The Magnetic Properties of Gd doped Bismuth-Telluride

For magnetic stability and magnetic phase of alloys doped with magnetic elements in the insulator, the mechanism of interaction is an important subject of Spintronics research and has been actively studied since 1992 when hole-mediated ferromagnetism was reported in a material doped with Mn, a magnetic element [1-4]. Mainly Si, Ge and 3d transition metals are applied to various hosts ranging from III-V groups such as (In, Ga) As to II-VI semiconductors [5-6].

Even though the results of extensive experiments and theoretical studies on dilute magnetic semiconductors (DMS) have been published, the magnetic elements did not develop to the practical level, because they are not evenly distributed in the host but exist as local masses [4,7-8].

In recent years, similar materials have been the subject of interest in the study of magnetic stability and magnetic interaction. They are 3d transition metal and a bismuth chalcogenides alloy which is magnetically doped with rare earth elements. Hosts bismuth telluride and selenide are the traditional and still the most widely used thermoelectric materials. Recent efforts to overcome environmental and energy problems by recycling unused heat through thermoelectric devices have led to the development of highly efficient thermoelectric materials to improve the thermoelectric efficiency of traditional thermoelectric materials. One representative effort is to improve the electrical conductivity of materials and to reduce the thermal conductivity to improve thermoelectric efficiency. Since it is known to be effective, materials with different phonon transfer properties so-called phonon through the formation of heterostructures such as superlattices or doping of heavy elements. Intensive research has been conducted to improve the thermal efficiency by blocking effect.

Among these, bismuth doped with magnetic elements with ferromagnetic and three-dimensional volumetric insulators (TI) -specific Dirac-like electronic structures have been reported in and selenides, attracting the attention of magnetic and phase insulator researchers. Doping elements such as Fe, Co, and Ni, the 3d transition metals with unfilled d bands and magnetically active in bulk, as well as Mn and Cr, which are known to be effective doping elements in DMS, have been studied. Phase surface between ferromagnetic stability, dirac-type electronic structure and bulk bandgap in middle Fe, Cr and Mn doped bismuth telluride / selenide band gap opening due to shift of the topological surface state has been reported.

On the other hand, research about the magnetic properties of the alloy doped with rare earth elements such as Gd or Ce on phase insulators have been relatively recently published. Ferromagnetic stability and quantum anomalous in GdBiTe3 thin films was predicted through the first principles calculation, but experimentally it is pointed out that there is a limit to the melting of Gd to displace Bi. Paramagnetic is reported in all Bi₂-xGd_xTe₃ thin films with x¡0.4 magnetic long-range order is not easily observed experimentally.

But seven Gd with unpaired 4f electrons is larger than the transition metal. Doping elements that have magnetic moments and substitute for +3 trivalent Bi are mainly transition metals with +2 valence. The role of impurity and the effect of charge doping seem to be mixed. On the other hand, the Gd of +3 can only expect the effect of pure magnetic impurity. In terms of magnetic and TI research, magnetic doping is very interesting. Very recently, the magnetic phase change from paramagnetic to antiferromagnetic in the vicinity of Bi₂-xGd_xTe₃ has beenqural optimization and magnetic stability, and discussed the +U, spin-orbit angular momentum interaction, and doping level dependence.

The principal principle of the electronic structure and magnetic stability of an alloy with Bi₂-xGd_xTe₃ bulk gauges with three doping levels of x=1, 1/3, and 1/6 is adopted by the FLAPW method. The Kohn-Sham equation based on the DFT is solved by self-sufficient feedback to obtain the eigenvalues and eigenstates of the ground state. A relatively strongly localized Gd 4f interelectron coulombic potential approaches +U was supplemented by adding a Hubbard term. For this, we used U = 7.7eV and J = 0.7eV, which are (Table 1) known as appropriate values or Gd. Core electrons dealt with completely relativistic by directly solving the Dirac equation. Valence electrons are treated in a quasi-relative manner and include Spin-Orbit Coupling (SOC) as the Second variational approach, but also self-sufficient feedback.

Table 1: Results of the total energy difference between the antiferromagnetic (AFM) and the Ferromagnetic (FM) configurations, ΔE = E_AFM-FM in meV/Gd, using different exchange correlation potentials for the GD bulk.

