Crystal structure of solid solutions REFe1−x(Al or Ga)xO3 (RE=Tb, Er, Tm) and the correlation between superexchange interaction Fe+3–O−2–Fe+3 linkage angles and Néel temperature
Introduction
Rare earth orthoferrites REFeO3 (RE=La…Lu and Y) create a family of compounds, which crystallise in an orthorhombically distorted perovskite structure belonging to the Pbnm (D2h16) space group. The elementary unit cell consists of four molecules. The RE+3 cations occupy nearly central positions (Wyckoff position-4(c)) in a parallelepiped formed by Fe+3 (4(b)) cations. The iron ions are nearly octahedrally coordinated with six O−2. Two of the O−2 occupies positions 4(c), and the other four occupy positions 8(d) (Table 1 and Fig. 1). The O−2(4c)–O−2(4c) axes of distorted octahedra are tilted alternately, forming a zigzag along the [0 0 1] direction with the tilt angle γThe dihedral angle () in the Fe+3 parallelepiped can be treated as a measure of the orthorhombic distortion of the perovskite structure in the ab plane. As the difference of lattice constants a and b approaches zero, the α angle approaches 90°, which means a decrease in the degree of distortion.
As the radius of the RE+3 cations located in deformed dodecahedral interstices between the oxygen octahedra increases (Lu+3(0.97 Å)→La+3(1.18 Å) [1]), all the ions apparently shift in such a way that lattice size increases [2], [3] (Fig. 2) and the distortion degree as well the tilt angle decrease (Fig. 3).
Among all the possible magnetic interactions in the REFeO3 orthoferrites, the superexchange coupling Fe+3–O−2–Fe+3 of iron magnetic moments is dominant and leads to a non-colinear antiferromagnetic (weak ferromagnetic) Fe+3 sublattice ordering. The direct Fe+3–Fe+3 coupling is much weaker, and magnetic RE+3–Fe+3 and RE+3–RE+3 couplings are of the 10−2–10−3 orders in relation to the Fe+3–O−2–Fe+3 ones [4], [5].
Phenomenologically, the Néel temperature TN of the antiferromagnetically ordered iron sublattice is proportional to the average number (Z=6) of linkages per Fe+3 ion, to the exchange constant () of Fe+3 ion pairs and to the average cosine of the Θ angle of the Fe+3–O−2–Fe+3 linkage [4], [6]where for Fe+3, and is defined by the Hamiltonian [4].
The above formula (2) can be written [4], [5] aswhere TN(Θ=180°) () coefficient is the Néel temperature of a hypothetical orthoferrite with the Fe+3–O−2–Fe+3 linkage angle of 180°.
An interesting question concerns the validity limits of that simple relation (3). A decrease in the exchange interaction can easily be achieved when the iron sublattice is diluted with non-magnetic atoms, as in the case of solid solutions of rare earth orthoferrites with correspondent orthoaluminates or orthogalates (REF1−xAlxO3, REFe1−xGaxO3). These compounds are, therefore, a suitable material for verifying the above mentioned dependence.
Section snippets
Crystal structure and Fe+3–O−2–Fe+3 superexchange linkage angles
In the REFeO3 elementary unit cell, each of the four Fe+3 ions interacts with six nearest Fe+3 ions through O−2 ions occupying common apices of two adjacent oxygen octahedra. The crystallographic symmetry of distorted perovskite allows two kinds of these linkages:
2 linkages (along the c-axis) with the first nearest neighbours—Fe+3–O−2(4c)–Fe′+3,
4 linkages (in the ab plane) with the second nearest neighbours—Fe+3–O−2(8d)–Fe″+3
with corresponding θI and θII angles, respectively (Fig. 1).
Hence,
Sample preparation and crystal structure
The polycrystalline samples of solid solutions: TbFe1−xAlxO3 (0⩽x⩽1), ErFe1−xAlxO3 (0⩽x⩽0.4), TmFe1−xAlxO3, TbFe1−xGaxO3, ErFe1−xGaxO3 and TmFe1−xGaxO3 (0⩽x⩽0.15) were prepared by the usual sintering method described in detail in Refs. [9], [10], [11], [12], [13]. Their structures were examined on a HZG4 X-ray diffractometer with a Cu tube. Assuming a random distribution of Fe+3, Al+3 or Ga+3 ions in 4(b) positions, the crystal structure parameters were determined (Table 2, Table 3, Table 4 and
Discussion and conclusions
Diluting the Fe+3 sublattice with Al+3 or Ga+3 ions leads to a monotonic decrease in lattice constants and in elementary unit cell volume (Table 2, Table 3, Table 4 and Fig. 5, Fig. 6, Fig. 7). Because the Al+3 ion radius (∼0.53 Å) is significantly smaller than that of Fe+3 (∼0.645 Å) [1], a visible decrease in elementary unit cell size and volume is observed with the increase in Al+3 concentration (x). The a(x), b(x), c(x) and V(x) non-linearity appearing in TbFe1−xAlxO3, which does not conform
Acknowledgements
The authors remain in gratitude to Ms. Justyna Leśniewska for her revision and proof-reading of the English version of the manuscript.
This work was partly supported by research grant No. 2 P03B 035 14 from the State Committee for Scientific Research.
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