Electronic and magnetic structures of Fe3O4 ferrimagnetic investigated by first principle, mean field and series expansions calculations

doi:10.1016/j.jmmm.2014.10.135

Journal of Magnetism and Magnetic Materials

Volume 378, 15 March 2015, Pages 37-40

https://doi.org/10.1016/j.jmmm.2014.10.135 Get rights and content

Highlights

•
Ab initio calculations, based on DFT approach and FLAPW are used to study the electronic properties of Fe₃O₄.
•
Magnetic moments of Fe₁ and Fe₂ are estimated to −/+3.44 µ_B.
•
HTSE method is used to calculate the Néel temperature of Fe₃O₄.

Abstract

Self-consistent ab initio calculations, based on density functional theory (DFT) approach and using a full potential linear augmented plane wave (FLAPW) method, are performed to investigate both electronic and magnetic properties of the Fe₃O₄. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Fe plans. Magnetic moment considered to lie along (010) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions (HTSEs) calculations to compute other magnetic parameters. The exchange interactions between the magnetic atoms Fe–Fe in Fe₃O₄ are given using the mean field theory. The high temperature series expansions (HTSEs) of the magnetic susceptibility of with the magnetic moments, m_Fe in Fe₃O₄ is given up to seventh order series in (1/k_BT). The Néel temperature T_N is obtained by HTSEs of the magnetic susceptibility series combined with the Padé approximant method. The critical exponent $γ$ associated with the magnetic susceptibility is deduced as well.

Introduction

Iron oxides have many different technological applications, ranging from coloring of glasses to magnetic recording. Among iron oxides, magnetite (Fe₃O₄) is a material that displays interesting magnetic properties, mostly when the particles are in the nanometric scale. Bulk magnetite is a ferrimagnetic compound with Curie temperature close to 860 K [1]. The oxygen anions form a face-cantered cubic lattice with Fe²⁺ and Fe³⁺ cations in interstitial sites. The tetrahedral (A) sites are occupied by Fe³⁺, and the octahedral (B) sites are randomly occupied by both Fe³⁺ and Fe²⁺, resulting in an inverse spinel structure [2]. For the spinel crystal structure, the scenario of electron transfer between different elemental ions on A and B sites has also been reported, e.g., with Fe₃O₄ [3] by magneto-optical effects. The synthesis and some physical properties of magnetite (Fe₃O₄) an particles is established by Ref. [4]. Another related ferrimagnetic oxide system, namely, (Fe₂O₃), has also been widely studied from the point of view of hysteretic behavior and exchange bias properties [5], [6], [7], [8], [9]. Magnetite has recently been of particular interest for being an excellent candidate for spintronics applications due to the high degree of spin polarization in one of the spin subbands at the Fermi level and at room temperature [10], [11], [12], [13]. Different facts point out to the surface of magnetite at nanoscale behaving in an entirely different manner than bulk magnetite. Surface studies in magnetite thin films showed the influence of surface morphology, roughness, and stoichiometric inhomogeneities on the electronic structure [14]. Ab initio calculations by employing density functional theory (DFT) with the generalized gradient approximation (GGA) and local-density approximation+U approaches to determine the electronic structure for five different (111) surfaces of Fe₃O₄ revealed that, depending on the particular cation distribution on the surface, either metallic or half-metallic (as in bulk Fe₃O₄) behavior can be found [11]. A half-metal to metal transition at the (100) Fe₃O₄ surface has been also observed by means of spin-resolved photoemission experiments on epitaxial and high quality thin films as well as by DFT-GGA calculations [15]. Such a half-metal to metal transition has also been confirmed by using first-principles calculations in four different Fe₃O₄ (001) surfaces [16].

Different theoretical models and numerical approaches, including recent experimental findings [9], have also been performed in order to contribute to the current understanding of exchange bias in nanoparticles [17], [18], [19], [20], [21], [22], [23].

In this work, three approaches self-consistent ab initio calculations, mean field and temperature series expansions (HTSEs) calculations are used to shed light on the magnetic structure. Firstly, FLAPW calculations based on DFT principle are performed on Fe₃O₄. Appropriate polarized spin and spin–orbit coupling as well as antiferromagnetic state are considered. Considering computed magnetic moment from FLAPW calculations as input data, we have used the mean field theory to find the first and second exchange interactions between the magnetic atoms Fe–Fe in Fe₃O₄. The high temperature series expansions (HTSEs) of the magnetic susceptibility of Fe₃O₄ combined with the Padé approximant [24] is studied up to tenth order series in (β=1/k_BT). Finally, the Néel temperature is deduced.

