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 ofthin "lms (along the normal to the "lm). O!-specular re#ectometry gives information about lateral structures (in theplane of the "lm) with typical lengthscales ranging from 5 to 100 lm. Furthermore, surface di!raction at grazing anglegives 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 resultsin 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

Magnetic thin "lms are now largely produced forfundamental studies and technological applications.Following the discovery of giant magnetoresistancein antiferromagnetically coupled multilayered "lms[1], there has been an extensive interest in theprecise measurement of the magnetic moment di-rections in each layer and at the interface between

*Corresponding author. Fax: 33-1-69-08-87-86; e-mail:cfermon@cea.fr.

layers. Owing to the large magnetic coupling be-tween the neutron and the magnetic moment,neutron di!raction is a powerful tool to obtaininformation about magnetic con"gurations.Polarised neutron re#ectometry (PNR) has beenused for several years [2,3] to investigate suchproblems. Polarised neutron re#ectometry withpolarisation analysis (PNRPA) has proved to bea useful tool to probe in-depth vectorial magneticpro"les [4,5].

In the last two years, new classes of challenges forPNR have appeared: the "rst one is to investigatethe 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

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 inthe plane perpendicular to the plane of incidence (along the `surface di!ractiona line).

through inelastic scattering [6]. The second one isto follow the evolution of the spin con"guration asa function of "eld or temperature in a reasonablebeam time [7]. The third is to obtain informationon thin "lms which are not magnetically homo-geneous in the plane of the "lm.

With the very high intensities available on syn-chrotron sources, it is possible to investigate lateralsizes of rough surfaces down to the nanometer. Wewill present here some o!-specular results obtainedby neutron scattering on magnetic thin "lms andmesoscopic structures patterned in thin "lms.

2. General ideas

A specular re#ectivity curve consists in the meas-urement of the intensities R re#ected by a "lm as afunction of the scattering vector q for each polarisa-tion state of the incident and re#ected neutron spin(R`` (resp. R~~) referring to incident and re#ected`upa (resp. `downa) neutrons, R`~"R~` refer-ring to the spin-#ip signals). For q smaller thana critical value q

#, the beam is totally re#ected;

for larger q (q'3q#), the intensity decreases as

the fourth power of q but presents oscillationswhose amplitude is related to the compositionand the magnetism of the thin "lm. Roughlyspeaking, R`` and R~~ depend on the chem-ical and the magnetic pro"le along the applied

magnetic "eld. In most cases, the spin-#ipsignals R`~"R~` depend mainly on the mag-netism perpendicular to the applied magnetic"eld.

In the case of homogeneous "lms, the neutronis sensitive only to the in-plane magnetisationand all the intensity is re#ected in the speculardirection. In the case of magnetically non-homo-geneous "lms, all the directions of the magnetisa-tion can be explored and intensity is scattered o!the specular direction.

The incidence plane is de"ned by the incidentwave vector and the perpendicular to the surface(Oz). Fig. 1 gives the corresponding geometry. Theconvention is to call `o!-speculara the intensitymeasured in the incidence plane (x, z) and `surfacedi!ractiona the intensity measured out of the re#ec-tion plane along the (Oy) direction.

The incident and re#ected wave vector k*

andk0are given by

k* K

k0

cos h*

0

!k0

sin h*K and k

0 Kk0

cos h0cos *h

yk0

cos h0sin *h

yk0sin h

0K,

where k0"2p/j is the value of the neutron wave

vector, h*is the incidence angle, h

0"h

*#*h

xis the

re#ection angle and *hy

is the angle of re#ectionrelative to the incidence plane. These angles arede"ned in the Fig. 1.

C. Fermon et al. / Physica B 267}268 (1999) 162}167 163

The scattering vector wave vector q de"ned byq"k

0!k

*is given by

qK!k

0(h

**h

x#(*h

x)2/2#(*h

y)2/2)

k0*h

yk0(2h

*#*h

x) K.

