Physica B 267}268 (1999) 162}167 Towards a 3D magnetometry by neutron re#ectometry C. Fermon *, F. Ott , B. Gilles , A. Marty , A. Menelle , Y. Samson , G. Lego! , G. Francinet DRECAM/SPEC CEA Saclay, 91191 Gif sur Yvette cedex, France Laboratoire Le&on Brillouin, CEA-CNRS 91191 Gif sur Yvette Cedex, France LTPCM, ENSEEG, B.P. 75, 38 042 Grenoble, France CEA-Grenoble, De&partement de Recherche Fondamentale sur la Matie%re Condense&e/SP2M, 17 rue des Martyrs, 38 054 Grenoble Cedex 9, France Abstract Specular polarised neutron re#ectometry with polarisation analysis allows one to probe in-depth magnetic pro"les of thin "lms (along the normal to the "lm). O!-specular re#ectometry gives information about lateral structures (in the plane of the "lm) with typical lengthscales ranging from 5 to 100 m. Furthermore, surface di!raction at grazing angle gives access to transverse dimensions between 10 nm and 300 nm with a resolution in that direction of a few nanometers. The combination of these three techniques applied to magnetic systems can lead to a 3D magnetic structure measure- ment. Such a technique is however not applicable to the study of a single magnetic dot, but it can generate unique results in several cases including patterns of domain walls in thin "lms with perpendicular anisotropy, arrays of magnetic dots, and patterned lines in magnetic thin "lms. 1999 Published by Elsevier Science B.V. All rights reserved. PACS: 61.12 Ha; 75.70 Kw; 75.70.!i Keywords: Magnetometry; Neutron re#ectometry; Polarisation analysis 1. Introduction layers. Owing to the large magnetic coupling be- tween the neutron and the magnetic moment, Magnetic thin "lms are now largely produced for neutron di!raction is a powerful tool to obtain fundamental studies and technological applications. information about magnetic con"gurations. Following the discovery of giant magnetoresistance Polarised neutron re#ectometry (PNR) has been in antiferromagnetically coupled multilayered "lms used for several years [2,3] to investigate such [1], there has been an extensive interest in the problems. Polarised neutron re#ectometry with precise measurement of the magnetic moment di- polarisation analysis (PNRPA) has proved to be rections in each layer and at the interface between a useful tool to probe in-depth vectorial magnetic pro"les [4,5]. In the last two years, new classes of challenges for * Corresponding author. Fax: 33-1-69-08-87-86; e-mail: PNR have appeared: the "rst one is to investigate cfermon@cea.fr. the dynamical properties of magnetic thin "lms 0921-4526/99/$ } see front matter 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 0 1 4 - 9 C. Fermon et al. / Physica B 267}268 (1999) 162}167 163 through inelastic scattering [6]. The second one is magnetic "eld. In most cases, the spin-#ip to follow the evolution of the spin con"guration as signals R>\"R\> depend mainly on the mag- a function of "eld or temperature in a reasonable netism perpendicular to the applied magnetic beam time [7]. The third is to obtain information "eld. on thin "lms which are not magnetically homo- In the case of homogeneous "lms, the neutron geneous in the plane of the "lm. is sensitive only to the in-plane magnetisation With the very high intensities available on syn- and all the intensity is re#ected in the specular chrotron sources, it is possible to investigate lateral direction. In the case of magnetically non-homo- sizes of rough surfaces down to the nanometer. We geneous "lms, all the directions of the magnetisa- will present here some o!-specular results obtained tion can be explored and intensity is scattered o! by neutron scattering on magnetic thin "lms and the specular direction. mesoscopic structures patterned in thin "lms. The incidence plane is de"ned by the incident wave vector and the perpendicular to the surface (Oz). Fig. 1 gives the corresponding geometry. The 2. General ideas convention is to call o!