$, and ($\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$)${}_{\mathrm{cub}}$ of SrFeO${}_{2.77}$. Magnetic intensity of the ($\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$)${}_{\mathrm{cub}}$ [(1, 1, 1)${}_{\mathrm{orth}}$ in the orthorhombic setting] appears spontaneously at 232(2) K due to the onset of antiferromagnetic ordering of the Fe atoms (phase VII) in orthorhombic Sr${}_4$Fe${}_4$O${}_{11}$. A second magnetic transition was observed at $T_{\mathrm{N}}$ $=$ 65(3) K. This can be ascribed to an antiferromagnetic ordering in a second phase, which could not be characterized so far. Furthermore, magnetic Bragg reflections with $T_{\mathrm{N}}$ $=$ 110(4) K were observed at the incommensurate positions ($h$±0.297, $k$±0.297, $\ell$±0.25)${}_{\mathrm{cub}}$ (phase V).

Figure 6

Neutron powder patterns of SrFeO${}_{3-\delta }$ with δ $=$ 0.13 at different temperatures between 20 and 80 K. The traces for temperatures below 80 K have been shifted for clarity. The neutron wavelength was λ $=$ 2.58 Å. Below $T_{\mathrm{N}}$ $=$ 133(1) K magnetic intensity appears at the position (0.13, 0.13, 0.13)${}_{\mathrm{cub}}$ due to the incommensurate ordering (phase I) of the end member SrFeO${}_3$. Below $T_{\mathrm{N}}$ $=$ 75(2) K incommensurate magnetic order of the iron moments (phase III) with ${\mathit{k}}_2$ $=$ (0.687, 0, 0.326)${}_{\mathrm{mon}}$ (using the monoclinic unit cell of low-temperature structure of Sr${}_8$Fe${}_8$O${}_{23}$). Further commensurate magnetic reflections are observable below $T_{\mathrm{N}}$ $=$ 65(4) K, suggesting the presence of a third magnetic phase (phase IV), with ${\mathit{k}}_3$ $=$ (0, 0, $\frac{1}{2}$)${}_{\mathrm{tetr}}$, of another oxygen-deficient ferrate, which could not be characterized so far.

Figure 7

Neutron powder patterns of Sr${}_8$Fe${}_8$O${}_{23}$. From the data sets collected at 2 and 90 K the crystal structure was refined in the monoclinic and tetragonal space groups $I$2/$m$ and $I$4/mmm, respectively. The calculated patterns (red) are compared with the observed ones (black circles). The difference patterns (blue) as well as the peak positions (black bars) of Sr${}_8$Fe${}_8$O${}_{23}$ (above) and the cubic phase SrFeO${}_3$ (below) are given in the lower part of each diagram. The inset indicates that the 2θ positions of reflections ($h$, $k$, $\ell$) with large $\ell$ showed the strongest changes below the structural phase transition.

Figure 8

Projection of the high-temperature tetra-gonal (top) and the low-temperature monoclinic (bottom) crystal structure of Sr${}_8$Fe${}_8$O${}_{23}$ along [001]. The network of distorted FeO${}_6$ octahedra in the $ab$ plane is shown at the level $z$ $=$ 0.25. In order to see the displacements of the O2 atoms in the monoclinic structure, the O2 atoms of the neighboring FeO${}_6$ octahedra at $z$ $=$ 0.75 are also shown. The values of particular interatomic Fe-O and O-O bond distances are also given.

Figure 9

Temperature dependence of the lattice parameters of Sr${}_8$Fe${}_8$O${}_{23}$. With decreasing temperature the tetragonal structure of Sr${}_8$Fe${}_8$O${}_{23}$ changes to a monoclinic structure at the transition temperature $T_{\mathrm{S}}$ $=$ 75(2) K. A significant decrease could be observed for the $c$ parameter, while the $a$ parameter shows only a slight increase below 30 K. The $b$ parameter (monoclinic axis) does not show any significant change in the monoclinic phase between 2 and 60 K.

Figure 10

Incommensurate magnetic structure of phase III with the propagation vector k $=$ (0.687, 0, 0.326), which can be attributed to the magnetic ordering in monoclinic Sr${}_8$Fe${}_8$O${}_{23}$. As found earlier for SrFeO${}_3$ the magnetic moments of the iron atoms are tilted with respect to the $c$ axis by angle of −35.3°. Thus the moments are aligned within a plane (marked with dashed lines) which is lying perpendicular to the direction [111] using the cubic setting. Due to the oxygen deficiency antiferromagnetic coupling occurs between those iron atoms along the $c$ axis, where sequences of alternating units of octahedral Fe${}^{4+}$O${}_6$ and square-pyramidal Fe${}^{3+}$O${}_5$ were found (Fe${}^{4+}$ and Fe${}^{3+}$ ions are marked in red and green, respectively).

Figure 11

Magnetic ordering of the iron moments in the system SrFeO${}_{3-\delta }$. The magnetic structures are shown as projections along the $b$ and $c$ axes of Sr${}_8$Fe${}_8$O${}_{23}$ and Sr${}_4$Fe${}_4$O${}_{11}$, respectively. For SrFeO${}_3$ the cubic unit cell is also shown. The iron moments in SrFeO${}_3$ and Sr${}_8$Fe${}_8$O${}_{23}$ show a helical and a sine-wave modulated magnetic ordering with a propagation vector k parallel to the direction [111] of the cubic unit cell, respectively. The canting angle of the moments with respect to the $c$ axis is θ $=$ −35.3°. A further decrease of oxygen content leads to commensurate magnetic ordering, where the moments are still canted with respect to the $c$ axis. For this phase the magnetic structure can be described with the propagation vector k $=$ (0, 0, $\frac{1}{2}$) using the tetragonal setting of Sr${}_8$Fe${}_8$O${}_{23}$. Thus the magnetic structure requires a doubling of the tetragonal $c$ axis. A further reduction of oxygen leads to a simple collinear structure of the Fe${}^{3+}$ sublattice of Sr${}_4$Fe${}_4$O${}_{11}$, whereas the moments of the Fe${}^{4+}$ ions in this phase are not three-dimensionally ordered.[8]