Pseudobinary Compounds Research Articles

Elaboration, Structural and Optical Characterization of the New Ternary Chalcogenide SnSb<sub>2</sub>S<sub>5</sub>

In this study, -antimony sulfide (SnSb2S5) thin films with 200 nm, 312 nm, and 431 nm thicknesses were successfully fabricated using thermal evaporation. These films' structural, optical, and photoanode properties were meticulously characterized to assess their suitability for photovoltaic applications. X-ray diffraction (XRD) analysis confirmed the presence of an orthorhombic symmetry phase within the <em>Pnma</em> space group, ensuring the crystalline quality of the films. Raman spectroscopy further validated the crystal structure and provided detailed identification of the vibrational active modes specific to this pseudo-binary chalcogenide compound. Optical characterization revealed that the SnSb<sub>2</sub>S<sub>5</sub> thin films possess direct optical bandgap energies ranging from 1.91 to 1.99 eV, making them ideal for efficient light absorption in photovoltaic devices. The refractive index (n) displayed minimal variation within the absorption region, indicating stable optical properties. At the same time, it increased proportionally with film thickness outside the absorption region, suggesting enhanced optical behavior with thicker films. This characteristic is particularly advantageous for improving the efficiency of photoanode materials. The combination of favorable structural properties, optimal bandgap energies, and tunable optical responses positions SnSb<sub>2</sub>S<sub>5</sub> thin films as promising candidates for advanced photovoltaic and optoelectronic applications. These findings highlight the potential of SnSb<sub>2</sub>S<sub>5</sub> in developing high-performance photoanodes, contributing to the advancement of solar energy conversion technologies.

Chemical tuning of photo- and persistent luminescence of Cr3+-activated β-Ga2O3 by alloying with Al2O3 and In2O3

An effect of alloying of the monoclinic β-Ga2O3 with Al2O3 and In2O3 on the photoluminescent, thermoluminescent and persistent luminescent properties of Cr3+ ions has been comprehensively investigated. For this purpose, various series of Cr3+ and Ca2+ co-doped microcrystalline phosphors were synthesized by the solution combustion method, including pseudobinary compounds like (Ga-Al)2O3 with up to 20 % Al and (Ga-In)2O3 with up to 50 % In as well as pseudoternary compounds (Ga-Al-In)2O3 with balanced proportion of Al, Ga and In. The phase composition and crystal structure of the obtained materials were examined by X-ray powder diffraction technique. Detailed luminescence studies were conducted for the (Ga-Al)2O3 and (Ga-In)2O3 compounds which exhibited a single-phase monoclinic structure. Low-temperature and time-resolved photoluminescence investigations of the Cr-doped pseudobinary compounds unveiled several types of Cr3+ centres, attributed to the Al-, Ga- and In-centred octahedra in the studied alloys. The obtained results underscore the benefit of bandgap engineering through alteration in the host lattice chemical composition for efficient tuning of the thermoluminescent and persistent luminescent properties of the near-infrared-emitting β-Ga2O3:Cr based phosphors. Furthermore, it was demonstrated that modification of the chemical composition of the host lattice also adjusts the thermometric performance of the studied phosphors. Indeed, the specific sensitivity of the β-Ga2O3:Cr3+ decay time luminescence thermometer showed nearly twofold enhancement when the host lattice was alloyed with 30 % of In2O3.

Modulation of the morphotropic phase boundary for high-performance ductile thermoelectric materials

The flexible thermoelectric technique, which can convert heat from the human body to electricity via the Seebeck effect, is expected to provide a peerless solution for the power supply of wearables. The recent discovery of ductile semiconductors has opened a new avenue for flexible thermoelectric technology, but their power factor and figure-of-merit values are still much lower than those of classic thermoelectric materials. Herein, we demonstrate the presence of morphotropic phase boundary in Ag2Se-Ag2S pseudobinary compounds. The morphotropic phase boundary can be freely tuned by adjusting the material thermal treatment processes. High-performance ductile thermoelectric materials with excellent power factor (22 μWcm−1 K−2) and figure-of-merit (0.61) values are realized near the morphotropic phase boundary at 300 K. These materials perform better than all existing ductile inorganic semiconductors and organic materials. Furthermore, the in-plane flexible thermoelectric device based on these high-performance thermoelectric materials demonstrates a normalized maximum power density reaching 0.26 Wm−1 under a temperature gradient of 20 K, which is at least two orders of magnitude higher than those of flexible organic thermoelectric devices. This work can greatly accelerate the development of flexible thermoelectric technology.