The Bi₂Te₃ bulkhead, which is the host substance, is small at around 150meV. An insulator with energy bandgap and multiple band maximal / minimum points away from the high-symmetry k-point direction. To obtain bandgaps and electronic structures like these experimental results, complementary exchange potentials such as Screened Exchange LDA. This utility is known, but Approximation (ASA) in Magnetic and Magnetic States.

It was confirmed that it did not affect the qualitatively and so was not adopted in this research. The wave function is described using different types of basic functions by dividing the muffin tin (MT) region around the atom and the interstitial region between them. Bi and Gd are 3.0 au. Te holds the MT region as a circle with a radius of 2.4 au, and within this MT region, it develops as spherical lattice harmonics with an angular momentum cutoff value of L_max=8, and in the lattice crevice region approximately about per atom An energy cutoff value was used to use 100 stiffened planar wave basis functions.

On the other hand, when the host Bi₂Te₃ is represented by hexagonal lattice, the experimental values of in-plane lattice constant a and perpendicular lattice constant c are atomic units, respectively. a=8.28 au and c=45.56 au. In the case of Gd magnetic doping, due to the large size of the doping atoms, not only the existing atomic position but also, the lattice constant can be changed according to the alternative atom type of the host material. After fixing the lattice constants a and c to the experimental values of the host Bi₂Te₃, doping substitution Gd, calculating the atomic forces acting on all atoms and moving the atoms until the forces become negligibly small. The structure was optimized by obtaining

For comparison, we first calculate the total energy difference of the ferromagnetic and sedimentation characteristics of the Gd bulk with the experimental lattice constant using GGA+U and GGA+U+SOC. The first principle calculation of the magnetic stability of the Gd bulk has been controversial for a long time. Earlier, reports of LDA and GGA calculations in the hexagonal structure showed that ferro magnetics had lower energies than antiferromagnetic, (Figure 1) and later Atomic shape approximation (ASA). The electronic structure of the ferromagnetic stability and the position of the filled majority spin band and empty minority spin band of 4f and the position of the empty minority spin band are known to be obtained by adopting the +U correction. have. As shown in our calculations in Table 1, the ΔE values are obtained positively with and without SOC, indicating that the ferromagnetic state is more stable because of the lower energy than the antiferromagnetic state. Considering this, the ferromagnetic stability is slightly increased, which is consistent with other calculations as shown in Table 1. In the case of Gd, the 4f band, which plays a decisive role in magnetism, is extremely localized to the nucleus and there is little overlap with other bands around it. The magnetic interaction is mainly Ruderman-Kittel- Kasuya-Yodsida (RKKY). In this case, as the distance between the Gd atoms increases, the magnitude of the magnetic interactions may not only change, but the ferromagnetic and antiferromagnetic properties may alternately stabilize. Also, in alloys doped with Gd in bismuth telluride, which will be discussed later, even the largest doping level, 50% Gd substitution doping, increases d compared to pure Gd bulk. Therefore, we calculated the delta E by increasing the lattice number of the Gd bulk larger than the experimental value, and the energy difference delta E even when the d increased from the experimental value of 6.76 au to 8.28 au by increasing the lattice constant of about 23%. It was found that ferromagnetic stability was maintained by obtaining = 55meV

Figure 1 shows the result of calculating the energy band and density of states (DOS) of the ferromagnetic Gd bulk with GGA+U+SOC. In the case of calculations involving SOC, the spin is no longer a well-defined quantum, so the two spin channels are not completely distinguished. Can be Fig The result of 1 shows that (i) the fully filled 4f majority spin band is located around -10 eV below the Fermi energy (EF , Fermi level) and the unfilled 4f minority spin band is about 2.5-3 eV above the E_F. 6s-5d character hybridized band is located near Fermi energy. The +U effect was found to significantly (Figure 2) increase the band spacing of the two 4f spin channels, especially when the 4f minority band was calculated as a partially occupied band located across the E_F in the GGA, which gave the wrong result of antiferromagnetic stability. The +U correction gives a correct result of the ferromagnetic stability because it is not occupied by moving upwards above the E_F . On the other hand, the spin separation of about 1eV in the hybridized 6s-5d band shown in the figure is in good agreement with 0.9 eV, which was recently obtained through spin-orbit and angle-resolved photoemission experiments. As a result, it is shown that the influence of the +U correction is hardly affected. On the other hand, the main effect of SOC was to separate the energy degenerate states. In particular, the 4f band has a noticeable effect, which shows a large increase in bandwidth, even in the 5d band near E_F . Small changes in the resulting band dispersion were observed.

