Magnetic anisotropy of ultrathin pd4co 111 film by first principles calculations

Journal of Science: Advanced Materials and Devices (2018) 243e253 Contents lists available at ScienceDirect Journal of Science: Advanced Materials and Devices journal homepage: www.elsevier.com/locate/jsamd Original Article Magnetic anisotropy of ultrathin Pd4Co(111) film by first-principles calculations Do Ngoc Son a, *, Ong Kim Le a, Mai Thanh Hiep a, Viorel Chihaia b a b University of Technology, VNU-HCM, 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Viet Nam Institute of Physical Chemistry “Ilie Murgulescu” of the Romanian Academy, Splaiul Independentei 202, Sector 6, 060021 Bucharest, Romania a r t i c l e i n f o a b s t r a c t Article history: Received 31 January 2018 Received in revised form 20 March 2018 Accepted 22 March 2018 Available online 29 March 2018 The PdeCo alloy is a suitable candidate for the perpendicular magnetic recording and related applications However, no research is available to clarify influences of local structures on the magnetic anisotropy of the PdeCo alloy Therefore, in this work, we studied the effects of Co arrangement on the magnetic anisotropy of ultrathin Pd4Co(111) film with 20% Co content by using the density functional theory calculations We found that a Co monolayer in the surface layer of the ultrathin film offers a large in-plane magnetic anisotropy while the Co atoms mixed inside the Pd matrix exhibit the perpendicular magnetic anisotropy Notably, a Co monolayer beneath the surface layer of the Pd matrix maximizes the perpendicular magnetic anisotropy up to 1.85 erg/cm2 Electronic properties were also analyzed to clarify the magnetic anisotropy of the ultrathin film © 2018 Vietnam National University in Ho Chi Minh City Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/) Keywords: Magnetic recording Magnetic anisotropy Density functional theory Electronic structure properties Ultrathin film Introduction Perpendicular magnetic anisotropy of Pd/Co multilayers has been intensively studied in the literature because of their high interface magnetism between the magnetic (Co) layer and the nonmagnetic (Pd) layer [1e18] Although it remains limitations such as considerable transition noise [15], the Pd/Co multilayers are one of the best perpendicular magnetic anisotropy materials, which have been applied in the hard disk drives (HDDs), optical devices, and magnetic random access memory [16e19] Conventional HDDs utilized the longitudinal magnetic recording technique with the maximum stored density of information reached 160 Gb/in2 [20] Since the first generation of perpendicular magnetic recording HDDs was realized [21], the high-density magnetic recording was established up to 500 Gb/in2 in 2010 It was predicted that the density of information could achieve up to 1.5 Tb/in2 before the perpendicular magnetic recording is replaced by a more advanced technology [22] The multilayered Pd/Co structures with their high magnetic stability due to the large perpendicular magnetic anisotropy are of particularly crucial for the applications [17,18] However, * Corresponding author E-mail address: dnson@hcmut.edu.vn (D.N Son) Peer review under responsibility of Vietnam National University, Hanoi the literature has concluded about the high perpendicular magnetic anisotropy of the Pd/Co multilayers based on the comparison to that of bulk Co [16] or multilayered structures of Co/Au and Co/Ag [19] There is no comparative research for various arrangements of the Co atoms in the Pd matrix for the PdeCo alloy It is clear that the layered structures are not the only ones found in the PdeCo alloy for a specific unit cell size and an atomic ratio of Pd to Co Furthermore, the literature has shown that as the thickness of the film decreases the perpendicular magnetic anisotropy increases Therefore, the ultrathin film of the PdeCo alloy becomes crucial for the perpendicular magnetic anisotropy [16] In this paper, we studied the influences of the Co arrangement on the magnetic anisotropy of the ultrathin Pd4Co(111) film with 20% Co content by using the density functional theory calculations Results of this work answer the questions: Whether the layered structures are superior regarding