High-pressure synthesis and low-temperature thermal expansion behavior of homogeneous phosphorus-rich pseudo-binary compound (V0.5Cr0.5)P4

A black phosphorus layered homogeneous phosphorus-rich compound – (V0.5Cr0.5)P4 is synthesized using a large volume press under conditions of P = 5 GPa, 1100 °C, and 1 h of heating. (V0.5Cr0.5)P4 has a monoclinic (C2/c) structure with lattice parameters and cell volume of a = 5.2307(3)Å, b = 10.861(4)Å, c = 5.8253(4)Å, β = 110.784°, and V = 309.41(4)Å3, respectively. The thermal expansion behavior above about 110K has been investigated by low-temperature synchrotron XRD. The coefficient of thermal expansion, α, was calculated to be αa = 0.57 × 10−5K−1, αb = 0.70 × 10−5K−1, αc = 0.92 × 10−5K−1, αβ = 0.13 × 10−5K−1 and αv = 2.10 × 10−5K−1 at 293K. This thermal expansion behavior presents an anisotropic expansion characteristic different from pure black phosphorus due to the V/Cr atom that bonded the black phosphorus layers together.

Mechanical and thermoelectric properties in Te-rich Ag2(Te,S) meta-phases

Ductile Ag2(Te,S) pseudobinary compounds have attracted great attention in thermoelectric community since they can be fabricated into high-performance flexible and hetero-shaped thermoelectric devices. However, in spite of the numerous studies, the ‘brittle–ductile’ transition boundary in Ag2(Te,S) is still unclear. In this work, a series of Te-rich Ag2(Te,S) pseudobinary compounds have been prepared. The structure characterizations confirm they belong to the new-concept of meta-phase. The systematically investigation on the mechanical properties demonstrate that the ‘brittle–ductile’ transition boundary appears around x = 0.1. Unexpected good ductility is observed in the Te-rich Ag2Te1–xSx crystalizing in the Ag2Te room-temperature monoclinic structure and high-temperature cubic structure, which are thought to be brittle before. Likewise, Ag content is found to be a very critical parameter determining the ductility of Te-rich Ag2Te1–xSx. Very slight Ag-deficiency can greatly deteriorate the ductility. The thermoelectric properties of these ductile Te-rich Ag2Te1–xSx pseudobinary compounds are investigated. A maximum thermoelectric figure-of-merit of 0.6 is obtained for Ag2Te0.9S0.1 at 600 K. This work sheds light on the future investigation of Ag2(Te,S) pseudobinary compounds.

Mechanochemical synthesis of pseudobinary Ti-V hydrides and their conversion reaction with Li and Na

Lithium-ion batteries (LiBs) based on insertion electrodes reach intrinsic capacity limits. Performance improvements and cost reduction require alternative reaction mechanisms and novel battery chemistries such as conversion reactions and sodium-ion batteries (NaBs), respectively. We here study the formation of Ti1-xVxH2 hydrides (0 ≤ x ≤ 1) and their electrochemical properties as anodes in LiBs and NaBs half-cells. Hydrides were synthesized by mechanochemistry of the metal powders under hydrogen atmosphere (PH2 ∼ 8 MPa). For V contents below 80 at. % (x < 0.8), single-phase pseudobinary dihydride compounds Ti1-xVxH2 are formed. They crystallize in the fluorite-type structure and are highly nanostructured (crystallite size ≤ 10 nm). Their lattice parameter decreases linearly with the V content leading to hydride destabilization. Electrochemical studies were first carried out in Li-ion half cells with full conversion between Ti1-xVxH2 hydrides and lithium. The potential of the conversion reaction is gradually tuned with the vanadium content as result of the hydride induced destabilization. Furthermore, different paths for the conversion reaction are observed for Ti-rich (x ≤ 0.25) and V-rich (x ≥ 0.7) alloys. Na-ion half-cell measurements prove the reactivity between (V, Ti)H2 hydrides and sodium, albeit with significant kinetic limitations.

