Physica B 192 (1993) 137-149
North-Holland ~

SDI: 0921-4526(93)EO120-6

G.P. Felcher

Argonne Nationa[ Laboratory, Argonne. IL, USA

A review is given of the role of polarized neutron reflectivity (PNR) in measuring the magnetic profile close to the
surface and in thin films of superconductors and magnetic materials. For type I and type II superconductors PNR provided
a new and direct determination of the penetration depth. For very thin ferromagnetic films PNR was able to determine the
absolute value of the magnetic moments. In magnetic superlattices, formed by the alternation of ferromagnetic layers and
nonmagnetic spacers, PNR was used to confirm the basic magnetic structure as well as to determine the direction of the
magnetic moments of the individual layers. In addition to reflectivity, forward magnetic scattering may very well extend the
usefulness of PNR to the case of laterally dishomogeneous systems.

I. Reflectivity from magnetic layers er equation for the neutron may be separated in
cartesian coordinates. Practically only the z
Polarized neutron reflectivity (PNR) has blos- component of the motion needs to be consid-
somed in recent years, because it is a simple ered: in the plane (x, y) (parallel to the surface)
method to measure the magnetic depth profile of the motion is that of a free particle and the
thin films and in proximity of the surface and of corresponding components of the wavevector
interfaces. Neutron reflectivity is an optical tech- are constant. The two spinor components
nique: thus the interaction of neutrons with 1/I+(z), 1/I-(z) of the neutron wave function obey,
matter, which gives rise to reflection, is ap- at a depth z in the medium, the Schrodinger
proached in a form slightly different from the equations r2,31:
conventional treatment of neutron scattering.
When neutrons propagate through a medium in
which the scattering centers are small compared ~ )(~ + (Vn + 2ILnBII)I/J
with the neutron wavelength, the effect of the 2m dz
medium may be represented by a smooth pseu- h2k;
dopotential whose magnitude is related simply to + 2J.Ln
B i 1/1 1/1
2m
the scattering density and the magnetic induction (2
in the material [11 as ( n2 )(d21/l-
2m d:;-z- ) + (Vn,- 2J.LnBII
)1/1-

27rfl~ nzkz
Vcff V +v =-bN+B.s
n m m + 2f.Ln B -L 1/1 + = -zrr:-1/l-

where b is the sum of all the scattering lengths where k z = 27r(sin (}j / A ) is the component of the
over the N atoms occupying a unit volume. If the momentum of the incident neutron normal to the
potential is a function only of the depth from the
surface (as in a stratified medium) the Schroding- surface, (}j the angle of incidence, A the neutron
wavelength and ILn its magnetic moment.
The z-axis is chosen to point from the vacuum
toward the surface which is placed at z = 0. The
Correspondence to: G.P. Felcher, MSD-223, Argonne Na.
tional Laboratory, Argonne, IL 60439, USA. wavefunction in the halfspace z < 0 is

138 G.P. Felcher I Magnetic depth profiling studies by polarized neutron reflection

1/1+ = exp(ikz .z) + R++ exp(-ikz .z) , , , ..
10v
(3)
1/1- = R exp( ik z) , ,"
;>, 10.'
for an incoming wavefunction fully polarized in ..-; ~
the + state. If at depths greater than ZF the >
.;jU
refractive index becomes constant and nonmag- 4) 10. \
1;:
netic the wavefunction can be described [4] by ~
~ :~. ...
1/1+ = T ++ exp(ikF+z) , o~
;.-
(4)
.1, = T 10-4 f
'1'- + exp(ikF-z) , , , , , .,
0 U.Ul U.U;! 003 004 005 006 0.07 008

q(A-I)
where
Fig. 1. Polarized neutron reflectivity of a film of permalloy
on Nio5CoO5O, at a temperature of 20 K. The abscissa i,
k q = 2k:o The permalloy is magnetized in the direction of the
applied field H. Full points: neutrons polarized parallel to
(5) H (R + ). Open circles: neutrons polarized opposite to H (R -)