The atomic structures for x=2, 1/3, and 1/6 of the Bi₂Te₃ alloy with Gd-substituted Bi in this calculation are shown in Figure 2. For the calculation of ferromagnetic and antiferromagnetic properties, two Gd atoms (Gd1 and Gd2) were taken per unit cell. You will align antiparallel. For antiferromagnetic the Gd1-Gd2 interatomic distances with antiparallel spin arrangements are given as 8.29 (when x =1 and 1/3) and 16.57 (when x=1/6) au. It is not experimentally known whether doped Gd prefers to be uniformly distributed or distributed in clusters of Gd in this type of alloy, and in which case the spin array has antiferromagnetic properties. In this study, the atom and spin structures shown in Figure 2 for each Gd composition are adopted for the convenience of calculation, and it is found that there may be more energy stable structures in each composition than ours. X=1/3 and 1/6 alloys have ferromagnetic Gd planes in the in-plane direction, as shown in the figure. Special spin structures arranged alternately (Table 2).

Table 2: Calculated results of the total energy difference between the antiferromagnetic (AFM) and the ferromagnetic (FM) configurations ΔE = E_AFM-EFM in meV/Gd, and the spin magnetic moments of GD (m_Gd) and TE (m_Te) Muffin-Tins in μ_B for the Bi₂-xGd_xTe₃ bulk alloys with X=1, 1/3, and 1/6.

Table 2 shows the calculation results of the energy difference delta E of their ferromagnetic and antiferromagnetic properties. The calculations show that x=1 for ΔE¡0, so that antiferromagneticity is stable, and x=1/3d = 1/6, positive

ΔE¿ 0 for ferromagnetic stability. However, note that the absolute value of ΔE is very small, about ~1 meV, and the magnetic stability of these alloys obtained by our calculations is very fragile and can easily change due to environmental changes such as slight structural changes or temperature. It can be seen. These ΔE values are very small, only about 1/50 of the delta E values of the Gd lumps shown above. This may be possible if the magnetic interaction is weakened with increasing distance typically seen in the action or if it is in an area where the ground state changes from ferromagnetic to antiferromagnetic. However, to check the possibility, as mentioned earlier, the calculation for a Gd mass with 8.28 au like that of an alloy with d=1 (or 1/3) yielded a large delta E value of 55 meV. This description is not suitable.

Note that the magnetic moment of up to 0.04 μ_B is induced only in the Te atom located closest to Gd. On the other hand, the spin magnetic moment in the MT of the Gd atom was reduced to about 7.04 μ_B in the alloy compared to 7.26 μ_B, which is the value of the Gd bulk having the same d value. In the case of x=1 alloy, which is calculated to be the only stable antiferromagnetic, the spin moment of Te was the highest in the ferromagnetic state. The mechanism of stabilization of Gd magnetic moment alignment through the mediation of Te is like pd hybridization in conventional DMS containing transition metals. Compared to the d band, the f band is much more strongly localized near the nucleus, so This is unusual because overlap is expected to be nearly negligible. In other words, hybridization with neighboring Te atoms could be an important contribution to the alignment of f-band-based magnetic moments

We investigate magnetic stability for Bismuth doped substituted Bismuth Telluride Alloy Bi₂Te₃ (x=1, 1/3, and 1/6). In order to study the electronic structure and to investigate the effect of +U correction and spin-orbit coupling (SOC) on the strongly localized 4f electron interaction, the first-principles calculation based on the density function was performed. And +U for Gd considering the SOCs, the ferromagnetic state is more stable with an energy difference of 77.33 meV/Gd from the antiferromagnetic state

We also show that the Gd-Gd interatomic distance is increased by 23% from the experimental value and is maintained even when calculated to be equal to the value in the alloy with x=1 and 1/3. As a result of the energy calculation, the antiferromagnetic state is stable at x=1, and the ferromagnetic state is stable at x=1/3 and 1/6, but in all cases the energy difference between ferromagnetic and antiferromagnetic is compared to very small ~1 meV/Gd, the magnetic stability of this alloy is very fragile, resulting in very small antisites, etc. It can be easily changed by defects or strains. For weak magnetism at element Te, the nearest neighbor of Gd, the moment is induced and the magnetic moment of Gd decreases, especially in the case of x=1 alloy with anti-ferromagnetic stability, which indicates that the direction of the spin moment induced in Te is antiparallel to the spin moment of Gd. It seems to play an important role in determining magnetic stability.

None.

No conflict of interest.

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