Magnetic, electronic and mechanical properties of SeXO₃ (X = Mn, Ni) with the LSDA + U framework

Highlights

• Depending on the U parameter, some physical properties of SeXO₃ were examined.

• Some physical properties of Se(Mn,Ni)O₃ have been predicted for the first time.

• The elastic parameters reveal that these compounds are mechanical stable.

• In the G-AFM phase, both compounds have an indirect band gap.

• Our calculated results can be seen as a prediction for future experimental work.

Abstract

We have investigated the influence of the Hubbard (effective) U correction parameter on the structural, local magnetic moment, electronic, mechanical and elastic anisotropy properties of SeXO₃ compounds from the first-principles computations. The equilibrium volumes, total energy, bulk moduli and its pressure derivative of the four different magnetic configurations of the SeXO₃ compound are assessed by the Murnaghan equation of state fittings. Comparing the ground state of total energy, we have found that the G-type antiferromagnetic configuration in SeXO₃ compounds is more stable than other magnetic configurations. Electronic band structure computations indicate that both compounds exhibit a semiconductor behavior. The elastic, polycrystalline elastic and anisotropic properties of both compounds in G-type antiferromagnetic phase were investigated. With the present research, the prediction of these mechanical properties of SeXO₃ compounds will guide the elastic constant measurements of these compounds in the future.

Introduction

The ABO₃ compounds mostly crystallize into an ideal perovskite structure which is cubic. The A- and B- site cations may contain different valence combinations and ionic radii. The stability condition of the cubic perovskite structure depends on the average radius of the A, B and O ions controlled by the Goldschmidt tolerance factor. In the perovskite structure, the tolerance factor can also be expressed in terms of the measured bond lengths instead of the ionic radius. For these two cases, the Goldschmidt tolerance factor (t) is defined by the following equation [1]:

$$t=\frac{(R_A+R_O)}{\sqrt{2}(R_B+R_O)}=\frac{(A-O)}{\sqrt{2}(B-O)}$$

where R_A, R_B and R_O are the ionic radii corresponding to the constituent atoms. (A - O) and (B–O) are the average of the measured bond lengths between the A cation and the O anions and between the B cation and the O anions, respectively. For the ideal cubic structure, the tolerance factor (t) should be equal to 1. Empirically, the tolerance factor is such that a cubic perovskite structure is a reasonable possibility if t is in the range of about 0.9–1.0. If the deviation of t is slightly less than one, tilting and rotations of the oxygen octahedral will be favored. In the case of a small/smaller deviation in t (i.e., t < 1), the crystal structure undergoes from a cubic phase to an orthorhombic or a rhombohedral phase [2]. The small ion radii of A and B cations give a lower t value and as a result, small value of t leads to structural distortion. The <B–O–B> bond angle is notably reduced from 180° with the increment in lattice distortion, which greatly influences many physical properties of many perovskites. For example, the <B–O–B> bond angle in BO₆ octahedra reduces from 180° to 125.48° for SeMnO₃ [3]. B ions are octahedrally coordinated by the O ions in the unit cell. This tilting of the octahedron is connected to the size of the A and B cotions. BO₆ octahedra tilts about the b- and c-axes for the orthorhombic structure. BO₆ octahedral takes an important role in the ferroelectricity and ferromagnetism properties of some ABO₃ compounds. Some ferroelectric perovskites are transition metal oxides containing transition metal ions with incompletely filled d-electrons. Some perovskite-type structures are compounds of the type A⁺⁴ B⁺² ${\text{O}}_3^{2-}$(e.g. SeMnO₃ and SeNiO₃). Due to the spins of partially filled 3d cations of transition metals, the ABO₃ perovskites have magnetic moments. Magnetic behavior is related to the organization between magnetic moments or spins on these cations.