(see ref. [5]).
The conditions of continuity of the wave function
and of its derivative at all values of z allow the
determination of R + + , R + -, T + + , T + -, and of 12 = IR
reflectivity, IR + I' which is an optical
the reflectivities IR++12 and IR+-12, which are transform of B .J.(z).
most directly compared with the experimental Figure 2 shows pictorially some of the cases
quantities. that can be encountered [9] .The + and -signs
If the sample magnetization is parallel to an refer to the relative polarizations of the neutron
applied magnetic field H (which is also the spin with respect to the applied magnetic field H .
quantization axis of the neutron) the two eqs. (2) which acts as a quantization axis for the polar-
do not contain crossterms. The neutron spin in ized neutrons. When a ferromagnetic layer is
its trajectory remains in its origina1 state, either magnetically saturated in the plane of the film
parallel to H ( + ) , or opposite to it ( -) .Figure 1 along the direction of H, the neutrons remain
shows a typical example [5] of spin-dependent polarized during the reflection process (fig. 2(a».
reflectivities for a 300 A layer of permalloy on If instead the direction of the magnetization
the top of an antiferromagnetic film of deviates from the quantization axis, the neutrons
NiosCoo.sO. Basically the reflectivity IR+(kz)12 undergo a partial precession during the reflection
is an optical transform of b(z)N(z) + cB(z) and process, so that the reflected beam appears as
similarly IR-(kz)12 is an optical transform of partially depolarized (fig. 2(b». If the ferromag-
b(z)N(z) -cB(z). Much work has been done netic film is not saturated, but for simplicity the
recently [6,7,8] to find the optimal way to exe- magnetization is uniaxial, the sample is divided
cute this transform which, for large values of kz , in magnetic domains aligned either parallel or
reduces to a Fourier transform. To present in antiparallel to the applied field. In this case there
more concise form the magnetic information of is no depolarization of the reflected beam, but
the reflectivity quantities such as IR + 12! IR -12 the values of IR+12 and IR-12 represent a weight-
have been introduced, conventionally named ed average over the reflectivities of the indi-
'flipping ratio'. More recently it has been pre- vidual domains (fig. 2(c». Finally, if H is applied
ferred to present the data as p = (R+ -R-)! perpendicular to the film and is sufficiently large
(R + + R -) ; this is called 'polarization' or 'spin to magnetize the sample in that direction, the
asymmetry'. When B1- Ą 0, analysis of the polari- neutron reflectivities become optical transforms
zation of the reflected beam gives a spin-flip of the nuclear profile only (fig. 2(d)). This is

G.P. Felcher Magnetic depth profiling studies by polarized neutron reflection l1Q

parallel to an applied magnetic field or opposite
to it. Similar devices, if inserted in the neutron
(a) path after reflection of the sample, allow polari-
zation analysis. Reflectometers have been con-
structed at both steady-state [10] and pulsed
neutron sources [2,11,12,13]. At steady state
sources the reflectivity as a function of kz =
27r sin 01},. is obtained in the following way. The
neutron beam is monochromatized to a wave-
length },.0. A suitable region of kz is spanned by
(b) varying the angle 0 between beam and sample
surface (and sample surfaceldetector). In con-
trast. at pulsed sources all the neutrons
contained in the source spectrum are utilized,
and their wavelength is sorted out by the time of
flight from source to detector. Here a substantial
region of k" is covered without changing the
~ angle of incidence 0. In all cases the maximum
(c)
-~/ value of k" spanned determines the resolution
0-- ~ ..::-:- . ~ length ~z in direct space: k" -1 I ~z .
Both types of instruments have distinct advan-
~ H tages. At a steady-state source one can choose
the k: region of interest with great flexibility,
taking data only where needed and with the
desired statistics. The neutron wavelength may
- be chosen at the top of the maxwellian which
/ (d)
characterizes the neutron spectrum. The resolu-
~--*-
~ tion,

