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  • Inducing and Manipulating Magnetization in Two-Dimensional ZnO by Strain and External Gating

    P. Taivansaikhan,1 T. Tsevelmaa,2 S. H. Rhim,2 S. C. Hong,2 and D. Odkhuu1∗ 1Department of Physics, Incheon National University, Incheon 22012, South Korea

    2Department of Physics, University of Ulsan and EHSRC, Ulsan 44610, South Korea

    Two-dimensional structures that exhibit intriguing magnetic phenomena such as perpendicular magnetic anisotropy and switchable magnetization are of great interests in spintronics research. Herein, the density- functional theory studies reveal the critical impacts of strain and external gating on vacancy-induced magnetism and its spin direction in a graphene-like single layer of zinc oxide (ZnO). In contrast to the pristine and defective ZnO with an O-vacancy, the presence of a Zn-vacancy induces significant magnetic moments to its first neigh- boring O and Zn atoms due to the charge deficit. We further predict that the direction of magnetization easy axis reverses from an in-plane to perpendicular orientation under a practically achieved biaxial compressive strain of ∼1–2% or applying an electric-field by means of the charge density modulation. This magnetization reversal is driven by the strain- and electric-field-induced changes in the spin-orbit coupled d states of the first-neighbor Zn atom to the Zn-vacancy. These findings open interesting prospects for exploiting strain and electric-field engineering to manipulate magnetism and magnetization orientation of two-dimensional materials.

    PACS numbers: 75.30.Gw, 75.60.Jk, 75.70.Tj, 71.20.Be, 71.15.Mb


    During the past two decades since the successful isola- tion of graphene from graphite [1, 2], the exploration of two- dimensional (2D) layered materials has received much atten- tion and is likely to remain one of the leading topics in mate- rial science into foreseeable future. Although there have been a number of experimental successes and theoretical predic- tions on discovering 2D materials, including graphene, hexag- onal boron nitride (h-BN), and transition metal dichalco- genides (TMDs) [1–5], their potentials in spintronic applica- tions have been limited by the lacks of spin orders and pos- sibilities of magnetization flip. Hence, the current research in this field primarily focuses on seeking a novel 2D material with intriguing magnetic properties [6–9], which would offer great advantages for exploring the internal quantum degrees of freedom of electrons and their potentials in nanoscale-down spin-based electronic applications.

    Zinc oxide (ZnO), as a 2D material, can possibly be a promising candidate in the same regard, since it has been re- cently reported that a (0001) oriented ultrathin ZnO film can be transformed into a new form of stable graphite-like struc- ture [10–14]. One to three or four atomic layers of ZnO(0001) have been successfully synthesized on a (111) surface of Ag [10] and Au substrates [15–17], where Zn and O atoms are arranged in the lateral lattice as a honeycomb shape, similar with the h-BN structure. Theoretical studies have also pre- dicted that thin films of ZnO prefer a graphite-like layered structure when the thickness is less than three atomic layers [12, 13], and the stability of even thicker graphitic layers can be improved by an epitaxial strain [14]. More remarkably, an epitaxial growth of ZnO monolayer on graphene has been very recently demonstrated in atomic resolution transmission electron microscopy (ARTEM) measurements [18].

    Numerous reports, on the other hand, have already shown that intrinsic defects and impurities can readily give rise to magnetism in ZnO allotropies, including monolayer, graphitic

    layers, thin films, nanowires and nanoribbons [19–29]. For instance, nonmetal (C, B, N, and K)-[27, 29] and rare- earth metal (Ce, Eu, Gd, and Dy)-doped ZnO monolayer [28] exhibits magnetic instability via first-principles calcula- tions. Moreover, it has been shown by both experimentally [20, 22, 26] and theoretically [19, 23, 24] that the Zn vacancy induces ferromagnetism in either thin films [20, 22, 24, 26] and graphitic layers [19, 23] of ZnO without the need of mag- netic impurities.

    In this article, we perform first-principles calculations to re- veal the synergistic effect of biaxial strain on magnetism and its spin direction of a graphene-like single layer of ZnO in- duced by a Zn-vacancy. Through the analyses of the spin- orbit Hamiltonian matrix elements and atom- and orbital- decomposed magnetic anisotropy energy (MAE), we eluci- date the underlying mechanism of magnetization reversal, which occurs at the compressive biaxial strain of only ∼1– 2%, in terms of the strain-induced changes in the spin-orbit coupled d states of the vacancy-neighbored Zn atom. More- over, this anisotropic magnetism is identified to even be re- versible upon the change in charge carrier density, suggesting the possibilities of chemical doping or magnetoelectric con- trol of magnetization reorientation.


