Spin Gapless Semiconductor–Nonmagnetic Semiconductor Transitions in Fe-Doped Ti₂CoSi: First-Principle Calculations

Abstract

Employing first-principle calculations, we investigated the influence of the impurity, Fe atom, on magnetism and electronic structures of Heusler compound Ti₂CoSi, which is a spin gapless semiconductor (SGS). When the impurity, Fe atom, intervened, Ti₂CoSi lost its SGS property. As Ti^A atoms (which locate at (0, 0, 0) site) are completely occupied by Fe, the compound converts to half-metallic ferromagnet (HMF) TiFeCoSi. During this SGS→HMF transition, the total magnetic moment linearly decreases as Fe concentration increases, following the Slate–Pauling rule well. When all Co atoms are substituted by Fe, the compound converts to nonmagnetic semiconductor Fe₂TiSi. During this HMF→nonmagnetic semiconductor transition, when Fe concentration y ranges from y = 0.125 to y = 0.625, the magnetic moment of Fe atom is positive and linearly decreases, while those of impurity Fe and Ti^B (which locate at (0.25, 0.25, 0.25) site) are negative and linearly increase. When the impurity Fe concentration reaches up to y = 1, the magnetic moments of Ti, Fe, and Si return to zero, and the compound is a nonmagnetic semiconductor.

1. Introduction

As one of the most outstanding material classes, Heusler compounds with a chemical formula of X₂YZ are a large family containing more than 1500 members [1,2]. When the number of valence electrons (VEs) of X atom is more than that of Y atom, Heusler compounds are known to be of a conventional type, i.e., Cu₂MnAl type with a space group of FM-3M, see Figure 1a [3]. While, when the number of VEs of X atom is less than that of Y atom, Heusler compounds crystallize in an inverse type, i.e., Hg₂CuTi type with space group of F-43M, see Figure 1b [4]. In addition, when two X atoms are different, the chemical formula of Heusler compounds converts to XX’YZ, and it is a quaternary type, i.e., LiMgPbSn type with space group of F-43M, see Figure 1c [5,6]. Owing to the fact that there is huge number of Heusler compounds that could be comprised by a combination of different elements, Heusler compounds exhibit diverse properties. Several Heusler compounds, such as Co₂MnSi, Ti₂CoAl, CoFeMnAl, and others, have been theoretically predicted and experimentally confirmed to be half-metallic ferromagnets [7,8,9,10,11,12,13]. Due to the special band structure, that the majority of the band shows metallicity, while an energy gap exists in the minority band, half-metallic Heusler compounds could offer theoretically 100% spin-polarized current. Besides, most of the half-metallic Heusler compounds possess high Curie temperature, and their lattice constants are very close to many semiconductors, such as MgO and GaAs. They are, therefore, regarded as one of the most excellent candidates for electrode materials of spintronics devices, such as magnetic tunnel junctions (MTJ) and current-perpendicular-to-plane spin valves (CPP-SV), and have a great application potential in magnetic random access memory (MRAM), ultra-high-speed reading in magnetic read heads of hard disk drivers (HDD) and spin transfer torque (STT) devices in spin random access memory [14,15,16,17,18,19,20,21]. In addition, a lot of Heusler compounds, especially half-Heusler compounds with chemical formula of XYZ, exhibit semiconductor character. Owing to high Seebeck coefficient, large electrical conductivity, good thermal stability, and environmentally friendly constituents, semiconducting Heusler compounds, such as n-type MNiSn (M = Ti, Zr, Hf) and p-type ErNiSn, HfPtSn, became promising thermoelectric materials which could recycle waste heat into electricity [22,23,24,25]. Hence, they are great useful for wearable devices like smart watches, and for sensors in industrial process monitoring. More recently, much attention has been paid to a new subfamily of Heusler compounds which were characterized with a novel band structure, that there is an energy gap that lies in minority bands, while the valence and conduction band edges of the majority of electrons touch at Fermi level, resulting in a zero-width gap. They are, therefore, classified to be spin gapless semiconductors (SGSs) [26]. Heusler compound Mn₂CoAl with SGS properties has been successfully fabricated, and high Curie temperature (T_C) of 720 K as well as magnetism of 2 μ_B were detected [27,28,29]. Others, like Ti₂CoSi and CoFeCrGa, also received intense research interest [30,31,32,33,34]. Owing to the extraordinary band structure, both electrons and holes of SGS Heusler compounds can be spin-polarized, and almost no threshold energy is required to move electrons from the valence band to the conduction band, as the mobility of carriers is stronger than that in regular semiconductors. Hence, they are considered to be possible candidates to substitute for diluted magnetic semiconductors (DMS) [35]. Due to the reason that diverse valence electrons configurations of Heusler compounds result in varied magnetic properties and electronic structures, in this paper, we studied the influence of impurity Fe atom on magnetism and electronic structures of Heusler compound Ti₂CoSi.

