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Magnetic anisotropy energy and effective exchange interactions in Co intercalated graphene on Ir(1 1 1)
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 476003 (http://iopscience.iop.org/0953-8984/26/47/476003) View the table of contents for this issue, or go to the journal homepage for more
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 476003 (6pp)
doi:10.1088/0953-8984/26/47/476003
Magnetic anisotropy energy and effective exchange interactions in Co intercalated graphene on Ir(1 1 1) A B Shick1 , S C Hong2 , F Maca1 and A I Lichtenstein3 1
Institute of Physics ASCR, Na Slovance 2, 18221 Prague, Czech Republic University of Ulsan, Department of Physics and Energy Harvest Storage Research Center, Ulsan 680-749, Korea 3 University of Hamburg, Jungiusstrasse 9, 20355 Hamburg, Germany 2
E-mail: [email protected] Received 19 August 2014, revised 22 September 2014 Accepted for publication 7 October 2014 Published 29 October 2014 Abstract
The electronic structure, magnetic moments, effective exchange interaction parameter and the magnetic anisotropy energy of [monolayer Co]/Ir(1 1 1) and Co intercalated graphene on Ir(1 1 1) are studied making use of the first-principles density functional theory calculations. A large positive magnetic anisotropy of 1.24 meV/Co is found for [monolayer Co]/Ir(1 1 1), and a high Curie temperature of 1190 K is estimated. These findings show the Co/Ir(1 1 1) system is a promising candidate for perpendicular ultra-high density magnetic recording applications. The magnetic moments, exchange interactions and the magnetic anisotropy are strongly affected by graphene. Reduction of the magnetic anisotropy and the Curie temperature are found for graphene/[monolayer Co]/Ir(1 1 1). It is shown that for graphene placed in the hollow-hexagonal positions over the monolayer Co, the magnetic anisotropy remains positive, while for the placements with one of the C atoms on the top of Co it becomes negative. These findings may be important for assessing the use of graphene for magnetic recording and magnetoelectronic applications. Keywords: magnetic anisotropy, Co monolayer, graphene (Some figures may appear in colour only in the online journal)
magnetic moments, the effective exchange interactions, and the MAE of the Co overlayer on the Ir(1 1 1) substrate, by making use of the first-principles density functional theory calculations. Knowledge of the MAE is essential for evaluating the magnetic bit stability over the superparamagnetic limit, and the effective exchange interaction parameter allows us to estimate the Curie temperature.
1. Introduction
The studies of new nanoscale materials with perpendicular magnetic anisotropy (PMA) are particularly timely and important due to the currently growing interest in perpendicular magnetic recording [1] and spin-transfer torque applications [2]. We focus on the influence of graphene on the anisotropic magnetic properties of ultra-thin magnetic films. Recent experiments using spin-polarized scanning tunnelling microscopy [3] observed magnetic moire patterns in Co intercalated graphene on Ir(1 1 1). Spin-polarized low-energy electron microscopy [4] experiments showed that the graphene film promotes PMA in the underlying Co film. However, with neither technique is it possible to extract quantitative information about the magnetic anisotropy energy (MAE). In the work reported here, we provide details of the effect of graphene on the electronic structure, the spin and orbital 0953-8984/14/476003+06$33.00
2. Method of calculation
We start with the supercell calculations for a Co overlayer on an Ir(1 1 1) surface. A supercell model is used that consists of a ten-layer Ir(1 1 1) substrate and Co monolayers (MLs) on each side of the substrate (see figure 1(a)). The in-plane interatomic distance for pure Ir (5.132 a.u.) was adopted and kept fixed in the calculations. The structural optimization used the standard VASP-PAW [5] program package without 1
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J. Phys.: Condens. Matter 26 (2014) 476003
A B Shick et al
spin–orbit coupling (SOC) employing the generalized gradient approximation, GGA-PBE. For [1ML Co]/Ir(1 1 1), we obtain a relatively large −8.4% relaxation of the inter-layer distance d[Co−Ir] = 3.84 a.u. The 2.5% change in the distance between Ir-interface (Ir-I) and Ir-sub-interface (Ir-I-1) layers, d[(Ir−I)−(Ir−I−1)] = 4.31 a.u., is substantial. Very small— practically negligible—changes in the positions of Ir atoms for the rest of the substrate are found in the calculations. Graphene forms a moire superstructure on Ir(1 1 1) due to the in-plane lattice mismatch. In order to directly model this superstructure, one would need to consider 10 × 10 graphene (with 200 C atoms) placed on 9×9 Ir(1 1 1) (with 81 Ir atoms in each Ir layer), and insert 9×9 Co layer(s) between the graphene and Ir(1 1 1) substrate. The application of density functional theory to such a superstructure is a difficult task when taking into account that high-accuracy relativistic calculations with the SOC included are necessary for the magnetic anisotropy calculations. Instead of considering a large superstructure, we place two C atoms of the graphene unit cell on the top of a ML Co/Ir(1 1 1) (GR/[1ML Co]/Ir(1 1 1)), and consider three different placements for the graphene overlayer: (1) top-hcp, one of the C atoms is on the top of the Co, the other is over the Ir interface ML; (2) top-fcc, one of the C atoms is on the top of the Co, the other is over the Ir sub-interface ML; and (3) hollow-hexagonal, one of the C atoms is on the top of the Ir interface ML, the other is over the Ir sub-interface ML. This supercell model, which consists of a ten-layer Ir(1 1 1) substrate and 1 ML of Co on each side of the substrate covered by a layer of graphene, is shown in figure 1(b). In addition 1 ML of Co on the Ir(1 1 1) surface [1ML Co]/Ir(1 1 1) is used in order to analyse graphene-induced changes in the magnetic properties of the Co atoms. As mentioned above, the structural optimization is performed using the standard VASP-PAW program package employing the GGA-PBE approximation. The in-plane interatomic distance of pure Ir (5.132 a.u.) was adopted and kept fixed in the calculations. For GR/[1ML Co]/Ir(1 1 1), for top-hcp and top-fcc, we obtain that graphene is strongly bonded to the Co atom, with d[C−Co] = 3.80 a.u., 3.72, respectively. For the hollow-hexagonal case, the C atoms are much less connected to the substrate, with d[C−Co] = 4.27 a.u. Once the structure relaxation is done, we use the relativistic version of the full-potential linearized augmented plane-wave method (FP-LAPW) [6], in which SOC is included in a self-consistent second-variational procedure [7]. The conventional (von Barth–Hedin) local spin-density approximation (LSDA) is adopted in the calculations, which is expected to be valid for itinerant metallic systems. The radii of the atomic muffin-tin spheres are set to 1.4 a.u. for C atoms, 2.2 a.u. for Co atoms and 2.5 a.u. for Ir atoms. The parameter RCo × Kmax = 7.7 defines the basis set size and the two-dimensional Brillouin zone (BZ) was sampled with 229 k points.
Figure 1. Schematic crystal structure used to represent the [1ML Co]/Ir(1 1 1) (a) and graphene/[1ML Co]/Ir(1 1 1) (b) surfaces.
