Half Metallic Properties of the Polymorphs of Rubidium Selenide Compound

Half-metallic ferromagnets denote a specific category of compounds where one spin channel exhibits a gap at the Fermi level, contrasting with the metallic nature of the other spin channel. This distinction results in complete carrier spin polarization, reaching 100% at the Fermi level. A first-principles pseudopotential plane-wave method is utilized to examine the structural, electronic, and magnetic characteristics of RbSe across various polymorphs. Our investigation covers the RbSe compound in the CsCl (B2), NaCl (B1), ZnS (B3), NiAs (B81) and wurtzite (B4) phases. The calculations were done using the quantum ESPRESSO code within the generalized gradient approximation. The lattice parameters, bulk moduli, and their pressure derivatives agrees with prior theoretical data for cubic structures. The electronic band structures and density of states indicate the emergence of half-metallic and magnetic properties in RbSe, which stem from the existence of spin-polarized p orbitals within the Se atom. RbSe shows half-metallic behaviour in all structures studied with an integer magnetic moment of 1μB per formula unit for CsCl, NaCl, ZnS; and 2μB for NiAs and wurtzite. Results showed that most energetically stable phase of all five crystal structures studied is the CsCl-type of RbSe.


HALF-METALLICITY IN BINARY COMPOUNDS
In 2000, Akinaga and colleagues made a noteworthy theoretical prediction that was subsequently confirmed through experimental observations, revealing the intriguing half-metallic behaviour exhibited by zinc-blende CrAs [1].Transition-metal chalcogenides and pnictides have gained much attraction in the last decade since most of these kinds of compounds were predicted to have half-metallic properties.The half-metallic trait and lattice structure, comparable to conventional binary semiconductors, make these zinc-blende pnictides and chalcogenides promising materials for spintronics applications.But for the majority of chalcogenides and transition-pnictides, the zinc-blende phase was established as the most stable ground-state structure for the majority of transition-metal chalcogenides and pnictides.Several such compounds, including CrTe, CrAs, MnAs, MnTe and CrSb in the structure of zinc-blende, have been effectively produced using cutting-edge methods like molecular beam epitaxy to create quantum dots and thin films [2], [3], [4].Unfortunately, these IOP Publishing doi:10.1088/1755-1315/1342/1/012011 2 experiments on zinc-blende transition-pnictides and chalcogenides are few due to the instability of the zincblende structure.
Similarly, Fe, Co, and Cr-doped ZnSe in the form of diluted magnetic semiconductors [5] and some binary materials which consist of transition metals such as TiTe and MnAs [6], [7], [8] possess half-metallic properties.Interestingly, some binary alloys without a transition element, as seen in MC (C = Ca, Sr, and Ba) and MS (M = Li, Na, K, and Cs) [9], [10], [11] are some materials known to be half-metals as well as potential ternary cubic alloys [12], [13].It is believed that amongst these half-metallic ferromagnets, the alloys lacking transition elements seems more suitable in spintronics applications because of the possibility of having high Curie temperatures [14], [15].An investigation into the magnetic and electronic characteristics of compounds KM (M = Se and Te) was conducted within various structural configurations including rock salt (NaCl), zinc-blende, CsCl and NiAs.The study, as documented by Rostami and Moradi in 2015 [9], explored these materials in their non-magnetic, ferromagnetic, and antiferromagnetic phases.The findings of Rostami's research revealed that KM (M = Se and Te) compounds, specifically those lacking transition elements, exhibit the highest stability when adopting the CsCl structural arrangement.Additionally, it was observed that these materials exhibit metallic properties when structured in the CsCl and NiAs structures.However, a noteworthy revelation was that in the rock salt and zinc-blende structures, they possessed half-metallic behaviour.With respect to KM (M = Se and Te), the rock salt structure exhibited a magnetic moment of 1  , which is indicative of a half-metallic ferromagnet.
The HM ferromagnetism in zinc-blende structures and rock salt of NaX (X = Po, O, S, Se, and Te) was found to have with an integer magnetic moment of 1  per unit formula [16], [17].The half-metallic property emerges from the hybridization between the p orbital of the X atom and s and p states of the Na atom.A few more examples of half-metallic ferromagnets involving binary compounds not based on transition metals are: i.
CsC in CsCl structure [14].The total energies versus the volume of different structures: CsCl, zincblende, rock salt, NiAs and wurtzite of CsC were compared.The result showed that the compound has a magnetic moment of 1  .ii.
The KS and RbS compounds in the CsCl structure [18], [19].Both compounds without transition elements, are HMFs with a magnetic moment of 1  per unit formula.iii.
Xie and coworkers in 2016 [20] first reported half-metallic behaviour in the cubic structure of RbSe and CrTe.Towards the end of the year 2016, the thermoelectric properties of the binary alloys in the CsCl structure only was reported [21].
This work explores the structural, magnetic and electronic properties of the five polymorphs of Rubidium Selenium (RbSe) using a spin-polarized first-principles calculation.The study encompasses both hexagonal and cubic structures.The subsequent sections provide a detailed breakdown of the paper's organization: Section 2 offers computational details, Section 3 presents comprehensive results and discussions, and the final section offers succinct conclusions.

