The influence of hydrogen adsorption on magnetic properties of NiCu(001) surface

a r X i v :c o n d -m a t /0302297v 1 [c o n d -m a t .m t r l -s c i ] 14 F e

b 2003

Czech.J.Phys.53(2003)33-39.

The in?uence of hydrogen adsorption

on magnetic properties of Ni/Cu(001)surface

Frantiˇs ek M′a ca,Alexander B.Shick

Institute of Physics ASCR,Na Slovance 2,CZ-18221Praha 8,Czech Republic

Josef Redinger,Raimund Podloucky and Peter Weinberger

Center for Computational Materials Science,TU Vienna,Getreidemark 9,A-1060Vienna,Austria Ni/Cu(001)is known as a unique system showing the spin-reorientation transition from an in-plane to out-of-plane magnetization direction when the Ni-overlayer thickness is increased.We

investigate di?erent relaxed multilayer structures with a hydrogen adlayer using the full-potential linearized augmented plane-wave method.The relaxed geometries,determined by total energy and atomic force calculations,show that H-monolayer strongly in?uences the interlayer distance between the Ni-surface and sub-surface layers yielding the outward relaxation of Ni-layer at H/Ni interface.Furthermore,large decrease of local magnetic moments at the top surface area is found for the surface covered by H.The magneto-crystalline anisotropy energies calculated for fully relaxed H/Ni-?lms.The spin-reorientation transition critical thickness of 4ML is found in good quantitative agreement with the experiment.

PACS numbers:75.70.Ak,75.30.Pd,75.30.Gw

I.INTRODUCTION

Ultrathin ferromagnetic ?lms grown on nonmagnetic substrate show peculiar magnetic behavior [1].One of the unique phenomena which is observed in the ultra-thin Ni ?lms on Cu(001)substrate is the spin direction reorientation transition (SRT)from an in-plane to out-of-plane magnetization direction when the Ni-overlayer thickness is increased [2,3,4].It is very important for the spintronic magnetic device applications and its mi-croscopic understanding attracted recently both experi-mental and theoretical [5,6]interest.The gas adsorp-tion on magnetic ?lm provides the way to monitor the surface magnetic properties resulting in strong in?uence on the SRT critical thickness d c .For Ni/Cu(001)?lms,the hydrogen adsorption is observed to reduce d c by ≈4monolayers (ML)from its value of ≈11ML for the vacuum/Ni/Cu-?lms [3,4].

The key quantity which drives the SRT in ultrathin magnetic ?lms is the magneto-crystalline anisotropy en-ergy (MAE).It determines the preferred ?lm magneti-zation orientation by minimizing the free energy of the system.For the free-standing Ni/Cu(001)?lms,the d c is found to be determined [5,6]by competition of the uni-axial MAE due to the tetragonal distortion of Ni-?lms (so called “volume”MAE)and the surface MAE.The adsorption of a gas produces non-trivial changes in ge-ometrical structure as well as magnetic properties of Ni ?lms [7,8]in?uencing both volume and surface MAE,and results in change of the SRT critical thickness.

In recent years it has become possible to make use of ab initio density functional theory to predict the MAE in ultra-thin ?lms [9].From theoretical and computational point of view,the MAE calculations are extremely di?-cult due to the very high energy resolution in the range of few μeV which is required.For the H/Ni/Cu(001)?lms,

the problem becomes even more complex due to the need of accurate account of structural relaxation.It requires us to use the most accurate total energy full-potential lin-earized augmented plane wave method (FP-LAPW)[7]in order to account simultaneously on equilibrium geo-metrical and magnetic structures.

II.

METHOD AND RESULTS OF

CALCULATIONS

The experiments show that H 2adsorbs dissociatively on Ni(001)surface in fourfold hollow sites [10].There-fore,as a structural model for ab-initio calculations we use free-standing Ni-?lms (H/Ni d /H,d =1-11)and Ni-?lms on Cu-substrate (H/Ni d /Cu 7/Ni d /H,d =1–6)with ordered p (1×1)H adsorbate overlayer as shown in Fig.1.