(I-1) layers. For the [1ML Co]/Ir(1 1 1) case, there is a reduction of the MS and ML values (MS = 1.80 µB and ML = 0.12 µB ) of the Co layer compared to the unrelaxed case (MS = 1.89 µB and ML = 0.13 µB ), and an enhancement of the magnetic polarization of the substrate. This is consistent with the structure relaxation-induced reduction of distance d[Co−Ir] , leading to an increase of hybridization between the Co overlayer and the Ir substrate. The Ir interfacial layer is spinpolarized parallel to the Co ML, while the spin-polarization for Ir-(I-1) is anti-parallel. For the GR/[1ML Co]/Ir(1 1 1) case, the spin moments are practically zero for the C atoms of the graphene ML for the hollow-hexagonal position, reflecting a very weak interaction between the Co ML and graphene. Once the C atom interacts with the Co atom underneath, as in the case of the top-fcc and top-hcp graphene placements, the spin magnetic moments are induced. The total induced spin moment in graphene is very small (≈0.01 µB ), and is oriented anti-parallel to the Co ML moment. The spin- and orbital-resolved projected densities of dstates (dDOS) for the Co layer (E1 : {xz, yz}, E2 : {x 2 − y 2 , xy}, A : {3z2 − r 2 }) are shown in figure 2. It is seen that there is only a minor difference between the Co atom
2.1. Electronic structure
Spin MS and orbital ML magnetic muffin-tin moments are shown in table 1 for the Co/Ir interface (I) and sub-interface 2
J. Phys.: Condens. Matter 26 (2014) 476003
A B Shick et al
Table 1. Spin (MS ) and orbital (ML ) magnetic moments in the muffin-tin sphere of the Co and Ir atoms (in Bohr magnetons), and effective exchange interaction parameter (J0 , eV) for [1ML Co]/Ir(1 1 1) and GR/[1ML Co]/Ir(1 1 1). In all calculations, the magnetization is directed along the z-axis along the surface normal.
Co MS ML J0
MS ML J0 MS ML J0 MS ML J0
Ir[I]
Ir[I-1]
[1ML Co]/Ir(1 1 1) 1.80 0.21 −0.06 0.12 0.01 −0.00 0.154 5 × 10−3 4 × 10−5 GR/[1ML Co]/Ir(1 1 1) hollow-hexagonal 1.57 0.19 −0.06 0.08 0.00 −0.00 0.109 4 × 10−3 5 × 10−5 top-fcc 1.16 0.10 −0.05 0.07 0.00 −0.01 0.084 1 × 10−3 2 × 10−4 top-hcp 1.29 0.13 −0.04 0.07 0.00 0.00 0.093 2 × 10−3 2 × 10−4
dDOS for [1ML Co]/Ir(1 1 1) and hollow-hexagonal GR/[1ML Co]/Ir(1 1 1). This is due to the weak bond between the C atoms and the Ir atoms. For the top-fcc position where one of the C atoms is over a Co, there is a substantial modification of the dDOS, especially for the partially occupied spin-minority A-state. 2.2. Effective exchange interaction parameter
A general expression for the effective exchange interaction of a given site for all magnetic environments [8, 9] is EF 1 J0 = − Im Tr ∆(G↑ − G↓ ) + ∆G↑ G↓ d, (1) 4π −∞ where Gσ =↑,↓ is the spin-diagonal elements of the on-site local LSDA Green function in the local basis of γ = (l, m, σ ) spin orbitals {φγ }, −1 1 GLSDA ( + iδ) = dk + iδ − HLDA (k) . γ1 γ2 γ1 γ2 VBZ BZ (2) Note that the SOC is included in the LSDA Hamiltonian HLSDA (k). is the on-site exchange splitting and EF is the Fermi energy. We have implemented equation (1) in the FP-LAPW basis making use of the previous implementation for the GLSDA in equation (2) as described in [14]. Since most of the muffintin magnetic moments MS are of d(l = 2) orbital character, only the d-states part of the [GLSDA ] matrix was considered in equation (1). For bulk hcp Co, we get J0 = 0.179 eV, in reasonable agreement with the previously reported value of 0.184 eV [15]. Applying equation (1) to [1ML Co]/Ir(1 1 1), we obtain a smaller value of J0 for the Co atom at the Ir(1 1 1) surface (see table 1) as a result of reduced dimensionality. The values
Figure 2. Spin-resolved d-projected DOS for (a) the Co layer in
[1ML Co]/Ir(1 1 1), and for the Co layer in (b) the GR/[1ML Co]/Ir(1 1 1) hollow-hexagonal position and (c) the top-fcc position.
of J0 at the Ir(I) interface and sub-interface Ir(I-1) are much smaller than the value for the Co atom, reflecting the smallness of the Ir local magnetic moments induced by the Co ML. The graphene placed on the top further reduces the magnitude of J0 (see table 1). The effective exchange interaction parameter can be used for the mean-field estimate of the magnetic ordering Curie temperature, TCMF = 3k2B J0 . This yields TCMF = 1383 K, in good agreement with the experimental value of 1388 K. 3
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Then the naive estimate for TC for [1ML Co]/Ir(1 1 1) will be 1191 K. For GR/[1ML Co]/Ir(1 1 1), the Curie temperature will be reduced further to 650–843 K. 2.3. Magnetic anisotropy energy
For hexagonal symmetry, the magnetic anisotropic energy EA (θ, φ) as a function of the spherical angles θ and φ is EA (θ, φ) = K1 sin2 θ + K2 sin4 θ + K3 sin6 θ + K4 sin6 θ cos 6φ,
(3)
where K1 and K2 are the uniaxial MAE constants, and K3 and K4 are the higher-order anisotropy constants [10]. The relativistic FP-LAPW method gives an accurate determination of the magneto-crystalline anisotropy energy. In order to evaluate the MAE of equation (3), we make use of the torque method [11]. For a FP-LAPW basis, the torque method was first implemented in [12]. It can be formulated as follows. We solve theKohn–Sham equations for a two↑ i component spinor | i = , ↓ i
β − ∇ 2 + Vˆeff + ξ(l · s) i (r) = ei αi (r) , (4) α,β
β
where the Vˆeff = V (r)Iˆ + σ · B(r) matrix consists of the sum of the scalar potential V and exchange field B parallel to the spin moment MS , and Hˆ SO = ξ(l · s) is the SOC operator. Here, to simplify the notation, we use a Pauli-like Hamiltonian including SOC, while the actual implementation contains in addition the scalar-relativistic terms. When the magnetic force theorem [8, 13] is used to evaluate the MAE, the MS is rotated and a single energy band calculation is performed for the new orientation of MS . The MAE results from SOC-induced changes in the band eigenvalues EA (θ, φ) = occ i i (θ, φ). In practice, it is more convenient to use the linear response theory, and evaluate the torque T (θ, φ) = ∂EA (θ, φ)/∂θ as T (θ, φ) =
occ
i |
i
†
∂U ∂U ξ(l · s)U† + Uξ(l · s) | i ∂θ ∂θ
Figure 3. (a) θ angular dependence of T (θ, φ = 0). (b) Layer-resolved (element-specific) contributions to the torque T (θ = π/4, φ = 0, π/6) per unit cell for Co/10Ir/Co. Table 2. Anisotropy constants K1 , K2 , K3 and K4 per unit cell (total and Co) for [1ML Co]/Ir(1 1 1) (meV).