    Density-functional theory (DFT) calculations were per- formed using the Vienna ab initio simulation package (VASP) with plane-wave basis set [30, 31]. The projector augmented wave (PAW) potentials [32] were used to describe the core electrons, and the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzernhof (PBE) was adopted for exchange-correlation energy [33]. As illustrated in Fig. 1(a), a 4×4 lateral unit cell of the hexagonal lattice was chosen as a model geometry of a single-layer ZnO. We also consider an intrinsic defect of an oxygen vacancy [Fig. 1(b)] as well as

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    FIG. 1: Top views of the atomic structures for (a) a single-layer ZnO with (b) a O-vacancy and (c) a Zn-vacancy. The larger gray and smaller red spheres are Zn and O atoms, respectively. In (b) and (c), the red and black dotted-circles correspond to the O and Zn vacan- cies, respectively.

    a zinc vacancy [Fig. 1(c)] in ZnO monolayer, which occurs notably often during sample preparation and treatments [35– 41]. In order to avoid spurious interactions between periodic images of ZnO layer, a vacuum spacing of no less than 15 Å perpendicular to the plane was employed. An energy cutoff of 500 eV and a 5×5×1 k mesh were imposed for the ionic relax- ation, where forces acting on atoms were less than 10−2 eV/Å. The MAE is obtained based on the total energy difference when the magnetization directions are in the xy plane (E‖) and along the z axis (E⊥), MAE = E‖ – E⊥, where convergence with respect to the k point sampling is ensured. To obtain reliable values of MAE, the Gaussian smearing method with a smaller smearing of 0.05 and dense k points of 15×15×1 were used in noncollinear calculations, where the spin-orbit coupling (SOC) term was included using the second-variation method employing the scalar-relativistic eigenfunctions of the valence states [34].

    TABLE I: Optimized in-plane lattice a (Å), formation energy H f (eV), magnetic moment µ (µB) and charge ρ (e) of Zn and O atoms in the nondefective (Vfree) and defective ZnO with an O- (VO) and a Zn-vacancy (VZn).

    a H f µZn µO µTotal ρZn ρO Vfree 3.290 – 0.0 0.0 0.0 10.81 7.18 VO 3.248 –3.75 0.0 0.0 0.0 10.86 7.15 VZn 3.296 –5.43 0.04 0.32 2.0 10.79 6.97

    FIG. 2: Spin- and orbital-decomposed PDOS of (a) Zn and (b) O atoms of the nondefective ZnO monolayer. The same PDOS for the defective ZnO with (a) and (b) a O-vacancy and (e) and (f) a Zn- vacancy. The singlet a1 (dz2 ) and doublet e

    ′ (dxy/x2y2 ) and e ′′ (dxz/yz)

    orbital states of Zn atom are shown in blue, black, and red lines, respectively. The px,y and pz orbital states of O atom are shown in blue and red lines, respectively. For reference, the total DOS per atom (shaded area) is also shown in each panel. The Fermi level is set to zero in energy.


    We first optimize the lattice parameters of the nondefective and defective ZnO monolayer and the results are shown in Table I. The lattice constant of the nondefective ZnO mono- layer is 3.29 Å, which agrees pretty well with experimental values of ∼3.29–3.30 Å [10, 16, 18], superior to the previ- ous theories (∼3.20–3.28 Å) [12, 13, 23]. While the lattice constant of the nondefective ZnO remains almost unchanged in the presence of a Zn-vacancy, it is reduced by ∼1% when an O-vacancy is introduced (in a 4×4 unit cell of ZnO mono- layer). The former is due to the direct repulsive interaction between O–O anions without Zn mediation. As presented in Table I, the further calculations of formation energy H f , defined as H f = ENondef−EDef−EZn/O, where ENondef, EDef, and EZn/O represent the total energies of the nondefective and defective ZnO with a Zn/O-vacancy, and a Zn/O atom in its bulk/O2-molecule form, indicate the favorable formation of a vacancy in ZnO, particularly for the Zn-site vacancy, as re- ported in experiments [35–41].

    The significance of induced magnetism, as fairly addressed in experimental [20, 22, 26] and previous theoretical studies [19, 23, 24], is then justified. Note that the magnetic moments

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    FIG. 3: (a) Magnetic moments µ of Zn (blue) and O (black) atoms and (b) MAE of a single-layer ZnO with a Zn-vacancy as a func- tion of strain (ε). The negative and positive ε correspond to the compressive and tensile strain, respectively. The insets in (b) show the schematics for magnetization switching from in-plane (bottom in negative MAE) to out-of-plane magnetization (top in positive MAE) at a compressiv