Insulator -- half metallic transition by the tetragonal distortion: A first-principles study of strain-induced perovskite RbMnF 3
N. Tsogbadrakh, N. Tuvjargal, Chun Feng, J.Davaasambuu, O.Tegus
IInsulator – half metallic transition by the tetragonal distortion:A first – principles study of strain – induced perovskite RbMnF Namsrai Tsogbadrakh , ∗ N. Tuvjargal , Chun Feng , , J. Davaasambuu , and O. Tegus Department of Physics, Natural Science Division, School of Arts and Sciences,National University of Mongolia, Ulaanbaatar 14201, Mongolia Inner Mongolia Key Laboratory for Physics and Chemistry of Functional Materials,Inner Mongolia Normal University, Hohhot 010022, China
From the spin polarized density functional total energy calculations, we shown that the groundstate of cubic perovskite Rubidium Trifluoromangate (RbMnF ) is an antiferromagnetic (AFM)insulator due to the super -exchange mechanism, in agreement with the other theoretical and exper-imental results. As included tetragonal distortion along the c - axis, keeping the predicted volume,our results indicated that strain -induced magnetic phase transition from an AFM insulator to ahalf metallic ferromagnetic (HMFM) state is available by the tetragonal distortion due to the Jahn– Teller distortion. We have shown that the easy axis of cubic perovskite RbMnF is changedfrom the [111] direction to the [001] direction, as created the strain - induced perovskite RbMnF without any external magnetic field. The predicted electronic and magnetic properties of strain - in-duced RbMnF show the HM - FM nature, making strain - induced RbMnF suitable for spintronicapplication. PACS numbers: 71.15.Mb, 75.30.Et, 75.50.Ee
I. INTRODUCTION
Although the most common perovskite compounds contain oxygen, there are few perovskite compoundsthat form without oxygen. The perovskite oxide (e.g., BiFeO , BaTiO , SiTiO etc) are known to undergoferro – or antiferro - electric phase transitions, which are accompanied by distortion of the lattice to a lowercrystallographic symmetry [1]. Many of the alkali transition metal fluorides (e.g., KMnF , RbFeF , KCoF etc) undergo similar phase transitions, which are apparently not associated with ferroelectric ordering [2–4]. After the discovery of antiferromagnetism for rubidium trifluoromangate (RbMnF ) [5], the elastic andmagnetoelastic properties, nuclear acoustic resonance, magnetostriction and magnetocrystalline anisotropy(MCA) of single crystal AFM RbMnF have experimentally investigated [6–10], and the magnetostrictionand magnetoelastic couplings were measured at the 4.2 K in the magnetic fields up to 137 kOe [9]. Thetheoretical and experimental investigations of Mn K – edge for RbMnF have shown the behaviors of 3d – 4pintra – atomic interaction in the conduction bands by resonant X – ray magnetic scattering (RXMS) [11, 12].In order to deeply understand the behavior of fluoroperovskite, the spintronic character and specially the ∗ Electronic address: [email protected] a r X i v : . [ c ond - m a t . m t r l - s c i ] D ec Namsrai Tsogbadrakh et. al., Insulator – half metallic transition by the tetragonal distortion: magnetic properties of the RbMnF compounds were studied by the first – principles calculations [13]. TheAFM materials have been considering renewed attention due to the emerging materials of AFM spintronics[14–20]. Commonly employed to pin the magnetization of an adjacent FM layer in spin valve devices throughthe interfacial exchange bias [21–23], among other developments AFM materials have been recently beenshown to be efficient spin current detectors by meaning of the spin Hall effect [24, 25]. Three AFM materialsthat attracted considerable attention in the past are the following fluoride insulators: FeF , MnF andRbMnF . These compounds show simple three dimensional AFM ordering with two sublattices at thetemperatures below the Neel temperature of 78, 67 and 83 K respectively [26]. Therefore, these insulatorsare not directly used to the AFM spintronics due to the low Neel temperatures, and are shown to be theparamagnetic (PM) phase at the room temperature.The magnetic interactions of FeF , MnF and RbMnF insulators are dominated by nearest neighbor ex-change having effective exchange fields on the same order of magnitude 540, 515 and 830 kOe respectively [26].However, their magnetic anisotropy fields are different by several orders of magnitude. In FeF compound,the ground state configuration of its magnetic Fe ions creates the D term, which has a finite orbital an-gular momentum and consequently a large effective anisotropy field of 190 kOe, arising from the spin – orbitcoupling of single ion [27, 28]. But in MnF and RbMnF compounds, the ground