Copyright © 1990 The American Physical SocietyFerromagnetic resonance (FMR) and SQUID magnetometry measurements have been made on multilayers of amorphous Fe70B30/Ag. The dependence of the magnetic surface anisotropy constant Ks on the magnetic layer thickness 2L has been determined in the range 1.6 Å16.5 Å, but decreases monotonically towards zero as 2L decreases from 16.5 Å towards zero. The FMR results can be well described by a theory developed for ultrathin amorphous ferromagnetic layers

B. Heinrich

C. Chappert

C. L. Chien

E. M. Gyorgy

F. J. A. den Broeder

G. A. Prinz

G. T. Rado

G. Xiao

Gang Xiao

L. Néel

L. Zhang

M. P. M. Luykx

P. Bruno

R. J. Hicken

U. Gradmann

Physical Review Letters

Hicken, R.J.

Rado, G.T.

Xiao, G.

Chien, C.L.

Open Research Exeter

VOLUME 64, NUMBER 15 PHYSICAL REVIEW LETTERS 9 APRIL 1990Observation of Thickness Dependence of Magnetic Surface Anisotropyin Ultrathin Amorphous FilmsR. J. Hicken, G. T. Rado, Gang Xiao, ' and C. L. ChienDepartment of Physics and Astronomy, The Johns Hopkins UniversityB, altimore, Maryland 212l8(Received 20 October 1989)Ferromagnetic resonance (FMR) and SQUID magnetometry measurements have been made on mul-tilayers of amorphous FeioB30/Ag. The dependence of the magnetic surface anisotropy constant K, onthe magnetic layer thickness 2L has been determined in the range 1.6 A ( 2L & 90 A using more thantwenty samples. It is found that K, is constant for 2L ) 16.S A, but decreases monotonically towardszero as 2L decreases from 16.S A towards zero. The FMR results can be well described by a theorydeveloped for ultrathin amorphous ferromagnetic layers.PACS numbers: 75.30.Pd, 75.50.Kj, 75.70.—i, 76.50.+gThere is currently much interest in artificially layeredmaterials consisting of magnetic and nonmagnetic layerswhich have thicknesses of a few tens of A or less. As thethickness 2L of the magnetic layer is decreased, thephysical properties of the multilayer as a whole are in-creasingly afl'ected by those of its interfaces. Of primaryimportance in the description of the magnetic propertiesof ultrathin films is the magnetic surface anisotropy en-ergy density E, first introduced by Neel. ' Its uniax-ial form for an amorphous material is given by E,= —K,cos 8, where 8 is the angle between the magneti-zation and the film normal while K, is the magnetic sur-face anisotropy constant. In our notation the magneticsurface anisotropy term E, favors an out-of-plane mag-netization for K, & 0. The value of K, can be most con-veniently determined in a flat-film geometry where thefilm thickness is varied. This approach has been used inseveral recent investigations. In most cases in which thinmagnetic films were used, whether single layers or multi-layers, K, appears to be independent of thickness, thevalue depending upon whether the specific magneticmedium was Co, Fe, Ni, or an amorphous fer-romagnet. In ultrathin films of Fe on Ag some varia-tion of K, has been noted among four samples. ' In thisLetter, we present the first systematic and conclusivestudy of a thickness dependence of K, . As discussedbelow, amorphous FeipB3o/Ag is particularly suitable forsuch an investigation. More than twenty samples wereused, the Fe70B30 thickness 2L spanning the range from1.6 to 90 k We demonstrate that K, is constant forthicker films (2L & 16.5 A) but becomes strongly thick-ness dependent in the ultrathin limit (2L ( 16.5 A). Theferromagnetic resonance (FMR) results at two frequen-cies in both perpendicular and parallel applied fields arein good agreement with each other and can be excellent-ly accounted for by the FMR theory of Zhang andRado, which was specifically developed for ultrathinamorphous ferromagnetic films. dc magnetometry mea-surements also agree very well with the FMR results.The use of amorphous magnetic materials in multilay-ered structures is particularly attractive for a number ofreasons. Amorphous films have no macroscopic in-planeanisotropies and may be combined with a variety ofspacer materials and substrates, since they are not sub-ject to the conditions required