PHYSICAL REVIEW B 66, 014439 ~2002!
`
`In-plane magnetocrystalline anisotropy observed on Fe(cid:213)Cu(cid:132)111(cid:133) nanostructures grown
`on stepped surfaces
`
`C. Boeglin,1,* S. Stanescu,1 J. P. Deville,1 P. Ohresser,2 and N. B. Brookes3
`1IPCMS-GSI-UMR 7504, F-67037 Strasbourg Cedex, France
`2LURE, F-91405 Orsay, France
`3ESRF, BP 220, F-38043 Grenoble Cedex, France
`~Received 21 February 2002; published 19 July 2002!
`
`Magnetic in-plane and out-of-plane anisotropies measured by angle dependent x-ray magnetic circular
`dichroism ~XMCD! on fcc Fe nanostructures are discussed and compared with fcc FeNi nanostructures. All
`studies were performed using XMCD at the Fe L 2,3 edges for Fe grown on a Cu~111! vicinal vic surface. The
`step induced in-plane anisotropy in the step decoration regime is analyzed by measuring the orbital magnetic
`moment dependence as a function of the in-plane azimuth and out-of-plane incidence angles. In the one-
`dimensional limit where the out-of-plane magnetic easy axis dominates, Fe/Cu~111! shows a large in-plane
`orbital magnetic moment anisotropy leading to a magnetocrystalline anisotropy energy of 0.4 meV/atom and an
`in-plane magnetic easy axis perpendicular to the steps. In the nanometer scale the aspect ratio of the elongated
`rectangular Fe stripes are found to be responsible for the in-plane and out-of-plane anisotropy. This is coherent
`with previous findings where the circular shaped fcc Fe0.65Ni0.35 nanostructures do not show any in-plane
`anisotropy. The three-dimensional nanostructures are characterized by magnetic orbital moments connected
`with the number of broken bonds in the direction of the quantization axis defined by the direction of the
`saturation field. The microscopic origin of the in-plane large orbital magnetic moment anisotropy is attributed
`to the nanometer size of the structures perpendicular to the steps and to the asymmetry of the number of broken
`bonds in the plane.
`
`DOI: 10.1103/PhysRevB.66.014439
`
`PACS number~s!: 75.70.Cn, 75.70.Ak, 78.70.Dm
`
`I. INTRODUCTION
`
`Magnetic nanostructures are nowadays among the most
`interesting subjects where the microscopic structures and the
`magnetic anisotropy are ultimately related. Reduced symme-
`try and cluster size effects of ferromagnetic nanostructures
`are challenging tasks for both experimentalists and theoreti-
`cians. In particular, ultrathin films can exhibit strong out-of-
`plane anisotropy. For
`thin films the magnetocrystalline
`anisotropies ~favoring out-of-plane magnetization! and the
`magnetostatic anisotropy ~favoring the in-plane one! are the
`mean contributions to the total macroscopic magnetic anisot-
`ropy. Strain relaxation in thin epitaxial films generally favors
`magnetocrystalline anisotropy whereas the bulk contribution
`favors the magnetostatic anisotropy. More recently our inter-
`est was focused on reduced one-dimensional ~1D! symmetry
`systems where oriented nanostructures lead to out-of-plane
`and in-plane magnetic anisotropies. In this framework it is of
`interest
`to look for the microscopic origin of 1D stripe
`anisotropies ~in the plane and out of the plane!. These
`anisotropies are known to be related either to strain relax-
`ation ~tetragonalisation! of the structures or to a large num-
`ber of broken bonds in one direction. Surfaces ~or interfaces!
`are known to be at the origin of the perpendicular magnetic
`anisotropy. We should thus be able to generalize this argu-
`ment to the in-plane geometry.
`Many self-organized systems have been studied recently
`~Co/Cu~100!, Fe/Cu~111!, Fe65Ni35 /Cu(111), Co/Au~111!,
`fl! in order to correlate the reduced dimensionality of clus-
`ters and surfaces to the increased magnetic moments.1–5 The
`mean results show that the magnetic orbital moments are
`
`strongly increased when reducing the size of the nanostruc-
`tures. This is explained by considering the contribution from
`the edge and surface atoms where the quenching of the or-
`bital magnetic moment is less effective than that of the bulk.
