HAN Hong-Pei, FENH Tuan-Hui, ZHANG Chun-Li, LI Ming, FENG Zhi-Bo, YAO Kai-Lun

(1. School of Electric and Mechatronics Engineering, Xuchang University, Xuchang 461000, China;2. School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China)

Abstract: First-principles calculations are employed to study the electronic structure and magnetism of bulk, (111) surfaces and (111) interfaces for rocksalt SrC. It is confirmed that bulk SrC with rosksalt structure is a well d0 half-metallic ferromagnet. The calculated results indicate that both C-surface and Sr-surface in (111) direction preserve the half-metallic characteristic of bulk system. For the four possible (111) interfaces of rocksalt SrC with semiconductor PbS, it is shown from the calculations on the density of states that this kind of half-metallicity still exists in C-Pb interface while it is lost in other three ones. The obtained results on d0 half-metallicity of (111) surfaces and (111) interfaces for rocksalt SrC would stimulate theoretical and experimental efforts toward the practical applications of spintronic devices with superior performance.

Key words: Half-metallicity; Surface and interface; Spintronic devices; First-principles

1 Introduction

In the past two decades, spintronics (also known as magnetoelectronics) has attracted increasing research interest because it can make full use of the spin as well as the electronic properties of electrons where information storage and processing can be performed in the same devices[1-3]. One of the crucial problems for the realization of spintronic devices is the high spin-polarization from ferromagnets into semiconductors[4]. The discovery of half-metallic (HM) ferromagnets provides ideal spin injection materials for spintronic devices due to the unique properties of 100% spin polarization, i.e., half-metallic materials are metallic for one spin channel while at the same time show semiconducting or insulating behavior at the Fermi level for the other spin channel[5].

Half-metallic materials are divided from the origin of magnetism into two classes:dhalf-metals andd0half-metals or sp half-metals. Indhalf-metals, the transition-metaldelectrons provide their main magnetic moments. So far, many compounds have been found to bedhalf-metals, e.g., full-Heusler alloys such as Co2FeSi[6]and Co2CrAl[7], rutile-type CrO2[8], perovskite compounds such as La0.7Sr0.3MnO3[9]and Sr2FeMoO6[10], spinel Fe3O4[11], pyrite-type CoS2[12], and some zinc-blende (ZB) transition-metal pnictides and chalcogenides[13-22]. For the other half-metals,d0half-metals, their magnetisms mainly originate from the anionpelectrons which are different from both the double exchange and thep-dexchange that are important indhalf-metals[23], and therefore this interesting behavior attracted much research interest. Gaoetal. investigated the electronic structures and magnetisms of BaC and SrC with rocksalt (RS) and ZB structure and found them exhibiting robust half-metallic character with respect to the lattice compression and expansion[24, 25]. NaN and KN in the RS structure are excellent HM ferromagnets with wide half-metallic gaps and high Curie temperature[26].

However, it is well known that for the realization of spintronic devices most of HM materials are designed with the form of thin films or multilayers. And so it is very important to investigate the half-metallicity of their surfaces and interfaces for HM ferromagnets since such HM behavior may be lost at the surfaces or interfaces even if a material is half-metallic in the bulk form. For thed0half-metallic thin films, several research groups have studied and found some interesting results. The electronic and the magnetic properties of the (001) surfaces of GeKCa and SnKCa with half-Heusler structure are studied and It is shown that only the surfaces terminated with a carbon group atom retain the half-metallic properties although the two compounds are half-metals in their bulk structures[27]. Gaoetal. investigate systematically the structural, electronic, and magnetic properties of surfaces and interfaces for some bulkd0half-metals of alkaline earth pnictides and carbides and found that the half-metallic properties are lost in many surface and interface structures[23, 28, 29]. Experimentally, Liuetalhave successfully prepared the self-assembled metastable CaN nanostructure[30]. Alkaline earth carbides, such as CaC2, are synthesized in a high yield and with a high purity in monoclinic structure[31]. In this paper, we use the first-principles to study systematically the structural, electronic and magnetic properties of bulk and two (111) surfaces of rocksalt SrC as well as its four possible interfaces with conventional semiconductor PbS. Our calculated results show the two surfaces of rocksalt SrC exhibit welld0half-metallicity and this characteristic is persevered in C-Pb interface of SrC/PbS.