Section snippets

Electronic structure calculations

We used the FLAPW method [25] which performs DFT calculations using the local density approximation with wave functions as a basis. The Kohn–Sham equation and energy functional were evaluated consistently using the full potential linearized augmented plane wave (FLAPW) method. For this method, the space was divided into the interstitial and the non-overlapping muffin tin spheres centered on the atomic site. The employed basis function inside each atomic sphere was a linear expansion of the

High temperature series expansion

In order to deduce the expression of the susceptibility of the system with two sublattices, the Hamiltonian of the Heisenberg with extern field $h$ may be put in the form $H = - 2 J_{A A} \sum_{〈 i, i^{`'} 〉} {\vec{S}}_{i} {\vec{S}}_{i'} - 2 J_{B B} \sum_{〈 j, j' 〉} {\vec{σ}}_{j} {\vec{σ}}_{j'} - 2 J_{A B} \sum_{〈 i, j 〉} {\vec{S}}_{i} {\vec{σ}}_{j} - μ_{B} h (g_{A} \sum_{i} S_{i}^{z} - g_{B} \sum_{j} σ_{j}^{z})$ where $\vec{S}$ and $\vec{σ}$ are spin vectors of magnitudes ${\vec{S}}^{2} = S (S + 1)$ and ${\vec{σ}}^{2} = σ (σ + 1)$ in sublattice $A$ and $B$ respectively. $g_{A}$ and $g_{B}$ are the corresponding gyromagnetic factors and $μ_{B}$ is the Bohr magneton. $h$ is an external magnetic field (z direction) introduced in

Results and discussions

FLAPW calculations were performed to investigate both electronic and magnetic structures for Fe₃O₄. They evidence that the DOS originates essentially from contributions of Fe atoms as seen in Fig. 1. The projected DOS on Fe₁ and Fe₂ at octahedral and tetrahedral sites, respectively, points out that DOS of both atoms is dominated by the Fe(3d) band contributions (Fig. 2, Fig. 3) whereas the projected DOS on O atoms shows only small contributions from O(2p) band contributions (Fig. 4). Magnetic

Conclusions

FLAPW calculations were performed to investigate both electronic and magnetic structures for Fe₃O₄. They evidence that the DOS originates essentially from contributions of Fe atoms. Magnetic moments carried by Fe atoms were computed as well and used as input data for HTSEs calculations. The magnetic properties are investigated using the high-temperature series expansions of magnetic susceptibility. As results, The Néel temperature T_N (K) is estimated from the divergence of the magnetic

References (30)

H. El. Ghandoor et al.
Int. J. Electrochem. Sci.
(2012)
E. Tronc et al.
J. Magn. Magn. Mater.
(2003)
Ó Iglesias et al.
Physica B
(2004)
E. Arisi et al.
J. Magn. Magn. Mater.
(2007)
Ó Iglesias et al.
Physica B
(2006)
K.N. Trohidou et al.
J. Magn. Magn. Mater.
(2007)
D. Kechrakos et al.
J. Magn. Magn. Mater.
(2007)
Ó Iglesias et al.
J. Magn. Magn. Mater.
(2007)
P. Blaha et al.
Comput. Phys. Common.
(1990)
P.G. Bercoff et al.
J. Magn. Magn. Matter.
(1997)

A.A. Farghali et al.

J. Mater. Process. Technol.

(2007)

L. Néel

Ann. Phys.

(1948)

W.C. Hamilton

Phys. Rev.

(1958)

W.F.J. Fontijn et al.

Phys. Rev. B

(1997)

B. Martínez et al.

Phys. Rev. Lett.

(1998)

Cited by (33)