COMPUTATIONAL METHOD
The calculations using DFT that were carried out using the QE simulation software package [22] uses pseudopotential and plane-wave methods to interpret the interactions between electrons and ions.In this work, the GGA with PBE [23] exchange-correlation functional was used.With the pseudopotential approach, only the valence electrons of Rb and Se were treated to define the Kohn-Sham orbitals described with plane-wave basis sets.Two key parameters, the ecutwfc i.e the wave cutoff and the k-points, determine how well the total IOP Publishing doi:10.1088/1755-1315/1342/1/0120113 electronic energy converges as computed in the plane-wave pseudopotential codes.In this work, the electronic wave function was truncated with energy-cutoff of about 70 Ry for RbSe in the CsCl, NaCl, ZnS, NiAs and wurtzite structure respectively.Due to the ultrasoft pseudopotential used, we set the charge-density cutoff was kept about 700 Ry.The Monkhorst-Pack scheme for the integration of the Brillouin zone [24] was employed.
The converged k-points mesh with a shifted mesh of 16 × 16 × 16 for CsCl, NaCl, ZnS, RbMoSe, RbMoTe and 16 × 16 × 8 for NiAs and wurtzite structures for the self-consistent field calculations.

STRUCTURAL PROPERTIES
The details of the atomic positions of in the crystal for each polymorph of RbSe is presented in Table I.
Geometry optimization for determination of structural properties involves volume optimization, cell shape determination and atomic position optimization so as to determine the ground state geometry.One way to determine the shape of a cell is to do density functional theory (DFT) calculations for all possible values of a=b and c, and find out which value gives the lowest total energy.An alternative (and faster) way is to use an automatic optimization procedure within QE that searches for the set of lattice parameters, unit cell angles and internal positions that makes the stress tensor zero (which corresponds automatically to a minimal total energy).
The optimized lattice constants of the RbSe compound in different configuration in the non-magnetic phase are deducted by fitting the obtained values with Murnaghan equation of states [25] The details of the bulk structural properties are presented in Table II.RbSe compound indicate that all structures studied are ferromagnetic around their equilibrium volume.By observing the ferromagnetic phase (FM) total energies as a function of volume for the RbSe compound, the CsCl structure exhibits the lowest energy (Fig. 3).The ferromagnetic phase of CsCl-type of all five structures considered, has the lowest energy as a function volume for the RbSe compound.This physically implies that the ferromagnetic phase of RbSe in the CsCl structure is found to be the most stable of all structures investigated.The compared results from the antiferromagnetic (AFM), non-magnetic (NM) and ferromagnetic (FM) of RbSe in the CsCl structure was reported by Jolayemi and collaborators [26], and the FM state remains the most stable in the CsCl phase.

MAGNETIC MOMENT
Another characteristic trait of a half-metallic ferromagnet is that its magnetic moment has integer value [27].
The results from this calculation shows that the total moments contain integer Bohr magnetons of 1  and 2  for the cubic and hexagonal structures studied respectively (see Table III).The contributions of each orbital in the five structures of the RbSe compound is stated in Table III.The significant contributions to half-metallic ferromagnetism in such materials arise from the spin polarization of the  and  states.Consequently, these specific compounds are categorized as sp half-metallic ferromagnets.These  half-metallic ferromagnets possess smaller magnetic moments, making them more favorable for applications in spintronic devices.It's well-established that materials exhibiting significant/large magnetic moments are impractical for spintronic applications due to their high stray field and elevated energy loss within the devices [28].In experiments, the molecular beam epitaxy (MBE) growth technique can be used to produce thin films over substrates.On the other hand, the thin film and substrate should almost exactly match in structure.Therefore, the possibility that the CsCl-type RbSe compound will maintain its half-metallic characteristics under pressure and at various unit cell lattice constants must be considered.It is observed that the total magnetic moments remained constant at an integer value equal to 1  as the lattice constant are contracted to 7.5589 a. u. (see Fig. 9).The half-metalicity can be preserved up to 3.78% compression of lattice constant relative to the lattice parameter in its equilibrium state.The result unveils preserved half-metallicity of the CsCl − RbSe compound as its lattice constant is expanded or compressed.Given that an integer magnetic moment is one of a half-metal's primary characteristics, the compound ceases being a half-metal at the lattice parameter with non-integer magnetic moment value.It is found that the compound can retain its HM character when its lattice constant is compressed and expanded thus, it can be grown over numerous substrates with the CsCl structure such as KSe and BSe.We further considered the effect of pressure on the total magnetic moment of RbSe in the CsCl being the most stable polymorph in this work.Similarly, from Fig. 10, as the pressure is increased from 0 to 2.12 GPa, the magnetic moment maintains an integer value of 1  after which the magnetic moment begins to drop.At the zero pressure, the magnetic moment corresponds to the equilibrium lattice constant.

CONCLUSION
The study's findings reveal the potential for half-metallic ferromagnetism in RbSe within non-cubic structures such as NiAs and wurtzite, identifying the CsCl structure as the most energetically favourable polymorph.This research significantly contributes by uncovering RbSe's previously unrecognized half-metallic ferromagnetic properties in hexagonal structures (NiAs and wurtzite), employing the DFT method via the quantum IOP Publishing doi:10.1088/1755-1315/1342/1/01201110 ESPRESSO code to examine RbSe's properties across various structures.Across all polymorphs, integral magnetic moments are observed, with electronic bands demonstrating metallic behaviour for one spin and semiconducting behaviour for the other, characteristic of half-metals.Given the potential applications in spinelectronics, exploring their transport properties is proposed, as modern electronics heavily rely on the movement of charged carriers.

Fig 2 :Fig. 3 :
Fig 2: Energy plot against volume of the Ferromagnetic (FM) and Non-Magnetic (NM) phases of the polymorphs of RbSe.

Fig. 4 :
Fig. 4: Band structure and density of state (DOS) for the spin-polarized state of the  - compound

Fig. 9 :
Fig. 9: Total magnetic moment   per formula unit for  in the  structure as the lattice constants increase in value.

Fig. 10 :
Fig. 10: Magnetic moment of RbSe in the CsCl structure with increasing pressure.

Table 3 .
The contributions made by each state-orbital to the RbSe compound's overall magnetic moment for all configurations under study.