Lattice Parameters, Electronic, and Magnetic Properties of Cubic Perovskite Oxides ARuO3 (A=Sr, Rb): A First Principles Study

Lattice Parameters, Electronic, and Magnetic Properties of Cubic Perovskite Oxides ARuO3 (A=Sr, Rb): A First‑Principles Study

Ahmed Memdouh YounsiLakhdar Gacem Mohamed Toufik Soltani 

University of Biskra, Laboratory of Physics of Photonics and Multifunctional Nanomaterials, BP 145, RP, Biskra 07000, Algeria

Materials Science and Informatics Laboratory, University of Ziane Achour Djelfa, PostOffice Box 3117, Djelfa 17000, Algeria

Corresponding Author Email:
5 November 2021
20 December 2021
31 December 2021
| Citation



Trioxides of rubidium, strontium, and ruthenium belong to the family of alkali and alkaline earth ruthenates. SrRuO3 crystallizes in various symmetry classes—orthorhombic, tetragonal, or cubic—whereas RbRuO3 is perovskite (cubic) structured and crystallizes only in the cubic space group Pm$\overline{3}$m(No. 221). In this study, we investigated the structural stability as well as the electronic and magnetic properties of two cubic perovskites SrRuO3 and RbRuO3. We established the corresponding lattice parameters, magnetic moments, density of states (DOS), and band structures using ab‑initio density‑functional theory (DFT). Both compounds exhibited a metallic ferromagnetic ground state with lattice parameter values between 3.83 and 3.96 Å; RbRuO3 had magnetic moments between 0.29 and 0.34 µBwhereas SrRuO3 had magnetic moments between 1.33 and 1.66 µB. This study paves way for further RbRuO3 research.


ab initio calculations, density-functional theory, cubic perovskites, ferromagnetic ground state, RbRuO3

1. Introduction

Owing to their physical and chemical properties, alkali and alkaline earth ruthenates play an important role in magnetics. With regard to this family of compounds, researchers have previously studied the superconductivity of Sr2RuO4 [1], the ferromagnetic transition in Ca2RuO4 [2], and the anti‑ferromagnetic behavior of Na2RuO4 [3]. These compounds form different crystalline lattices as influenced by varying external conditions such as temperature. The lattices may be orthorhombic (space groups Pnma, Imma, etc. tetragonal (space group I4/mcm), or cubic (Pm$\overline{3}$m space group) [4, 5].

Cubic perovskites (ABO3) have been studied extensively in the last two decades. For example, Xiao et al. [6] reported lattice parameters between 3.50 and 3.61 Å for SrSiO3. Tariq et al. [7] theoretically computed lattice parameters between 3.80 and 3.85 Å for cubic perovskites of SrAO3 (A = Cr, Fe, and Co).

SrRuO3 has been observed to crystallize into a cubic perovskite structure at temperatures as high as 1273 K [4]. In their study on thin films, Choi et al. [5] demonstrated that a cubic perovskite structure (Pm$\overline{3}$m space‑symmetry group) can be obtained upon annealing SrRuO3 at 950 K.

SrRuO3 is a metallic oxide that exhibits both electronic and magnetic characteristics owing to the transition metal ruthenium [4, 8]. The theoretical study conducted by Granas et al. [9] investigated the magnetic and electronic properties of the orthorhombic and cubic structures of SrRuO3.

Rubidium is an important alkali metal; located alongside strontium in period VI of the periodic table, rubidium has a large number of valence electrons and consequently has various electrical, electronic, and chemical applications [10].

In their pioneering work, Fischer et al. synthesized rubidium oxoruthenate (Rb2RuO4) from rubidium peroxide and ruthenium dioxide and also calculated its magnetic properties [11]. The trioxide of rubidium and ruthenium (RbRuO3) decomposes to Rb2RuO4 and RuO2, where RuO2 crystallizes with tetragonal rutile structure (P42/mmm) [12], whereas Rb2RuO4 crystallizes with an orthorhombic structure (Pnma) [11]. These products, under certain physical–chemical circumstances such as thermal treatment, combine to produce the perovskite RbRuO3 in Pm$\overline{3}$m space‑symmetry group [4, 13].