-speculara the intensity measured in the incidence plane (x, z) and surface A specular re#ectivity curve consists in the meas- di!ractiona the intensity measured out of the re#ec- urement of the intensities R re#ected by a "lm as a tion plane along the (Oy) direction. function of the scattering vector q for each polarisa- The incident and re#ected wave vector k tion state of the incident and re#ected neutron spin and k (R>> (resp. R\\) referring to incident and re#ected  are given by upa (resp. downa) neutrons, R>\"R\> refer- ring to the spin-#ip signals). For q smaller than k and k , a critical value q kcos 0  kcos cos W k cos  sin W , the beam is totally re#ected; !k k for larger q (q'3q  sin  sin  ), the intensity decreases as the fourth power of q but presents oscillations where k whose amplitude is related to the composition "2 / is the value of the neutron wave vector, and the magnetism of the thin "lm. Roughly is the incidence angle, " # V is the re#ection angle and speaking, R>> and R\\ depend on the chem- W is the angle of re#ection relative to the incidence plane. These angles are ical and the magnetic pro"le along the applied de"ned in the Fig. 1. Fig. 1. Setup of the experiment. It is possible to study o!-specular di!usion in the plane of incidence (along the o!-speculara line) and in the plane perpendicular to the plane of incidence (along the surface di!ractiona line). 164 C. Fermon et al. / Physica B 267}268 (1999) 162}167 The scattering vector wave vector q de"ned by q"k!k is given by q !k( V#( V)/2#( W)/2) k W . k(2 # V) We have supposed that all the angles were small and performed a second-order Taylor expansion. It appears clearly that qV is a second-order term and qW is a "rst-order one. The lateral sizes which are probed are typically given by 2 /qV and 2 /qW which are very di!erent. For example, on the re#ectometer PADA, which is monochromatic with a wavelength of 0.4 nm, we have 10 nm(2 /q Fig. 2. Di!raction map in the (q W(400 nm and 1 m( V, qX) plane on a grating of nickel 2 /q lines (width 5 m, periodicity 10 m, thickness 90 nm) deposited V(50 m. The upper limit is given by the resolution of the re#ectometer and the lower limit on a glass substrate. The line qV"0 corresponds to the specular re#ection, the other lines correspond to di!raction modes. by the lack of intensity. It appears that except for a region in the micron size range, due mainly to the lack of intensity, it is possible to probe a large range In Fig. 3, the specular signal and the "rst two of lateral scales by re#ectometry. di!raction modes #1 and !1 have been plotted versus qX. For clarity, the intensities of the mode !1 (resp #1) have been divided by a factor of 100 3. Non-specular neutron di4raction on periodic (resp. 10 000). Numerical "ts based on a dynamical gratings formalism [8] are plotted in black lines. They are in good agreement for the #1 mode but the intensity It is possible to produce periodic gratings using of the !1 mode is overestimated by a factor of 4. lithographic techniques. Optical lithography is es- The typical re#ectivity oscillations are not present pecially suited for producing gratings in the micron because the resolution was lowered to increase the size range. The di!erent etching processes are dry available neutron #ux. etch by argon milling, reactive ion etching (RIE) or chemical etching. A nickel grating with a 10 m periodicity and 4. Di4raction on periodic magnetic stripe domains 5 m wide lines has been etched chemically in a solution of FeCl in a nickel thin "lm (90 nm thick) We have measured magnetic surface di!rac- deposited on a glass substrate. O!-specular di!u- tion on magnetic stripe domains appearing in sion has been measured on this sample using a Fe time-of-#ight re#ectometer, by measuring a rocking  Pd  thin "lms. The sample was prepared by molecular beam epitaxy under ultra-high vacuum curve around 0.753, the detector being "xed at 1.53. (10\ Pa). A 2 nm seed layer of Cr was deposited The intensity map is plotted in Fig. 2 in the (qV, qX) onto a MgO (0 0 1)-oriented substrate in order to plane. One can observe di!erent lines at constant allow the epitaxial growth of the 60 nm single- qV. The line qV"0 corresponds to the specular crystal Pd bu!er layer. After a 10 min annealing at signal. The other lines (along qV"$0.0006, 700 K, a 50 nm thick Fe $0.0012, $0.0018 nm\) correspond to the dif-  Pd  alloy layer was deposited at room temperature using a monolayer ferent di!raction modes. Fig. 2 shows that it is (ML) by monolayer growth method in order to possible to observe up to three di!raction orders. induce a chemical order similar to the one found in C. Fermon