Rare earth based Mg- chalcogenides MgDy<inf>2</inf>(S/Se)<inf>4</inf> as an emerging aspirant for spintronic and thermoelectric applications
2024, Materials Science in Semiconductor Processing
The magnesium based spinel chalcogenides are outstanding materials for spintronic technology and energy applications. Herein, the modified Becke Johnson potential (TB-mBJ) was employed to investigate the electrical, ferromagnetism, and thermoelectric properties of MgDy₂(S/Se)₄ spinels comprehensively. The energy emitted during optimization as well as formation energy has both been used to demonstrate the stability of the cubic phase. The density of states, Curie temperature, exchange coupling, and spin polarization are elaborated to address the nature of ferromagnetism. Further, half metallic ferromagnetism is studied in terms of hybridization, exchange energies, and exchange constants. In contrast to the clustering effect of the internal magnetic of Dy atoms in the structure, the lowering of Dy's magnetic moment and its transferring on Mg, and S/Se sites demonstrate that the ferromagnetism is caused by the exchange of electron spin. Furthermore, thermoelectric properties were studied and various thermoelectric parameters such as electrical and thermal conductivities, Seebeck coefficient (S), and power factor (PF) of the examined spinels have been determined.
Field induced metamagnetic transition and mixed charge transfer Mott-Hubbard character in nanocrystalline FeCo<inf>2</inf>O<inf>4</inf> spinel oxide: A combined study using experimental and first principles techniques
2024, Journal of Alloys and Compounds
Unusual magnetic behavior of nanocrystalline FeCo₂O₄ (FCO) has been observed at different annealing temperatures. FCO nanoparticles have been prepared by co-precipitation method and the prepared sample annealed at different temperatures to vary its crystallite size. The powder x-ray diffraction analysis confirms the presence of pure spinel phase in the samples annealed at 900 $℃$ and 1000 $℃$ . The increase in particle size with annealing temperature has been confirmed by field emission scanning electron microscopy (FESEM) analysis. High resolution x-ray photoelectron spectroscopy (HRXPS) analysis reveals the presence of mixed oxidation states of Fe⁺²/ Fe⁺³ and Co⁺³/Co⁺² in the sample annealed at 900 $℃$ . The as-synthesized sample at 80 °C shows strong antiferromagnetic behavior due to their smaller particle size, but all the annealed samples have strong ferromagnetic behavior with large coercive field and remanence due to their larger particle size. We have observed a sharp rise in magnetization near small field values in the virgin curve and also the presence of virgin curve completely outside the main hysteresis loop in the M(H) curves measured at 5 K for the samples annealed at and above 1000 $℃$ reveal the characteristic of first order nature of field induced metamagnetic transition. Structural parameters obtained after Rietveld refinement of powder x-ray diffraction pattern for sample annealed at 900 $℃$ have been used for investigating the magnetic properties using first principles density functional theory. Our calculations using hybrid exchange-correlation functional, HSE06 captures the correct insulating ferromagnetic ground state and band gap for inverse spinel structure in broad agreement with our experimental results while calculations within GGA+U leads to a wrong half metallic ferromagnetic ground state. The partial density of states obtained for inverse spinel structure with HSE06 functional suggests a mixed charge transfer and Mott-Hubbard character in our system. We have explored the interplay among structural, magnetic and transport properties of FCO using experiment as well as first principles density functional theory.
Study of electronic, optical and photovoltaic properties of lead-free double perovskite Cs<inf>2</inf>AgXBr<inf>6</inf> (X = Bi, Sb): An ab initio calculations
2024, Computational Materials Science
In this work, the electronic, optical, and photovoltaic properties of the two double perovskites were determined, represented, and interpreted using ab initio calculations. The calculations were based on the generalized gradient of Perdew, Burke and Ernzerhof and Tran-Blaha-modified Becke-Johnson approximations within the framework of density functional theory. Quantities that predict the use of dual perovskites in photovoltaic, such as external quantum efficiency, open-circuit voltage and short-circuit current were calculated. These quantities were calculated based on optical properties, in particular the dielectric function, reflectivity, and absorption coefficient. Based on the electronic properties, the gap values obtained with TB-mBJ are 2.13 eV and 1.65 eV, while those obtained with GGA-PBE are 1.48 eV and 1.07 eV for Cs₂AgBiBr₆ and Cs₂AgSbBr₆, respectively. The variations in external quantum efficiency and optical absorption coefficient show a strong evolution around the range of energies making up the visible spectrum. This makes them promising materials for the photovoltaic industry. We will apply various pressure values, ranging from 0 to 30GPa, to our structures in order to gain an improved comprehension of the effect of pressure on the energy loss function.