The SeMnO₃ and SeNiO₃ have perovskite-type structures. The SeNiO₃ and SeMnO₃ compounds are described by partly filled 3d orbitals and a related local magnetic structure in which the Mn and Ni atoms are antiferromagnetically aligned [3]. The symmetry of both compounds belongs to Pnma (#62) space group in the orthorhombic structure [3,4] at room temperature. A site in ABO₃ perovskites is occupied by voluminous Se⁺⁴ cations and B site by Mn⁺² or Ni⁺² ion. The compounds of the SeXO₃ (X = Mn, Ni) perovskite family have the ability to contain the lone-pair electrons in crystal structure, usually occupied by the Se⁺⁴ cations. Escamilla et al. [5] recommended that SeMnO₃ compound changed its magnetic ground state from a small ferromagnetic to antiferromagnetic phase at 52 K, probably due to strong octahedral distortion. The perovskite SeMnO₃ and SeNiO₃ are synthesized at elevated pressure and temperature (3.5 GPa and 850 °C) [3,6]. By the neutron powder diffraction and susceptibility measurements [3], the magnetic structure of these compounds are described as antiferromagnetic (AFM) at a Néel temperature 53.3 K (SeMnO₃) and 104 K (SeNiO₃) with the magnetic moments along the c direction. The moments are antiferromagnetically coupled along the b direction. Also, the AFM states of SeNiO₃ was confirmed in a numerical calculation study using the LSDA + U method [7] and first principles method [8]. Similarly, the AFM states of SeMnO₃ was proved in a computation study by Perdew, Burke and Ernzerhof (PBE) + U calculation, using hybrid functional [8], and experimentally by Escamilla at al [5]. In addition, SeXO₃ includes a violently tilted XO₆ octahedron structure, because the average radius of X²⁺ cation is larger than Se⁴⁺. Thus, the SeXO₃ compounds have a large X-O-X super-change φ angle which leads to the surprising magnetic properties. These compounds have the same magnetic structure and are given by their basic vectors (0, 0, A_z). The four possible spin configurations in the ground state for SeXO₃ represent one ferromagnetic (FM) and three antiferromagnetic (AFM) (A-, C-, G-type) ordering. In the case of FM, all magnetic moments of X⁺² ions are arranged parallel to the c-crystal axis direction in ab plane. In A-type AFM (A-AFM) ordering, ferromagnetically aligned X ions in ac planes are coupled antiferromagnetically along b-axis. The magnetic moment chain of the C-type (C-AFM) X⁺² ions is ferromagnetic in the direction of the b axis, and in the ac plane, the closest neighbors form the antiferromagnetic order. In G-type AFM (G-AFM), the magnetic moments of X⁺² ions that are antiferromagnetically double along the b-direction are arranged antifromagnetically along the c axis. Our calculations used the homogeneous and collinear spin arrangements.

The standard local spin density approach (LSDA) technique can not accurately define the conductor and semiconductor behavior and is well known to give small values for forbidden band gap and magnetic moment of localized d/f electrons in rare earth and transition metal oxide compounds. Various approaches have been developed beyond density functional theory (DFT) to harmonize the forbidden band gap with the experimental values. One of these implemented approaches is the LSDA + U method [9] with two additional parameters. One of these parameters is the Hubbard parameter U, which projects the strength of the on-site electronic interaction. The other parameter J sets the strength of the exchange interaction term. Dudarev et al. [9] combined the U and J parameters as a single effective parameter, U_eff = U - J, using the rotational invariant method. The LSDA + U method describes the strong correlation of the 3d electronic states of the X²⁺ ion. This method can give electronic band gap that is in very good agreement with the optical band gap for some materials. So far, only a few limited theoretical work have been conducted on the structural, magnetic and electronic properties of the SeMnO₃ and SeNiO₃ compounds [[4], [5], [6], [7], [8],10]. In the present study, the structure, electronic structure, magnetic properties, elastic constants, elastic moduli, elastic anisotropy factor and Debye temperature properties of SeXO₃ have been analyzed in detail within the framework of LSDA and LSDA + U calculations. Until now, neither an experimental study nor a theoretical calculation has been made on the elastic constants of the SeXO₃ compounds. The mechanical properties of SeXO₃ compounds were determined for the first time in this study.