for epitaxial growth. Theamorphous film is likewise not subject to the defects thatsuch constraints may produce in a crystalline film" andwhich may cloud the magnetic properties of the system.The spacer layers of Ag were chosen because of their im-miscibility with Fe. Characterization studies of our sam-ples are described more fully in Ref. 12 but we shall re-state the main findings here because of their relevanceto the present work. Large-angle x-ray diA'raction con-firmed that the Fe7oB3o layers were indeed amorphouswhile the Ag layers were crystalline. Small-angle x-raydiÃraction revealed superlattice peaks appearing atscattering vector magnitudes given by integer multiplesof 2tr/d, where d is the bilayer thickness. Cross-sectionalelectron microscopy revealed flat continuous layers ofFe7pB3o and Ag with no sign of island structure for asample in which 2L =10 A. Resolution of the layerstructure in the thinnest of our samples is of course verydifficult and beyond the capabilities of the instrumentsavailable. However, even these films have a continuousand island-free layer structure because there is no hint ofsuperparamagnetism from either SQUID measure-ments' or the FMR measurements that will be de-scribed belo~. %'e note that the frequencies used in theFM R rneasurernents diAer from those used in theSQUID measurements by 10 orders of magnitude. Thesaturation magnetization at T =8 K was measured for anumber of values of 2L, the smallest of which was 3 A,and was found to be independent of 2L. This impliesthat the magnetization at the surface of the Fe70830 lay-er is unafTected by the interface and hence that there isno interdict'usion between the Fe70830 and Ag layers.This is not entirely unexpected since Fe and Ag havenegligible mutual solubilities. Finally, the temperaturedependence of the magnetization M(T) for various layerthicknesses has also been determined. ' These favorable1990 The American Physical SocietyVOLUME 64, NUMBER 15 PHYSICAL REVIEW LETTERS 9 APRIL 1990conditions facilitate the exploration of magnetic surfaceanisotropy in ultrathin films.In order to explore the 2L dependence of K, we havemade FMR measurements at room temperature onFe7oB3o/Ag multilayers grown on Kapton substrates.The use of multilayers rather than single layers wasessential for the observation of a strong FMR signal.The ratio of the Ag thickness to the Fe70B30 thickness 2Lwas maintained at 3:1 throughout. ' The multilayersamples contain from 32 to 726 bilayers. Details of fa-brication and of the 2L dependence of the magnetizationas determined by SQUID magnetometry measurementswere given previously. ' More than twenty samples wereused to cover the range of 1.6 A & 2L & 90 A. The sam-ple used for FMR typically had a lateral dimension ofabout 1 mm to assure uniform film thickness across thesample. The FMR field was measured with the staticapplied field both parallel and perpendicular to the planeof the sample at frequencies of 9.52 and 23.9 6Hz.Some of the perpendicular resonance fields could not bemeasured since they exceeded the 14 kOe available fromour magnet.Some representative FMR signals are shown in Fig. 1.The signals are clean despite the presence of ultrathinlayers with 2L =3 A. Thus they attest to the quality ofsamples consisting of several hundred layers and to thefact that the data reveal the behavior of a single layer.In the perpendicular configuration, the relevant FMRequations areco/y =H 4rrM 2A—k '/M-,Aktanh(kL) = —K, , (2)where H is the applied magnetic field, k is the wave10H (koe)11I I I7H (koe)FIG. 1. FMR traces at 23.9 GHz for a 3.0-A sample. Thefirst derivative of the absorption is plotted against the appliedstatic magnetic field H. The upper and lower traces are for theperpendicular and parallel configurations, respectively.number of the microwave magnetic field, co is the circu-lar frequency, and, for Fe7oB3o, A =1.38x10 erg/cmand y=18.38 MHz/Oe. Since the resonance field can bemeasured, K, can be determined from Eqs. (1) and (2).In the parallel configuration, the corresponding rela-tions are equally well known but more