To the best of our knowledge, the cubic perovskite RbRuO3 has yet to be synthesized in experiments or studied theoretically; so far, the material has only been simulated [13]. Pearson simulated it and determined its properties such as lattice parameters, elasticity, and band structure using VASP code and generalized gradient approximation (GGA). Accordingly, we investigated the similarities between SrRuO3 and RbRuO3; we compared their structural stability as well as electronic and magnetic properties. To this end, we employed several ab‑initio methods from the density‑functional theory (DFT) implemented in the CASTEP (Cambridge Serial Total Energy Package) code.

The rest of the paper is devoted to presenting some computational aspects and details of the proposed approach followed by a description of the simulation results and a discussion of key findings. Finally, we conclude by retracing the important findings of our work.

2. Computational Methodology

We investigated the structural stability, electronic and magnetic properties of the RbRuO3 and SrRuO3 perovskites with space‑group number 221 (Pm$\overline{3}$m). All calculations presented in this paper were performed using CASTEP [14]. CASTEP utilized DFT to compute the solution of the Schrödinger equation. The electron wave functions were developed on a plane‑wave basis via periodic boundary conditions and Bloch’s theorem.

Bloch's theorem [15] states can be written as Eq. (1).

$\psi_{i, K}(r)=u_{j}(r) e^{i K . r}$       (1)

ui(r) is a function that defines the periodicity of the potential. For example, ui(r+L)=ui(r), where L is the length of the unit cell and K is a wavevector confined to the first Brillouin region. As ui(r) is a periodic function, we can express its Fourier expansion as Eq. (2).

$u_{j}(r)=\sum_{G} C_{j}, G e^{i G . r}$       (2)

The reciprocal lattice vectors are defined by $G \cdot R=2 \Pi \mathrm{m}$, where m is an integer and R is a real‑space lattice. Ci and G are plane‑wave expansion coefficients. Therefore, the wave functions of the electron can be written as a linear set of plane waves.

$\psi_{j, K}(r)=\sum_{G} C_{j, K+G} e^{i(K+G) \cdot r}$       (3)

Brillouin zone integration and the Monkhorst–Pack scheme were adopted to determine the energy‑band structure of the studied material using special k‑points and the 6×6×6 grids of a 340‑eV plane‑wave cut‑off. CASTEP used the Monkhorst–Pack scheme [16] to sample the Brillouin zone. After applying a series of convergence tests, we designated 340 eV as the energy cut‑off. Further, we designated 10 k‑points corresponding to the 6×6×6 Monkhorst–Pack meshes as a sampling of the first Brillouin zone. Self‑consistent field algorithms were implemented in the CASTEP code to determine the electronic ground state of the systems studied. With the same code, the total energy of the systems was minimized via Vanderbilt ultrasoft pseudo‑potentials [17, 18] and exchange‑correlation functionals from GGA. The following exchange‑correlation functionals were employed: Perdew–Burke–Erzerhof (PBE) [19], PBEsol (PBE for solids) [19, 20], Wu–Cohen functional (WC) [21], and Perdew–Wang (PW91) [22]. In addition, we employed local‑spin‑density approximation (LSDA) [23, 24], and LSDA with Hubbard correction (LSDA+U) [25, 26].

3. Results and Discussion

3.1 Lattice parameters

Before calculating the electronic and magnetic properties, we adjusted the lattice parameters. The cube in Figure 1 illustrates the atomic positions in the primitive cell of the crystal lattice. Based on the Wyckoff positions for group Pm$\overline{3}$m, the ruthenium atom was placed at the center of the cube, Ru (0.5, 0.5, 0.5); atom A (A = Rb, Sr) was placed at each corner of the cube, 8A (0, 0, 0); and the oxygen atom was placed at the center of each face, 2O1(0, 0.5, 0.5), 2O2 (0.5, 0.5, 0), 2O3 (0.5, 0, 0.5) [27].