the out-of-plane magnetic anisotropy as compared to the other structures of the Pd4Co(111) alloy? If it is the case, ones should design the Co layer on the surface of or sandwich within the Pd matrix? This work also explains the magnetic anisotropy of the ultrathin Pd4Co(111) alloy film based on electronic structure properties and provide a sharper picture of the magnetic anisotropy in the super-thin Pd4Co(111) film Therefore, the results should be useful for designing the super-thin PdeCo alloy film for the applications of perpendicular magnetic anisotropy https://doi.org/10.1016/j.jsamd.2018.03.004 2468-2179/© 2018 Vietnam National University in Ho Chi Minh City Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) 244 D.N Son et al / Journal of Science: Advanced Materials and Devices (2018) 243e253 The remaining of this manuscript was organized as follows: In sect 2, we gave details of the computational method In sect 3, we sequentially presented the computational results and discussion, and lastly, in sect 4, we made the conclusion Computational method We performed the total energy calculations based on the density functional theory using the Vienna ab initio simulation package (VASP) [23e25] The PerdeweBurkeeErnzerhof derivative of the generalized gradient approximation was used for the exchangecorrelation energy [26,27] The electroneion interaction was described by using the projector-augmented-wave method [28,29] with the cutoff energy of 400 eV for the plane wave expansion The calculations were performed with a five-layer slab of the  unit cell and a vacuum space of times of the smallest distance between two nearest neighbors in the supercell The surface Brillouin zone integration was done by using the special k-point sampling Fig The sampling structures for the study of magnetic anisotropy The Co atoms arrange in single (S), double (D), triple (T), and quadruple (Q) layer The blue and orange spheres represent the Co and Pd atoms, respectively Four Co atoms correspond to 20% Co in the Pd matrix D.N Son et al / Journal of Science: Advanced Materials and Devices (2018) 243e253 technique of Monkhorst and Pack [30] All the atomic positions in the slab were allowed to fully relax before the post calculations for the total energy with the k-point mesh of 13  13  The dipole correction was also included in the simulation for the periodic supercell to correct the interaction between the repeated images [31,32] The cutoff energy, the k-point mesh, and the vacuum space were tested to ensure the convergence of the obtained results We used the Fermi-Dirac smearing with the width of 0.2 eV and the €chl corrections [33] for the caltetrahedron smearing with the Blo culations of the geometry optimization and the total energy, respectively The spineorbit coupling was taken into account, and the fully relativistic calculation was performed for the magnetic anisotropy energy (MAE) [34], which is calculated by the following formula: DE ¼ EX;Y À EZ : (1) here, X and Y denote for the in-plane directions and Z for the outof-plane direction of the unit cell We followed the method presented in the VASP manual for the calculation of the MAE, where the spineorbit coupling couples the spin to the crystal structure We first calculated the total energy of the unit cell for each direction (X, Y, Z) of spin We then substituted to the equation (1) Convergence check on energies was done to confirm the accuracy of MAE to 0.01 meV We also estimated the spin polarization at the Fermi level by using the expression: Pẳ r[ rY : r[ ỵ rY (2) here, r[ and rY are the total density of states (DOS) of the spin-up and spin-down bands at the Fermi level, respectively In the  unit cell of the ultrathin Pd4Co(111) film, many different arrangements of the Co atoms are possible, which can be in the surface layer or the Pd matrix We not intend to study all the possible structures exhaustively Therefore, we selected the sampling structures as presented in Fig for the 245 study of the magnetic anisotropy These structures were arranged in the order with an increase of the scattering level from the monolayer to two, three, and four layers of the Co atoms spreading throughout the unit cell of the ultrathin Pd4Co(111) film The