DFT Simulations of ZnxMg1–XO Solid Solutions for Solar-Blind UV Sensors: Evaluation of Electronic Structure and Phase Stability

Abstract In this research, density functional theory accompanied with linear combination of atomic orbitals (LCAO) method is applied to study the atomic and electronic structure of wurtzite and rocksalt ZnxMg1−xO pseudobinary compounds in their bulk phases. Calculated band gaps of ZnxMg1−xO solid solutions under study are further validated by means of spectroscopic ellipsometry and optical absorption. In agreement with an experiment, it is predicted that increase of Zn content in ZnxMg1−xO leads to narrowing of its band gap for both wurtzite and rocksalt phases. The calculated infra-red (IR) spectra show that the IR peaks are shifted towards larger frequencies along with decrease of Zn content. Presence of imaginary phonon frequencies in rocksalt ZnxMg1−xO of x &gt; 0.625 allows us to suggest that it is necessary to use properly oriented substrates for epitaxial growth to overcome polycrystallinity inZnxMg1−xO thin films at concentration x = 0.4 – 0.6.

Strong-coupling superconductivity with Tc ∼ 10.8 K induced by P doping in the topological semimetal Mo5Si3

By performing P doping on the Si sites in the topological semimetal Mo5Si3, we discover strong-coupling superconductivity in Mo5Si3−xPx (0.5 ≤ x ≤ 2.0). Mo5Si3 crystallizes in the W5Si3-type structure with space group of I4/mcm (No. 140), and is not a superconductor itself. Upon P doping, the lattice parameter a decreases while c increases monotonously. Bulk superconductivity is revealed in Mo5Si3−xPx (0.5 ≤ x ≤ 2.0) from resistivity, magnetization, and heat capacity measurements. Tc in Mo5Si1.5P1.5 reaches as high as 10.8 K, setting a new record among the W5Si3-type superconductors. The upper and lower critical fields for Mo5Si1.5P1.5 are 14.56 T and 105 mT, respectively. Moreover, Mo5Si1.5P1.5 is found to be a fully gapped superconductor with strong electron-phonon coupling. First-principles calculations suggest that the enhancement of electron-phonon coupling is possibly due to the shift of the Fermi level, which is induced by electron doping. The calculations also reveal the nontrivial band topology in Mo5Si3. The Tc and upper critical field in Mo5Si3−xPx are fairly high among pseudobinary compounds. Both of them are higher than those in NbTi, making future applications promising. Our results suggest that the W5Si3-type compounds are ideal platforms to search for new superconductors. By examinations of their band topologies, more candidates for topological superconductors can be expected in this structural family.

The effect of Pd on hydride formation in Zr(PdxM1−x)2 intermetallics where M is a 3d element

We report how the substitution of 3d metal atoms M by Pd in Zr(PdxM1−x)2 pseudobinary compounds affects the stability of the corresponding hydrides. For the lighter elements in the M=3d metal row, V and Cr, the Pd substitution creates less stable hydrides while it yields almost no change in the stability of the hydrides for Mn, of the middle of the 3d row. We further demonstrate that the two factors determining the stability of the hydrides of these compounds are the heat of formation of the compound, ΔHalloy, and its crystal volume, V. Using a combination of these two parameters we predict that the substitution of the heavier 3d metals Fe and Co by Pd stabilizes the Zr(PdxM1−x)2 hydrides, i.e. they would require lower hydrogenation pressures than those necessary for ZrFe2 and ZrCo2 hydride formations. These findings support other authors’ theoretical prediction for ZrPdFe hydride formation. The empirically fitted constants that link ΔHalloy and V are related to the energies needed to expand or compress the crystal lattice and thus have basic physical meaning. We further evaluate the critical temperatures, Tc, for Zr(PdxMn1−x)2-H2 systems from the experimental pressure hysteresis in the absorption-desorption loops. This enables us to show that the electronic contribution to the H-H interaction in the ZrM2 hydride is unexpectedly neutral for M=Mn, it is positive, i.e. repulsive, for the lighter 3d element M=Cr, and surprisingly negative, i.e. attractive, for the binary PdH0.6 hydride.