.,
k::12 = [/lOIO]
I f.lk [~A/A]-

~ consists of two terms of comparable size which
Fig. 2. Effccts of tho: film magl1ctizatio!l On thc ncutro!l do not vary greatly with angle. This means that
rellectivity a!ltl p()larizati\\il In conliguratio!ls (a) and (h) the high resolution can be obtained at large angle.
reflectivity is spin-dcpcndc!lt: ho\vcvcr, in (h) the spin of the On the other hand, the instruments at pulsed
reflectctl hcam is partially rotatcd. For (c) thc rcflectivity is sources have their own advantages: they permit
averagL' for that of the two !lCutro!l spin states while for
co!lliguration (tI) the rcflectivity is duc only to nuclear the observation of the entire reflectivity pattern
interactions (see rcf. [lJI). at ollce; the footprint of the beam on the sample
is fixed; since Ilk / k .-IlA / A is constant the
z .
because B;: , the component of B normal to the resolution is excellent for k- values close to the
surface, is continuous across the surface. region of total reflection. The choice of the 'best'
Conceptually (and to a great deal even practi- instrument is thus dictated by the experiment to
cally) a reflectometer is a very simple instru- be performed.
ment. A narrow beam of neutrons of wavelength The review presented here covers only the
A hits a sample surface at an angle () (of the order PNR work done in selected areas of research
of one degree) and is reflected at the same angle where rapid development is taking place. The list
() into the detector. Appropriate devices polarize is not all-inclusive. For instance, PNR has been
the neutrons before the samnle in the direction used to study the effects of thermal and chemical

G.P. Felcher Magnetic depth profiling studies by polarized neutron refieclion

treatment on the surface magnetism of ferrites netism exist only in a shallow surface layer when
[14]. It has also been used to study the magnetic the field is applied parallel to the plate. The
depth profiles of relatively thin films, when latter state occurs between H c2 and a surface
deposited either on grossly mismatched lattices nucleation field Hc3.
(like strained layers of Fe and Co on GaAs) [15], Only a few experiments have been made on
or on antiferromagnetic substrates (like permal- superconductors (mostly below Hcl) and yet
loy on NiO) [5,9] which provide a unidirectional there is a fair amount of disagreement between
bias. the results of different groups. The earliest PNR
experiment was carried out on a Nb film, 5 IJ.m
thick, deposited onto a polished silicon substrate
2. Superconductivity [19]. The superconducting properties of this film
were found to be satisfactory, with Hcl = 1.0 kOe
The magnetic state of a body is always per- at T = 5 K and a critical temperature T c = 9.2 K.
turbed at the surface, and the perturbation From PNR a penetration depth A = 430 :t: 40 A
extends over a thickness that depends on the at 4.6 K was obtained and the temperature
range of the interaction forces. In a ferromagnet, variation of A was found to be consistent with a
at T = O the magnetic moments are significantly zero-temperature value A(O) = 410 :t: 40 A. This
different from the bulk value up to three atomic value is in excellent agreement with theoretical
planes from the surface. Such distance is too calculations and most of other, less direct mea-
short to be detectable by reflectivity at present surements. However. independent measure-
day neutron sources. The thickness of the 'mag- ments from another group [20] gave different
netic surface layer' increases with the tempera- o .
results: at T = 4.9 K, for a film 7000 A thick the
ture [16] and actually becomes infinite at the penetration depth was found to be A = 900 :t:
magnetic transition temperature. However, in 100 A; for a second film, 2550 A thick, ,1 =
practice the span of temperatures over which 1450:t: 150A.
surface effects become visible is small and at- Even larger discrepancies marred the deter-
tempts made up to now [ 17] have not provided mination of the penetration depth of the high- T "
reliable values for the critical exponents. More superconductor YBa2CuJO7-,. The first mea-
promising is the case of superconductors. surement, made on a syntered pellet [21], gave a
As is well known [18], magnetic fields always penetration depth A = 225 A. a value unexpec-
penetrate to some extent the surface of a super- tedly low for a material with a very short
conducting material. For an applied field H less coherence length and hence a large penetration
than a critical field ( the thermodynamic critical depth. For two other measurements the sample
field Hc for type-I superconductors; the lower was a thin film deposited epitaxially onto a
critical field Hcl for type-II superconductors) the substrate of SrTiO3. In both cases the c-axis of
penetration is restricted to a depth of the order the YBa2Cu3O7-, lamellar structure was perpen-
of a few hundred Angstroms. At higher field the dicular to the film and the penetration depth was
penetration is more dramatic: for instance for measured with the magnetic field applied parallel
type-II superconductors, in fields between Hcl to the surface. The two results, A = 1400 A [22]
and H c2 ( the upper critical field) a mixed state of and A = 900 (+600, -250) A [23], are in sub-
quantized vortex lattice has been observed both stantial agreement with each other and with the
by small angle neutron diffraction and decora- values obtained by muon resonance. All the
tion techniques utilizing small magnetic particles. measurements on superconductors were plagued
There are two situations that are strictly surface by the presence of a sizeable surface roughness.
effects and cannot be conveniently studied by the which not only causes the 'surface' to be ill-
preceding techniques. These are the Meissner defined but that -at least in the extreme case -
state, in which the field penetrates only a small may cause a shortcircuit of the magnetic flux.
distance into the superconductor, and the surface What is the functional dependence of the
sheath, in which superconductivity and diamag- magnetic field close to the surface of a supercon-