Figure 1. Crystal structure of primitive cell of (ARuO3; A = Rb, Sr) in cubic system Pm$\overline{3}$m (No. 221)

Figure 2. Structural parameter as a function of the energy of cubic perovskite; a) RbRuO3 and b) SrRuO3, using the Hubbard correction U = 1.0 eV

First, we used GGA and LSDA to optimize and calculate the equilibrium lattice constant (a0) of the stable crystal structure of the primitive cell; for LSDA, we applied a high spin polarization on the ruthenium atom. As shown in Figures 2 a and b, the lattice parameters were traced as a function of energy, and through fitting, the curves were corrected according to the Birch–Murnaghan equation of state [28].

$E(V)=E_{0}+\frac{9 V_{0} B_{0}}{16}\left\{\left[\left(\frac{V_{0}}{V}\right)^{2 / 3}-1\right] B_{0}^{\prime}+\left[\left(\frac{V_{0}}{V}\right)^{2 / 3}-1\right]^{2}\left[6-4\left(\frac{V_{0}}{V}\right)^{2 / 3}\right]\right\}$        (4)

The equilibrium lattice parameter (a0) was selected at ground state, i.e., when the energy resulting from all interactions between electrons and ions in the studied systems was the lowest. Table 1 lists the results for the equilibrium lattice parameter and ground‑state energy of the studied crystals according to the different functional calculation techniques. Furthermore, we observed that GGA is better than LSDA at estimating ionic bonding in molecular systems.

For RbRuO3, we obtained lattice parameter values between 3.83 and 3.95 Å; these values were similar to those for SrRuO3, which ranged between 3.85 and 3.96 Å. Notably, the SrRuO3 values are consistent with the experimental results of Cuffini et al. [4] and theoretical findings of Abbes and Noura [27], as shown in Table 1. We also calculated the bulk moduli; we obtained values between 287 and 298 GPa for RbRuO3, and between 278 and 291 GPa for SrRuO3. Among the various computational methods, GGA–PBE yielded the most optimal results.

3.2 Electronic structure and magnetic properties

3.2.1 Density of states and magnetic moments

The transition metal ruthenium is responsible for the magnetic nature of SrRuO3 and RbRuO3. In this study, we applied ferromagnetic ordering, which is suitable for cubic ground states prior to ferromagnetic ordering; the structures with Pm$\overline{3}$m space‑symmetry group. In this regard, we applied high spin-up and high spin-down polarization on the ruthenium atom. We then calculated the magnetic moments of the materials. The results are presented in Table 2.

For SrRuO3, we obtained total magnetic moments between 1.33 and 1.66 µB; these results are in good agreement with those reported in other works [9, 29]. For RbRuO3, the magnetic moments were lower, between 0.29 and 0.34 µB. As previously mentioned, there are no published articles reporting the laboratory synthesis or the theoretical examination of this compound. As such, we could not compare the corresponding results with known benchmarks. We noted that these two compounds had ferromagnetic ground‑state energies shown in Tables 1 and 2 decreased after ferromagnetic ordering.

Figure 3 shows the total‑ and partial‑density‑of‑states (TDOS and PDOS) curves of our materials. These results were obtained using the GGA–PBE functional with high spin-up and spin-down polarization.