Investigation of the phase occurrence and H sorption properties in the Y33.33Ni66.67-xAlx (0 ≤ x ≤ 33.33) system

The Y33.33Ni66.67-xAlx system has been investigated in the region 0 ≤ x ≤ 33.3. The alloys were synthesized by induction melting. Phase occurrence and structural properties were studied by X-Ray powder Diffraction (XRD). The Al solubility in each phase has been investigated by XRD and Electron Probe Micro-Analysis (EPMA). The hydrogenation properties were characterized by pressure-composition isotherm measurements and kinetic curves at 473 K. For x = 0, the binary Y33.33Ni66.67 alloy crystallizes in the cubic superstructure with F4̅3m space group and ordered Y vacancies. For 1.67 ≤ x ≤ 8.33, the alloys contain mainly Y(Ni, Al)2 and Y(Ni, Al)3 pseudobinary phases; while for 16.67 ≤ x ≤ 33.33 they are mainly formed by ternary line compounds Y3Ni6Al2, Y2Ni2Al and YNiAl. Contrary to the binary Y33.33Ni66.67, Y(Ni, Al)2 pseudo-binary compounds crystalize in C15 phase (space group Fd3¯m) with disordered Y vacancies. The solubility limit of Al in the C15 YNi2-yAly phase is y = 0.11 (i.e., x = 3.67). The Y(Ni, Al)3 phase changes from rhombohedral (PuNi3-type, R3¯m) to hexagonal (CeNi3-type, P63/mmc) structure for x increasing from 5.00 to 6.67. Upon hydrogenation, the disproportion of C15 Y(Ni, Al)2 and losses of crystallinity of YNi and Y2Ni2Al are the main reasons causing capacity decay of Y33.33Ni66.67-xAlx (0 ≤ x ≤ 33.33) alloys upon cycling.

Collective magnetism of a single-crystalline nanocomposite FeCoCrMnAl high-entropy alloy

We have investigated the nature of the magnetic state of a single-crystalline FeCoCrMnAl nanocomposite high-entropy alloy (HEA), composed of crystallographically oriented magnetic nanoplatelets embedded in a magnetic matrix of different magnetic order. The two-phase nanocomposite was formed by a bcc-B2 spinodal decomposition. Due to the single-crystalline nature of the material, there is no symmetry breaking of the surface atomic monolayer at the borders between the two phases and there are no interface regions between the nanoplatelets and the matrix. The material also does not exhibit grain structure, allowing for the observation of the true intrinsic magnetism of a nanocomposite HEA. Upon cooling, the predominantly Fe‒Cr‒Mn chemically disordered bcc matrix orders first at TC1≈ 425 K in an asperomagnetic-type magnetic state. Below TC2≈ 370 K, the B2 nanoplatelets that are predominantly an Al30(Co,Mn)70 pseudo-binary intermetallic compound, start to order in a ferromagnetic (FM)-type manner. We have focused to the question whether the magnetic state of the nanocomposite below TC2 is a collective state of the interacting nanoplatelets and the matrix or their coupling is weak enough that the magnetic ordering of each of them can be treated independently. Experimental results support the development of a single collective, disordered FM-type magnetic state upon cooling due to the exchange coupling between the nanoplatelets and the matrix. The nanocomposite is magnetically soft and the strong variation of the magnetization with the temperature in a large interval ΔT≈ 125 K just above room temperature due to two successive magnetic phase transitions make this material promising for the application in magnetocaloric refrigeration.

Correlation between the structure and thermomagnetic properties of pseudo-binary (Tb,Er)Ni2 solid solutions

Magnetic and thermodynamic properties, the isothermal magnetic entropy change ΔSmag is among them, of the polycrystalline pseudo-binary Tb1-xErxNi2 (x = 0.25, 0.5, and 0.75) solid solutions are studied in accordance with the erbium substitution for terbium, which causes changing the crystal structure. The Tb1-xErxNi2 solid solutions at room temperature were found to have the C15 Laves-phase superstructure rather than the C15 structure typical of the parent compounds, TbNi2 and ErNi2. Moreover, as was shown by magnetic measurements, the substitution of Er for Tb in Tb1-xErxNi2 results in the decrease in the ordering temperature of the pseudo-binary compounds, which corresponds to the second-order ferromagnet to paramagnet magnetic phase transition; in the case of x = 0.25 and x = 0.75, the decrease is from 29.0 to 13.6 K, respectively.The isothermal magnetic entropy change, which is estimated to characterize the magnetocaloric properties of the pseudo-binary compounds, was analyzed using the thermomagnetic Maxwell relation and in terms of the Landau theory of phase transitions. The maximum magnetic entropy change of the Tb0·75Er0·25Ni2, Tb0·5Er0·5Ni2 and for Tb0·25Er0·75Ni2 compositions reaches 6.6 (12.7), 6.9 (13.8) and 7.5 (14.9) J/kgK for a magnetic field change of 2 (5) T, respectively.The relatively large reversible and close values of ΔSmag allow us to state that these pseudo-binary solid solutions show promise as materials for magnetic refrigerators operating within a specific low-temperature range.