2 Computational method

We use the first-principles full-potential linearized augmented plane-wave (FPLAPW) method implemented in the Wien2k package[32]to study the structural, electronic and magnetic properties of the (111) surfaces for rocksalt SrC and its (111) interfaces with semiconductor PbS. In the present calculations, theRmtKmaxis set to be 7.5 and the expansion is made up tol= 10 in the muffin tins. We choose the radiiRmtof the muffin tins for Sr, C, Pb and S to be 2.3, 2.3, 2.3 and 2.0 a.u., respectively. For the exchange-correlation functional, the generalized gradient approximation (GGA) in the scheme of Perdew-Burke-Ernzerhof (PBE) is adopted[33]. The relativistic effects are taken into account in the scalar approximation, while the spin-orbit coupling is not considered since it has only a small effect on the ferromagnetism of the systems. For the Brillouin zone integration, the 14 × 14 × 1kmeshes is used for considered surfaces and interfaces. The self-consistency calculations are considered to be converged only when the total energy difference between succeeding iterations is less than 10-5Ry/f.u., we also make the corresponding calculations for bulk SrC using the same computational conditions as those of thin films except for 14 × 14 × 14kmeshes for bulk systems to compare the electronic and magnetic properties of bulk SrC with those of their surfaces and interfaces.

3 Results and discussion

3.1 Bulk half-metallicity

To better understand the origin of the half-metallicity for rocksalt SrC, we first construct the crystal cell of SrC with rocksalt structure in Fig. 1 (a) to calculate its electronic and magnetic properties. From the total densities of states (DOSs) for Sr and C atoms of rocksalt SrC in Fig. 1 (b), one can clearly find that rocksalt SrC exhibits well half-metallicity and this characteristic originates mainly from the spin-splitting of C atom of SrC, which show that rocksalt SrC is a kind ofd0half-metal. Moreover, the calculated equilibrium lattice constant of 5.67 Å and magnetic moment of 2.00 μBare same to the previous calculations,[3, 24]which illustrate that our adopted computational method is feasible.

Fig. 1 (Color online) (a) The crystal structure of rocksalt SrC. (b) The total densities of states for Sr and C atoms of bulk SrC with rocksalt structure.

3.2 Surface structure and properties

After understanding the half-metallicity of bulk SrC with rocksalt structure, we next pay our attention to its surface and interface properties. In (111) direction, there are two kinds of surface terminations including C-termination and Sr-termination (for short, C-term and Sr-term). To investigate the electronic and magnetic properties of SrC (111) surfaces, we adopt the relaxed lattice parameter 5.67 Å to simulate these two surfaces by constructing a slab of 19 atomic layers for both C-term and Sr-term. Meanwhile, 12 Å vacuum is added symmetrically on both identical sides of the slabs in order to avoid the interaction of adjacent slabs (see the C-term in Fig. 2 (a) as an example). According to our previous calculations[34-37], 19 atomic layers and 12 Å vacuum are sufficient to simulate the surface properties.

Fig. 2 (Color online) The models of C-terminated surface (a) and C-Pb interface (b) for SrC (111) thin films.

To obtain the equilibrium structures of these two (111) surfaces, we first make structure optimization for them. In the process of structure optimization, the topmost five atomic layers are allowed to relax by the total energy and atomic force calculations. After finishing the structure relaxation of these two surfaces, we turn our eyes on the calculations of electronic and magnetic properties concerned mostly for them. According to our calculated data, we plot in Fig. 3 the atomic DOSs of surface layer for both C-term and Sr-term. For comparison, the corresponding atomic DOSs of bulk system are presented in Fig. 3. It is clearly found from Fig. 3 that both C-term and Sr-term exhibit half-metallic characteristic since there is an energy gap at the Femi level in spin-up electrons while spin-down electrons cross the Femi level. Note that the half-metallic gap (the minimum between the bottom energy of majority (minority) spin conduction bands with respect to the Fermi level and the absolute values of the top energy of majority (minority) spin valence bands[38]) of both two surfaces becomes small with respect to that of the bulk system due to the fact that the DOSs of spin-up electrons shift toward the high energy region. In a word, the existence of half-metallicity for (111) surfaces is greatly beneficial to spin injection from rocksalt SrC to conventional semiconductors.

Fig. 3 (Color online) The surface-layer atomic DOSs (red line) of both C-terminated and Sr-terminated surfaces for SrC in (111) direction. The corresponding atomic DOSs (Grey shaded regions) in bulk systems are also presented for comparison. The dashed line indicates the Fermi level at 0 eV.