`But for most of these systems, the strain and the broken
`bond effects are almost indistinguishable because the films
`show both effects simultaneously in a given growth regime.
`Our aim is to separate the regime where no strain relaxation
`occurs in order to relate the anisotropies of the nanostruc-
`tures to the broken bonds and aspect ratio of the structures.
`This is the case for stripes in Fe/Cu~111! grown at room
`temperature on vicinal surfaces and below the 2D coales-
`cence. We will show that the magnetocrystalline anisotropy
`measured on Fe/Cu~111! nanostructures can be attributed to
`the effect of the anisotropy of the number of broken bonds
`and the associated electronic structure. At a given tempera-
`ture the anisotropy of these materials are given in a simpli-
`fied approach by a constant volume and a 1/d ~where d is the
`thickness of the film! surface-dependent term. A generaliza-
`tion of this concept along any direction is thought to be
`possible inside the plane when specific structural or configu-
`ration anisotropies are present. For instance, this is the case
`by growing self-similar magnetic nanostructures through dif-
`fusion on controlled surface defects such as regular steps on
`vicinal surfaces.
`Magneto-optic Kerr experiments performed on thin ferro-
`magnetic layers @Fe/W~001!, Co/Cu~100!, Fe/Ag~100!#6–11
`deposited on vicinal surfaces show the existence of step in-
`duced uniaxial anisotropies. Depending on the thin ferro-
`magnetic layers, the growth mode and the step density12 the
`in-plane orientation of the easy axis remains parallel or per-
`pendicular to the steps irrespectively to the crystallographic
`
`0163-1829/2002/66~1!/014439~6!/$20.00
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`66 014439-1
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`©2002 The American Physical Society
`
`Lambeth Magnetic Structures, LLC Exhibit 2003
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`LMBTH-000112
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`

`
`BOEGLIN, STANESCU, DEVILLE, OHRESSER, AND BROOKES
`
`PHYSICAL REVIEW B 66, 014439 ~2002!
`
`orientation. The important remaining question is to know
`what is responsible for the either parallel or perpendicular
`orientation of the magnetic easy axis for these systems. In
`this framework, recent self-consistent
`tight-binding MAE
`calculations from J. Dorantes-Davila13 show that for 3d met-
`als the easy axis of magnetization for 1D chains and 2D
`ladders is oriented either out of plane, in-plane parallel or
`in-plane perpendicular to the chains, depending on the elec-
`tronic configuration. For example, Fe infinite monatomic
`chains show a parallel in-plane easy axis of magnetization
`whereas multichains with interchain packing of triangular
`symmetry show a perpendicular easy axis of magnetization,
`demonstrating the crucial role of the structure in the low-
`dimensional systems.
`At present, the element specific orbital (M L) and spin
`(M S) magnetic moments can be derived by x-ray magnetic
`circular dichroism ~XMCD! applying the sum rules. The
`high sensibility of the XMCD technique has favored recently
`many experimental works
`in the nanostructured 0.01-
`monolayer ~ML!–1-ML range. In the absence of alloying the
`magnetic moment M S relates generally to the atomic volume
`of the element and M L to the electronic structure influenced
`by the hybridization and strain in the film. Conversely, the
`magnetic orbital moment anisotropies are far less understood
`in this thickness range. Besides the effect of the electronic
`hybridization at the interfaces and of tetragonalization in the
`strain relaxation regime, in the very low thickness range ~0–
`0.8 ML! the microscopic origin of the strong orbital moment
`anisotropy is still an open question. The strong electron lo-
`calization caused by low atomic coordination occurring for
`the low-dimension nanostructures is thought to be the main
`origin of the strong orbital moments and anisotropies. Nev-
`ertheless, for most of the experimentally grown thin films,
`the two parameters ~structure and reduced symmetry! are of-
`ten superimposed so that no simple relationship can be
`drawn between one and the other microscopic phenomena
`and the observed moments. Using well characterized Fe
`nanostructures grown on a Cu~111! vicinal surface14,15 in the
`pseudomorphic ~Fe fcc! thickness range we have the possi-
`bility to measure along the 3D coordinates all the magnetic
`parameters and to compare them to the density of broken
`bonds.
