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Electronic and magnetic properties of SnO_{2}/CrO_{2} thin superlattices
Nanoscale Research Lettersvolume 6, Article number: 146 (2011)
Abstract
In this article, using firstprinciples electronic structure calculations within the spin density functional theory, alternated magnetic and nonmagnetic layers of rutileCrO_{2} and rutileSnO_{2} respectively, in a (CrO_{2})_{ n }(SnO_{2})_{ n }superlattice (SL) configuration, with n being the number of monolayers which are considered equal to 1, 2, ..., 10 are studied. A halfmetallic behavior is observed for the (CrO_{2})_{ n }(SnO_{2})_{ n }SLs for all values of n. The ground state is found to be FM with a magnetic moment of 2 μ_{B} per chromium atom, and this result does not depend on the number of monolayers n. As the FM rutileCrO_{2} is unstable at ambient temperature, and known to be stabilized when on top of SnO_{2}, the authors suggest that (CrO_{2})_{ n }(SnO_{2})_{ n }SLs may be applied to spintronic technologies since they provide efficient spinpolarized carriers.
Introduction
A variety of heterostructures have been studied for spintronics applications, and they have proved to have a great potential for highperformance spinbased electronics [1]. A key requirement in developing most devices based on spins is that the host material must be ferromagnetic (FM) above 300 K. In addition, it is necessary to have efficient spinpolarized carriers. One approach to achieve the spin injection is to create builtup superlattices (SLs) of alternating magnetic and nonmagnetic materials. One attempt has already been made by Zaoui et al. [2], through ab initio electronic structure calculations for the one monolayer (ZnO)_{1}(CuO)_{1} SL, with the aim of obtaining a halfmetallic behavior material, since they are 100% spin polarized at the Fermi level and therefore appear ideal for a welldefined carrier spin injection.
In this study, the magnetic and electronic properties of (CrO_{2})_{ n }(SnO_{2})_{ n }SLs with n = 1, 2, ..., 10 being the number of monolayers are investigated. These systems are good candidates to obtain a halfmetallic behavior material since bulk rutileCrO_{2} has shown experimentally this behavior [3] and recently magnetic tunnel junctions based on CrO_{2}/SnO_{2} epitaxial layers have been obtained [4].
Theoretical method
All the calculations were based on the spin density functional theory. The ProjectorAugmented Wave method implemented in the Vienna Abinitio Simulation Package (VASPPAW) [5, 6] was employed in this study, and for the exchangecorrelation potential, the generalized gradient approximation and the Perdew, Burke, and Ernzerhof (GGAPBE) approach was used [7]. The valence electronic distribution for the PAWs representing the atoms were Sn 4d ^{10} 5s ^{2} 5p ^{2}, Cr 3d ^{5} 5s ^{1}, and O2s ^{2} 2p^{4}. Scalar relativistic effects were included. For simulation of the one monolayer (CrO_{2})_{1}(SnO_{2})_{1} SL, a supercell with 12 atoms (2Sn, 2Cr, and 8O) in the rutile structure as shown in Figure 1a was used. For this case, a 4 × 4 × 3 mesh of MonkhorstPack kpoints was used for integration in the SL BZ. All the calculations were done with a 490 eV energy cutoff in the planewave expansions.
Results and discussion
For the (CrO_{2})_{1}(SnO_{2})_{1} SL, the calculation was started with the experimental lattice parameters of the tin dioxide, a = 4.737 Å, c/a = 0.673, and u = 0.307 [8–10]. The system was relaxed until the residual forces on the ions were less than 10 meV/Å. Good agreement between the calculated and the available experimental values for the lattice parameters is obtained, as seen in Table 1. Figure 1b shows that the ground state is ferromagnetic (FM), being the most stable state compared with the nonmagnetic (NM) and antiferromagnetic (AFM) ones. For the ground state, the total magnetic moment gives a value of 2 μ_{B} per chromium atom. Figure 2a,b presents the total density of states (TDOS) and the projected density of states (PDOS), respectively for the Cr 3d orbital, showing that the system has a half metallic behavior, with the Cr 3d orbital appearing in the gap region, characterizing a metalliclike behavior for the majority spin and a semiconductorlike behavior for the minority spin. The band structures of the SL for spin up and spin down are depicted in Figure 2c. A band gap of approximately 1.71 eV