complicated inform and will not be reproduced here. The FMR equa-tions mentioned above were obtained from the equationof motion of the magnetization in which the surface an-isotropy was introduced via the general exchange bound-ary conditions. These and other aspects of the theoreti-cal background of the experimental observations (suchas the nature of the k values and the associated excita-tions) are presented elsewhere. The magnetization Mwas determined independently by SQUID magne-tometry. While M(0 K) is independent of 2L, M(300 K)does depend on 2L. It is found that M(300 K) can beadequately described by M(300 K) =[1054—1194(1/2L)] emu/cm' for 2L & 6.8 A and M(300 K) =[942434(1/2L—)] emu/cm for 2L & 6.8 A.The resonance fields at 9.52 and 23.9 GHz with bothperpendicular and parallel applied fields are shown inFig. 2. The values of K, calculated from each FMRmeasurement have been averaged and plotted in Fig. 3for each thickness. To demonstrate the self-consistencyof the results, the four theory curves (shown in Fig. 2)have been generated from Eqs. (1) and (2) and othersusing the single set of K, values shown in Fig. 3. FromFig. 3 it can be seen that K, has a constant value of 0.34erg/cm for 2L & 16.5 A but then decreases monotoni-cally towards zero as 2L is decreased from 16.5 A, con-clusively demonstrating that in the ultrathin limit K, de-creases with film thickness.We have also determined K, for 2L =4.1, 6.7, 10.2,and 16.7 A by extracting the "knee field" Hk„„ from theSQUID-determined perpendicular magnetization curvesat T=300 K. In the perpendicular configuration of themagnetization measurement, Hk„„ is defined as the fieldat which M is just saturated. With the inclusion of themagnetic surface anisotropy, Hk„„=4aM —(4K,/M)x (1/2L), from which K, can be determined. The valuesof K, obtained from the SQUID data are also plotted inFig. 3 and are seen to be in very good agreement withthose determined from the four sets of FMR measure-ments.It must be emphasized that the decrease in the valueof K, for 2L & 16.5 A is certainly not an artifact result-ing from the 2L dependence of M(300 K). If a constantvalue of M equal to 1054 emu/cm is assumed for allvalues of 2L, then K, again decreases towards zero for2L & 16.5 A but now the value of K, for 2L & 16.5 A isfound to be slightly higher, being about 0.40 erg/cm .The excellent agreement between five independent mea-surements of K„ four at microwave frequencies and oneessentially static, strongly supports the validity of themodel used, and rules out the possibility of the film1821VOLUME 64, NUMBER 15 PHYSICAL REVIEW LETTERS 9 APRIL 199014Il2I10f=9.52 GHz128OA~r Z ~~ 7 ~(b)f=9.52 GHz)0—A'aS08—0NQf=23.9 GHz(d)f=23.9 GHz0.6 0.0 0.2 0.60.2 0.4 04I jaL (A ') I jul. (A ')FIG. 2. Dependence of the magnetic-resonance field on the reciprocal of the magnetic layer thickness 2L. The applied magneticfield is parallel to the film plane in (a) and (c), and perpendicular to the film plane in (b) and (d). The four curves were calculatedon the basis of Ref. 9 by using the method described in the text.'4 I I I IfI I I IiI I I I ( I I I I t I I00.30.1I I I I I I I I I l I I I I I I I I I I I I10 20 302L (A)40FIG. 3. Dependence of the magnetic surface anisotropy con-stant EC, on the magnetic layer thickness 2L. Data points ob-tained by FMR and SQUID measurements are denoted by tri-angles and squares, respectively. The solid line is an interpola-tion of the data points.breaking up into an island structure as an explanationfor the decrease of EC, with decreasing 2L. Furthermore,for an island structure the profound difference betweenthe perpendicular and parallel FMR configurationswould be strongly diminished. As shown in the picturereproduced in Ref. 12, cross-sectional transmission elec-tron microscopy revealed the layer structure to be verygood for 2L 10 A; that is, well below the value of 2L atwhich K, begins to decrease. We wish to stress that theexperimental data on K, shown in Fig. 3 differ from aproportionality to 2L by an amount exceeding experi-mental error. Even if K, were exactly proportional