Superconductivity in the Electron-Doped Chevrel Phase Compound Mo6S6.8Te1.2.

Chevrel-phase superconducting compounds AyMo6Q8 (A = Pb, Mg, etc. and Q = S, Se, Te) have attracted much attention due to their ultrahigh upper critical magnetic fields (Hc2). However, the binary compounds Mo6S8 and Mo6Te8 show no superconducting properties above 2 K. In this work, the new Chevrel-phase pseudobinary compound Mo6S6.8Te1.2 with a superconducting transition temperature (Tc) of 3.6 K was successfully synthesized by a two-step process. A detailed investigation implies that the superconductivity in Mo6S6.8Te1.2 may derive from the increased electronic density near the Fermi level in comparison to Mo6S8. Our work provides a feasible scheme to search for new superconducting compounds.

Phase-change properties related to anharmonicity of local structure

Ge-Sb-Te pseudo-binary compounds are known to be phase-change materials (PCM). Most of these chalcogenide compounds are candidate for future phase-change random access memory (PCRAM) applications since they show abrupt change on crystalline-amorphous phase-change process. For the use in next-generation applications, increase of retention properties and decrease of power needed for phase-change process are required. These phase-change properties depend on various material characteristics, and thermal conductivity is one of them. In this study, to introduce an easier method for evaluating the local structural anharmonicity of phase-change materials, optical pump terahertz (THz) probe experiments were performed. By investigating the phonon behaviours in PCM by this method and comparing them with local structural information extracted from extended X-ray absorption fine structure (EXAFS) on Ge1Sb2Te4 and Ge2Sb2Te5 films, the effects of resonant bonding on lattice anharmonicity and thermal conductivity were determined. As resonant bonding in the local structure get enhanced, local distortion of the system decrease which cause the decrease in anharmonicity. The quantitatively-measured anharmonicity obtained from the optical pump THz probe experiments can be closely related to the structural and electrical properties, thus reflecting well the difference of phase-change properties between Ge1Sb2Te4 and Ge2Sb2Te5 films.

Thermodynamic and corrosion study of Sm1-xMgxNiy (y = 3.5 or 3.8) compounds forming reversible hydrides

AB5 compounds (A = rare earth, B = transition metal) have been widely studied as anodes for Ni-MH applications. However, they have reached their technical limitations and the search for new promising materials with high capacity is foreseen. ABy compounds (2 < y < 5) are good candidates. They are made by stacking [AB5] and [A2B4] units along the c crystallographic axis. The latter unit allows a large increase in capacity, while the [AB5] unit provides good cycling stability. Consequently, the AB3.8 composition (i.e. A5B19 with three [AB5] for one [A2B4]) is expected to exhibit better cycling stability than the AB3.5 (i.e. A2B7 with two [AB5] for one [A2B4]). Furthermore, substitution of rare earth by light magnesium improves both the capacity and cycling stability. In this paper, we compare the hydrogenation and corrosion properties of two binary compounds, SmNi3.5 and SmNi3.8, and two pseudo-binary ones, (Sm, Mg)Ni3.5 and (Sm, Mg)Ni3.8. A better solid-gas cycling stability is highlighted for the binary SmNi3.8. The pseudo-binary compounds also exhibit higher cycling stability than the binary ones. Furthermore, their resistance to corrosion was investigated.

Magnetic and transport behaviors of non-centrosymmetric Nd7Ni2Pd

Crystallographic, magnetic, electrical transport and thermodynamic properties of pseudo-binary Nd7Ni2Pd compound have been studied using temperature-dependent x-ray powder diffraction and physical property measurements. Compared to the ferromagnetic parent Nd7Pd3, the ground state of Nd7Ni2Pd is antiferromagnetic, and it exhibits strong metamagnetism. The measurements indicate two antiferromagnetic transitions in fields less than 8 kOe: a second-order paramagnetic to antiferromagnetic at TN2 = 29 K and a weak first-order antiferromagnetic to antiferromagnetic transition at TN1 = 24.5 K. The compound becomes ferromagnetic in fields of 8 kOe and higher with TC = 30 K. Temperature dependence of lattice parameters is anomalous, most prominently in the basal plane at ∼30 K; however, there is no detectable structural distortion or clear volume discontinuity around 25 K, suggesting a significant weakening of the first-order transition when compared to the binary Nd7Pd3.