sampling structures are symmetrically independent For example, the Co atoms were not arranged in the bottom layer because the uppermost layer and the bottom one are considered to be equivalent Results and discussion We performed the geometry optimization before calculating the total energy for each structure The total energy for each spin direction was calculated by taking into account the spineorbit coupling within the non-collinear magnetic calculations of VASP The magnetic anisotropy energy was then estimated following the eq (1), which is listed in Table and presented in Fig Fig shows the behavior of the MAE for the different structures We found that EX-EZ varies in a similar manner with EY-EZ However, most of the Co double layer structures have EX-EZ greater than EY-EZ while the Co triple and quadruple layer structures exhibit EX-EZ smaller than EY-EZ For the structures with a higher atomic ratio of Co to Pd in the surface layer such as S1 and D1, the MAE is welldefined with a negative value However, the structures with the number of the Co atoms less than or equal to that of the Pd atoms in the uppermost layer such as D5, D7, D9, T1, and Q, the sign of the magnetic anisotropy energy is likely to depend on the combination with the other Co atoms in the beneath layers Even though, it seems that the more the number of Co atoms in the surface layer, the more the negative MAE of the structures becomes For instance, the in-plane magnetization is of the order: S1 > D1 > D5 > Q, which has 4, 3, 2, and Co atoms in the surface layer, respectively Furthermore, the Co layered structures S1 and S2 have the most negative and positive MAE, correspondingly The negative magnetic anisotropy energy of the structure S1 with the Co monolayer on the surface implies that the easy magnetization axis is parallel to the surface of the structure While the Co monolayer in the inner layers as the structures S2 and S3 offer the positive magnetic anisotropy Table The magnetic anisotropy energy per unit cell, the magnetic moment per Co atom, the total Bader charge of the Co atoms, and the spin polarization at the Fermi level of the ultrathin Pd4Co(111) film Structure EX-EZ (meV) EY-EZ (meV) Sign  Max(EX-EZ, EY-EZ) (meV) Magnetic moment per Co atom (mB) Total Bader charge of the Co atoms (eÀ) Spin polarization at Fermi level S1 S2 S3 D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 Q À7.75 17.45 0.08 À5.52 10.76 0.22 12.51 À1.61 3.45 4.09 3.79 5.39 3.32 4.03 0.18 0.05 À0.04 À0.02 À0.32 À0.32 7.52 5.60 0.02 0.00 À1.16 À2.65 11.5 3.70 À2.29 6.76 2.20 6.55 À0.60 2.17 0.40 2.02 1.83 1.83 1.20 0.25 1.60 1.70 1.48 1.30 2.03 5.67 4.81 1.55 0.95 À1.1 À7.75 17.45 3.70 À5.52 10.76 2.20 12.51 À1.61 3.45 4.09 3.79 5.39 3.32 4.03 0.25 1.60 1.70 1.48 1.30 2.03 7.52 5.60 0.55 0.95 À1.16 2.72 3.23 3.01 2.69 3.23 3.09 3.25 2.90 3.13 2.95 3.24 2.92 3.24 3.19 3.16 3.17 3.27 3.26 3.36 3.36 3.35 3.35 3.35 3.28 3.31 À0.612 À1.486 À1.388 À0.934 À1.453 À1.381 À1.581 À1.181 À1.474 À1.402 À1.717 À1.403 À1.701 À1.403 À1.608 À1.619 À1.733 À1.743 À1.852 À1.880 À1.791 À1.794 À1.864 À1.745 À1.731 À0.212 À0.409 À0.432 À0.159 À0.539 À0.101 À0.555 À0.302 À0.511 À0.190 À0.515 À0.248 À0.528 À0.273 À0.478 À0.527 À0.668 À0.669 À0.461 À0.705 À0.368 À0.431 À0.713 À0.351 À0.738 246 D.N Son et al / Journal of Science: Advanced Materials and Devices (2018) 243e253 Fig The magnetic anisotropy energy per unit cell of the ultrathin Pd4Co(111) film energy meaning that the easy magnetization axis is now perpendicular to the structure's surface For the Co atoms dispersed in the Pd matrix, most of the structures exhibit the perpendicular magnetic anisotropy but with a smaller value compared to that of the Co monolayer in the Pd matrix The maximum absolute value of MAE, listed in the fourth column of Table 1, shows that the Co double layer structures exhibit a higher MAE in comparison to the Co triple-layer structures The average MAE of (EX-EZ, EY-EZ) for each typical Co arrangement was found to be (8.43, 5.95) > (5.07, 2.67) > (1.65, 2.05) > (1.16, 1.10) meV for the Co single, double, triple, and quadruple layer structures, respectively This result implies that as the Co layer thickness increases the out-of-plane magnetic anisotropy decreases, which is in