`Thus in the absence of tetragonalization ~before the relax-
`ation of the epitaxial strain! the M L anisotropy can be shown
`to be configurational
`in origin. Epitaxial nanostructures
`grown by self-diffusion on patterned substrates can thus
`show specific directions along which reduced coordinations
`are found and thus lead to a direction dependent orbital mo-
`ment which provides the macroscopic magnetic anisotropy.
`We will show that this is the case for elongated Fe stripes
`grown along the step edges of vicinal surfaces where a re-
`duced number of nearest neighbors ~NN’s! is obtained along
`the perpendicular to the step direction whereas parallel to the
`steps large NN numbers are found. We will also show that
`the reduced number of NN’s along the growth direction leads
`to large out-of-plane anisotropies of the orbital magnetic mo-
`ment. These anisotropies are coherent with those measured
`in the plane considering the number of NN’s. The local elec-
`tronic structures associated with the number of broken bonds
`
`are directionally dependent and related to the directional de-
`pendence of M L .
`In Sec. II we shall describe the angle-dependent MCXD
`results obtained at the Fe L 2,3 edges and we shall discuss the
`results with respect to the growth mode and morphology of
`Fe in the submonolayer regime on vicinal Cu~111! surface.
`Finally in Sec. III we shall discuss the origin of the measured
`orbital magnetic moment anisotropies.
`
`II. EXPERIMENT
`
`A. Experimental setup
`The structural studies have been carried out in a UHV
`system with a base pressure of 1310210 mbar equipped with
`Auger electron spectroscopy ~AES!, low-energy electron dif-
`fraction ~LEED! and scanning tunneling microscopy ~STM!.
`The substrate, further labeled as Cu~111!-vic, is cut from a
`Cu~111! single crystal at 1.2° from the @111# direction. The
`monoatomic steps are parallel to the @11¯ 0# direction and
`perpendicular to the @1¯ 1¯ 2# one, leading to ~111! microfacets.
`The substrates were cleaned by repeated cycles of Ar1 sput-
`tering and annealing at 850 K. After elimination of all impu-
`rities, checked by AES, it was verified by STM that straight
`and parallel steps with an average terrace length of 9 nm for
`the 1.2° miscut sample were obtained. In agreement with
`previous studies on Fe/Cu~111!-vic 1.2° ~Ref. 14! a p(1
`31) LEED pattern with a threefold symmetry was observed
`up to 2-ML Fe deposition indicating a pseudomorphic
`growth of the Fe fcc film.
`For the XMCD experiments the Cu~111! single-crystal
`substrates were prepared under ultrahigh vacuum conditions
`(13 10210 mbar). During these experiments the thickness of
`the thin film was checked by measuring the x-ray-absorption
`Fe L 3 edge heights as previously reported for Fe65Ni35 ultra-
`thin films.3 The XMCD experiments were performed at the
`ID12B beamline of the European Synchrotron Radiation Fa-
`cility in Grenoble by monitoring the total electron yield. The
`XMCD measurements were performed at saturation for dif-
`ferent incidence and azimuthal angles of the light, applying
`the magnetic field parallel to the incident circular polarized
`light. The XMCD spectra were obtained by reversing both
`the magnetic field ~64 T! and the helicity of the light at 10
`K. In order to check and insure the magnetic saturation along
`the quantization axis we record the XMCD magnetization
`cycles at the Fe L 3 edge.
`
`B. XMCD measurements
`X-ray magnetic circular dichroism in the L 2,3 absorption
`edges gives access to an element specific local magnetic mo-
`ment. A theoretical analysis performed in an atomic frame-
`work predicts that for 2p-3d transitions the ground-state ex-
`pectation values for the spin and orbital magnetic moments
`can be derived.16,17 In this paper we will use these sum rules
`to extract the values of the orbital magnetic moment M L and
`eff per hole. A constant
`the effective spin magnetic moment M S
`hole number of 3.34 per iron atom has been introduced and
`eff . This
`does not affect any relative variation of M L or M S
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`IN-PLANE MAGNETOCRYSTALLINE ANISOTROPY . . .
`
`PHYSICAL REVIEW B 66, 014439 ~2002!