(5)
where U(θ, φ) is a conventional spin rotation matrix and | = U(θ, φ)| . From the angular dependence of the torque,
MAE constants
K1
K2
K3
K4
Total Co
2.59 0.09
−0.16 0.01
0.05 −0.02
−0.01 0.01
The θ angular dependence of T (θ, φ) in equation (6) with φ = 0 is shown in figure 3(a) for a Co/Ir(1 1 1)/Co unit cell (see figure 1(a), note that it contains two Co atoms). For T (θ, φ = π/6), the angular dependence was found to be very similar. It is seen that the Co contribution to the total torque is rather small. The corresponding anisotropy constants, K1 , K2 , K3 and K4 , per unit cell are shown in table 2. MAE = EA [M||x] − EA [M||z] = 1.24 meV/Co was calculated. This agrees reasonably well with the Co/Ir(1 1 1) MAE = 1.395 meV/Co calculated in [17]. Since the higherorder anisotropy constants are small (see table 2), then MAE ≈T (θ = π/4, φ = 0) holds. In figure 3(b) the layer-resolved (element-specific) contributions to the torque T (θ = π/4, φ = 0, π/6) per unit cell are shown (note that these are twice the MAE contributions from individual Co-, Ir(I)-, Ir(I-
T (θ, φ) = K1 sin 2θ + K2 sin 2θ (1 − cos 2θ ) 3 + (K3 + K4 cos 6φ) sin 2θ (1 − cos 2θ )2 , (6) 4 the uniaxial MAE constants, K1 and K2 , and the higherorder anisotropy constants, K3 and K4 , are evaluated. An advantage of this approach is that it allows separation of equation (5) into the sum of the element-specific contributions from different atoms in the unit cell [16], and the evaluation of the element-specific contributions to the anisotropy constants and the total MAE. We point out that care should be taken with the convergence of the torque T (θ, φ) in equation (6) with respect to the two-dimensional BZ integration. For [1ML Co]/Ir(1 1 1), we found that the torque converges to better than 0.1 meV/Co for 3482 k points in the BZ. 4
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Table 3. Anisotropy constants K1 , K2 , K3 and K4 per unit cell (total and Co) for GR/[1ML Co]/Ir(1 1 1) (meV).
MAE constants Total Co Total Co Total Co
K1
K2
hollow-hexagonal 0.55 0.17 0.08 0.01 top-fcc −0.325 −0.06 0.244 0.00 top-hcp −0.95 −0.11 −0.02 −0.01
K3
K4
0.22 0.01
−0.04 0.01
0.02 0.00
0.00 0.00
0.16 0.01
0.025 −0.01
Table 4. Layer- (element-specific) and spin-resolved torques T↑↑ , T↑↓ and T↓↓ , and the total torque T = T↑↑ + T↑↓ + T↓↓ , evaluated at (θ = π/4, φ = 0) (per unit cell, meV) for [1ML Co]/Ir(1 1 1) and GR/[1ML Co]/Ir(1 1 1).
MAE constants [1ML Co]/Ir(1 1 1) Co Ir interface Ir interface-1 GR/[1ML Co]/Ir(1 1 1) Co Ir interface Ir interface-1 GR/[1ML Co]/Ir(1 1 1) Co Ir interface Ir interface-1 GR/[1ML Co]/Ir(1 1 1) Co Ir interface Ir interface-1
1,2,3,4)-layers in the unit cell). It is seen that most of the MAE comes from the Ir(I) interface and Ir(I-1) sub-interface layers. The positive MAE sign indicates the perpendicular magnetic anisotropy for [1ML Co]/Ir(1 1 1). Next, we applied the torque method to evaluate the MAE for GR/[1ML Co]/Ir(1 1 1). The calculated anisotropy constants, K1 , K2 , K3 and K4 , per unit cell are shown in table 3 for different arrangements of the graphene overlayer unit cell (see figure 1(b), note that it contains two Co atoms). For the hollow-hexagonal placement, the uniaxial MAE = EA [M||x] − EA [M||z]/Co = 0.46 meV/Co was calculated. In addition, there is non-negligible in-plane MAE = 0.04 meV/Co. Thus, in this case graphene reduces the uniaxial MAE but it remains positive. The elementspecific Co and Ir substrate contributions are also positive. For the top-fcc position, MAE = −0.18 meV/Co. Here, the positive anisotropy of the Co layer is overcome by the negative contribution of the Ir substrate. For the top-hcp case, the MAE becomes even more negative, −0.44 meV/Co (see table 3). Also we note that the C atoms of graphene do not yield any noticeable contribution to the MAE since their induced magnetic moments are small (∼0.01 µB ) and the SOC is small. Furthermore, we analyse the layer- (element-specific) and spin-resolved torques T↑↑ , T↑↓ and T↓↓ , together with the total torque T = T↑↑ + T↑↓ + T↓↓ evaluated at (θ = π/4, φ = 0) (per unit cell, meV) for [1ML Co]/Ir(1 1 1) and GR/[1ML Co]/Ir(1 1 1). As was already mentioned, MAE ≈ T (θ = π/4, φ = 0) holds. We found that placement of graphene leads to the changes in the torque contributions mainly from the Co interface, Ir interface and Ir interface-1 layers. These layerand spin-resolved torques are shown in table 4. In the top-fcc case, a graphene overlayer affects the Co layer contribution to the MAE. This is mainly due to enhancement of the T↓↓ positive contribution. This can be explained within the SOC perturbation theory, which is valid for Co [18], as the SOC to the exchange splitting ratio ξ ∼ 0.05 is small. As follows from the spin- and orbital resolved Co dDOS shown in figure 2, the changes in the spin-down channel near EF for the top-fcc placement of graphene are: (i) a downward shift of the E1 : {xz, yz} peak away from EF and (ii) an upward shift of the A : {3z2 − r 2 } peak. According to SOC perturbation theory, the coupling z2 |x |{xz, yz} (where x is the operator for the x-axis projection of the orbital moment) makes a negative contribution to the MAE. These changes in the spin-minority
T↑↑ 0.34 −2.42 0.06 0.75 −1.71 −0.56 0.27 −4.91 1.00 0.36 −5.31 0.62
T↑↓
T↓↓
without GR −1.41 1.15 4.62 −0.97 1.65 −0.13 hollow-hexagonal −1.70 1.01 4.51 −1.37 0.73 −0.40 top-fcc −1.51 1.49 6.80 −2.29 −0.01 −1.21 top-hcp −1.70 1.38 8.15 −2.91 −0.62 −0.30
T 0.09 1.23 1.58 0.07 1.43 −0.23 0.25 −0.41 −0.22 −0.02 −0.06 −0.30