good agreement in comparison to the result of the experiment [9,10,35] We can see that the Co arrangement strongly influences the magnetic anisotropy of the ultrathin film The Co monolayer structures have rather high positive MAE compared to the others supporting for the reality that the metallic Fig Total spin-up (positive) and spin-down (negative) DOS and the species-projected DOS for the structures S1, S2, D1, and D4 The Fermi level is set to eV D.N Son et al / Journal of Science: Advanced Materials and Devices (2018) 243e253 magnetic multilayers such as sandwiched and over-layered structures have been commonly chosen for perpendicular magnetic anisotropy applications, for instance, in magnetic recording devices and spin valves [36e39] The calculated MAE of the Co monolayer structures S2 and S3 are in good agreement with the theoretical [40] and experimental works [35,41e44] in the sense that these structures exhibit the out-of-plane orientation of magnetization 247 The calculated MAE of the monolayer structures can be interpreted as uniaxial anisotropy energy Ku studied in the interface magnetic anisotropy experiments [35] To compare to the experimental data, the absolute values of product (DE)  tCo must be calculated, where tCo is the thickness of the Co layer The interface anisotropy plays an essential role in multilayered structures The study of the interface anisotropy requires the fabrication of ideal interfaces of Pd and Co Fig The layer projected density of states of the most negative MAE structures S1 and D1, and of the most positive MAE structures S2 and D4 Majority and minority spin components are positive and negative, respectively The uppermost layer is denoted as the layer 248 D.N Son et al / Journal of Science: Advanced Materials and Devices (2018) 243e253 layers because the structural complexity of interfaces and the interdiffusion of the atoms between the layers are not readily incorporated into the study As seen in Fig 1, most of the structures are not ideally layered at the Pd/Co interfaces except for the structures S1, S2, and S3, and some Co atoms are mixed into the Pd matrix Even though, Engel and coworkers have experimentally prepared the structures with a good interface of Pd and Co layers Therefore, we can compare the calculated MAE of the Co monolayer structures in our work with those obtained in the experiment [35] The value of tCo is 2.34 Å for the Co monolayer in the present work With the unit cell volume of 234.96  10À24 cm3, we have obtained the average value of (DE) x tCo z 1.35 erg/cm2 for the Co monolayer structures with the average MAE of DE ¼ 8.43 meV Comparing this calculated value with the experimental data in the work of Engel [35], Ku x tCo z 1.2 erg/cm2, the obtained result in our study is in good agreement with the experiment Furthermore, the structure S2 with the Co monolayer beneath the Pd skin provides the highest perpendicular magnetic anisotropy up to 1.85 erg/cm2 This value of the ultrathin Pd4Co(111) film is much higher than that experimentally obtained for the Pd/Co multilayers [35], and comparable with that of the best perpendicular magnetic anisotropy materials so far [45] Table The layer-resolved Bader charge of the structures The error of the charge calculation is about 0.01 eÀ Structure Maximum value of (EXeEZ, EYeEZ) (meV) S1 S2 S3 D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 Q À7.75 17.45 3.7 À5.52 10.76 2.2 12.51 À1.61 3.45 4.09 3.79 5.39 3.32 4.03 0.25 1.6 1.7 1.48 1.3 2.03 7.52 5.6 0.55 0.95 À1.16 Bader charge (eÀ) layer layer layer layer layer À0.612 0.787 0.222 À0.254 0.595 0.181 0.611 0.075 0.438 0.088 0.476 0.070 0.471 0.301 0.296 0.299 0.289 0.293 0.430 0.437 0.416 0.415 0.292 0.414 0.108 0.497 À1.486 0.484 0.047 À0.925 0.302 À0.951 À0.393 À0.432 À0.429 À0.467 À0.414 À0.461 À0.469 À0.120 À0.121 À0.248 À0.248 À0.684 À0.690 À0.511 À0.512 À0.234 À0.515 À0.105 0.098 0.583 À1.388 0.172 0.134 À0.841 0.119 0.267 À0.337 0.276 À0.372 0.280 À0.372 À0.022 À0.359 À0.364 0.094 0.092 0.504 0.503 0.030 0.032 0.067 0.050 À0.039 À0.110 0.011 0.470 À0.079 0.057 0.068 0.075 À0.071 0.176 À0.052 0.189 À0.059 0.194 0.053 À0.105 À0.112 À0.560 À0.567 À0.690 À0.677 À0.230 À0.228 À0.576 À0.237 À0.255 0.127 0.105 0.212 0.115 0.139 