G.P. Felcher I Ma,s;'netic depth profiling studies by polarized neutron reflection 141

ductor? Provided that electronic response is reason. In vacuum the magnetic induction B
entirely local, the magnetic field decays exponen- reduces to H. Hence the discontinuity of the
tially in the material [18]. Nonlocality is pre- interaction potential at the surface is /l.n .(BII -
dicted to have visible effects only in the case of H): in a diamagnetic material, such as a super-
'extreme' type I superconductors. A careful conductor, the neutron sees a negative magnetic
study of films of pure lead and Pb-Bi alloys was field. The polarization of the Pb(Bi) film at
made to explore this point [24]. Pure lead is a 323 Oe is compared with the results of different
type-I superconductor for which Hcl equals the calculations. If for a magnetic profile an ex-
thermodynamic critical field Hc. Adding an im- ponential decay is adopted, certain features of
purity level of 0.8% Bi brings the system to just the polarization are not satisfied: for instance,
below the crossover point to type-Il, where Hcl with an exponential decay length of 260 A, the
and Hc2 separate and the region in between is minimum is matched but not the values of the
characterized by the mixed state. polarization for higher values of kz. Much better
The polarization of Pb(Bi) at T = 6 K is pre- fit is obtained with a magnetization profile that
sented in fig. 3. The sample, in a field H = decays from the surface first less rapidly, then
323 Oe, is in the Meissner state. The polarization more rapidly an exponential function (fig. 3).
appears to be entirely negative, for the following Such behavior might be explained in terms of
nonlocal effects; however it is hard to justify the
persistance of these effects in such a 'dirty'
superconductor. New independent measure-
ments [25] are now in progress to verify these
0.02
i finding and also to expand earlier observations of
~ a superconducting surface sheath predicted to
occur at the superconductor/vacuum interface in
to these materials at higher magnetic fields.

3. Magnetic thin films

Only for film thicknesses below a few nanome-
, ,
I i i i i
0.12 ters the magnetization of ferromagnetic is sig-
0.003 0.004 0.005 0.006 0.007 0.008 0.009 nificantly altered from the bulk value, in size,
k (;..01)
. direction of magnetization and even type of
magnetic order [26]. These new properties are
the result of a complex set of circumstances.
Free standing films, ideally one atomic plane
thick, are expected to exhibit magnetic moments
larger than the bulk: since the orbital compo-
nents are less quenched, the moments are ex-
pected to tend toward the free atom values. On
the other hand, the lower dimensionality is
, ~ expected to reduce, and even to suppress, the
00 --I temperature of magnetic order. Experimental
0 200 400 600 800 1000 1200 films have to be deposited on a substrate, which
Depth from surface (A) perturbs the magnetization of the proximate
Fig. 3. Above: polarization of a film of Pb(Bi) in a field of layer on two accounts. In the first place the
323 Oe and 5.5 K. The dashed line is calculated for an magnetic atoms which are deposited from vapor
exponential decay of the magnetic field in the material, with
a penetration depth of 300 A. The continuous line is obtained or from a plasma arrange themselves in a struc-
for the parametric model profile shown below (see ref. [24]). ture, which tends to mimic that of the substrate.