is obtained for the minority spin at the Гpoint. There is a smaller gap for spin flip excitations from the Fermi level, which is approximately 0.86 eV. For the (SnO_{2})_{ n }(CrO_{2})_{ n }SLs with n >1, considered here up to n = 10, it was observed that the ground state remains as FM. The interplay of the SnO_{2} and CrO_{2} layer thicknesses does not change the halfmetallic behavior, as can be verified through the DOS shown in Figure 3a,b for n = 10. The magnetic moment per Cr atom, in all the studied cases, is the same and equal to 2 μ_{B}. Moreover, the SL magnetization does not depend on the number of monolayers. This has been verified by performing calculations with one monolayer of CrO_{2} grown between 3, 7, and 11 monolayers of SnO_{2}. It was observed that the SL magnetization remained equal to 2 μ_{B}. Our results show a 100% spin polarization at the Fermi level, ideal for a welldefined carrier spin injection.
An investigation, related to strain effects along the zdirection for the rutile phase of CrO_{2}, was made by simulating bulk rutileCrO_{2}, on top of tin dioxide, assuming for CrO_{2} the lattice parameter a of SnO_{2}, i.e., a situation in which the chromium dioxide is tensile. By varying the ratio c/a _{SnO2} and minimizing the total energy of the system, the authors obtained the curves shown in Figure 4a for the FM, AFM, and NM states, showing that the transition from a FM to an AFM state occurs when c/a _{SnO2} is about 0.544. At this value, a magnetic moment reduction is observed, as depicted in Figure 4b. These results suggest a magnetization change when the SL is under strain or, in other words, when CrO_{2} is compressed. A similar behavior was found by Srivastava et al. for bulk rutileCrO_{2} under pressure [11].
The advantage in using the SnO_{2}/CrO_{2} SLs, despite the fact that CrO_{2} is unstable at room temperature, is that its stability becomes possible when grown on SnO_{2}[12]. Our results showed that the interface effects due to the lattice mismatch do not change the chromium dioxide magnetism characteristics. If the distances between two planes perpendicular to the rutile caxis containing the Cr_{2} and Sn_{1} are compared (see Figure 1a), at the interface region of the SL, before and after full relaxations, then changes of only approximately 4% are observed for all the studied SLs.
Conclusions
In conclusion, the results of firstprinciples electronic structure calculations, within the spin density functional theory, carried out for (CrO_{2})_{ n }(SnO_{2})_{ n }SLs formed by alternating magnetic and nonmagnetic layers of rutileCrO_{2} and rutileSnO_{2}, where the number of monolayers n was varied from 1 to 10, have been reported in this article. A halfmetallic behavior is observed for all the studied (CrO_{2})_{ n }(SnO_{2})_{ n }SLs. The ground state is FM, with a magnetic moment of 2 μ_{B} per chromium atom, which is independent of the number of monolayers. As the FM rutileCrO_{2} is unstable at ambient temperature, and known to be stabilized when on top of SnO_{2}, it is suggested that (CrO_{2})_{ n }(SnO_{2})_{ n }SLs may be applied to spintronic technologies since they provide efficient spinpolarized carriers.
Abbreviations
 AFM:

antiferromagnetic
 FM:

ferromagnetic
 GGAPBE:

generalized gradient approximation and the Perdew, Burke, and Ernzerhof
 NM:

nonmagnetic
 PDOS:

projected density of states
 SL:

superlattice
 TDOS:

total density of states
 VASPPAW:

Vienna Abinitio Simulation Package and the Projected Augmented Wave.
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Acknowledgements
The authors would like to thank the partial support from the Brazilian funding agencies FAPEMIG, FAPESP, CAPES, and CNPq, and from the Material, Science, Engineering and Commercialization Program at the Texas State University in San Marcos.
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The authors declare that they have no competing interests.
Authors' contributions
PB performed the ab initio calculations, participated in the analysis, and drafted the manuscript. LS and PB conceived of the study. HA, ES, LA, and LS participated in the analysis and in the production of a final version of the manuscript. All authors read and approved the final manuscript.
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Keywords
 SnO2
 Spin Injection
 Chromium Atom
 Magnetic Tunnel Junction
 Minority Spin