0.290 0.146 0.122 0.155 0.117 0.175 0.123 0.168 0.136 0.287 0.297 0.424 0.430 0.440 0.427 0.294 0.293 0.450 0.287 0.291 Fig The maximum value of magnetic anisotropy energy (EX-EZ, EY-Ez) and the Bader point charge of the first and second atomic layer of the super-thin Pd4Co(111) film D.N Son et al / Journal of Science: Advanced Materials and Devices (2018) 243e253 The fifth column of Table shows that the average value of magnetic moment per Co atom in the unit cell is correspondingly 2.99 < 3.06 < 3.28 < 3.31 mB for the Co single, double, triple, and quadruple layer structures The trend of the magnetic moment is inversely proportional to that of the average value of the MAEs implying that the more scattered the Co arrangement in the Pd matrix, the higher the bulk magnetization is Simultaneously, the interface magnetization of the ultrathin film decreases due to the higher Co scattering degree Therefore, the better concentration of the Co atoms in a single layer such as S2 and S3 enhances the interface magnetic anisotropy due to the presence of the large interface of the nonmagnetic (Pd) and magnetic (Co) layers Fig presents the total electronic DOS of the most negative and positive MAE structures This figure shows that the spin-up and spin-down components not equally distribute with respect to the energy Notably, the spin-down DOS dominates the unoccupied states in which the far end of these states is attributed to the spindown DOS of the Co atoms, while the states near and below the 249 Fermi level is assigned to those of the Pd atoms The electronic properties at the Fermi level play an essential role in the understanding of the magnetic properties of materials Therefore, we also calculated the magnetization of the sampling structures of the super-thin Pd4Co(111) film by using the eq (2) The result is listed in the last column of Table We found that the spin polarization is negative and quite large for every structure due to a rather large spin-down DOS compared to the spin-up component at the Fermi level, implying that all the structures exhibit ferromagnetic property Fig shows the layer projected DOS of the structures S1, S2, D1, and D4 We see that the DOS of the layers 1e2 of S1 and D1, and the layers 1e3 of S2 and D4, are much more significantly modified compared to the other layers for each structure The DOS of the remaining layers of each structure exhibit the behavior similar to that of the total DOS of the Pd atoms (see Fig 3) The results indicate the crucial role of the upper layers toward the magnetic anisotropy of the ultrathin film It is worthy to note that we have selected the Fig Charge density difference of the structures S1, D1, S2, and D4 Occupied and unoccupied states are presented in red and green, respectively 250 D.N Son et al / Journal of Science: Advanced Materials and Devices (2018) 243e253 sampling structures with the consideration of symmetric equivalence of the upper and lower layers of the structures In the ultrathin Pd4Co(111) film, the states of the surface layers are crucial as qualitatively shown in the layer-projected DOS However, to quantitatively examine the dependence of the MAE on the electronic structure properties, we now focus on the analysis of the point charge calculated by the Bader partition technique We have tested two different scenarios of the MAE versus: (1) the total point charge exchange between the Co atoms and the Pd atoms and (2) the layer-resolved charge of all the structures For the first one, the point charge of each Co atom was calculated and then summed into the total contribution of all the Co atoms for every structure, which is listed in the sixth column of Table Because the charge of the unit cell should be neutral, the total charge of the Pd atoms should be in opposite sign with that of the Co atoms Table shows that the Co atoms always donate the charge implying that the Pd atoms gain the charge Although the charge donation of the Co atoms does not have a correlation in details with the MAE of the structures, the behavior of the average charge donation is 1.162 < 1.432 < 1.730 < 1.731 e for the Co single, double, triple, and quadruple layer structures, respectively This behavior is inversely proportional to the average MAE