dDOS promote a reduction of the absolute value of the negative MAE contribution, and the total positive MAE for the Co layer is increased. The change from positive to negative sign of the MAE for the top-fcc and top-hcp cases is due to the changes of the MAE contributions from the Ir interface and Ir interface1 layers (see table 4). For the Ir interface layer, the parallel spin contributions T↑↑ and T↓↓ are negative, and compete with the positive T↑↓ term. In the top-fcc and top-hcp cases, the negative MAE contributions prevail over the positive. Note that the absolute values of the individual spin-resolved torques for the Ir interface are substantially bigger than for the Co layer, and reflect the enhanced strength of the SOC of Ir over Co ( ξξCoIr ∼ 6.6). The sub-interface layer yields the negative contribution to the MAE, which is similar for all graphene placements. Note that the SOC perturbation theory of [18] is not valid for the MAE evaluation for 5d element atoms with strong SOC, where the SOC to the exchange splitting ratio is large, ∼4 for the Ir interface, and ∼10 for Ir interface-1 layers. We estimate the magnetic recording density limit that would correspond to the MAE of the considered Co/Ir(1 1 1) system. For [1ML Co]/Ir(1 1 1), MAE = 1.24 meV/Co atom plus the shape anisotropy Esa = −0.09 meV/ Co atom yield the total MAE, = 1.15 meV/Co atom. We use the standard criterion [N]/[kB Troom ] = 60 [1] needed to ensure the thermal stability of the information bit for 10 years. This yields N = 1300 Co atoms in the information bit with corresponding areal density of 8 × 1012 bit in−2 . Taking into account the Curie temperature TC estimate of 1190 K, which is well above room temperature, we conclude that the Co/Ir(1 1 1) system is a promising candidate for perpendicular ultra-high density applications. For Co intercalated graphene on Ir(1 1 1), we found a reduction of the positive MAE for the hollow-hexagonal placement of a graphene overlayer. In this case, the PMA remains, but the MAE is reduced by a factor of 3. This means that the corresponding bit size is increased by the same 5
J. Phys.: Condens. Matter 26 (2014) 476003
A B Shick et al
factor of 3 and the areal recording density is decreased to 2.7 × 1012 bit in−2 . Still, the estimated Curie temperature of 843 K is reasonably high. However, for the top-fcc and top-hcp placements of graphene, the MAE becomes negative, which makes GR/[1ML Co]/Ir(1 1 1) unsuitable for PMA applications. The above calculations show that the MAE of [1ML Co]/Ir(1 1 1) changes with a graphene overlayer. Experimental studies of the magnetic properties of cobalt intercalated in graphene on Ir(1 1 1) show an enhancement of the PMA [4]. These results were obtained for films that were a few Co MLs thick, and not a single Co overlayer. Moreover, we have used the commensurate in-plane unit cell of graphene instead of the experimental moire superstructure. This can lead to neglecting strong interface effects, such as charge transfer-induced polarization in the adsorbed graphene. From the computational point of view, the MAE evaluation for GR/[1ML Co]/Ir(1 1 1) in a realistic moire superstructure remains a challenge.
Acknowledgments
This work has been supported by the Czech Republic grants GACR No. P204/10/0330 and No. 14-37427G. SCH acknowledges the support by the Priority Research Centers Program (NRF 2009-0093818). AIL acknowledges the support from the Deutsche Forschungsgemeinschaft (SFB668). References [1] Weller D, Moser A, Folks L, Best M E, Wen M F, Schwickert M, Thiele J-U and Doerner M F 2000 IEEE Trans. Magn. 36 10 [2] Mangin S et al 2006 Nat. Mater. 5 210 [3] Decker R, Brede J, Atodiresei N, Caciuc V, Bluegel S and Wiesendanger R 2013 Phys. Rev. B 87 041403 [4] Rougemaille N, N’Diaye A T, Coraux J, Vo-Van C, Fruchart O and Schmid A K 2012 Appl. Phys. Lett. 101 142403 [5] Kresse G and Hafner J 1993 Phys. Rev. B 47 R558 Kresse G and Furthmuller J 1996 Comput. Mater. Sci. 6 15 Kresse G and Joubert D 1999 Phys. Rev. B 59 1758 [6] Singh D J 1994 Planewaves, Pseudopotentials and the LAPW Method (Boston: Kluwer Academic) p 115 [7] Shick A B, Novikov D L and Freeman A J 1997 Phys. Rev. B 56 R14259 [8] Lichtenstein A I, Katsnelson M I, Antropov V P and Gubanov V A 1987 J. Magn. Magn. Mater. 67 65 [9] Katsnelson M I and Lichtenstein A I 2000 Phys. Rev. B 61 8906 [10] Chikazumi S 1997 Physics of Ferromagnetism (Oxford: Oxford University Press) p 655 [11] Turzhevskii S A, Lichtenstein A I and Katsnelson M I 1990 Fiz. Tverd. Tela 32 1952 [12] Wang X, R. Wu, Wang D-S and Freeman A J 1996 Phys. Rev. B 54 61 [13] Methfessel M and Kubler J 1982 J. Phys. F 12 141 [14] Shick A B, Koloren˘c J, Lichtenstein A I and Havela L 2009 Phys. Rev. B 80 085106 [15] Gubanov V A, Liechtenstein A I and Postnikov A V 1992 Magnetism and the Electronic Structure of Crystals (Springer Series in Solid-State Sciences) vol 98 (Berlin: Springer) [16] Khmelevskyi S, Shick A B and Mohn P 2011 Phys. Rev. B 83 224419 [17] Etz C, Zabloudil J, Weinberger P and Vedmedenko E Y 2008 Phys. Rev. B 77 184425 [18] Wang D S, Wu R Q and Freeman A J 1993 Phys. Rev. B 47 14932
3. Conclusions
The first-principles FP-LAPW calculation of the electronic structure, magnetic moments, effective exchange interaction parameter and MAE of [monolayer Co]/Ir(1 1 1) and Co intercalated graphene on Ir(1 1 1) have been performed. The large positive magnetic anisotropy of 1.24 meV/Co was found for [monolayer Co]/Ir(1 1 1), and a high Curie temperature of 1190 K was estimated. These findings make the Co/Ir(1 1 1) system a promising candidate for perpendicular ultra-high density magnetic recording applications. It is shown that the magnetic moments, exchange interactions and the magnetic anisotropy are strongly affected by graphene. For a graphene/[monolayer Co]/Ir(1 1 1), a reduction of the magnetic anisotropy as well as the Curie temperature were found. It was shown that for graphene placed in the hollow-hexagonal positions over the ML Co, the magnetic anisotropy remains positive. For other placements with one of the C atoms on top of Co, the MAE becomes negative. These findings may be important for assessing the use of graphene for future applications and developments of nanoscience and nanotechnology, such as ultrahigh-density magnetic recording media, spin torque based magnetic random-access memories, magnetic tunnel junctions and tunnelling anisotropic magnetoresistance devices.