`
`point is supported by Sto¨hr18 showing that reduced symmetry
`does not change significantly the electron or hole distribu-
`eff values with
`tion. This allows to compare our M L and M S
`that of bcc iron grown after 2.5-ML Fe/Cu~111!-vic. We can
`neglect the saturation effects in total electron yield at the Fe
`L 2,3 edges because the thickness of our films does not exceed
`8 Å which is small compared to the escape depth ~17 Å! and
`to the x-ray penetration at 710 eV.19 Assuming this limited
`thickness of the films the orbital moment and the effective
`spin magnetic moment can be measured as a function of the
`film thickness. Moreover, in the case of the nanostructures
`studied in this work, the incidence angle dependence of the
`XMCD signal is affected by errors less than 5% due to satu-
`ration effects in total yield measurements.20 The azimuth
`variations of the in-plane spin and orbital magnetic moments
`are insensitive to such effects.
`The Fe L 2,3 XMCD spectra, recorded in the total yield
`detection mode were performed using a 7-T cryomagnet. The
`sample holder allowed polar ~u! and azimuthal rotations ~w!
`of the sample around the surface normal as already described
`by Cherifi et al.3 The incidence angle ~u! dependence of the
`XMCD signal was measured along different azimuthal
`angles defined by the direction of the steps. These measure-
`ments where performed in order to extract the out-of-plane
`magnetic anisotropies relative to the in-plane step directions
`and the in-plane magnetic anisotropies. The magnetization
`direction could thus be tuned between parallel (w50°) and
`perpendicular (w590°) to the steps at a constant incidence
`angle u. The incident x-ray beam is 90% circularly polarized
`and is kept parallel to the saturated magnetization direction
`during the XMCD measurements. In Fig. 1 we present a pair
`of typical normalized x-ray-absorption spectra at the Fe L 2,3
`edges for 0.15-ML Fe/Cu~111!-vic 1.2° obtained by revers-
`ing the magnetic field from the parallel to the antiparallel
`alignment in respect to the photon spin. Below we show two
`XMCD differences and the related integrated spectra ob-
`tained for two different geometries in respect to the steps.
`eff are extracted from the
`The magnetic moments M L and M S
`XMCD spectra using the sum rules16,17 where for the L 2,3
`edges one has
`
`M L52
`
`4qN h
`3R iso
`
`,
`
`eff5M S1M T~u!52
`M S
`
`~6p24q !N h
`R iso
`
`,
`
`~1!
`
`~2!
`
`where p and q are, respectively, the integrals over L 3 and
`L 21L 3 of the XMCD difference and R iso is the integrated
`isotropic spectrum assumed to be equal to the magnetization-
`averaged absorption cross section. N h is the number of holes
`in the 3d electronic states. M T ~u! is the dipolar spin mo-
`ment, generally neglected for 3d metals.
`Between the direction parallel to the steps (w50°) and
`perpendicular to the steps (w590°) the Fe L 2,3 integrated
`value q doubles and can be correlated with the in-plane or-
`bital magnetic moment anisotropy. For each azimuth a com-
`plete set of values of M L ~u! and M S ~u! is measured be-
`
`This will allow us to define the easy axis of magnetization if
`one assumes that for 3d metals it is related to the largest
`component of the orbital magnetic moment measured at
`saturation.19–24 As will be discussed later, XMCD is re-
`stricted to the magnetocrystalline part of the magnetic anisot-
`ropy. Thus we will be able to define the easy axis of magne-
`
`014439-3
`
`FIG. 1. Two XMCD spectra at the Fe L 2,3 edges obtained for
`0.15 ML at u550° for the parallel and the antiparallel alignment
`between the incident light and the applied magnetic field. The nor-
`malized differences of the XMCD spectra are presented at the bot-
`tom and we compare the results obtained parallel to the steps and
`perpendicular to the steps ~w50° and w590°, respectively!. The
`difference is noticeable at the L 2 edge. The integration over the Fe
`L 2,3 is plotted in order to evidence the large orbital magnetic mo-
`ment difference ~proportional to q! between the two geometries. In
`the inset we present the XMCD geometry defining the incidence
`angle uand the azimuth w with respect to the iron stripes.
`
`the out-of-plane
`
`tween 0,u,50°
`to extract
`in order
`anisotropy of the magnetic moments.