and similar to that of the average magnetic moment For the second one, the total charge of each layer was calculated and listed in Table We have already checked the correlation of the MAE versus the charge of each atomic layer for all the structures We found that although the charge of the layers 3, 4, and does not exhibit any correlations, the charge variation of the layers and correlates well with the change of the MAE Fig shows the charge for only the layers and We can see that although there are the fluctuations of the charge for the structures with the small MAE ranging around 0e5 meV, the charge of the layer increases, while the charge of the layer decreases with the MAE The charge of the layer has a better behavior compared to that of the layer implying that the state of the uppermost (surface) layer should play a vital role in the determination of the magnetic anisotropy of the ultrathin film We also see that the most negative MAE structures such as S1 and D1 exhibit the negative Bader charge, while the most positive MAE structures (D2, D4, S2) show a significant positive Bader charge of the layer This result indicates that a substantial charge loss at the surface layer causes the in-plane magnetic anisotropy, while a vast charge accumulation at the surface causes the out-of-plane magnetic anisotropy Therefore, we will focus on the analysis of the charge density difference of the uppermost atomic layer in the following part Fig shows the charge density difference of the most negative and positive MAE structures In this figure, we also draw the lattice vectors of the unit cell, where the vector a is perpendicular to and point toward the page For the ultrathin film, the characteristics of the charge cloud those exposed to the vacuum area would be fundamental and influence the direction of magnetic anisotropy of the structures Therefore, we pay close attention to the characteristics of the charge clouds of the surface atomic layer of each structure We found that the charge clouds exhibit the shape of the d orbitals The states are d2z , (dyz, dxz), and (dxy, d2xÀy2) for those along the vector c, in the (bc, ac) plane, and in the ab plane, respectively At first glance, we found that for each structure the charge clouds of the uppermost layer, where the atomic layer contains the Co atoms or is close to the Co-containing layers, are more expanded in the space than those of the bottom layer The bottom layer of the perpendicular magnetic anisotropy structures, S2 and D4, exhibits the more considerable charge clouds compared to that of the in-plane magnetic anisotropy structures, S1 and D2 All the d2z orbitals of the uppermost layer of S2 and D4 are unoccupied, while some of them are occupied for the topmost layer of S1 and D1 Simultaneously, the dxy and d2xÀy2 orbitals are completely occupied for the structure S2 or partially occupied for the structure D4, while most of the dxy and d2xÀy2 orbitals are unoccupied for the cases of S1 and D1 The occupied orbitals provide the orbits for the motion of the electrons Furthermore, the orbit motion of the electrons generates the magnetic moment Fig The projected DOS of the sampling structures S1, S2, D1, D4, T2, and Q The dxy and d2xÀy2 orbitals (similarly the dxz and dyz orbitals) are identical for S1 and S2 D.N Son et al / Journal of Science: Advanced Materials and Devices (2018) 243e253 perpendicular to the plane of an orbital Therefore, when the spineorbit coupling is taken into account, the magnetic moment interacts with the electron spin resulting in the magnetic anisotropy The electron motion on the dxy and d2xÀy2 orbitals creates the magnetic moment along the c vector, while on the d2z orbital creates the magnetic moment in the ab plane [46] This picture explains for the in-plane magnetic anisotropy of S1 and D1 due to the portion of the occupied d2z orbitals, and for the out-of-plane magnetic anisotropy of S2 and D2 because of the more part of the occupied dxy and d2xÀy2 orbitals The anisotropy energy due to 251 the rotation of the magnetization from dxz to dyz or vice versa is also an essential contribution to the total perpendicular anisotropy energy [47], which is corresponding to the orbital motion of the electron around the Z