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Magnetic anisotropy energy and effective exchange interactions in Co intercalated graphene on Ir(1 1 1)
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 476003 (http://iopscience.iop.org/0953-8984/26/47/476003) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 193.255.248.150 This content was downloaded on 19/01/2015 at 04:42
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 476003 (6pp)
doi:10.1088/0953-8984/26/47/476003
Magnetic anisotropy energy and effective exchange interactions in Co intercalated graphene on Ir(1 1 1) A B Shick1 , S C Hong2 , F Maca1 and A I Lichtenstein3 1
Institute of Physics ASCR, Na Slovance 2, 18221 Prague, Czech Republic University of Ulsan, Department of Physics and Energy Harvest Storage Research Center, Ulsan 680-749, Korea 3 University of Hamburg, Jungiusstrasse 9, 20355 Hamburg, Germany 2
E-mail: [email protected] Received 19 August 2014, revised 22 September 2014 Accepted for publication 7 October 2014 Published 29 October 2014 Abstract
The electronic structure, magnetic moments, effective exchange interaction parameter and the magnetic anisotropy energy of [monolayer Co]/Ir(1 1 1) and Co intercalated graphene on Ir(1 1 1) are studied making use of the first-principles density functional theory calculations. A large positive magnetic anisotropy of 1.24 meV/Co is found for [monolayer Co]/Ir(1 1 1), and a high Curie temperature of 1190 K is estimated. These findings show the Co/Ir(1 1 1) system is a promising candidate for perpendicular ultra-high density magnetic recording applications. The magnetic moments, exchange interactions and the magnetic anisotropy are strongly affected by graphene. Reduction of the magnetic anisotropy and the Curie temperature are found for graphene/[monolayer Co]/Ir(1 1 1). It is shown that for graphene placed in the hollow-hexagonal positions over the monolayer Co, the magnetic anisotropy remains positive, while for the placements with one of the C atoms on the top of Co it becomes negative. These findings may be important for assessing the use of graphene for magnetic recording and magnetoelectronic applications. Keywords: magnetic anisotropy, Co monolayer, graphene (Some figures may appear in colour only in the online journal)
magnetic moments, the effective exchange interactions, and the MAE of the Co overlayer on the Ir(1 1 1) substrate, by making use of the first-principles density functional theory calculations. Knowledge of the MAE is essential for evaluating the magnetic bit stability over the superparamagnetic limit, and the effective exchange interaction parameter allows us to estimate the Curie temperature.
1. Introduction
The studies of new nanoscale materials with perpendicular magnetic anisotropy (PMA) are particularly timely and important due to the currently growing interest in perpendicular magnetic recording [1] and spin-transfer torque applications [2]. We focus on the influence of graphene on the anisotropic magnetic properties of ultra-thin magnetic films. Recent experiments using spin-polarized scanning tunnelling microscopy [3] observed magnetic moire patterns in Co intercalated graphene on Ir(1 1 1). Spin-polarized low-energy electron microscopy [4] experiments showed that the graphene film promotes PMA in the underlying Co film. However, with neither technique is it possible to extract quantitative information about the magnetic anisotropy energy (MAE). In the work reported here, we provide details of the effect of graphene on the electronic structure, the spin and orbital 0953-8984/14/476003+06$33.00
2. Method of calculation
We start with the supercell calculations for a Co overlayer on an Ir(1 1 1) surface. A supercell model is used that consists of a ten-layer Ir(1 1 1) substrate and Co monolayers (MLs) on each side of the substrate (see figure 1(a)). The in-plane interatomic distance for pure Ir (5.132 a.u.) was adopted and kept fixed in the calculations. The structural optimization used the standard VASP-PAW [5] program package without 1
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spin–orbit coupling (SOC) employing the generalized gradient approximation, GGA-PBE. For [1ML Co]/Ir(1 1 1), we obtain a relatively large −8.4% relaxation of the inter-layer distance d[Co−Ir] = 3.84 a.u. The 2.5% change in the distance between Ir-interface (Ir-I) and Ir-sub-interface (Ir-I-1) layers, d[(Ir−I)−(Ir−I−1)] = 4.31 a.u., is substantial. Very small— practically negligible—changes in the positions of Ir atoms for the rest of the substrate are found in the calculations. Graphene forms a moire superstructure on Ir(1 1 1) due to the in-plane lattice mismatch. In order to directly model this superstructure, one would need to consider 10 × 10 graphene (with 200 C atoms) placed on 9×9 Ir(1 1 1) (with 81 Ir atoms in each Ir layer), and insert 9×9 Co layer(s) between the graphene and Ir(1 1 1) substrate. The application of density functional theory to such a superstructure is a difficult task when taking into account that high-accuracy relativistic calculations with the SOC included are necessary for the magnetic anisotropy calculations. Instead of considering a large superstructure, we place two C atoms of the graphene unit cell on the top of a ML Co/Ir(1 1 1) (GR/[1ML Co]/Ir(1 1 1)), and consider three different placements for the graphene overlayer: (1) top-hcp, one of the C atoms is on the top of the Co, the other is over the Ir interface ML; (2) top-fcc, one of the C atoms is on the top of the Co, the other is over the Ir sub-interface ML; and (3) hollow-hexagonal, one of the C atoms is on the top of the Ir interface ML, the other is over the Ir sub-interface ML. This supercell model, which consists of a ten-layer Ir(1 1 1) substrate and 1 ML of Co on each side of the substrate covered by a layer of graphene, is shown in figure 1(b). In addition 1 ML of Co on the Ir(1 1 1) surface [1ML Co]/Ir(1 1 1) is used in order to analyse graphene-induced changes in the magnetic properties of the Co atoms. As mentioned above, the structural optimization is performed using the standard VASP-PAW program package employing the GGA-PBE approximation. The in-plane interatomic distance of pure Ir (5.132 a.u.) was adopted and kept fixed in the calculations. For GR/[1ML Co]/Ir(1 1 1), for top-hcp and top-fcc, we obtain that graphene is strongly bonded to the Co atom, with d[C−Co] = 3.80 a.u., 3.72, respectively. For the hollow-hexagonal case, the C atoms are much less connected to the substrate, with d[C−Co] = 4.27 a.u. Once the structure relaxation is done, we use the relativistic version of the full-potential linearized augmented plane-wave method (FP-LAPW) [6], in which SOC is included in a self-consistent second-variational procedure [7]. The conventional (von Barth–Hedin) local spin-density approximation (LSDA) is adopted in the calculations, which is expected to be valid for itinerant metallic systems. The radii of the atomic muffin-tin spheres are set to 1.4 a.u. for C atoms, 2.2 a.u. for Co atoms and 2.5 a.u. for Ir atoms. The parameter RCo × Kmax = 7.7 defines the basis set size and the two-dimensional Brillouin zone (BZ) was sampled with 229 k points.
