Parameterization of dilute Ising model for iron-containing lanthanum gallate and aluminate solid solutions based on first-principles calculations

Highlights

• Solid solution is represented as a set of configurations with estimated probabilities.

• The dilute Ising model considers both magnetic and covalent contributions to energy.

• The proposed model reproduces well the relative energies of different configurations.

• Ga ↔ Fe and Al ↔ Fe interchange energies have different signs in the considered compounds.

• Fe-clustering is more beneficial in Fe-doped LaGaO₃ in comparison with LaAlO₃.

Abstract

Calculations of the cubic models of two solid solutions LaGa_0.5Fe_0.5O₃ and LaAl_0.5Fe_0.5O₃ have been performed within the hybrid density functional theory. Multiple configurations have been considered for the solid solutions resulting from a different distribution of Fe atoms over the p-metal (Ga or Al) positions accounting for different spin orientation for Fe atoms themselves. It was demonstrated that 27 structures for both LaGa_0.5Fe_0.5O₃ and LaAl_0.5Fe_0.5O₃ should be treated to account for all the possible configurations in case of cubic 2 × 2 × 2 supercell. Optimized geometry, energy, and electron properties were calculated for all the obtained configurations_. Statistical weights and probabilities were estimated for each symmetry non-equivalent configuration of the solid solutions within the canonical ensemble. A new parameterization for the dilute Ising model has been proposed. In this model, we account for non-magnetic contributions, which are absent in the simple Ising model, using the lattice approach based on the concept of interchange energy. Two model parameters (the magnetic coupling constant and interchange energy) were fitted to the calculated total energies of all considered configurations of both solid solutions. The dilute Ising model confirmed the benefit of Fe-clustering in doped lanthanum gallate against aluminate. Different signs of the estimated interchange energy enable us to explain the reasons for such differences.

Introduction

For the last decades and until today, the perovskite-type oxides are being actively explored due to a wide range of their applications. The slightest impurities in the perovskite structure can cause significant distinction in the electronic, optical, and magnetic properties. At the same time, the perovskite structure itself is tolerant for various substitutions in both A and B crystallographic orbits of ABO₃, which opens large possibilities for doping with dia- and paramagnetic elements to obtain the necessary target products. That is the reason why complex oxides with perovskite structure became so popular.

A great number of works suggests some applications for the doped LaGaO₃. For example, the increasing number of studies are focused on the photoluminescence properties of LaGaO₃ doped with lanthanides (Sm³⁺, Tb³⁺, Bi³⁺, Eu³⁺, Tm³⁺, Yb³⁺) [[1], [2], [3]]. Besides this, the doped LaGaO₃ oxides being mixed electronic-ionic conductors are frequently mentioned as promising candidates for solid oxide fuel cells (SOFC) [4,5]. Nevertheless, the practical applications of SOFCs are still limited due to the high costs of component materials: LaGaO₃ is rather expensive material. In contrast, lanthanum aluminate, LaAlO₃, is much cheaper and also studied profoundly [6]. However, a markedly smaller number of works relates to doped LaAlO₃ systems.

Published experimental results [[7], [8], [9]] show that LaGaO₃- and LaAlO₃-solid solutions differ in properties. Thus, the studies of magnetic properties of LaMO₃–LaAlO₃ and LaMO₃–LaGaO₃ diluted solid solutions (M = Fe, Cr) [7,9] showed that the distribution of d-elements over B sites in perovskite structure is far from random. It was found that the fractions of dimer clusters in the diluted solutions exceeded the statistically probable fraction by a factor of about 2 in aluminates and 2.5 in gallates, whereas as was shown for lanthanum aluminate the fraction of clusters did not depend on the nature of 3d-element, but only on the composition of the host diamagnetic lattice. This means that in lanthanum gallate the clustering of paramagnetic M atoms is essentially greater than in the aluminate. A good example of such behavior is the systems LaFe_xAl_1−xO₃ [8] and LaFe_xGa_1−xO₃ [9]. The plots of paramagnetic components of magnetic susceptibility calculated per 1 mol of iron atoms are given in Fig. 1. Solid solutions of composition LaFe_xGa_1−xO₃ and LaFe_xAl_1−xO₃ (x = 0.01–0.10) were synthesized by ceramic method. The magnetic susceptibility χ_g was measured by Faraday method in the temperature range 77–400 K at 10 fixed values of magnetic field strength. The accuracy of measuring χ_g is 1%. The diamagnetic increments were introduced taking into account the susceptibility of diamagnetic matrix – LaGaO₃ and LaAlO₃ measured over the same temperature range. We are currently working on the paper with a more detailed discussion on the given experimental results. The slope of the isotherms shows that long order exchange interactions are antiferromagnetic in both systems and the paramagnetic component decreases with concentration to a greater extent in gallate. However, at low concentrations a large ferromagnetic component appears in the exchange according to magnetic susceptibility data for LaFe_xGa_1−xO₃. This suggests that clustering of iron atoms in gallate is stronger than in aluminate. Nevertheless, these are model estimations based on experimental data, though carried out for a series of d-elements.

