In this article, using first-principles electronic structure calculations within the spin density functional theory, alternated magnetic and non-magnetic layers of rutile-CrO_{2} and rutile-SnO_{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 half-metallic 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 rutile-CrO_{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 spin-polarized carriers.

Introduction

A variety of heterostructures have been studied for spintronics applications, and they have proved to have a great potential for high-performance spin-based 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 spin-polarized carriers. One approach to achieve the spin injection is to create built-up superlattices (SLs) of alternating magnetic and non-magnetic 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 half-metallic behavior material, since they are 100% spin polarized at the Fermi level and therefore appear ideal for a well-defined 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 half-metallic behavior material since bulk rutile-CrO_{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 Projector-Augmented Wave method implemented in the Vienna Ab-initio Simulation Package (VASP-PAW) [5, 6] was employed in this study, and for the exchange-correlation potential, the generalized gradient approximation and the Perdew, Burke, and Ernzerhof (GGA-PBE) 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 O-2s^{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 Monkhorst-Pack k-points was used for integration in the SL BZ. All the calculations were done with a 490 eV energy cutoff in the plane-wave 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 non-magnetic (NM) and anti-ferromagnetic (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 metallic-like behavior for the majority spin and a semiconductor-like 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 Г-point. 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 half-metallic 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 well-defined 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

An investigation, related to strain effects along the z-direction for the rutile phase of CrO_{2}, was made by simulating bulk rutile-CrO_{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 rutile-CrO_{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 c-axis 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 first-principles electronic structure calculations, within the spin density functional theory, carried out for (CrO_{2})_{
n
}(SnO_{2})_{
n
}SLs formed by alternating magnetic and non-magnetic layers of rutile-CrO_{2} and rutile-SnO_{2}, where the number of monolayers n was varied from 1 to 10, have been reported in this article. A half-metallic 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 rutile-CrO_{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 spin-polarized carriers.

Abbreviations

AFM:

anti-ferromagnetic

FM:

ferromagnetic

GGA-PBE:

generalized gradient approximation and the Perdew, Burke, and Ernzerhof

NM:

non-magnetic

PDOS:

projected density of states

SL:

superlattice

TDOS:

total density of states

VASP-PAW:

Vienna Ab-initio Simulation Package and the Projected Augmented Wave.

Declarations

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.

Authors’ Affiliations

(1)

Instituto de Física, Universidade de São Paulo

(2)

Department of Physics, Texas State University

(3)

Universidade Federal de São João Del Rei

(4)

Departamento de Fisica, Universidade Federal de Pernambuco

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