Figure 1. Schematic crystal structure used to represent the [1ML Co]/Ir(1 1 1) (a) and graphene/[1ML Co]/Ir(1 1 1) (b) surfaces.
(I-1) layers. For the [1ML Co]/Ir(1 1 1) case, there is a reduction of the MS and ML values (MS = 1.80 µB and ML = 0.12 µB ) of the Co layer compared to the unrelaxed case (MS = 1.89 µB and ML = 0.13 µB ), and an enhancement of the magnetic polarization of the substrate. This is consistent with the structure relaxation-induced reduction of distance d[Co−Ir] , leading to an increase of hybridization between the Co overlayer and the Ir substrate. The Ir interfacial layer is spinpolarized parallel to the Co ML, while the spin-polarization for Ir-(I-1) is anti-parallel. For the GR/[1ML Co]/Ir(1 1 1) case, the spin moments are practically zero for the C atoms of the graphene ML for the hollow-hexagonal position, reflecting a very weak interaction between the Co ML and graphene. Once the C atom interacts with the Co atom underneath, as in the case of the top-fcc and top-hcp graphene placements, the spin magnetic moments are induced. The total induced spin moment in graphene is very small (≈0.01 µB ), and is oriented anti-parallel to the Co ML moment. The spin- and orbital-resolved projected densities of dstates (dDOS) for the Co layer (E1 : {xz, yz}, E2 : {x 2 − y 2 , xy}, A : {3z2 − r 2 }) are shown in figure 2. It is seen that there is only a minor difference between the Co atom
2.1. Electronic structure
Spin MS and orbital ML magnetic muffin-tin moments are shown in table 1 for the Co/Ir interface (I) and sub-interface 2
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Table 1. Spin (MS ) and orbital (ML ) magnetic moments in the muffin-tin sphere of the Co and Ir atoms (in Bohr magnetons), and effective exchange interaction parameter (J0 , eV) for [1ML Co]/Ir(1 1 1) and GR/[1ML Co]/Ir(1 1 1). In all calculations, the magnetization is directed along the z-axis along the surface normal.
Co MS ML J0
MS ML J0 MS ML J0 MS ML J0
Ir[I]
Ir[I-1]
[1ML Co]/Ir(1 1 1) 1.80 0.21 −0.06 0.12 0.01 −0.00 0.154 5 × 10−3 4 × 10−5 GR/[1ML Co]/Ir(1 1 1) hollow-hexagonal 1.57 0.19 −0.06 0.08 0.00 −0.00 0.109 4 × 10−3 5 × 10−5 top-fcc 1.16 0.10 −0.05 0.07 0.00 −0.01 0.084 1 × 10−3 2 × 10−4 top-hcp 1.29 0.13 −0.04 0.07 0.00 0.00 0.093 2 × 10−3 2 × 10−4
dDOS for [1ML Co]/Ir(1 1 1) and hollow-hexagonal GR/[1ML Co]/Ir(1 1 1). This is due to the weak bond between the C atoms and the Ir atoms. For the top-fcc position where one of the C atoms is over a Co, there is a substantial modification of the dDOS, especially for the partially occupied spin-minority A-state. 2.2. Effective exchange interaction parameter
A general expression for the effective exchange interaction of a given site for all magnetic environments [8, 9] is EF 1 J0 = − Im Tr ∆(G↑ − G↓ ) + ∆G↑ G↓ d, (1) 4π −∞ where Gσ =↑,↓ is the spin-diagonal elements of the on-site local LSDA Green function in the local basis of γ = (l, m, σ ) spin orbitals {φγ }, −1 1 GLSDA ( + iδ) = dk + iδ − HLDA (k) . γ1 γ2 γ1 γ2 VBZ BZ (2) Note that the SOC is included in the LSDA Hamiltonian HLSDA (k). is the on-site exchange splitting and EF is the Fermi energy. We have implemented equation (1) in the FP-LAPW basis making use of the previous implementation for the GLSDA in equation (2) as described in [14]. Since most of the muffintin magnetic moments MS are of d(l = 2) orbital character, only the d-states part of the [GLSDA ] matrix was considered in equation (1). For bulk hcp Co, we get J0 = 0.179 eV, in reasonable agreement with the previously reported value of 0.184 eV [15]. Applying equation (1) to [1ML Co]/Ir(1 1 1), we obtain a smaller value of J0 for the Co atom at the Ir(1 1 1) surface (see table 1) as a result of reduced dimensionality. The values
Figure 2. Spin-resolved d-projected DOS for (a) the Co layer in
[1ML Co]/Ir(1 1 1), and for the Co layer in (b) the GR/[1ML Co]/Ir(1 1 1) hollow-hexagonal position and (c) the top-fcc position.
of J0 at the Ir(I) interface and sub-interface Ir(I-1) are much smaller than the value for the Co atom, reflecting the smallness of the Ir local magnetic moments induced by the Co ML. The graphene placed on the top further reduces the magnitude of J0 (see table 1). The effective exchange interaction parameter can be used for the mean-field estimate of the magnetic ordering Curie temperature, TCMF = 3k2B J0 . This yields TCMF = 1383 K, in good agreement with the experimental value of 1388 K. 3
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Then the naive estimate for TC for [1ML Co]/Ir(1 1 1) will be 1191 K. For GR/[1ML Co]/Ir(1 1 1), the Curie temperature will be reduced further to 650–843 K. 2.3. Magnetic anisotropy energy
For hexagonal symmetry, the magnetic anisotropic energy EA (θ, φ) as a function of the spherical angles θ and φ is EA (θ, φ) = K1 sin2 θ + K2 sin4 θ + K3 sin6 θ + K4 sin6 θ cos 6φ,
(3)
where K1 and K2 are the uniaxial MAE constants, and K3 and K4 are the higher-order anisotropy constants [10]. The relativistic FP-LAPW method gives an accurate determination of the magneto-crystalline anisotropy energy. In order to evaluate the MAE of equation (3), we make use of the torque method [11]. For a FP-LAPW basis, the torque method was first implemented in [12]. It can be formulated as follows. We solve theKohn–Sham equations for a two↑ i component spinor | i = , ↓ i
β − ∇ 2 + Vˆeff + ξ(l · s) i (r) = ei αi (r) , (4) α,β
β
where the Vˆeff = V (r)Iˆ + σ · B(r) matrix consists of the sum of the scalar potential V and exchange field B parallel to the spin moment MS , and Hˆ SO = ξ(l · s) is the SOC operator. Here, to simplify the notation, we use a Pauli-like Hamiltonian including SOC, while the actual implementation contains in addition the scalar-relativistic terms. When the magnetic force theorem [8, 13] is used to evaluate the MAE, the MS is rotated and a single energy band calculation is performed for the new orientation of MS . The MAE results from SOC-induced changes in the band eigenvalues EA (θ, φ) = occ i i (θ, φ). In practice, it is more convenient to use the linear response theory, and evaluate the torque T (θ, φ) = ∂EA (θ, φ)/∂θ as T (θ, φ) =
occ
i |
i
†
∂U ∂U ξ(l · s)U† + Uξ(l · s) | i ∂θ ∂θ
Figure 3. (a) θ angular dependence of T (θ, φ = 0). (b) Layer-resolved (element-specific) contributions to the torque T (θ = π/4, φ = 0, π/6) per unit cell for Co/10Ir/Co. Table 2. Anisotropy constants K1 , K2 , K3 and K4 per unit cell (total and Co) for [1ML Co]/Ir(1 1 1) (meV).
