Magnetic anisotropy of ultrathin pd4co 111 film by first principles calculations

Original Articlecalculations Do Ngoc Sona,*, Ong Kim Lea, Mai Thanh Hiepa, Viorel Chihaiab a University of Technology, VNU-HCM, 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City,

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Original Article

calculations

Do Ngoc Sona,*, Ong Kim Lea, Mai Thanh Hiepa, Viorel Chihaiab

a University of Technology, VNU-HCM, 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Viet Nam

b 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

Article history:

Received 31 January 2018

Received in revised form

20 March 2018

Accepted 22 March 2018

Available online 29 March 2018

Keywords:

Magnetic recording

Magnetic anisotropy

Density functional theory

Electronic structure properties

Ultrathin ﬁlm

a b s t r a c t

The PdeCo alloy is a suitable candidate for the perpendicular magnetic recording and related applica-tions 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 ultrathinfilm 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 ultrathinfilm

© 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/)

1 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

anisot-ropy are of particularly crucial for the applications[17,18] However,

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 thefilm decreases the perpendicular magnetic anisotropy increases Therefore, the ultrathinfilm of the PdeCo alloy becomes crucial for the perpen-dicular 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 calcula-tions Results of this work answer the questions: Whether the layered structures are superior regarding the out-of-plane mag-netic 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) alloyﬁlm 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

* Corresponding author.

E-mail address: dnson@hcmut.edu.vn (D.N Son).

Peer review under responsibility of Vietnam National University, Hanoi.

Contents lists available atScienceDirect Journal of Science: Advanced Materials and Devices

j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / j s a m d

https://doi.org/10.1016/j.jsamd.2018.03.004

Journal of Science: Advanced Materials and Devices 3 (2018) 243e253

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The remaining of this manuscript was organized as follows: In

sect 2, we gave details of the computational method Insect 3, we

sequentially presented the computational results and discussion,

and lastly, insect 4, we made the conclusion

2 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 exchange-correlation 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 aﬁve-layer slab of the 2 2 unit cell and a vacuum space of 6 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 1 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

D.N Son et al / Journal of Science: Advanced Materials and Devices 3 (2018) 243e253

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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 1 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

tetrahedron smearing with the Bl€ochl corrections[33]for the

cal-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:

here, X and Y denote for the in-plane directions and Z for the

out-of-plane direction of the unit cell We followed the method

pre-sented in the VASP manual for the calculation of the MAE, where

the spineorbit coupling couples the spin to the crystal structure

Weﬁrst calculated the total energy of the unit cell for each direction

(X, Y, Z) of spin We then substituted to the equation(1)

Conver-gence 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:

P¼r[rY

here,r[andrYare the total density of states (DOS) of the spin-up

and spin-down bands at the Fermi level, respectively

In the 2 2 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 do not intend to

study all the possible structures exhaustively Therefore, we

selected the sampling structures as presented in Fig 1 for the

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

3 Results and discussion

We performed the geometry optimization before calculating the total energy for each structure The total energy for each spin di-rection 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 inTable 1and presented inFig 2

Fig 2shows the behavior of the MAE for the different structures

We found that EX-EZvaries in a similar manner with EY-EZ However, most of the Co double layer structures have EX-EZgreater 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

well-deﬁned 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 1 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 1

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 Pd 4 Co(111) ﬁlm.

Structure E X -E Z (meV) E Y -E Z (meV) Sign Max(E X -E Z , E Y -E Z ) (meV) Magnetic moment

per Co atom (mB )

Total Bader charge of the Co atoms (e)

Spin polarization

at Fermi level

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energy meaning that the easy magnetization axis is now

perpen-dicular to the structure's surface For the Co atoms dispersed in the

Pd matrix, most of the structures exhibit the perpendicular

mag-netic 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 ofTable 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 im-plies 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 anisot-ropy of the ultrathinﬁlm

The Co monolayer structures have rather high positive MAE compared to the others supporting for the reality that the metallic

Fig 2 The magnetic anisotropy energy per unit cell of the ultrathin Pd 4 Co(111) ﬁlm.

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magnetic multilayers such as sandwiched and over-layered

struc-tures 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

The calculated MAE of the monolayer structures can be interpreted

as uniaxial anisotropy energy Kustudied in the interface magnetic anisotropy experiments[35] To compare to the experimental data, the absolute values of product (DE) tComust be calculated, where

tCois 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 4 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

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layers because the structural complexity of interfaces and the

inter-diffusion of the atoms between the layers are not readily

incorpo-rated into the study As seen inFig 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

tCois 2.34 Å for the Co monolayer in the present work With the unit

cell volume of 234.96 1024cm3, we have obtained the average

value of (DE) x tCoz 1.35 erg/cm2for the Co monolayer structures with the average MAE ofDE¼ 8.43 meV Comparing this calculated value with the experimental data in the work of Engel[35], Kux

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 experi-mentally obtained for the Pd/Co multilayers[35], and comparable with that of the best perpendicular magnetic anisotropy materials

so far[45]

Table 2

The layer-resolved Bader charge of the structures The error of the charge calculation is about 0.01 e.