direction Fig also shows that the electron occupation of the dxz and dyz orbitals of S2 and D4 is more significant than those of S1 and D1 Fig shows that for the Co monolayer structures S1 and S2 the dxz and dyz orbitals are identical and therefore degenerate A similar result was also found for the dxy and d2xÀy2 orbitals However, for the structures with the Co atoms dispersed in the Pd matrix, the Fig (continued) 252 D.N Son et al / Journal of Science: Advanced Materials and Devices (2018) 243e253 degeneracy of these orbitals are less profound The spin-up and spin-down DOS of the Pd atoms are not so different at the Fermi level Contrastingly, the density of states of the Co atoms at the Fermi level is attributed only to the spin-down component Therefore, the contribution to the magnetic anisotropy should mainly come from the Co d orbitals The degeneracy of the dxy and d2xÀy2 orbitals and the dxz and dyz orbitals was found for the Co monolayer structures of the ultrathin Pd4Co(111) film with the presence of the spineorbit coupling This result is different compared to the case of the Pd/Co multilayers found in the literature that a break of the degeneracy of these orbitals near the Fermi level occurs whenever taking into account the spineorbit coupling We also see that there is the beak of the degeneracy of the dxz and dyz or the dxy and d2xÀy2 orbitals for the case of the lower magnetic anisotropy structures such as D1 and D4 Fig also shows that the in-plane magnetic anisotropy structures (S1, D1) have a more significant portion of the d2z orbital, while the out-of-plane magnetic anisotropy structures (S2, D4) have a more substantial part of the dxy and d2xÀy2 orbitals around the Fermi level in comparison to the other orbitals This result supports the analysis of the charge density difference We also observe the same consequence for the projected DOS of the other structures those have a rather small MAE such as Q and T2 Conclusion The picture of magnetic anisotropy of the ultrathin Pd4Co(111) film has been revealed by using the density functional theory calculations The results were found to be in good agreement with those of the previous theoretical and experimental works We pointed out that the Co monolayer grown on the surface exhibits the most significant in-plane magnetic anisotropy, while the Co monolayer grown beneath the surface layer displays the highest out-of-plane magnetic anisotropy For the Co atoms in the Pd matrix, most of the structures exhibit the magnetic anisotropy perpendicular to the film's surface The electronic structure analysis indicated that the surface states are the most important ones dominating the magnetic anisotropy, in which the dxy and d2xÀy2 orbitals contribute to the perpendicular easy magnetization axis, while the d2z state dominates the in-plane magnetic anisotropy Acknowledgments This research was funded by Vietnam National University in Ho Chi Minh City (VNU-HCM) under grant number C2015-20-21 We acknowledge the usage of the computer time and software granted by the Institute of Physical Chemistry of Romanian Academy, Bucharest (HPC infrastructure developed under the projects Capacities 84 Cp/I of 15.09.2007 and INFRANANOCHEM 19/ 01.03.2009) References [1] P.F Carcia, A.D Meinhaldt, A Suna, Perpendicular magnetic anisotropy in Pd/ Co thin film layered structures, Appl Phys Lett 47 (1985) 178e180 [2] H.J.G Draaisma, W.J.M de Jonge, F.J.A den Broeder, Magnetic interface anisotropy in Pd/Co and Pd/Fe multilayers, J Magn Magn Mat 66 (1987) 351e355 [3] F.J.A den Broeder, H.C Donkersloot, H.J.G Draaisma, W.J.M de Jonge, Magnetic properties and structure of Pd/Co and Pd/Fe multilayers, J Appl Phys 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orbitals, and for the out -of- plane magnetic anisotropy of S2 and D2 because of the more part of the occupied... in the understanding of the magnetic properties of materials Therefore, we also calculated the magnetization of the sampling structures of the super-thin Pd4Co( 111) film by using the eq (2) The... maximum value of magnetic anisotropy energy (EX-EZ, EY-Ez) and the Bader point charge of the first and second atomic layer of the super-thin Pd4Co( 111) film D.N Son et al / Journal of Science: Advanced