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.
Figure 1. The supercell model and total energies for the systems. (a) Supercell used to study the (SnO_{2})_{1}(CrO_{2})_{1} SL, and (b) Total energies for the nonmagnetic (NM) and antiferromagnetic (AFM) states relative to the ferromagnetic (FM) state. The dashed lines connecting the points are to guide the eyes.
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 [810]. 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.
Table 1. Experimental and calculated values for the lattice parameters of the SnO_{2}, CrO_{2}, and of the (CrO_{2})_{1}(SnO_{2})_{1 }and (CrO_{2})_{10}(SnO_{2})_{10 }SLs in the rutile structure
Figure 2. Density of states and band structure for the (SnO_{2})_{1}(CrO_{2})_{1} SL. (a) Total density of states (TDOS), (b) Project density of states (PDOS) for the Crd orbital, (c) Band structure, for spin up and spin down, along the main symmetry lines of the SL BZ. The Fermi level, E_{F}, is set to zero in (a), (b), and (c).
Figure 3. Density of states and total energies for the SL with n=10. (a) Total density of states (in black) and project density of states (in gray) for the Cr3d. (b) Total energies for the non magnetic (NM) and antiferromagnetic (AFM) states relative to the ferromagnetic (FM) state. The Fermi level, E_{F}, is set to zero. The dashed lines connecting the points are to guide the eyes.
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].
Figure 4. Study of strain effects on the magnetic behavior. (a) Total energy versus the c/a_{SnO2} parameter for bulk rutileCrO_{2} for AFM, FM, and NM states. (b) Magnetic moment per cell versus the c/a_{SnO2} parameter.
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.
Competing interests
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.
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.
References

Wolf SA, Awschalom DD, Buhrman RA, Daughton JM, von Molnár S, Roukes ML, Chtchelkanova AY, Treger DM: Spintronics: A SpinBased Electronics Vision for the Future.
Science 2001, 294:1488. PubMed Abstract  Publisher Full Text

Zaoui A, Ferhat M, Ahuja R: Magnetic properties of (ZnO)1/(CuO)1 (001) superlattice.
Appl Phys Lett 2009, 94:102102. Publisher Full Text

Anguelouch A, Gupta A, Xiao Gang, Abraham DW, Ji Y, Ingvarsson S, Chien CL: Nearcomplete spin polarization in atomicallysmooth chromiumdioxide epitaxial films prepared using a CVD liquid precursor.
Phys Rev B 2001, 64:180408R. Publisher Full Text

Miao GX, LeClair P, Gupta A, Xiao G, Varela M, Pennycook S: Magnetic tunnel junctions based on CrO2/SnO2 epitaxial bilayers.
Appl Phys Lett 2006, 89:022511. Publisher Full Text

Kresse G, Furthmuller J: Efficiency of abinitio total energy calculations for metals and semiconductors using a planewave basis set.
Comput Mater Sci 1996, 6:15. Publisher Full Text

Kresse G, Furthmuller J: Efficient iterative schemes for ab initio totalenergy calculations using a planewave basis set.
Phys Rev B 1996, 54:11169. Publisher Full Text

Perdew JP, Burke K, Ernzerhof M: Generalized Gradient Approximation Made Simple.
Phys Rev Lett 1996, 77:3865. PubMed Abstract  Publisher Full Text

Wycokoff R: Crystal Structures. Volume 1. 2nd edition. New York, London: John Wiley & Sons; 1963.

Borges PD, Scolfaro LMR, Leite Alves HW, da Silva EF Jr: DFT study of the electronic, vibrational, and optical properties of SnO2.
Theor Chem Acc 2010, 126:39. Publisher Full Text

Maddox BR, Yoo CS, Kasinathan D, Pickett WE, Scalettar RT: Highpressure structure of halfmetallic CrO2.
Phys Rev B 2006, 73:144111. Publisher Full Text

Srivastava V, Sanyal SP, Rajagopalan M: First Principles study of pressure induced magnetic transition in CrO2.

Zabel H, Bader SD, (Eds): Magnetic Heterostructures: Advances and Perspectives in Spinstructures and Spintransport STMP 227. Berlin: Springer; 2008.