2. Structures and Calculation Methods

All calculations are performed by employing the VASP Package based on the density functional theory (DFT) [36]. Plane-wave basis sets, together with the projector-augmental wave (PAW) [37] method, are chosen to deal with electron–ion interaction. The valence-electron configurations of Ti (3d²4s²), Fe (3d⁶4s²), Co (3d⁷4s²), and Si (3s²3p²) are selected. The 7 × 7 × 7 mesh of special k-points in the Brillouin zone is applied. In the self-consistent calculation, we select the refined 1 × 10⁻⁶ eV/atom as the SCF convergence criterion, and 360 eV as energy cutoff, respectively. When the positions of atoms are relaxed, we set a convergence criterion of 0.02 eV/Å. All structures are built with 2 × 1 × 1 supercell. For the doped compound calculations, we geometrically optimize all supercells by using the same parameters employed in the bulk calculation. All technical parameters have been tested carefully to ensure the accuracy of the results.

3. Results and Discussion

Interface Structures

The electronic structure of Ti₂CoSi is firstly calculated. In Figure 2, there is a large energy gap of 0.671 eV exists in spin down band, and the Fermi level locates at the top of the gap. Such an energy gap is a result of exchange splitting between spin down unoccupied antibonding bands (which are localized at Co, Ti^A and Ti^B atoms) and spin down occupied bands (which are predominantly of Co character). As for spin up band, it exhibits an obvious zero-width gap around the Fermi level. It also can be seen from Figure 3 that the maximum of the valence band sits at Γ point, while the minimum of the conduction bands locates at X point; such a closed spin up gap, therefore, is an indirect gap.

When Fe atom is introduced into Ti₂CoSi, it could lead to four doping structures, thus, X(Fe) doping structure where X atom (X = Ti^A, Ti^B, Co, Si) is substituted by an Fe atom. In order to determine which doping structure is more favorable, the formation energy is calculated by the following equation $E_f=E^{\prime }-E-{\displaystyle \sum _i{n}_i{\mu }_i}$, where E_f is formation energy, and E′ and E are total energy of the doping structure and undoping structure, respectively. The integer n_i is the number of atoms that has been removed from (n_i is negative value) or added to (n_i is positive value) to form the disorders, and μ_i is the corresponding chemical potential which represents the energy of the reservoirs. According to our calculation, the highest E_f of 1.028 eV belongs to Ti^B(Fe) doping structure, and that of Co(Fe) and Si(Fe) are also as high as −0.023 eV and −0.018 eV, respectively, while the minimal E_f of −0.927 eV occurs in Ti^A(Fe) doping structure. It reveals that Ti^B, Co, and Si atoms are hard to be replace by Fe atom, however, Ti^A atom could be easily replaced with Fe atom. Therefore, we focus on the Ti^A_1−xFe_xTi^BCoSi doping structure, where the doping concentration x = 0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, and 1.

In Figure 4, when the Fe atom intervenes in Ti₂CoSi and the doping concentration increases, the zero-width gap in spin up states is destroyed, and the spin up band strides over the Fermi level and shows metallic behavior. On the other hand, doping Fe atom produces a negative impact on the spin down energy gap, causing the width of the gap to vanish, and the Fermi level drops into a spin down conduction band. As a result, the SGS character of Ti₂CoSi is completely destroyed by the impurity Fe atom. When the doping concentration x = 0.875, the top of the spin down valence band and the bottom of spin down conduction band touch at Fermi level, and form an indirect closed spin down gap. The doping structure, Ti^A_0.125Fe_0.875Ti^BCoSi, is a gapless half-metal. As the doping concentration increases up to x = 1, the closed spin down gap is opened, while the spin up states still cross the Fermi level. Therefore, when x = 1, the structure converts to a quaternary Heusler alloy TiFeCoSi with half-metallic character.

It can be seen from Figure 5 that TiFeCoSi possesses a wide half-metallic energy gap of about 0.56 eV, and the Fermi level is located slightly above the middle of the gap and, hence, it is predicted to have stable half-metallicity. Both spin down occupied bonding bands and spin down unoccupied antibonding bands are mainly localized by Co and Fe atoms. Figure 6 shows the half-metallicity of TiFeCoSi as a function of the lattice constant, and it holds the half-metallic energy gap when its lattice constant increases from 5.4 Å to 6.1 Å. When the lattice constant is 5.4 Å, the Fermi level lies at the top of spin down valence band, and when TiFeCoSi is further compressed, the Fermi level would drop into the valence band and lose its half-metallicity. With the lattice constant increases, the Fermi level gradually moves from a low energy zone to a high energy zone. As the lattice constant increases up to 6.1 Å, the Fermi level locates at the bottom of spin down conduction band, and when TiFeCoSi is further stretched, the Fermi level would move into the conduction band, and half-metallicity is also destroyed.