We observed that the electron states were distributed on 2s2 and 2p4 orbital configurations for oxygen atoms; 4s2, 4p6, and 5s1 for rubidium atoms; 4s2, 4p6, and 5s2 for strontium atoms; and 4s2, 4p6, 4d7, and 5s1 for the ruthenium atoms. The Fermi level was fixed at 0 eV, where the overlap was clear at this level. We observed a metallic ground state for both compounds. For RbRuO3, this metallic nature was attributed to the contribution of the electron states of the 5s1 orbital of Rb, the 2p4 orbital of O, and the 4d7 orbital of Ru. Conversely, for SrRuO3, the electrons of the 5s2 orbital of Sr, the 2p4 orbital of O, and the 4d7 orbital of Ru contributed to the metallic behavior. A more detailed illustration of this metallic ground state presented in the band–structure curves.

Table 1. Equilibrium lattice parameter a0 calculated via different methods in conjunction with GGA (without spin polarization) and LSDA (with Hubbard correction U = 1.0 eV)

Exchange–Correlation DFT functional




Ground‑state energy (eV)

Lattice constant a0 (Å)

Bulk modulus B0(GPa)

Ground‑state energy (eV)

Lattice constant a0 (Å)

Bulk modulus B0(GPa)













































3.96 [4]





163-213 [27]

Table 2. Total magnetic moments Mtot calculated by different methods in conjunction with GGA (with high spin‑up and spin‑down polarization) and LSDA (with Hubbard correction U = 1.0 eV)

Exchange–Correlation DFT functional




Ground‑state energy (eV)


Ground‑state energy (eV)


































1.190 [29]



1.320–1.800 [9]

Figure 3. PDOS and TDOS using GGA–PBE functional with spin‑up and spin‑down polarization

3.2.2 Band structures

The outcome of the band–structure calculations is shown in Figures 4 and 5. For these computations, we used the GGA–PBE functional with and without spin polarization; the energy eigenvalues of the systems under consideration were traced using a function of reciprocal‑space k‑points. The Brillouin zones are defined at four zones in our calculation because the materials studied here crystallize in the cubic symmetry system. We observed overlapping of valence and conduction bands at Fermi level as well as at the end of the second and third Brillouin zones. This overlap is visible—with and without spin polarization—at the points between M and Γ (see Figures 4 and 5).

Figure 4. Band structure, using GGA–PBE functional without spin polarization

Figure 5. Band structure with A. spin-up polarization and B. spin-down polarization, using GGA–PBE functional

For RbRuO3, the maximum energy values of the valence bands were found to be 0.556, 0.502, and 0.681 eV without spin polarization, with spin ascent, and with spin descent, respectively, whereas the corresponding minimum energy values of the conduction bands were -0.236, -0.254, and -0.148 eV.

Similarly, for SrRuO3, the maximum energy values of the valence bands were 0.425, -0.007, and 0.963 eV, whereas the minimum energy values of the conduction bands were 0.008, -0.256, and 0.332 eV. These values indicate a larger overlap between the two bands. So, there are no band gaps. We conclude that all the specimens studied here are conductors.

4. Conclusion

We used ab‑initio DFT calculations to determine the electronic and magnetic properties of two cubic perovskite oxide compounds, RbRuO3 and SrRuO3, belonging to a family of alkali and alkaline earth ruthenates. We observed that both compounds had similar lattice parameter values. Moreover, both were ferromagnetic conductors. However, they had different degrees of magnetization; compared to SrRuO3, RbRuO3 had lower magnetic moments. This theoretical study confirmed that both RbRuO3 and SrRuO3 can potentially be used in ferromagnetic conductivity-based technologies, for example, in metallic ultra‑thin nanoribbons and magnetic thin‑film domains. Furthermore, RbRuO3 may be useful in applications requiring a small magnetic moment, such as layered hetero‑structures with magnetic/nonmagnetic layers. Laminated heterogeneous structures are composed of multiple ferromagnetic and nonmagnetic layers. These composites have potential applications in spintronics, and several investigations—including interface magnetism, interlayer exchange coupling, and magnetization reversal from ferromagnetic to paramagnetic—have been conducted to this end. We believe our study will encourage experimental efforts to synthesize this compound.


The authors would like to thank the material science department team of the University of Biskra for funding this work.


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