state configuration of theirmagnetic Mn ions creates the S / term with no single ion angular momentum, so that their crystallineanisotropy is small. In MnF , the tetragonal arrangement of the magnetic ions results in a sizable anisotropyof 10 kOe due to the dipolar interaction [29, 30]. However, RbMnF has a cubic perovskite structure with nomeasurable distortion, so that dipolar anisotropy vanishes. As this result, cubic perovskite RbMnF has thevery small magnetic anisotropy of 4.5 Oe [5]. Recently Lopez Ortiz was shown to occur the AFM – spin flop(SF) and SF – FM transitions due to the very small magnetic anisotropy, and obtained the critical magneticfield and SF temperature for the transition from the AFM phase to the SF phase [10].In this study, we consider to occur the insulator – half metallic transition of strain – induced perovskiteRbMnF driving by tetragonal distortion by the first - principles calculations within the framework of spinpolarized density functional theory (DFT). Our results have shown the influence of tetragonal distortion tothe magnetic property of strain – induced perovskite RbMnF . II. COMPUTATIONAL METHOD
The RbMnF usually crystallizes in the cubic perovskite structure with the space group of Pm – 3m ( has the 5 atoms and the atomic positions in RbMnF are sited as follows:Rb atom at the (0, 0, 0), Mn atom at the (1/2, 1/2, 1/2), and F atoms at the (0, 1/2, 1/2), (1/2, 0, 1/2),(1/2, 1/2, 0). In order to create the AFM state, we used the (1 x 1 x 2) supercell in all the calculations.Our calculations are based on the pseudopotential projector augmented wave (PAW) and plane wave (PW)self – consistent field methods using the generalized gradient approximation (GGA) by Perdew, Burke andErnzerhof (PBE) [31] within the framework of DFT [32, 33], as implemented in the QUANTUM ESPRESSO6.3 package [34, 35]. The interactions between the ions and valence electrons are expressed as the nonrelativistic ultrasoft [36] and PAW [37] pseudopotentials taken from the Pslibrary 1.0.0 utility generatedby A. Dal Corso [38, 39]. The following electronic states are treated as valence states: Rb(4s , 4p , 5s ),Mn(3s , 3p , 3d , 4s ) and F(2s , 2p ). The wave functions are expressed as plane waves up to a kineticenergy cutoff of 40 Ry and the kinetic energy cutoff for charge density and potential is chosen by 320 Ry.Three - dimensional Fast Fourier Transform (FFT) meshes for charge density, SCF potential and wavefunctionFFT and smooth part of charge density are chosen to be (60 x 60 x 120) grids. There might be need to usefiner k – points meshes for a better evaluation of on - site occupations due the strong correlated system. Thesummation of charge densities is carried out using the special k – points restricted by the (10 x 10 x 5) gridsof Monkhorst – Pack scheme due to the computer power ability [40]. The linear tetrahedral method is usedwhen the electronic densities of state (DOS) are evaluated [41]. To obtain optimized atomic structures, ionicpositions and lattice parameters are fully relaxed until the residual forces are less than 0.05 eV/˚ A for eachatom. The occupation numbers of electrons are expressed Gaussian distribution function with an electronictemperature of kT = 0.02 Ry. The mixing mode of charge density is chosen to be local density dependentTomas – Fermi (TF) screening for highly inhomogeneous systems. Its mixing factor for self – consistency isto be 0.2 and the number of iterations used in mixing scheme is 5. The generalized eigenvalue problem issolved by the iterative diagonalization using the conjugate gradient (CG) minimization technique, and thestarting wave function is chosen from superposition of atomic orbitals plus a superimposed ”randomization”of atomic orbitals in all our calculation [34, 42]. In order to express the strong correlated effect of electronsin the Mn(3d) state, we first checked the U parameter of Hubbard – based Hamiltonian on – site Coulombinteraction from 2 eV to 7 eV, and was chosen to be U = 5 eV the using the simplified rotational – invariantformulation based on the linear – response method [43]. Atomic wavefunctions used for GGA + U projectorare not orthogonalized. In order to perform the MCA calculations [44–46], we have done the spin polarizeddensity functional total energy calculations of non collinear magnetism (GGA + SOC) including the spin –orbit coupling, using the fully relativistic ultrasoft and PAW pseudopotentials taken from the Pslibrary 1.0.0utility. III. RESULTS AND DISCUSSION