`In Fig. 2 we show the evolution of the three components
`Y with the Feof the orbital magnetic moments M LZ , M LX M L
`
`
`
`film thickness. These components are extracted applying the
`sum rules and the sin2(u) dependence of the orbital moment
`anisotropy21,22 along the specific azimuths in order to extract
`Y!. For ex-the projected in-plane components ~M LX and M L
`
`
`X component following
`ample, one can extract the in-plane M L
`the expression
`
`
`
`Z#sin2~u!.M L~u, w50 !5M LX1@M LX2M L
`
`
`
`
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`BOEGLIN, STANESCU, DEVILLE, OHRESSER, AND BROOKES
`
`PHYSICAL REVIEW B 66, 014439 ~2002!
`
`FIG. 2. Evolution of the magnetic orbital moment as a function
`of the thickness plotted for the X, Y, and Z direction. The open
`Z magnetic orbital moments. The
`symbols are the out-of-plane M L
`
`Y defined respec-full symbols indicate the evolution of M LX and M L
`
`tively by the two azimuths w50° and w590°.
`
`tization for the samples when the magnetocrystalline effect is
`dominant in the total macroscopic magnetic anisotropy.
`The overall evolution observed in Fig. 2 corresponds to
`the results of Ohresser et al.4 and shows that the moments
`are dependent on the fcc to bcc structural phase transition
`which occurs at 2.3-ML Fe/Cu~111!-vic 1.2°. If we compare
`i (i5x, y, z) along different direc-
`the relative values of M L
`tions of the Fe nanostructures we clearly find two thickness
`regimes. The first one is located before the 2D coalescence at
`i
`is
`1.5-ML Fe where a splitting of all three components M L
`observed and the second one occurs after 1.5-ML Fe where
`i are equivalent. Qualitatively, be-
`both in-plane values of M L
`
`
`
`Zfore 1.5 ML’s the splitting of the values M LX , M LY , and M L
`can be understood by the pseudomorphic fcc structure of iron
`on copper. In the absence of structural tetragonalization as
`reported by Shen et al.15 the magnetocrystalline term reduces
`to the aspect ratio and broken bond effects of the Fe stripes.
`After the 2D coalescence a bct transformation of the struc-
`ture leads to a Kurdjumov-Sachs ~KS! superstructure. The
`structural phase transformation was shown to bring up a
`compression of the bcc structure in the z direction leading to
`a bct phase where the surface plane is ~110! and defined by a
`threefold domain orientation.15 This can be correlated to our
`XMCD data which show strongly enhanced magnetic orbital
`Y .moments M LZ compared to the in-plane values M LX and M L
`
`
`
`Moreover, due to the threefold symmetry of the KS domains
`in the plane of the 2D iron films neither the structure nor the
`morphology are expected to induce uniaxial anisotropies. We
`find by XMCD that no in-plane magnetic anisotropy is
`Y). The orbital mag-present at this stage of growth (M LX5M L
`
`
`netic moments measured by XMCD are restricted to the
`magnetocrystalline contribution of the magnetic anisotropy.
`The macroscopic measurements by magneto-optic Kerr
`effect15 evidences the magnetic out-of-plane–in-plane transi-
`tion of the easy magnetization axis at 2.3 ML’s for Fe/
`Cu~111!-vicinal 1.2°. We thus show, comparing Kerr effect
`and XMCD data, that after the 2D coalescence and the fcc
`
`i plotted as a function of
`FIG. 3. Magnetic orbital moments M L
`the ratio Ri defined by the normalized number of broken bonds
`along direction i. All moments are extracted from the XMCD data
`obtained for stripes below the 2D coalescence.
`
`!bcc transition the magnetostatic anisotropy, which favors
`in-plane anisotropy, is clearly dominating over the magneto-
`crystalline anisotropy.
`In order to describe more quantitatively the magnetic an-
`isotropy for the Fe stripes ~0–1.5 ML’s! we will focus spe-
`cifically on this morphology. As described by Shen et al.14
`the first stage of growth of the Fe nanostructures is defined as
`elongated stripes 10–20 nm in the x direction, parallel to the
`steps, and 2–3 nm along the y direction, perpendicular to the
`steps. Thus along the y direction, a section with 10–15 atoms
`is obtained almost up to an equivalent thickness of 0.8 ML.