Figure 1:Surface layers of H/Ni n /Cu(100)system.

The in-plane experimental lattice constant of Cu a Cu =3.615?A [11]is used which remains unchanged in the calculations.All interlayer spacings d ij (see Fig.1)are relaxed to the equilibrium values.In order to deter-mine the equilibrium slab geometry we employ the FP-LAPW method in FLAIR implementation (unpublished improved and rewritten version of the original FLAPW

2

3.23.4

3.6

d 23d 34d 45d 56d 67d 78

I n t e r l a y e r d i s t a n c e (a . u .)

Figure 2:Relaxation of interlayer distances for H/Ni n /Cu(001)for n =3?6and for n =∞.For clarity,the data sets are shifted by 0.1a.u.Lines serve as guide to the eye.

codes [7]).The scalar-relativistic atomic force technique is employed for the total energy minimization.Here,the Perdew and Wang [12]approximation for exchange-correlation potential is used with the plane wave energy cuto?E cut of 13Ry,and the 28special k-points in the 1/8th irreducible part of 2-dimensional Brillouin zone (2D BZ)are used for the BZ integrations.The con-vergence better than 1×10?6e/(a.u.)3is achieved for charge/spin densities,and better than 0.2mRy/a.u.for the atomic force acting on individual atom.

The relaxed interlayer distances for di?erent free-standing ?lms (H/Ni n /Cu 7/Ni n /H,n =3–6)are shown in Fig.2and compared with the relaxation of tetragonal p (1×1)H Ni(100)surface.Clearly,we can distinguish the outward relaxation of top Ni layer as well as the strong in-?uence of Ni/Cu interface on inter-layer distances in the close vicinity of the interface.The relaxation of Ni/Cu subsurface is di?erent only for 5ML Ni.The deeper in-terlayer distances (thicker ?lm)approach the bulk value.

Table I:Interlayer distances in a.u.

HNi 6Cu 7Ni 6H

0.63d 23

3.28

3.18d 45

3.19The equilibrium values of inter-layer distances for two model systems:eleven-layer tetragonal Ni-?lm covered with H and seven-layer Cu-?lm with overlayer of six Ni layers covered with H are shown in Table 1.Both in-terfaces (H/Ni,Ni/Cu)in?uence strongly the interlayer distances in the overlayer slab.Note,that the calcu-lated bond length d H ?Ni of 3.48a.u.is slightly shorter than the bond length for the bulk nickel hydride (3.52a.u.).The outward relaxation of top Ni-layer is found,the H-ML in?uences strongly only the interlayer distance between the Ni-surface and Ni-subsurface layer.Below the interface,the interlayer distances oscillate around the bulk value for strained tetragonal Ni bulk (d ⊥=3.20a.u.).The electron screening in the metal is responsible for fast damping of these oscillation.

Table II:Magnetic moments in μB

HNi 6Cu 7Ni 6H

0.238

Ni 2

0.588

0.640

Ni 4

0.633The layer-resolved spin magnetic moments M s for these systems are shown in Table 2.These values cor-respond to the magnetic moments in the Ni “mu?n-tin”spheres (R MT =2.2a.u.).It is seen that there is strong reduction of the spin magnetization for the top Ni-layer due to the interaction with the H-adlayer.The strong hybridization of the H s state with the ?lled majority Ni d band changes the band structure and the surface density of states (SDOS)leading to the decrease of spin-majority and increase of the spin-minority SDOS.Away from the interface,the spin magnetic moments are slowly converging to their bulk values.The layer-resolved mag-netic moments for di?erent H/Ni n /Cu 7-?lms (n =3–6)on Cu-substrate are shown in Fig. 3.We note that for very thin H/Ni n /Cu 7-?lms with n=1,2the Ni-local mo-ments disappear and the system becomes non-magnetic.With the increase of the Ni-?lm thickness,the local Ni M s of 0.24μB is formed at the Ni-interface and then in-creases away from the H/Ni interface.When approach-ing the Ni/Cu interface,the Ni-atom magnetic moments start to decrease again and become ≈0.45μB for Ni/Cu interface layer (depending of the Ni-?lm thickness).