(5)
where U(θ, φ) is a conventional spin rotation matrix and | = U(θ, φ)| . From the angular dependence of the torque,
MAE constants
K1
K2
K3
K4
Total Co
2.59 0.09
−0.16 0.01
0.05 −0.02
−0.01 0.01
The θ angular dependence of T (θ, φ) in equation (6) with φ = 0 is shown in figure 3(a) for a Co/Ir(1 1 1)/Co unit cell (see figure 1(a), note that it contains two Co atoms). For T (θ, φ = π/6), the angular dependence was found to be very similar. It is seen that the Co contribution to the total torque is rather small. The corresponding anisotropy constants, K1 , K2 , K3 and K4 , per unit cell are shown in table 2. MAE = EA [M||x] − EA [M||z] = 1.24 meV/Co was calculated. This agrees reasonably well with the Co/Ir(1 1 1) MAE = 1.395 meV/Co calculated in [17]. Since the higherorder anisotropy constants are small (see table 2), then MAE ≈T (θ = π/4, φ = 0) holds. In figure 3(b) the layer-resolved (element-specific) contributions to the torque T (θ = π/4, φ = 0, π/6) per unit cell are shown (note that these are twice the MAE contributions from individual Co-, Ir(I)-, Ir(I-
T (θ, φ) = K1 sin 2θ + K2 sin 2θ (1 − cos 2θ ) 3 + (K3 + K4 cos 6φ) sin 2θ (1 − cos 2θ )2 , (6) 4 the uniaxial MAE constants, K1 and K2 , and the higherorder anisotropy constants, K3 and K4 , are evaluated. An advantage of this approach is that it allows separation of equation (5) into the sum of the element-specific contributions from different atoms in the unit cell [16], and the evaluation of the element-specific contributions to the anisotropy constants and the total MAE. We point out that care should be taken with the convergence of the torque T (θ, φ) in equation (6) with respect to the two-dimensional BZ integration. For [1ML Co]/Ir(1 1 1), we found that the torque converges to better than 0.1 meV/Co for 3482 k points in the BZ. 4
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Table 3. Anisotropy constants K1 , K2 , K3 and K4 per unit cell (total and Co) for GR/[1ML Co]/Ir(1 1 1) (meV).
MAE constants Total Co Total Co Total Co
K1
K2
hollow-hexagonal 0.55 0.17 0.08 0.01 top-fcc −0.325 −0.06 0.244 0.00 top-hcp −0.95 −0.11 −0.02 −0.01
K3
K4
0.22 0.01
−0.04 0.01
0.02 0.00
0.00 0.00
0.16 0.01
0.025 −0.01
Table 4. Layer- (element-specific) and spin-resolved torques T↑↑ , T↑↓ and T↓↓ , and the total torque T = T↑↑ + T↑↓ + T↓↓ , evaluated at (θ = π/4, φ = 0) (per unit cell, meV) for [1ML Co]/Ir(1 1 1) and GR/[1ML Co]/Ir(1 1 1).
MAE constants [1ML Co]/Ir(1 1 1) Co Ir interface Ir interface-1 GR/[1ML Co]/Ir(1 1 1) Co Ir interface Ir interface-1 GR/[1ML Co]/Ir(1 1 1) Co Ir interface Ir interface-1 GR/[1ML Co]/Ir(1 1 1) Co Ir interface Ir interface-1
1,2,3,4)-layers in the unit cell). It is seen that most of the MAE comes from the Ir(I) interface and Ir(I-1) sub-interface layers. The positive MAE sign indicates the perpendicular magnetic anisotropy for [1ML Co]/Ir(1 1 1). Next, we applied the torque method to evaluate the MAE for GR/[1ML Co]/Ir(1 1 1). The calculated anisotropy constants, K1 , K2 , K3 and K4 , per unit cell are shown in table 3 for different arrangements of the graphene overlayer unit cell (see figure 1(b), note that it contains two Co atoms). For the hollow-hexagonal placement, the uniaxial MAE = EA [M||x] − EA [M||z]/Co = 0.46 meV/Co was calculated. In addition, there is non-negligible in-plane MAE = 0.04 meV/Co. Thus, in this case graphene reduces the uniaxial MAE but it remains positive. The elementspecific Co and Ir substrate contributions are also positive. For the top-fcc position, MAE = −0.18 meV/Co. Here, the positive anisotropy of the Co layer is overcome by the negative contribution of the Ir substrate. For the top-hcp case, the MAE becomes even more negative, −0.44 meV/Co (see table 3). Also we note that the C atoms of graphene do not yield any noticeable contribution to the MAE since their induced magnetic moments are small (∼0.01 µB ) and the SOC is small. Furthermore, we analyse the layer- (element-specific) and spin-resolved torques T↑↑ , T↑↓ and T↓↓ , together with the total torque T = T↑↑ + T↑↓ + T↓↓ evaluated at (θ = π/4, φ = 0) (per unit cell, meV) for [1ML Co]/Ir(1 1 1) and GR/[1ML Co]/Ir(1 1 1). As was already mentioned, MAE ≈ T (θ = π/4, φ = 0) holds. We found that placement of graphene leads to the changes in the torque contributions mainly from the Co interface, Ir interface and Ir interface-1 layers. These layerand spin-resolved torques are shown in table 4. In the top-fcc case, a graphene overlayer affects the Co layer contribution to the MAE. This is mainly due to enhancement of the T↓↓ positive contribution. This can be explained within the SOC perturbation theory, which is valid for Co [18], as the SOC to the exchange splitting ratio ξ ∼ 0.05 is small. As follows from the spin- and orbital resolved Co dDOS shown in figure 2, the changes in the spin-down channel near EF for the top-fcc placement of graphene are: (i) a downward shift of the E1 : {xz, yz} peak away from EF and (ii) an upward shift of the A : {3z2 − r 2 } peak. According to SOC perturbation theory, the coupling z2 |x |{xz, yz} (where x is the operator for the x-axis projection of the orbital moment) makes a negative contribution to the MAE. These changes in the spin-minority
T↑↑ 0.34 −2.42 0.06 0.75 −1.71 −0.56 0.27 −4.91 1.00 0.36 −5.31 0.62
T↑↓
T↓↓
without GR −1.41 1.15 4.62 −0.97 1.65 −0.13 hollow-hexagonal −1.70 1.01 4.51 −1.37 0.73 −0.40 top-fcc −1.51 1.49 6.80 −2.29 −0.01 −1.21 top-hcp −1.70 1.38 8.15 −2.91 −0.62 −0.30
T 0.09 1.23 1.58 0.07 1.43 −0.23 0.25 −0.41 −0.22 −0.02 −0.06 −0.30