Antiferromagnetic-paramagnetic transition at T_N ≃ 215 K was experimentally investigated by Komine et al. in the study of electronic conduction in LaGa_0.5Fe_0.5O₃ [10]. The nature of the pre-peaks in the oxygen K-edge XANES (X-ray absorption near-edge structure) spectra of LaGa_xFe_1−xO₃ was discussed by Lafuerza et al. [11]. Their existence was interpreted in terms of a molecular-orbital bonding theory. The first pre-peak A is related to a 2p-3d bond (OFe) and remains independent of Fe neighbors. The second pre-peak B is affected by the Ga substitution in LaFeO₃, which changes both energy and intensity. This peak represents the states of σ symmetry, where 3d orbitals are strongly correlated with the coordination octahedra. The intensity of the peak B decreases with Ga substitution of one Fe atom in FeOFe triplet, and with the substitution of the two Fe atoms the peak is completely missing. In this respect, a more sensitive method is necessary for examination the orbital mixing at low concentrations of the 3d metal, i.e., the existence of Fe-clusters in the diluted solutions cannot be observed in XANES spectra.

Kuznetsov et al. [12] examined the magnetic properties of LaAl_1−xFe_xO₃ solutions. Unexpectedly, the orthorhombic (Pbnm) → rhombohedral (R$\overline{3}$c) phase transition was not observed over the whole range of concentrations, in contrast to other works [8,13]. The Mossbauer spectra of the LaFeO₃, LaFe_0.7Al_0.3O₃, and LaFe_0.2Al_0.8O₃ confirm that the valence state of Fe atoms (3+) does not change with Al appearance. Ahmed et al. [14] recommended Fe-doped LaAlO₃ as a prospective material for tunable capacitors and ferroelectric random access memory. The multiferroic LaAl_yFe_1−yO₃ (0 < y < 0.2) were prepared by citrate autocombustion method. It was shown [14] that the value of the Neel temperature in general decreases with the increasing of Al content (T_N = 795 K for LaAl_0.2Fe_0.8O₃).

In the theoretical study by Singh et al. [15], the photoluminescence properties of Fe-doped LaGaO₃ were considered. First-principles density functional theory (DFT) calculations were carried out. The antiferromagnetic ordering of the solid solutions was established. The calculations showed that LaGa_xFe_1−xO₃ solutions have the direct band gap, which enables the observed photoluminescence. It is important that the calculations were carried out assuming the solid solution to be ordered and represented by a single structure. This approximation is the most commonly used in the first-principles calculations. Therefore, the interchange interactions between paramagnetic and diamagnetic atoms were ignored. However, it is these interatomic interactions that determine the magnetic and electrical performance of perovskites. The ions of Al³⁺ and Ga³⁺ have a similar valence electron structure and taking into account the disordered nature of the solid solutions is a key to the explanation of the observed differences. This means the discussed approximation becomes inappropriate for modeling of the solid solutions under consideration.

In this work, we do not assume that the solid solution is represented by a single ordered structure. We present an ab initio approach, which allows modeling of the magnetic properties of the solid solutions considering different distributions of the dopant atoms. To the best of our knowledge, the papers where the properties of LaFe_xGa_1−xO₃ and LaFe_xAl_1−xO₃ solid solutions were compared theoretically on ab initio level are absent.

Our paper is organized as follows: In Section 2, we discuss the choice of the computational scheme, the basics of the solid solutions calculations considering multiple configurations are presented in Section 3. In Section 4, we focus on the discussion of the results: Fe-clustering is analyzed in Section 4.1, 4.2 The dilute Ising model, 4.3 Stability investigation are devoted to the suggested parameterization of the dilute Ising model and stability investigation, respectively. Finally, the conclusions of the study are summarized.