The anisotropic energy density of a tetragonal ferro-magnetic ?lm is written as [13]:

E/V =?K v 1m 2z ?K v 2m 4z ?K v 3m 2x m 2

y

?

2

3

00.2

0.4

0.6

0.8

1

S-1

S-3

S-5S-7

M a g n e t i c m o m e n t (μB )

Layer

Figure 3:Layer-resolved magnetic moments of H/Ni n /Cu(001)for n =3?6and for n =∞.For clarity,the data sets are shifted by 0.1(n ?1)μB .Layers are labeled S,S-1,...,starting with the surface layer S.Lines serve as guide to the eye.

type 2nd and 4th-order anisotropy constants,m x,y,z are magnetization cosines with respect to the crystal axes,and d is a thickness of magnetic ?lm.We assume that the 4th-order terms in Eq.(1)are signi?cantly smaller

than 2nd-order uniaxial anisotropy constant K v

1,and ne-glect them.The MAE then can be characterized with the di?erence in the total energy when magnetization is oriented along [100](in-plane, )and [001](out-of-plane,⊥)axes (MAE =E [100]?E

[001]).

We use the relativistic version [14]of the FP-LAPW method to solve self-consistently the Kohn-Sham-Dirac equations with spin-orbit coupling included to obtain the ground state charge and spin densities for the magne-tization directed along [001]-axis.The fully optimized interlayer distances as discussed above are used for free-standing Ni-?lms and Ni-?lms on Cu-substrate with H-adlayer.The MAE is obtained by applying the force theorem to the spin -axis rotation [15]:from the self-consistent ground state charge and spin density obtained for the [001]spin axis,a calculation of the band structure for [100]spin axis orientation is performed,and di?erence of the single particle eigenvalue sums is then taken to be the MAE.For the MAE calculations the k-points mesh equivalent to 6400k-points in the full 2D BZ is used guaranteeing the MAE convergence better than 10μeV.The MAE as a function of the Ni-?lm thickness for the H/Ni d /H ?lms with d =3,5,7,9ML is shown in Fig. 4.For the d =3we found small and negative MAE (-0.02meV)keeping the Ni-?lm magnetization in [100]plane.It becomes positive for the d =5(0.432meV)resulting in the out-of-plane magnetization switch-ing.The MAE is positive with further increase of d and

13

579

Ni layers

-0.25

0.25

0.75

M A E (m e V )

Figure 4:The MAE (circles)and MAE+SAE (diamonds)for the fully relaxed H/Ni d /H ?lms as a function of the ?lm thick-ness d (in ML).

shows pronounced oscillations.The linear interpolation MAE =d ·K V +2·K I yields the estimates for the “volume”K V =0.106meV/atom and “interface”K I =-0.127meV/atom MAE contributions.The calculated “volume”MAE agrees well with K V =0.0835meV/atom calculated for free-standing unrelaxed Ni-?lms without H-adlayer [6]and extrapolated to T=0K experimental value of 0.072meV/atom of Ref.[16].The H/Ni “inter-face”K I is calculated to be substantially smaller than vacuum/Ni “surface”K S =-0.447meV/atom [6]for free-standing Ni-?lms and extrapolated to T=0K experimen-tal value of -0.7meV/atom [3].We note that for the very thin Ni-?lms considered here,validity of the linear ?t for the MAE and its separation into “volume”and “surface”contributions is not well justi?ed due to the strong depen-dence of the Ni-?lm magnetic properties on the thickness of the ?lm,especially in the presence of the H-adlayer.In order to estimate the d c critical thickness for SRT,we take into account the shape anisotropy energy (SAE)due to the magnetic dipole interaction,which provides additional in-plane anisotropy.This anisotropy is esti-mated using the relation SAE =?2πM 2to the spin magnetization density M (in CGS units).It yields for the SAE the values of -0.016meV,-0.032meV,-0.055meV and -0.073meV corresponding respectively to the H/Ni d /H ?lms with d =3,5,7,9layers (which are consis-tent with experimentally derived SAE/Ni atom of -0.0075meV [3]).This additional negative SAE slightly shifts the MAE in Fig.4downwards yielding the d c =4.