We have first done the full relaxed total energy calculations of nonmagnetic (NM), FM and AFM statesusing both the PW and PAW methods by GGA and GGA + U approaches. We presented the results ofpredicted lattice parameters, band gap, magnetic energy gain between the FM and AFM states (∆ E = E F M − E AF M ), magnetic moments per atom and total magnetization of magnetic ions of RbMnF on TableI. Our results are shown that the ground state of cubic perovskite RbMnF is antiferromagnetically stable.In the PW and PAW methods, the AFM state is found to be energetically more stable by 24.49 and 26.72meV/cell, respectively, than the FM one due to the super - exchange mechanism through Mn – F – Mnbonding by the GGA approach. In these cases, the lattice parameter is predicted to be 4.16 ˚ A , and thesevalues agree with the experimental values of 4.24 ˚ A [47]. The magnetic moment of Mn ion is found to be 4.69 µ B /atom by both the methods. But the band gaps are found to be 1.28 and 1.14 eV by the PW and PAWmethods respectively. These values are different from the experimental value of 2.50 eV for cubic perovskiteRbMnF [12]. Therefore, we considered the strong correlated effect of magnetic Mn ion by the U parameter Namsrai Tsogbadrakh et. al., Insulator – half metallic transition by the tetragonal distortion: of Hubbard – based Hamiltonian on – site Coulomb interaction.For the GGA + U approach, the band gaps are found to be 3.00 and 2.92 eV by the PW and PAWmethods respectively. It is shown an insulating behavior for both the majority and minority channels. Wehave shown the electronic total and orbital projected densities of state (TDOS and PDOS) of AFM and FMstates for cubic perovskite RbMnF using the PAW and PW methods by the GGA + U approach in theFigures (1a, 1b) and (1c, 1d) respectively. The electronic structure of GGA approach is similar to that ofGGA + U approach. These values of band gap of AFM state for cubic perovskite RbMnF agree with theother theoretical value of cubic perovskite RbMnF [12]. In this case, we note that the magnetic momentsincrease up to 4.79 and 4.77 µ B /atom by the PW and PAW methods respectively. The magnetic energy gainsare found to be 6.04 and 11.16 meV/cell by the PW and PAW methods respectively. It is shown that themagnetic energy gain decreases, as included the strong correlated effect of magnetic Mn ion. These resultsaffect to the lattice parameter and predicted lattice parameter decreases up to 4.10 and 4.04 ˚ A by the PWand PAW methods respectively.For the AFM state, the Mn(3d) states are symmetrically and are splitting to the Mn(t g ) and Mn(e g )states by the octahedral crystal field of F ions. The F(2p) state is spreading from -8.6 eV to -2.4 eV andhybridized with the Mn(t g ) state of Mn ion in both the PW and PAW methods. The main peaks of F(2p)states are sited at the positions of -4.6 eV and -5.0 eV by the PW and PAW methods respectively. TheMn(e g ) state is located above the Mn(t g ) state of Mn ion. For the unoccupied states, the separation ofunoccupied Mn(t g ) and Mn(e g ) states is to be smaller than that of occupied states. The intra - atomicexchange splitting (Hund’s coupling) is larger than the band gap of cubic perovskite RbMnF . For the FMstate the majority and minority states are unbalancing and the band gap of minority state is increasing upto 7.14 and 7.52 eV by the PW and PAW methods respectively. These values are shown to be an insulatingbehavior for the minority channel. But the band gap of majority state is decreasing up to 2.69 and 2.59 eVby the PW and PAW methods respectively. It is shown a semiconducting behavior for the majority channel.These results agree with the theoretically results by Hashmi [13].For the PW and PAW methods by the GGA + SOC approach, the lattice parameter is increasing up to 4.30˚ A . The magnetic energy gains between the FM and AFM states are found to be 23.17 and 19.05 meV/cell,and the AFM state is favored to be the ground state of cubic perovskite RbMnF . The magnetic momentsof magnetic ions is found to be 4.21 and 4.20 µ B /atom in the GGA + SOC approach by the PW and PAWmethods respectively. These results are similar to the above results. While the GGA + SOC approach showsthat the SOC is not small and it is affected to the lattice parameter of cubic perovskite RbMnF .The theoretical work is shown that the bulk modulus of cubic perovskite RbMnF is smaller than that ofother cubic perovskites RbXF (X = V, Co and Fe) [13]. Therefore, we created the tetragonal distortionalong the c - axis to the cubic perovskite RbMnF and the total energy calculations of NM, FM and AFMstates have performed at the predicted volume. The magnetic energy gain and magnetic moments of Mn ionare shown in Figs. 2(a) and 2(b) by the GGA and GGA + U approaches, respectively. For the tetragonaldistortion, when the ratio of c and a parameters becomes greater than 1.2 