`During the first equivalent monolayer growth ~0–1 ML! of
`Fe/Cu~111!-vic 1.2° this in-plane morphology undergoes
`only small changes, whereas along the growth direction z the
`single atomic layer Fe is progressively completed by the sec-
`ond layer. In this early stage of growth, the iron stripes show
`a strong in-plane anisotropy along @11¯ 0# arising from the
`high aspect ratio. We should thus be able to describe the
`three orbital magnetic moments and their evolution up to the
`2D coalescence by a simple model assuming a surface and a
`i . The related magnetocrystalline anisot-
`volume term for M L
`ropy will thus be connected to the difference of the surface to
`bulk ratio along both in-plane directions X and Y. In Fig. 3
`i values obtained for different nanostructures
`we plot the M L
`below 1-ML Fe/Cu~111! as a function of the ratio R i , where
`R i represents the number of broken bonds over the total
`number of atoms along the i direction (i5x, y, z). The lin-
`ear dependence shows clearly that independently from the
`i
`is defined by a
`direction i the orbital magnetic moment M L
`‘‘volume’’ iron fcc term of 0.035mB /atom and a ‘‘surface’’
`term of 0.125mB /atom.
`Moreover, the evolution of the differences DM L ~Fig. 4!
`shows that the magnetocrystalline anisotropy, proportional to
`x , before the 2D coalescence, decreasesDM L5M Lz 2M L
`
`
`y
`strongly whereas in the plane the differences DM L5M L
`x keeps constant. This is related to the double layer
`2M L
`growth in the out of plane direction z, whereas only a slight
`enlargement of the stripes is expected in the plane up to 1
`ML. For the 3d elements where the ground-state spin-orbit
`coupling j is small compared to the crystal field and to the
`exchange interaction E ex the MAE can be expressed by the
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`IN-PLANE MAGNETOCRYSTALLINE ANISOTROPY . . .
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`PHYSICAL REVIEW B 66, 014439 ~2002!
`
`FIG. 4. Evolution of two orbital moment anisotropies DM L ~left
`axis! and calculated MAE’s ~right axis! with the thickness: The
`difference between the out-of-plane and the in-plane magnetic or-
`
`
`X) is plotted for the out-of-bital moments DM Lof-plane5(M LZ2M L
`
`plane magnetic anisotropy ~filled triangles! and compared to the
`in-plane magnetic orbital moment anisotropies ~open circles! given
`
`
`X). The vertical dotted line at 2.3-MLby DM Lin-plane5(M LY2M L
`
`thickness define the fcc!bcc phase transition.
`
`following expression given by Bruno21,22 linking the orbital
`anisotropy DM L to the anisotropy energy:
`
`MAE52
`
`1
`
`
`
`
`
`j
`4mB
`3j2
`2E exmB
`
`
`
`X!##@~ M LZ2M LX!"2~ M LZ2M L
`
`
`
`
`X!.~7M TZ27M T
`
`
`
`FIG. 5. Evolution of the orbital magnetic moment anisotropies
`X) ~left axis! and calculated MAE’s ~right axis! as a
`
`DM L5(M Li 2M L
`function of the inverse thickness of the iron stripes (2/d) along
`direction i. The plotted DM L
`i values are obtained with respect to the
`X axis, assuming that the stripes are infinite along the X direction.
`
`evolution of the effective magnetic anisotropy as a function
`of 1/d and including the in and out of plane anisotropy on the
`same footing we plot in Fig. 5 the effective magnetic anisot-
`ropy energy extracted from Bruno’s formula21 and stemming
`from all our data points for fcc Fe below 1-ML Fe/Cu~111!.
`The linear evolution scales with 1/d in the restricted thick-
`ness range considered. This can thus be described by an ef-
`fective anisotropy energy per atom:
`
`~3!
`
`MAES .
`
`2 d
`
`MAEeff5MAEV1
`
`The straight-line fit shows that all directions can be coher-
`ently described by a broken bond effect and that we can
`extract a direction independent magnetocrystalline surface
`anisotropy energy MAES51 meV/atom and a volume anisot-
`ropy energy of MAEV50.1 meV/atom. This shows that sur-
`face MAE is ten times larger than the bulk contribution.
`Recent calculations25 show that the surface contribution to
`the MAE turns out to be an order of magnitude higher ~0.1
`meV/atom! than the volume contribution ~0.01 meV/atom!.