3.3 Interface structure and properties

For the investigation of rocksalt SrC (111) interface properties, it is very important to select a suitable conventional semiconductor in order to obtain high spin-polarized interface structures[39,40]. PbS, as a conventional semiconductor, is considered as an ideal candidate for forming interface structures with rocksalt SrC. On the one hand, PbS has a similar crystal structure with rockaslt SrC (same space group No. 225) and the lower lattice mismatch rate of 4.5% between the lattice constants 5.67 Å, 5.94 Å of SrC and PbS, respectively[24]. On the other hand, PbS presents non-typical electronic and transport properties, such as higher carrier mobilities, higher dielectric constants, narrow band gaps and positive temperature coefficients, which make it a potential candidate for different technological applications including spintronic devices[41-43]. In (111) direction, similar to SrC, PbS has also two surface terminations that are Pb-termination and S-termination. Therefore, there are four different interface structures of C-Pb, C-S, Sr-Pb and Sr-S in (111) SrC/PbS thin film. Taking into account both high-efficient computation and realistic simulation, we use 21 layers of SrC and 13 layers of PbS to construct a slab for simulating every (111) interface (see a model of C-Pb configuration in Fig. 2 (b)). Note that the two interfaces in the slab are equivalent due to the symmetry with respect to the center. With the aim of forming an epitaxial interface, we set the in-plane lattice parameters of the slabs to the lattice parameter 5.94 Å of PbS and then make structure optimization for these four interfaces of (111) SrC/PbS thin films. For the structure optimization, the first five atomic layers of both SrC and PbS near the interface are allowed to relax by the total energy and atomic force calculations.

To check whether the half-metallicity of surface structures exists in the corresponding interfacial structures, we calculate the interfacial layer atomic DOSs of the four optimized interfaces mentioned above. For comparison, the corresponding atomic DOSs of the bulk SrC are showed together in Fig. 4. For C-Pb interface showed in Fig. 4, it is exciting that not only C atom from SrC preserves the half-metallicity of bulk system but also Pb atom from semiconductor PbS exhibits half-metallic properties due to the strongly spin-polarization caused by the interaction between the interfacial atoms C and Pb. That is to say, C-Pb interface displays well half-metallicity which is significant for the practical applications of spintronic device in form of thin films or multilayer films. In addition, one can also find that the half-metallic gap of C-Pb interface is decreased compared to that of bulk SrC because of the reduction of the spin-splitting between the interfacial atoms C and Pb. However, for C-S and Sr-Pb interfaces in Fig. 4, it is very regrettable that the half-metallicity is destroyed by some interfacial states formed by the shift of spin-up DOS to high energy region leading to crossing the Femi level. And for the last Sr-S interface in Fig. 4, the interfacial S atom from PbS exhibits metallic properties in both spin up and spin down electrons and has nearly no magnetism. Therefore, the half-metallicity is also lost for Sr-S interface as shown in Fig. 4. Based on the analysis of the DOSs for the four (111) interfaces of rocksalt SrC with semiconductor PbS, we obtain one half-metallic interface structure of C-Pb although the other three ones have no such properties as we expected.

Fig. 4 (Color online) The interface-layer atomic DOSs of C-Pb, C-S, Sr-Pb and Sr-S (111) interfaces for SrC/PbS thin film (red line for the atom of SrC, blue line for that of PbS). The corresponding atomic DOSs (Grey shaded regions) in bulk SrC are also presented for comparison. The dashed line indicates the Fermi level at 0 eV.

4 Conclusions

Using the full-potential linearized augmented plane-wave (FPLAPW) method from the first-principles, we investigate systematically thed0half-metallicity of the bulk, (111) surfaces and (111) interfaces for rocksalt SrC. It is confirmed that rocksalt SrC is ad0half-metallic ferromagnet originated from the spin-splitting of C atom through our calculations on the bulk system, which is in agreement with other results presented. For the two (111) surfaces of rocksalt SrC, the calculated DOSs show that both C-term and Sr-term exhibit well half-metallic properties only that the HM gap becomes small compared to that of the bulk structure. Based on the half-metallicity of (111) surfaces for rocksalt SrC, we construct its (111) interfaces with semiconductor PbS and also make calculations on their DOSs. It is indicated from the atomic DOSs of interfacial layers that C-Pb interface preserves such half-metallicity while the remaining three interfaces of C-S, Sr-Pb and Sr-S lose this characteristic due to the emergence of interfacial states. The calculated results are helpful to grow experimentally 100% spin-polarized thin films or multilayer films and provide certain theoretical guidance for the design and practical applications of spintronics devices.