Structure Maximum value of (E X eE Z , E Y eE Z ) (meV) Bader charge (e)

layer 1 layer 2 layer 3 layer 4 layer 5

ﬁrst and second atomic layer of the super-thin Pd ﬁlm D.N Son et al / Journal of Science: Advanced Materials and Devices 3 (2018) 243e253

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Theﬁfth column ofTable 1 shows that the average value of

magnetic moment per Co atom in the unit cell is correspondingly

2.99< 3.06 < 3.28 < 3.31mBfor 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 ultrathinﬁlm 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 3presents the total electronic DOS of the most negative and

positive MAE structures Thisﬁgure shows that the spin-up and

spin-down components do 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

spin-down DOS of the Co atoms, while the states near and below the

Fermi level is assigned to those of the Pd atoms The electronic properties at the Fermi level play an essential role in the under-standing 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 ofTable 1 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 4shows 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 (seeFig 3) The results indicate the crucial role of the upper layers toward the magnetic anisotropy

of the ultrathinﬁlm It is worthy to note that we have selected the

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sampling structures with the consideration of symmetric

equiva-lence 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 theﬁrst 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 ofTable 1 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 1shows

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 inTable 2 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 5 does not exhibit any correlations, the charge variation of

the layers 1 and 2 correlates well with the change of the MAE.Fig 5

shows the charge for only the layers 1 and 2 We can see that

although there are theﬂuctuations of the charge for the structures

with the small MAE ranging around 0e5 meV, the charge of the

layer 1 increases, while the charge of the layer 2 decreases with the

MAE The charge of the layer 1 has a better behavior compared to

that of the layer 2 implying that the state of the uppermost

(sur-face) layer should play a vital role in the determination of the

magnetic anisotropy of the ultrathinﬁlm 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 1 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 dif-ference of the uppermost atomic layer in the following part

Fig 6shows the charge density difference of the most negative and positive MAE structures In thisfigure, we also draw the lattice vectors of the unit cell, where the vector a is perpendicular to and point toward the page For the ultrathinfilm, 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 charac-teristics 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 dz, (dyz, dxz), and (dxy, dx y2) for those

along the vector c, in the (bc, ac) plane, and in the ab plane, respectively Atﬁrst 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 dzorbitals 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 dxyand dxy2orbitals are completely occupied for the structure S2 or partially occupied for the structure D4, while most of the dxyand dx y2orbitals are

un-occupied for the cases of S1 and D1 The un-occupied orbitals provide the orbits for the motion of the electrons Furthermore, the orbit motion of the electrons generates the magnetic moment

Fig 7 The projected DOS of the sampling structures S1, S2, D1, D4, T2, and Q The d xy and dxy2 orbitals (similarly the d xz and d yz orbitals) are identical for S1 and S2.

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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

anisot-ropy The electron motion on the dxyand dxy2orbitals creates the

magnetic moment along the c vector, while on the dz 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 dzorbitals, and for the out-of-plane

magnetic anisotropy of S2 and D2 because of the more part of

the occupied dxyand dx y2orbitals The anisotropy energy due to

the rotation of the magnetization from dxzto dyzor 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 5also shows that the electron occupation of the dxzand dyzorbitals of S2 and D4 is more

sig-niﬁcant than those of S1 and D1

Fig 7shows that for the Co monolayer structures S1 and S2 the

dxzand dyzorbitals are identical and therefore degenerate A similar result was also found for the dxyand dx y2orbitals However, for the

structures with the Co atoms dispersed in the Pd matrix, the

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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 dxyand

dx y2 orbitals and the dxzand dyzorbitals 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

litera-ture 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 dxzand

dyzor the dxyand dxy2orbitals for the case of the lower magnetic

anisotropy structures such as D1 and D4.Fig 7also shows that the

in-plane magnetic anisotropy structures (S1, D1) have a more

sig-niﬁcant portion of the dzorbital, while the out-of-plane magnetic

anisotropy structures (S2, D4) have a more substantial part of the

dxyand dx y2orbitals around the Fermi level in comparison to the

other orbitals This result supports the analysis of the charge

den-sity 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

4 Conclusion

The picture of magnetic anisotropy of the ultrathin Pd4Co(111)

ﬁlm has been revealed by using the density functional theory

cal-culations 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

ma-trix, most of the structures exhibit the magnetic anisotropy

perpendicular to theﬁlm's surface The electronic structure analysis

indicated that the surface states are the most important ones

dominating the magnetic anisotropy, in which the dxyand dxy2

orbitals contribute to the perpendicular easy magnetization axis,

while the dzstate 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

Ca-pacities 84 Cp/I of 15.09.2007 and INFRANANOCHEM 19/

01.03.2009)

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