Research articles
Various challenges in realizing spin-gapless semiconductivity in Ti2CoSi

https://doi.org/10.1016/j.jmmm.2020.167188Get rights and content

Highlights

  • Ti2CoSi is a potential spin-gapless semiconductor (SGS).

  • Regular Heusler phase of this material is non-magnetic while the inverted phase is nearly SGS.

  • 100% spin polarization in inverted Heusler phase is detrimentally affected by surface states.

Abstract

Spin-gapless semiconductors are recently discovered class of materials that behave as an insulator for one spin channel and as a zero-gap semiconductor for the opposite spin. Here, we show from first-principle calculations that one such material Ti2CoSi predicted to exhibit spin-gapless semiconductivity has an energetically close non-spin-polarized phase. In particular, we show that the regular Heusler phase of this material is non-magnetic, while the inverted Heusler phase is nearly spin-gapless semiconducting, with a very small energy difference of 0.1 eV per 16-atom cell, in favor of the regular Heusler structure. Moreover, we also show that a 100% spin polarization in inverted Heusler phase is detrimentally affected by the emergence of surface states in thin-film geometry. These results need to be taken into account for realistic implementations of this and similar materials in nano-device applications, which rely on highly spin-polarized current in thin-film geometry.

Introduction

A high degree of spin polarization in electron transport (defined as P=NEF-NEFNEF+NEF, where NEF is the spin-dependent density of states (DOS) at the Fermi level, EF) [1] is a cornerstone of spin-based electronics (spintronics). An ideal candidate material should provide a spin-polarization of the current close to 100%, at room temperature. Two types of materials have been suggested to exhibit this property: half-metals, and spin-gapless semiconductors. Half-metal is a material that behaves as an insulator for one spin channel and as a conductor for the opposite spin channel, while spin-gapless semiconductor is a recently discovered class of materials that behaves as an insulator for one spin channel and a zero-gap semiconductor for the opposite spin.

The concept of a spin gapless-semiconductor (SGS) was theoretically proposed a few years ago by X. L. Wang [2]. In SGS materials, both electrons and holes can be 100% spin polarized. The characteristic feature of a gapless semiconductor (e.g. graphene) is that no energy is required to excite electrons from the valence band to the conduction band. In SGS materials, these excited electrons are spin polarized, with the degree of spin polarization potentially reaching 100%, depending on the excitation energy.

Since the original proposal by X. L. Wang [2], spin-gapless semiconductors attracted significant attention due to their potential applications in spintronics [3], [4], [5], [6], [7], [8]. These materials combine advantages of half-metallic magnets and zero-gap semiconductors, which may result in 100% spin polarization of both the electrons and holes, voltage-tunable spin polarization, and the ability to switch between spin-polarized n- and p-type conduction [9]. Several materials, such as Ti2MnAl, Ti2CoSi, Mn2CoAl, have been predicted theoretically to exhibit SGS properties [10], while few materials, such as Heusler-type Mn2CoAl and CoFeCrAl, have been realized experimentally [5], [6].

In general, there are several mechanisms which could modify the degree of spin polarization, such as mechanical strain, atomic disorder, temperature, termination surface/interface in thin film multilayer geometry, etc. The latter is typically reported to reduce the spin polarization due to the emergence of surface states. For example, it has been shown that NiMnSb in its thin film geometry loses bulk half-metallicity due to the segregation of Sb and Mn atoms at the surface [11], [12], [13], [14], [15], [16], [17], while IrMnSb suffers a reduced spin polarization due to the emergence of the minority-spin surface states [18]. Surface states may have a detrimental impact on other types of materials as well, e.g. magnetic semiconducting spin-filters [19]. At the same time, we recently demonstrated that certain half-metals (Co2CrAl and Ti2MnAl0.5Sn0.5) retain a 100% spin-polarization in thin-film geometry for certain surface terminations, contrary to the commonly accepted opinion that reduced geometry destroys half-metallicity [20], [21]. To the best of our knowledge, the effect of reduced geometry on spin polarization of SGS materials has not received sufficient attention so far. In this article, we analyze this question from first principles, by studying the electronic structure of Ti2CoSi in both the bulk and thin-film geometries. This material has been predicted by Skaftouros et al. [10] to exhibit SGS properties in bulk geometry, while a more recent study by Feng et al. reported a non-magnetic transition in this compound upon Fe-doping [22]. Here, we show that Ti2CoSi may co-exist in two energetically close phases, regular Heusler which is non-magnetic, and inverted Heusler which is nearly spin-gapless semiconducting in the bulk. Further, we show that while the inverted Heusler phase of Ti2CoSi may retain its bulk SGS properties under practically feasible values of external biaxial strain, its spin polarization is strongly reduced in thin-film geometry, due to the emergence of minority-spin surface states.

The rest of the paper is organized as follows. Section 2 outlines the computational methods. Structural, electronic, and magnetic properties of bulk Ti2CoSi are reported in Section 3, while in Section 4 we report how these properties are modified in thin-film geometry. Section 5 is devoted to concluding remarks, followed by acknowledgments and references.

Section snippets

Computational methods

We perform density functional calculations of bulk and thin-film Ti2CoSi full Heusler alloy, using the projector augmented-wave method (PAW) [23], implemented in the Vienna ab initio simulation package (VASP) [24] within the generalized-gradient approximation (GGA) [25]. The integration method [26] with a 0.05 eV width of smearing is used. The cut-off energy of the plane-waves is set to 500 eV. Structural optimization is performed with the energy convergence criteria of 10−2 meV, which results

Electronic, magnetic, and crystal structure

Fig. 1(a) and (b) show the unit cells of Ti2CoSi in inverted and regular Heusler structures. The former has been previously reported by Skaftouros et al. [10] to exhibit SGS electronic structure. Here, we analyze both phases, as these two structures have been reported in the past to be energetically close for similar materials, e.g. for Ti2MnAl [8].

We optimized the geometry of both inverted and regular Heusler phases, with the calculated lattice constants being a=6.015Å for the former and a=

Thin-film Ti2CoSi in inverted Heusler structure

In general, spin-polarization of bulk and thin-film phases of the same material is not necessarily the same, since the crystallographic symmetry is reduced when surface termination is taken into account [18]. To analyze how the transition to low dimensional geometry affects the electronic structure of Ti2CoSi in the inverted Heusler structure, we next perform calculations for the thin film.

Fig. 9 presents a schematic view of the inverted Heusler Ti2CoSi cell used for thin-film calculations.

Conclusions

We showed from first-principles that Ti2CoSi has two energetically close phases: non-spin-polarized, and nearly spin-gapless semiconducting. Our calculations indicate that in its magnetic phase this material is not a truly spin-gapless semiconductor, as there is a majority-spin band crossing at the Fermi level. Since the energy of the band crossing is fairly small (less than 0.1 eV), this material could be categorized as “nearly” spin-gapless semiconducting. We demonstrated that the regular

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

Research at the University of Northern Iowa (UNI) is supported by the UNI Faculty Summer Fellowship. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562. This work used the XSEDE Regular Memory (Bridges) and Storage (Bridges Pylon) at the Pittsburgh Supercomputing Center (PSC) through allocation TG-DMR180059.

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