et al. / Physica B 267}268 (1999) 162}167 165 Fig. 3. Intensity of the di!racted modes #1 and !1 (triangles and squares) versus qX. Numerical "ts are plotted in black lines. For clarity, the intensities of the mode !1 (resp. #1) have been divided by a factor of 100 (resp. 10 000). the tetragonal structure L1. This structure consists created by the stripes. In this case, the di!use of alternate atomic layers of Fe and Pd on a body cross-section can be written as [14] centred tetragonal lattice [9]. After a magnetisation along the easy axis, a stripe domain structure is "k(1!n)" observed (see bottom picture in Fig. 4) [10]. d "(¸ d V¸W) 16  The di!raction measurement has been performed using a small angle neutron scattering spectrometer ;"¹(k (the spectrometer PAPOL at the Laboratoire LeHon )" "¹(k)" S(q) Brillouin). In the experiment, the lines were aligned with along the plane of incidence. An example of di!rac- tion in shown in Fig. 4. One can observe a bright exp(![(qRX)#(qRHX)] /2) specular spot and two weaker (10\) o!-specular S(q)" "qR peaks. The positions of these peaks along the (Oy) X" axis re#ects the periodicity of the stripe domains (100 nm). The maximum intensity of these peaks is ; dXd>(exp("qRX"C(X,>))!1) obtained in the direction correponding to the criti- 1 cal angle of the layer whatever the incidence ;exp(i(q angle is. The absolute maximum intensity of the VX#qW>)), di!raction peaks is obtained when the incidence where C(X, >) is the magnetic roughness correla- angle is . These peaks have a behaviour similar to tion function, q is the di!usion vector k Yoneda peaks (or anomalous re#ections) [11}13]. !k and q As a "rst approach, it is possible to explain these  is the wave-vector transfer in the medium. Maxima are obtained in the di!use scattering when observations by using a DWBA approach. The k considered unperturbed system is the #at FePd  or k makes an angle close to since in these positions, the Fresnel coe$cients T reach a max- layer; the perturbation is the magnetic structure imum. 166 C. Fermon et al. / Physica B 267}268 (1999) 162}167 In the case of our magnetic lines, we de"ne the correlation function of the magnetic roughness as: 1 C(X, >)" M(x, y) M(x#X, y#>) dx dy. S   1 The magnetic correlation function is a sawtooth function if we assume sharp interfaces between the domains. Fig. 4 shows an MFM picture of the magnetic stripe domains with the corresponding experimental di!usion pattern. If qRX is small, S(q) reduces to the Fourier trans- form of the magnetic roughness correlation func- tion: S(q)" dXd>C(X,>)exp(i(qVX#qW>)). 1 The surface di!raction signal measures the Fourier transform of the magnetic correlation function. The Fig. 5 shows the o!-specular signal calculated for two di!erent incidence angles, the critical angle "0.53 and "0.73. The peak positions are un- changed whatever the incidence angle is. The max- Fig. 4. Di!raction geometry and o!-specular di!usion signal imum intensity is obtained when the incidence measured on a network of magnetic domains using a multidetec- angle is equal to the critical angle tor (top picture). The top peaks are the specular and o!-specular . However, the DWBA approach is not well suited peaks. The bottom signal is due to the refracted wave. The to this problem since the magnetic roughness ex- bottom picture is a MFM image of magnetic domains observed in the Fe tends over the full thickness of the magnetic layer  Pd  thin "lms. so that the #at layer as a basis state is very far from Fig. 5. Calculated o!-specular signal as measured on a multidetector for two di!erent incidence angles (a)  " "0.53 and (b)  "0.73. The peaks maximum does not move but the intensity decreases as soon as the incidenceangle is moved away from the critical angle . C. Fermon et al. / Physica B 267}268 (1999) 162}167 167 the real eigenstates of the system. The determina- [2] C.F. Majkrzak, J.W. Cable, J. Kwo, M. Hong, D.B. tion of quantitative magnetic information will re- McWhan, Y. Yafet, J. Waszcak, Phys. Rev. Lett. 56 (1986) quire a fully dynamical theory. 2700. [3] G.P. Felcher, R.O. Hilleke, R.K. Crawford, J. Haumann, R. Kleb, G. Ostrowski, Rev. Sci. Instr. 58 (1987) 609. 5. Conclusion [4] S.J. Blundell, J.A.C. Bland, Phys. Rev. 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