`Our XMCD measured surface versus bulk MAE’s are in per-
`fect agreement with this calculations but lead to one order of
`magnitude larger numerical values. This has recently been
`explained by the fact that XMCD measurements of the MAE
`differ fundamentally from those obtained by the macroscopic
`~SMOKE,
`low-energy
`techniques
`ferromagnetic
`resonance!.26
`As compared with previously published data of MAE for
`fcc Fe65Ni35 nanostructures on Cu~111!-vic 1.2° the present
`values scales by a factor of 2 in the thickness range between
`0.7 and 1.5 ML’s. But unlike with the previous data, the
`in-plane anisotropy is present on the oriented Fe stripes be-
`low the coverage of 0.5 ML whereas the Fe65Ni35 islands do
`
`The MAE is obtained neglecting the majority spins and in-
`troducing a spin-orbit coupling constant j550 meV. 21 We
`shall also neglect the dipolar spin magnetic-moment anisot-
`ropy energy which is quadratic in j. This approximation is
`confirmed by our measurements on the Fe nanostructures
`eff(u) show no angular depen-
`studied in this work where M S
`dence inside the error bars related to low dipolar magnetic
`moments M T .
`In this framework a large out of plane MAE value of 1
`meV/atom is found for the 1-ML-height Fe stripes @0.15-ML
`Fe/Cu~111!# in the Z direction decreasing to less to 0.4 meV/
`atom for the double layer stripes ~0.8-ML Fe!. The out-of-
`plane anisotropy vanishes completely at the phase transition
`~2.3 ML’s!. The large in-plane anisotropy ~0.4 meV/atom!
`related to the constant aspect ratio in the plane decreases
`down to 0 at the 2D coalescence confirming the role of shape
`of the iron stripes. As compared to theoretical work the
`1-meV/atom MAE of the 1-ML situation is close to the free-
`standing monolayer ~111!-oriented fcc iron value found by
`Bruno and Renard22 in the range 0.6–1.2 meV/atom.
`Assuming that at 0.1 ML the stripes are infinite in the x
`direction parallel to the steps, the two previous magnetic
`x , i5z or y! cananisotropies defined using XMCD ~M Li 2M L
`
`
`be considered as a combination of a surface term and a vol-
`ume term. Thus in order to verify the validity of the linear
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`BOEGLIN, STANESCU, DEVILLE, OHRESSER, AND BROOKES
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`PHYSICAL REVIEW B 66, 014439 ~2002!
`
`not show any in-plane anisotropy in this range. We attribute
`the absence of anisotropy in the plane to the in-plane isotro-
`pic circular shape of the Fe65Ni35 nanostructures. This is one
`further indication that the in-plane uniaxial morphology is
`mandatory for in-plane MAE in the ultrathin film limit.
`
`III. CONCLUSION
`
`Epitaxially grown Fe stripes show strong in-plane and
`out-of-plane magnetic anisotropies related to the growth on a
`Cu~111! vicinal surface. A huge increase of M L is observed
`depending on the direction of saturation of the applied field.
`i and the number of Fe atoms
`The correlation between M L
`leads to the conclusion that the enhancement of the orbital
`moment along one direction is connected to the number of
`broken bonds along this direction. A ratio of 4 is obtained
`between surface and bulk orbital moments. According to our
`model the influence of the copper interface is absent both in
`the direction dependence of M L and in the anisotropy of the
`
`moments. This will induce an isotropic electronic structure
`of the pseudomorphic Fe/Cu interface.
`One monolayer thick iron stripes show a 1 meV/at MAE
`whereas the value in the plane is 0.4 meV/atom for the Fe
`stripes below 1-ML Fe. This is related to the size of the
`in-plane stripes compared to the monolayer-high stripes in
`the first stage of the growth. The orbital magnetic moment
`show a directionally independent correlation with the num-
`ber of broken bonds. We determine a volume and a surface
`contribution of the orbital moment and of the MAE. The
`surface contribution is shown to be one order of magnitude
`larger than the volume MAE of fcc Fe.
`
`ACKNOWLEDGMENTS
`
`The authors thank K. Larsson, B. Muller, and J. G. Faul-
`lumel for technical help during the XMCD experiments. This
`work was supported by the Center National de la Recherche
`Scientifique ~CNRS-ULTIMATECH program!.
`
`*Corresponding author. Fax: ~133! 3 88 10 72 48. Email address:
`christine.boeglin@ipcms.u-strasbg.fr
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