Indeed,the H/Ni d /H model is a way too simple to de-scribe quantitatively the SRT in in Ni/Cu layers with H-adlayer.As it was already mentioned in Ref.[3,5]the Ni/Cu interface can play an important role.In order to evaluate the in?uence of Ni/Cu interface on SRT we perform the calculations for H/Ni d /Cu 5/Ni d /H (d =3,4)?lms,where the 5Cu layers play a role of the substrate.The use of 5ML of Cu layers instead of 7ML allows to reduce computational e?ort without producing any sig-ni?cant impact on the magnetic properties and the MAE

4

of H/Ni/Cu-?lms,since they are originated from Ni mag-netic?lm and not the Cu non-magnetic substrate,and the relaxed Cu-interlayer distance below the Ni-interface is found to be very close to its bulk value of3.427a.u. For the d=3we found negative MAE of-0.192meV and SAE of-0.036meV keeping the Ni-?lm magnetiza-tion in[100]plane.Already for d=4the MAE becomes positive0.543meV while the SAE is small and negative-0.052meV.Again as in the case of free-standing H/Ni d/H ?lms we get the SRT critical thickness d c=4.

To summarize,we found that hydrogen adsorption for the Ni?lms on Cu substrate yields the reduction of the SRT critical thickness.The calculated d c=4for both H/Ni d/H and H/Ni d/Cu5/Ni d/H?lms agrees well with the experimental d c of7ML[3].We show that the MAE has strong and oscillatory dependence on the Ni-?lm thickness which deviates substantially from the lin-ear?t.We attribute the decrease of the d c due to the H adsorption to originate from strong reduction of the mag-nitude for the Ni“surface”MAE contribution.In turn, this is caused by strong decrease of the exchange splitting at the H/Ni interface due to the strong hybridization of the H s state with the Ni-bands.

Acknowledgment

The?nancial support was provided by the Academy of Sci-ences of the Czech Republic(Grant No.A1010214),CMS Vi-enna(GZ45.504),and by the RTN project”Computational Magnetoelectronics”of the European Commission(HPRN-CT-2000-00143).

[1]S.Bl¨u gel:Phys.Rev.Lett.68(1992)851and references

therein.

[2]B.Schulz and K.Baberschke:Phys.Rev.B50(1994)

13467.

[3]R.Vollmer et al.:Phys.Rev.B60(1999)6277.

[4]S.van Dijken,R.Vollmer,B.Poelsema,J.Kirschner:J.

Magn.Magn.Mater.210(2000)316.

[5]C.Uiberacker et al.:Phys.Rev.Lett.82(1999)1289.

[6]A.B.Shick,Y.N.Gornostyrev,A.J.Freeman:Phys.Rev.

B60(1999)3029.

[7]E.Wimmer,H.Krakauer,A.J.Freeman:Adv.Electron.

Electron Phys.65(1985)357.

[8]M.Weinert and J.W.Davenport:Phys.Rev.Lett.54

(1985)1547.

[9]H.J.F.Jansen:Phys.Rev.B59(1999)4699and refer-

ences therein.

[10]I.Stensgaard and F.Jakobsen:Phys.Rev.Lett.54

(1985)711.

[11]W.B.Pearson:A handbook of lattice spacings and struc-

tures of metals and alloys.Pergamon Press,Oxford,1958.

[12]J.P.Perdew and Y.Wang:Phys.Rev.B45(1992)13244.

[13]https://www.sodocs.net/doc/984379791.html,ndau,E.M.Lifshitz,and L.P.Pitaevskii:Elec-

trodynamics of Continuous Media.Oxford,1995,p.138.

[14]A.B.Shick,D.L.Novikov and A.J.Freeman:Phys.

Rev.B56(1997)R14259.

[15]I.V.Solovyev,P.H.Dederichs and I.Mertig:Phys.Rev.

B52(1995)13419and references therein.

[16]M.Farle at al.:Phys.Rev.B55(1997)3708.