and 1.3 by the PW and PAWmethods, respectively, the FM state is favored due to the insulator - half metallic transition. We haveshown the PDOS of Mn(3d) state in Figs. 2(c) and 2(d) using the PAW and PW methods by the GGA+Uapproach, respectively. The broadening of majority Mn (e g ) state for Mn ion is filling the majority band gapand crossing the Fermi level due to the Jahn-Teller distortion. The band gap of minority state is reduced upto 5.03 and 5.08 eV by the PAW and PW methods by the GGA+U approach, respectively. Therefore, thestrain - induced RbMnF is shown a half metal behavior by tetragonal distortion due to the Jahn – Tellerdistortion. The magnetic moment of Mn ion is decreasing up to 3.79 and 3.71 µ B /atom by the PW andPAW methods by the GGA + U approach, respectively. We have shown the TDOS of NM state for strain -induced RbMnF by the PAW and PW methods into the insets of Figs. 2(c) and 2(d), respectively.In our MCA calculations, we first estimated the MCE defined, as to be MCE=E [100] / [010] / [001] E [111] in thecubic perovskite RbMnF . Our result is shown that the MCE is found to be 4.5 meV/cell. It is shown thatthe easy axis is located along the [111] direction and agrees with the experimental result of cubic perovskiteRbMnF [9]. For the HM – FM strain – induced perovskite RbMnF , we found to be the easy axis alongthe [001] direction, and the MCEs of other spin orientations along the [100]/[010] and [111] directions arefound to be higher than that along the [001] direction by 225 and 126 meV/cell, respectively. Therefore,we observed that the easy axis of cubic perovskite RbMnF is changed from the [111] direction to the [001]direction without any magnetic field.In finally, we should note that all the results of the PAW methods by the GGA, GGA + U and GGA +SOC approaches are indicated to occur the AFM insulator – half metallic ferromagnetic transition by thetetragonal distortion. It is shown that the HM - FM state is favored by the Stoner mechanism of itinerantelectrons. This behavior of strain - induced RbMnF show the HM - FM nature, making strain - inducedRbMnF suitable for spintronic application. IV. CONCLUSION
In conclusion, we have predicted that the ground state of cubic perovskite RbMnF is an AFM insulatordue to the super - exchange mechanism. As included tetragonal distortion along the c - axis, keeping thepredicted volume, our results indicated that the strain - induced magnetic phase transition from an AFMinsulator to a HM - FM state occurs by the tetragonal distortion due to the Jahn – Teller distortion. Weobserved that the easy axis of cubic perovskite RbMnF is changed from the [111] direction to the [001]direction, as created the strain - induced perovskite RbMnF without any external magnetic field. Thepredicted electronic and magnetic properties of strain - induced RbMnF suitable for spintronic application. Acknowledgments
This work has supported by the research project of the Asia Research Center (Korean Foundation forAdvanced Studies) titled Study of rare – earth magnetic materials (code P2017 – 1303) and Fundamentalresearch project SSA 014/2016 funded by the Mongolian Foundation for Science and Technology. We thanksfor performing the calculations on the server computers at the School of Applied Science and Engineering
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TABLE I: The predicted lattice parameters, band gap, magnetic energy gain between the FM and AFMstates (∆ E = E F M − E AF M ), magnetic moments per atom and total magnetization of magnetic ions ofRbMnF using the PW and PAW methods by the GGA, GGA + U and GGA + SOC (U = 5 . A ) 4.16 4.10 4.30 4.16 4.04 4.30 E g (eV) 1.28 3.00 1.14 2.92∆ E (meV/cell) 24.49 6.04 23.17 26.72 11.16 19.05M(Mn )( µ B /atom) 4,69 4.79 4.21 4.49 4.77 4.20M(Mn )( µ B /atom) -4,69 -4.79 -4.21 -4.49 -4.77 -4.20M tot ( µ B /cell) 0.00 0.00 0.00 0.00 0.00 0.00 FIG. 1: (Color online) The total and orbital projected electronic densities of states (TDOS and PDOS) of RbMnF using the PW and PAW methods by the GGA + U approach. The valence band maximum (VBM) corresponds tothe zero. FIG. 2: (Color online) The magnetic energy gains between the FM and AFM states (∆E = E FM - E AFM ) andmagnetic moments of RbMnF using the PW and PAW methods by the (a) GGA and (b) GGA + U approachesrespectively. The orbital projected electronic densities of states (PDOS) of Mn (3d) state for strain – induced perovskiteRbMnF (by the tetragonal distortion of c / a = 1.3) using the (c) PAW and (d) PW methods by the GGA + Uapproach respectively. The VBM of minority state corresponds to the zero. For the inserted figures, the total densityof state (TDOS) of NM states for strain induced RbMnF3