dDOS promote a reduction of the absolute value of the negative MAE contribution, and the total positive MAE for the Co layer is increased. The change from positive to negative sign of the MAE for the top-fcc and top-hcp cases is due to the changes of the MAE contributions from the Ir interface and Ir interface1 layers (see table 4). For the Ir interface layer, the parallel spin contributions T↑↑ and T↓↓ are negative, and compete with the positive T↑↓ term. In the top-fcc and top-hcp cases, the negative MAE contributions prevail over the positive. Note that the absolute values of the individual spin-resolved torques for the Ir interface are substantially bigger than for the Co layer, and reflect the enhanced strength of the SOC of Ir over Co ( ξξCoIr ∼ 6.6). The sub-interface layer yields the negative contribution to the MAE, which is similar for all graphene placements. Note that the SOC perturbation theory of [18] is not valid for the MAE evaluation for 5d element atoms with strong SOC, where the SOC to the exchange splitting ratio is large, ∼4 for the Ir interface, and ∼10 for Ir interface-1 layers. We estimate the magnetic recording density limit that would correspond to the MAE of the considered Co/Ir(1 1 1) system. For [1ML Co]/Ir(1 1 1), MAE = 1.24 meV/Co atom plus the shape anisotropy Esa = −0.09 meV/ Co atom yield the total MAE, = 1.15 meV/Co atom. We use the standard criterion [N]/[kB Troom ] = 60 [1] needed to ensure the thermal stability of the information bit for 10 years. This yields N = 1300 Co atoms in the information bit with corresponding areal density of 8 × 1012 bit in−2 . Taking into account the Curie temperature TC estimate of 1190 K, which is well above room temperature, we conclude that the Co/Ir(1 1 1) system is a promising candidate for perpendicular ultra-high density applications. For Co intercalated graphene on Ir(1 1 1), we found a reduction of the positive MAE for the hollow-hexagonal placement of a graphene overlayer. In this case, the PMA remains, but the MAE is reduced by a factor of 3. This means that the corresponding bit size is increased by the same 5
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factor of 3 and the areal recording density is decreased to 2.7 × 1012 bit in−2 . Still, the estimated Curie temperature of 843 K is reasonably high. However, for the top-fcc and top-hcp placements of graphene, the MAE becomes negative, which makes GR/[1ML Co]/Ir(1 1 1) unsuitable for PMA applications. The above calculations show that the MAE of [1ML Co]/Ir(1 1 1) changes with a graphene overlayer. Experimental studies of the magnetic properties of cobalt intercalated in graphene on Ir(1 1 1) show an enhancement of the PMA [4]. These results were obtained for films that were a few Co MLs thick, and not a single Co overlayer. Moreover, we have used the commensurate in-plane unit cell of graphene instead of the experimental moire superstructure. This can lead to neglecting strong interface effects, such as charge transfer-induced polarization in the adsorbed graphene. From the computational point of view, the MAE evaluation for GR/[1ML Co]/Ir(1 1 1) in a realistic moire superstructure remains a challenge.
Acknowledgments
This work has been supported by the Czech Republic grants GACR No. P204/10/0330 and No. 14-37427G. SCH acknowledges the support by the Priority Research Centers Program (NRF 2009-0093818). AIL acknowledges the support from the Deutsche Forschungsgemeinschaft (SFB668). References [1] Weller D, Moser A, Folks L, Best M E, Wen M F, Schwickert M, Thiele J-U and Doerner M F 2000 IEEE Trans. Magn. 36 10 [2] Mangin S et al 2006 Nat. Mater. 5 210 [3] Decker R, Brede J, Atodiresei N, Caciuc V, Bluegel S and Wiesendanger R 2013 Phys. Rev. B 87 041403 [4] Rougemaille N, N’Diaye A T, Coraux J, Vo-Van C, Fruchart O and Schmid A K 2012 Appl. Phys. Lett. 101 142403 [5] Kresse G and Hafner J 1993 Phys. Rev. B 47 R558 Kresse G and Furthmuller J 1996 Comput. Mater. Sci. 6 15 Kresse G and Joubert D 1999 Phys. Rev. B 59 1758 [6] Singh D J 1994 Planewaves, Pseudopotentials and the LAPW Method (Boston: Kluwer Academic) p 115 [7] Shick A B, Novikov D L and Freeman A J 1997 Phys. Rev. B 56 R14259 [8] Lichtenstein A I, Katsnelson M I, Antropov V P and Gubanov V A 1987 J. Magn. Magn. Mater. 67 65 [9] Katsnelson M I and Lichtenstein A I 2000 Phys. Rev. B 61 8906 [10] Chikazumi S 1997 Physics of Ferromagnetism (Oxford: Oxford University Press) p 655 [11] Turzhevskii S A, Lichtenstein A I and Katsnelson M I 1990 Fiz. Tverd. Tela 32 1952 [12] Wang X, R. Wu, Wang D-S and Freeman A J 1996 Phys. Rev. B 54 61 [13] Methfessel M and Kubler J 1982 J. Phys. F 12 141 [14] Shick A B, Koloren˘c J, Lichtenstein A I and Havela L 2009 Phys. Rev. B 80 085106 [15] Gubanov V A, Liechtenstein A I and Postnikov A V 1992 Magnetism and the Electronic Structure of Crystals (Springer Series in Solid-State Sciences) vol 98 (Berlin: Springer) [16] Khmelevskyi S, Shick A B and Mohn P 2011 Phys. Rev. B 83 224419 [17] Etz C, Zabloudil J, Weinberger P and Vedmedenko E Y 2008 Phys. Rev. B 77 184425 [18] Wang D S, Wu R Q and Freeman A J 1993 Phys. Rev. B 47 14932
3. Conclusions
The first-principles FP-LAPW calculation of the electronic structure, magnetic moments, effective exchange interaction parameter and MAE of [monolayer Co]/Ir(1 1 1) and Co intercalated graphene on Ir(1 1 1) have been performed. The large positive magnetic anisotropy of 1.24 meV/Co was found for [monolayer Co]/Ir(1 1 1), and a high Curie temperature of 1190 K was estimated. These findings make the Co/Ir(1 1 1) system a promising candidate for perpendicular ultra-high density magnetic recording applications. It is shown that the magnetic moments, exchange interactions and the magnetic anisotropy are strongly affected by graphene. For a graphene/[monolayer Co]/Ir(1 1 1), a reduction of the magnetic anisotropy as well as the Curie temperature were found. It was shown that for graphene placed in the hollow-hexagonal positions over the ML Co, the magnetic anisotropy remains positive. For other placements with one of the C atoms on top of Co, the MAE becomes negative. These findings may be important for assessing the use of graphene for future applications and developments of nanoscience and nanotechnology, such as ultrahigh-density magnetic recording media, spin torque based magnetic random-access memories, magnetic tunnel junctions and tunnelling anisotropic magnetoresistance devices.
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