We have supposed that all the angles were smalland performed a second-order Taylor expansion. Itappears clearly that q

xis a second-order term and

qyis a "rst-order one.The lateral sizes which are probed are typically

given by 2p/qx

and 2p/qy

which are very di!erent.For example, on the re#ectometer PADA, which ismonochromatic with a wavelength of 0.4 nm, wehave 10 nm(2p/q

y(400 nm and 1 lm(

2p/qx(50 lm. The upper limit is given by the

resolution of the re#ectometer and the lower limitby the lack of intensity. It appears that except fora region in the micron size range, due mainly to thelack of intensity, it is possible to probe a large rangeof lateral scales by re#ectometry.

3. Non-specular neutron di4raction on periodicgratings

It is possible to produce periodic gratings usinglithographic techniques. Optical lithography is es-pecially suited for producing gratings in the micronsize range. The di!erent etching processes are dryetch by argon milling, reactive ion etching (RIE) orchemical etching.

A nickel grating with a 10 lm periodicity and5 lm wide lines has been etched chemically in asolution of FeCl

3in a nickel thin "lm (90 nm thick)

deposited on a glass substrate. O!-specular di!u-sion has been measured on this sample using atime-of-#ight re#ectometer, by measuring a rockingcurve around 0.753, the detector being "xed at 1.53.The intensity map is plotted in Fig. 2 in the (q

x, q

z)

plane. One can observe di!erent lines at constantqx. The line q

x"0 corresponds to the specular

signal. The other lines (along qx"$0.0006,

$0.0012, $0.0018 nm~1) correspond to the dif-ferent di!raction modes. Fig. 2 shows that it ispossible to observe up to three di!raction orders.

Fig. 2. Di!raction map in the (qx, q

z) plane on a grating of nickel

lines (width 5 lm, periodicity 10 lm, thickness 90 nm) depositedon a glass substrate. The line q

x"0 corresponds to the specular

re#ection, the other lines correspond to di!raction modes.

In Fig. 3, the specular signal and the "rst twodi!raction modes #1 and !1 have been plottedversus q

z. For clarity, the intensities of the mode

!1 (resp #1) have been divided by a factor of 100(resp. 10 000). Numerical "ts based on a dynamicalformalism [8] are plotted in black lines. They are ingood agreement for the #1 mode but the intensityof the !1 mode is overestimated by a factor of 4.The typical re#ectivity oscillations are not presentbecause the resolution was lowered to increase theavailable neutron #ux.

4. Di4raction on periodic magnetic stripe domains

We have measured magnetic surface di!rac-tion on magnetic stripe domains appearing inFe

0.5Pd

0.5thin "lms. The sample was prepared by

molecular beam epitaxy under ultra-high vacuum(10~7 Pa). A 2 nm seed layer of Cr was depositedonto a MgO (0 0 1)-oriented substrate in order toallow the epitaxial growth of the 60 nm single-crystal Pd bu!er layer. After a 10 min annealing at700 K, a 50 nm thick Fe

0.5Pd

0.5alloy layer was

deposited at room temperature using a monolayer(ML) by monolayer growth method in order toinduce a chemical order similar to the one found in

164 C. Fermon et al. / Physica B 267}268 (1999) 162}167

Fig. 3. Intensity of the di!racted modes #1 and !1 (triangles and squares) versus qz. 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 L10. This structure consists

of alternate atomic layers of Fe and Pd on a bodycentred tetragonal lattice [9]. After a magnetisationalong the easy axis, a stripe domain structure isobserved (see bottom picture in Fig. 4) [10].