TbMgNi4-xCox–(H,D)2 System. I: Synthesis, Hydrogenation Properties, and Crystal and Electronic Structures

A series of cubic TbMgNi4-xCox (x = 0–4) pseudo-binary compounds have been synthesized by either a solid-state reaction or mechanical alloying with further annealing treatment. Their hydrogenation properties have been studied by pressure–composition–temperature (PCT) measurements, showing the formation of α-, β-, and γ-hydrides. The Co for Ni substitution yields a lowering of the equilibrium pressure and an increase of the hydrogen capacity. An improvement of the kinetics of hydrogen absorption was observed with an increasing Co content. β-TbMgNi4-xCoxH∼4 (x = 0–3) hydrides show an orthorhombic distortion (Pmn21 space group), whereas the β-TbMgCo4H3.3 hydride crystallizes in a monoclinic structure (Pm space group) derived from the orthorhombic structure. Sensitivity of the formation of the β-TbMgCo4H3.3 hydride to temperature has been observed in PCT curves to exist below 50 °C. γ-TbMgNi4-xCoxHy (x = 2–4, y > 5) hydrides preserve the parent cubic structure (F43m space group) with a hydrogen-induced volum...

Origin of Band Modulation in GeTe-Rich Ge–Sb–Te Thin Film

Germanium tellurides and its pseudo binary compounds offer interesting properties that are important in thermoelectric and phase-change applications. Despite being a class of materials under scrutiny since its discovery, unique properties and functionalities kept on emerging in recent years. In this work, we observed another unique property of Ge-Sb-Te (GST) thin film that can be beneficial in its development for thermoelectric application. A rapid heating and quenching process of the GST film resulted in a metastable rock-salt cubic structure, exhibiting a unique electronic-transition-like behavior. Above the transition temperature at 150 °C, we observed a temperature-induced band modulation, corroborated with changes in its effective mass and valence band position that leads to favorable electronic and thermoelectric properties. Charge transfer between Sb and Te occurred, accompanied by a distorted cubic-to-cubic structural change. The interplay of the electronic and lattice structure born out of the co...

Mutual impact of crystal volume and heat of alloy formation on hydride stabilities in Zr(PdxCr1−x)2 and similar intermetallics

Hydrides of Zr(PdxCr1−x)2 pseudobinary compounds (x = 0.05, 0.1, 0.175) exhibit slight destabilization and more sloped hydrogen plateau pressures with the increase of the palladium content. The former feature conforms to the rule of reverse stability but violates the trend of increased hydride stability upon increasing the unit cell intermetallic volume. A combination of the two effects, the heat of alloy formation and the crystal volume, shows better correlation with the hydride stabilities than considering separately each property. Hydrogen absorption is found in ZrPd2 at ∼60 atm and associated with its moderate shear modulus.

Structural and magnetic properties of Pr5Si3-xGex compounds

The crystal structures, magnetic properties and electronic structures of pseudo-binary compounds Pr5SixGe3-x were investigated. With the increase of the Ge content, structure of Pr5SixGe3-x gradually changes from the tetragonal Cr5B3-type to the hexagonal Mn5Si3-type. For the compounds with the tetragonal structure, the unit cell volumes as well as the magneto-crystalline anisotropy energy (MAE) increase with the Ge content, leading to the diminishing of the magnetization and the maximum magnetic entropy changes -ΔSM. As compared to the binary compound Pr5Si3, the intermetallic compounds with Ge doping show broader working temperature span and considerably large relative cooling power (213.9, and 184.8 J kg−1 at ΔH = 50 kOe for Pr5Si2.5Ge0.5 and Pr5Si2Ge, respectively). For the hexagonal compound Pr5Ge3, a large MAE and an easy magnetization direction close to c axis (polar angle θ ∼7°) were calculated, which is related to the macroscopic magnetic transition behavior at low temperature.