to2L, it would be unreasonable to describe the experimen-tal data by introducing a constant (i.e., thickness-independent) effective volume anisotropy K,, of some un-known origin for 2L ( 16.5 A while retaining a constantsurface anisotropy K, for 2L ) 16.5 k This is becauseit is highly improbable that the values of K,, and E„which are independent, satisfy the equality K,, =K,/2Lfor 2L =16.5 A, as demanded by the continuity of theexperiinental data.The main result of this paper is that K, is constant for2L & 16.5 A but decreases monotonically and continu-ously towards zero as 2L decreases from 16.5 A towardszero. Although several mechanisms have been suggestedthat may reduce' the value of K„ it is by no meansclear that one or more of these mechanisms would ac-count for a monotonic decrease of K, with decreasing 2Lin an amorphous material. We suggest that the funda-mental interactions contributing to the surface anisotro-py energy in our samples have a range up to half of 16.5A. It seems conceivable that such relatively long-rangeinteractions perhaps arise from the single-ion mechanism1822VOLUME 64, NUMBER 15 PHYSICAL REVIEW LETTERS 9 APRIL 1990described (after an appropriate averaging over the atom-ic sites) by the quadratic axial spin Hamiltonian termDS, , where the z axis is now perpendicular to the film.This term involves, in our case, the combined action ofthe electrostatic field at the magnetic surface ions of theamorphous ferromagnet and the spin-orbit coupling. Wenote that in a ferrite a D term has already been shown toproduce' a surface anisotropy energy in agreement withexperiment. In the present case, of course, it would beessential to include in the calculations of D the electro-static field arising from ions located farther than nearestneighbors.The success of our model in fitting the experimentaldata reaffirms the utility of the concept of a surface an-isotropy energy. Moreover, we have demonstrated con-clusively that the value of this energy is thickness depen-dent in ultrathin films and therefore cannot simply be in-ferred from experimental or theoretical investigations ofthe surface of a bulk solid.This work was supported in part by National ScienceFoundation Grant No. DMR 88-22559 and by the U.S.Naval Research Laboratory.' Present address: Department of Physics, Brown Universi-ty, Providence, RI 02912.'L. Neel, J. Phys. Radium 15, 225 (1954). Magnetic sur-face anisotropy is sometimes alternatively referred to as mag-netic interface anisotropy.~For a recent revie~, see U. Gradmann, J. Magn. Magn.Mater. 54-57, 733 (1986).3C. Chappert and P. Bruno, J. Appl. Phys. 64, 5736 (1988).4F. J. A. den Broeder, D. Kuiper, and H. C. Donkersloot, J.Phys. (Paris), Colloq. 49, C8-1663 (1988).5M. P. M. Luykx, C. H. W. Swuste, H. J. G. Draaisma, andW. J. M. de Jonge, J. Phys. (Paris), Colloq. 49, C8-1769(1988).G. A. Prinz, G. T. Rado, and J. J. Krebs, J. Appl. Phys. 53,2087 (1982); G. T. Rado, Phys. Rev. B 26, 295 (1982); 32,6061(E) (1985).~E. M. Gyorgy, J. F. Dillon, Jr., D. B. McWhan, L. W.Rupp, Jr., L. R. Testardi, and P. r. Flanders, Phys. Rev. Lett.45, 57 (1980).sG. Xiao and C. L. Chien, J. Appl. Phys. 61, 4061 (1987).9L. Zhang and G. T. Rado, Phys. Rev. B 36, 7071 (1987).' B. Heinrich, K. B. Urquhart, A. S. Arrott, J. F. Cochran,K. Myrtle, and S. T. Purcell, Phys. Rev. Lett. 59, 1756 (1987).''U. Gradmann, H. J. Elmers, and M. Przybylski, J. Phys.(Paris), Colloq. 49, C8-1665 (1988).' G. Xiao, C. L. Chien, and M. Natan, J. Appl. Phys. 61,4314 (1987).' Rather than 4:1 as stated in Ref. 12 of the present paper.'4P. Bruno and J. Seiden, J. Phys. (Paris), Colloq. 49, C8-1645 (1988).'sG. T. Rado, Phys. Rev. B 18, 6160 (1978).1823

Observation of thickness dependence of magnetic surface anisotropy in ultrathin amorphous films

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Observation of thickness dependence of magnetic surface anisotropy in ultrathin amorphous films.

Observation of thickness dependence of magnetic surface anisotropy in ultrathin amorphous films.

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