The di!raction measurement has been performedusing a small angle neutron scattering spectrometer(the spectrometer PAPOL at the Laboratoire LeH onBrillouin). In the experiment, the lines were alignedalong the plane of incidence. An example of di!rac-tion in shown in Fig. 4. One can observe a brightspecular spot and two weaker (10~3) o!-specularpeaks. The positions of these peaks along the (Oy)axis re#ects the periodicity of the stripe domains(100 nm). The maximum intensity of these peaks isobtained in the direction correponding to the criti-cal angle h

#of the layer whatever the incidence

angle is. The absolute maximum intensity of thedi!raction peaks is obtained when the incidenceangle is h

#. These peaks have a behaviour similar to

Yoneda peaks (or anomalous re#ections) [11}13].As a "rst approach, it is possible to explain theseobservations by using a DWBA approach. Theconsidered unperturbed system is the #at FePdlayer; the perturbation is the magnetic structure

created by the stripes. In this case, the di!usecross-section can be written as [14]

AdpdXB

$*&&

"(¸x¸y)Dk2

0(1!n2)D216p2

]D¹(k1)D2 D¹(k

2)D2 S(q

5)

with

S(q5)"

exp(![(qtz)2#(qtH

z)2]p2/2)

DqtzD2

]P PS

dX d>(exp(DqtzD2C(X,>))!1)

]exp(i(qxX#q

y>)),

where C(X, >) is the magnetic roughness correla-tion function, q is the di!usion vector k

2!k

1and

q5

is the wave-vector transfer in the medium.Maxima are obtained in the di!use scattering whenk1

or k2

makes an angle close to h#

since in thesepositions, the Fresnel coe$cients T reach a max-imum.

C. Fermon et al. / Physica B 267}268 (1999) 162}167 165

Fig. 5. Calculated o!-specular signal as measured on a multidetector for two di!erent incidence angles (a) h*/#

"h#"0.53 and (b)

h*/#

"0.73. The peaks maximum does not move but the intensity decreases as soon as the incidence angle is moved away from the criticalangle h

#.

Fig. 4. Di!raction geometry and o!-specular di!usion signalmeasured on a network of magnetic domains using a multidetec-tor (top picture). The top peaks are the specular and o!-specularpeaks. The bottom signal is due to the refracted wave. Thebottom picture is a MFM image of magnetic domains observedin the Fe

0.5Pd

0.5thin "lms.

In the case of our magnetic lines, we de"ne thecorrelation function of the magnetic roughness as:

C(X, >)"1

S0PP

S0

M(x, y) M(x#X, y#>) dx dy.

The magnetic correlation function is a sawtoothfunction if we assume sharp interfaces between thedomains. Fig. 4 shows an MFM picture of themagnetic stripe domains with the correspondingexperimental di!usion pattern.

If qtz

is small, S(q5) reduces to the Fourier trans-

form of the magnetic roughness correlation func-tion:

S(q5)"P P

S

dX d> C(X, >)exp(i(qxX#q

y>)).

The surface di!raction signal measures the Fouriertransform of the magnetic correlation function. TheFig. 5 shows the o!-specular signal calculated fortwo di!erent incidence angles, the critical angleh#"0.53 and h

*"0.73. The peak positions are un-

changed whatever the incidence angle is. The max-imum intensity is obtained when the incidenceangle is equal to the critical angle h

#.

However, the DWBA approach is not well suitedto this problem since the magnetic roughness ex-tends over the full thickness of the magnetic layerso that the #at layer as a basis state is very far from

166 C. Fermon et al. / Physica B 267}268 (1999) 162}167

the real eigenstates of the system. The determina-tion of quantitative magnetic information will re-quire a fully dynamical theory.

5. Conclusion

We have shown that it is possible to observeo!-specular neutron di!usion on thin "lms in allthe directions of the reciprocal space. We haveobserved surface di!raction from periodic magneticdomains. By a simple DWBA approach, it is pos-sible to account qualitatively for the results. Itshould soon be possible to describe these resultsquantitatively by using a matricial dynamical ap-proach. We hope that our e!orts will pave the wayfor a new technique of 3D magnetometry; this willmake it possible to measure quantitatively struc-tures with an in-depth and in-plane resolution.

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