Half-metallic ferromagnetism and thermoelectric effect in spinel chalcogenides SrX<inf>2</inf>S<inf>4</inf> (X = Mn, Fe, Co) for spintronics and energy harvesting
2023, Journal of Physics and Chemistry of Solids
Spintronics is an emerging technology in advanced quantum electronics, which has multidirectional applications. In this study, the electronic, magnetic, and thermoelectric characteristics of SrX₂S₄ (X = Mn, Fe, Co) are computed systematically. The stability in ferromagnetic states is verified by energy released from optimized structures and enthalpy of formation. The Heisenberg model is applied for Curie temperature. The band structures are plotted for both spin ↑ and ↓ configurations, which ensure 100% spin polarization and integer magnetic moments. Furthermore, the metallic behavior in spin ↑ and insulating behavior in spin ↓ confirm half-metallic ferromagnetism. The crystal field energy, direct exchange energy, indirect exchange energy, and exchange constants indicate that ferromagnetism is due to spin of electrons rather than any clusters of transition metals. The effect of thermoelectric parameters on spin functionality of electrons is addressed to enhance the device reliability. The thermoelectric performance is reported by power factor in the temperature span 100–500 K, which is important for energy harvesting.
Study of role of spin in ferromagnetism and thermoelectric characteristics of spinel chalcognides MgEr<inf>2</inf>(S/Se)<inf>4</inf> for spintronic and clean energy
2023, Journal of Solid State Chemistry
The rare earth elements are become emerging source of ferromagnetism in spinel chalcogenides which can open the new ways for spintronic industry. Therefore, here in this article, the electronic, ferromagnetic, and transport features of MgEr₂(S/Se)₄ are studied systematically. The enthalpy of formation (ΔH) has been reported for assurance of thermodynamic existence and energy release during optimization in ferromagnetic state (FM) guarantee the magnetic stability. Curie temperature (T_c) describes by Heisenberg through classical model. The spin polarization density, and band structures (BS) evaluation depict the ferromagnetism and complete spin polarization. The densities of states (DOS) are elaborated the role of p-d coupling in terms of exchange energies Δ_x(pd) and Crystal field energy Δ_CF. The exchange mechanism of electrons spin, and exchange constants are calculated to note the energy lowering in spin down which confirm the stable ferromagnetism. Furthermore, thermoelectric characteristics are evaluated for energy harvesting and their effect on electrons spin functionality. The large power factor, and ultralow thermal conductivity make them appealing for thermoelectric generators.
Influence of vacancy on the elastic, thermodynamic and electronic properties of LaMgNi<inf>4</inf> alloys from first-principles calculations
2023, Vacuum
In this work, the structural stability, mechanical, electronic, and thermodynamic characteristics of LaMgNi₄ alloys with different vacancies are discussed in detail. The calculated results of formation enthalpy (ΔH) of LaMgNi₄ alloys with Mg_-Va, Ni_-Va2, La_-Va1 and La_-Va2 vacancies are −0.294eV/atom, −0.273eV/atom, −0.241eV/atom and −0.241eV/atom, respectively, and the results of phonon dispersion curves show that these vacancy models do not exhibit imaginary frequency in any high symmetry direction, which indicates that these models have stable structure. In addition, different vacancies have different effects on the mechanical properties of LaMgNi₄ alloys. For example, the existence of Mg_-Va, La_-Va1, and La_-Va2 vacancies enhances the mechanical properties of LaMgNi₄ alloys, while the existence of Ni_-Va2 vacancy weakens its mechanical properties. From the perspective of electronic structure, the change of mechanical properties of LaMgNi₄ alloys is probably caused by the change of electronic state density at the Fermi level due to the existence of different vacancies. The thermodynamic properties such as the specific heat (C_v) and Debye temperature (Θ_D) of the LaMgNi₄ alloys with different vacancies are calculated by phonon calculations for wide temperature range from 0 K to 1000 K, and further discussed in detail. Finally, the adsorption of O atom on LaMgNi₄ (110) surface and the elastic constants and the elastic modulus of random solid solution alloys of La₄Mg₄Ni₁₄Cu₂ are also investigated.

View all citing articles on Scopus

View full text

Electronic and magnetic structures of Fe3O4 ferrimagnetic investigated by first principle, mean field and series expansions calculations

Highlights

Abstract

Introduction

Section snippets

Electronic structure calculations

High temperature series expansion

Results and discussions

Conclusions

Int. J. Electrochem. Sci.

J. Magn. Magn. Mater.

Physica B

J. Magn. Magn. Mater.

Physica B

J. Magn. Magn. Mater.

J. Magn. Magn. Mater.

J. Magn. Magn. Mater.

Comput. Phys. Common.

J. Magn. Magn. Matter.

J. Mater. Process. Technol.

Ann. Phys.

Phys. Rev.

Phys. Rev. B

Phys. Rev. Lett.

Electronic and magnetic structures of Fe₃O₄ ferrimagnetic investigated by first principle, mean field and series expansions calculations