The atom-resolved spin magnetic moment (AMM) and total magnetic moment (TMM) of Fe doped Ti₂CoSi as a function of Fe concentration is shown in Figure 7. As for pure Ti₂CoSi, Ti^A and Ti^B contribute the main part of TMM, while Co offers a small part, due to the reason that low valence transition metal Ti atom has larger spin splitting than the high valence transition metal Co. When Fe atom doping in Ti₂CoSi forms Ti^A_1−xFe_xTi^BCoSi, the contribution of Fe atom to the TMM is lower than Ti^A atom. As the Fe doping concentration increases, the AMM of Ti^A, Ti^B, and Fe atoms lineally decline, while AMM of the Co atom is enhanced, and it is almost as high as Fe atom when the doping concentration increases to x = 1. It also can be seen that when x ranges from 0 to 0.625, the AMMs of Ti^A, Ti^B, Fe, and Co are positive values, indicating the ferromagnetic arrangement among these transition metal elements. While, when x > 0.625, the AMM of Ti^B atom reverses to a negative value, leading to the fact that the doped structure changes into a ferrimagnet. Overall, the TMM lineally decreases with Fe concentration increases, and it is in good agreement with the Slater–Pauling rule, which can be written as TMM = Z − 24, where Z is the total number of valence electrons.

Based on the half-metallic TiFeCoSi, we continue to introduce the impurity, Fe atom, and impurity Fe may occupy Ti, Co, or Si atoms, forming a Ti(Fe), Co(Fe), or Si(Fe) doping structure, respectively. The formation energy of these three possible doping structures are also calculated by Equation (1). Si(Fe) and Ti(Fe) doping structures respectively exhibit high formation energies of 1.895 eV and 1.437 eV, revealing that Si and Ti are hard to be replaced by Fe atom. While Co(Fe) doping structure possesses the minimal formation energy of −0.153 eV, indicating that the Co atom is easily occupied by Fe atom and forms the TiFeCo_1−yFe_ySi doping structure, where y is the concentration of the impurity Fe atom, and y = 0.125, 0.25, …, 0.875, 1. Figure 8 shows the band structures of TiFeCo_1−yFe_ySi. When impurity Fe concentration y ranges from 0.125 to 0.625, spin up bands stride over the Fermi level, while there is an obvious energy gap that exists in the spin down bands. Therefore, TiFeCo_1−yFe_ySi maintains its half-metallicity when the impurity Fe concentration increases from 0.125 to 0.625. As y increases to 0.75, the Fermi level drops into the spin down conduction band, and the doping structure loses its half-metallicity, and the spin polarization decreases to about 74%. In addition, with an increase of the impurity Fe concentration, the overlap degree between spin up valence band and spin down valence band increases. When y reaches up to 0.875, the Fermi level still exists in the spin down conduction band, and there is much overlap between the spin up and spin down bands, and the energies of the spin up and spin down bands are almost the same, making the spin polarization seriously drop to only 3%. Hence, the doping structure TiFeCo_0.125Fe_0.875Si can be regarded as pseudo-semiconductor. As the impurity Fe concentration further increases up to y = 1, the spin up and spin down bands completely overlap, and there is an energy gap of 0.418 eV that exists in both spin up and spin down band, and the structure Fe₂TiSi therefore converts to a semiconductor.

The AMM and TMM of Fe doped TiFeCoSi as a function of impurity Fe concentration is exhibited in Figure 9. When impurity Fe concentration increases from 0.125 to 0.75, AMM of Co atom has a slight increase, while that of the Fe atom descends obviously. In addition, the absolute value of AMMs of Ti^B and impurity Fe are weakened. It should be noted that when the impurity Fe concentration y increases to 0.875, the AMM of Co atom suffers a sharp decline, and AMMs of all atoms are extremely close to zero, owing to the fact that TiFeCo_0.125Fe_0.875Si shows a pseudo-semiconductor property. Furthermore, AMMs of Co and Fe are positive values, while that of Ti^B and impurity Fe are negative values, indicating that doping structure TiFeCo_1−yFe_ySi is a ferrimagnet when y ranges from 0.125 to 0.75. As the impurity Fe concentration further increases up to y = 1, AMMs of all atoms are zero. As a result, Fe₂TiSi is a nonmagnetic semiconductor.

4. Conclusions

We investigated the influence of impurity Fe atom on magnetism and electronic structures of Heusler compound Ti₂CoSi by using the first-principle calculations within density functional theory (DFT). Ti₂CoSi is a spin gapless semiconductor (SGS) with an indirect closed spin down energy gap. It lost its SGS property when the impurity Fe atom intervened, and when the concentration of impurity Fe atom increases to x = 0.875, the compound shows gapless metal character. At the doping concentration of x = 1, Ti^A atoms are completely occupied by impurity Fe atoms, and the compound converts to TiFeCoSi, which is a half-metallic ferromagnet (HMF). During this SGS→HMF transition, the total magnetic moment linearly decreases with the concentration of impurity Fe atom increasing, which follows the Slate–Pauling rule well. When the impurity Fe further increases from y = 0.125 to y = 0.625, the doping compounds maintain their half-metallicity. While, when the doping concentration increases up to y = 1, the compound converts to semiconductor Fe₂TiSi. During this HMF→nonmagnetic semiconductor transition, when the concentration of impurity Fe atom ranges from y = 0.125 to y = 0.625, the magnetic moment of Fe atom is positive and linearly decreases, while that of impurity Fe and Ti^B are negative and linearly increase. When all Co atoms are substituted by Fe atoms, the magnetic moments of Ti, Fe, and Si return to zero, and the compound, therefore, is a nonmagnetic semiconductor.