14 G.P. Felcher Magnetic depth profiling studies by polarized neutron reflection

In comparison with the bulk material, the thin easier to take into account the weak magnetic
film is expanded (or compressed): this may response of overlayer and substrate, even when
change drastically the coupling of magnetic elec- they are much more massive than the magnctic
trons. In the second place, if both magnetic film film.
and substrate are metallic a transfer of electrons To perform a PNR experiment it is not neces-
takes place. Numerous ab initio calculations sary that the thin film is at the surface: the film
have been made for epitaxial films [27] ; table 1 may be covered with a nonmagnetic layer, which
o .
shows the magnetic moments predicted for one- could be a few hundred Angstroms thIck. Actu-
atomic-Iayer-thick metals on several substrates ally such coverage enhances [30] the spin depen-
dence of the reflectivity. However, the polariza-
[28].
A wealth of experimental information has tion is proportional to the linear magnetic flux.
been accumulated in recent years on the magnet- i.e. the product of the internal field and iron
ism of thin films [29]. For instance, ultrathin thickness (8 dFe). To the extent that k= .dFe ~ 1.
films of iron have been epitaxially deposited on the experiment is insensitive to the variation of B
single crystal substrates of Cu, Ag, Au, Pd, W within the layer, or for that matter to the
and MgO and studied by spin-polarized photo- thickness of the layer itself. Once known 8, the
emission, Kerr effect, conversion electrons, mean magnetic moment per atom JiF can be
Mossbauer spectroscopy and spin-polarized obtained with precision without detailed kno\\'-
LEED. These studies have demonstrated the ledge of the number of magnetic atoms in thc
presence of ferromagnetic ordering and perpen- layer or their density. This is because the optical
dicular surface anisotropy in monolayer thick potential of eq. ( 1) can be shown [ 1] to be
iron films [27]. However, the determination of proportional to (b ::!:: C'Jir )N , where c' is a con-
the absolute magnetic moment per atom of an stant (c' =0.02695 x 10-'2cm/Jiu) and N is thc
ultra-thin film is still a tremendous challenge for atomic density per unit volume. The simulta-
experimentalists. Experiments were proposed neous fitting of II~+I~.IRI2 strongly constrains
[30] and later successfully implemented [31-35] the ratio between atomic moment of an atom
to determine by polarized neutron reflection and its well-known neutron scattering length.
(PNR) the magnetic moments in Fe and Co films The first magnetic thin film studied by PN R
as thin as two monolayers. Being an optical was face-ccntcred-cubic (FCC) cobalt on
technique, PNR goes well beyond conventional Cu(001), overcoated with copper [31]. For a
magnetometry. To start with, if the magnetic film 18 A thick it was found an in-plane mag-
layer is covered, its depth in the sample is netization of 1.8Jiu /Co, slightly larger than the
localized. At the same time, the optical signal bulk value ( 1.6JiB ). Subsequent measurements
assures that iron is conformed as a film. and not [32,33] on even thinner films of FCC cobalt on
(for instance) in an assembly of droplets having Ag indicated a moment enhancement up to
equivalent thickness. Finally. in PNR is much 2.15JiB/Co. Although these measurements were
taken at 4.2 K, the cobalt magnetization was
found to be virtually unchanged up to room
Table 1 temperature. The behavior of thin films of body-
Magnetization of thin films: theory and PNR experiments. 0
centered iron was entirely different. A 14 A film
Monolayer Calculated Experimental Magnetic moment sandwiched in copper was fitted [31] with
JLI1 / atom JLB / atom in solid
2.2JiB /Fe, a value virtually undistinguishable
Cr!Vacuum 12 :0.1 from that of the bulk. Even for a 4.3 A film (on a
Cr!Ag :0.1
nonmagneti rather rough surface) the ferromagnetic moment
Fe!Cu 23 2.2
2.97 2.2 did not exceed 2.35JiB /Fe at liquid helium tem-
Fe!Ag
Fe!MgO 3.07 2.2 2.2 perature [15]. A systematic study of BCC iron
Co!Cu 1.79 1.8 1.7 films 4,6,8,16 A thick on MgO and capped with
1 '7
Co!Ag gold [35] showed a dramatic decrease of the

G.P. Felcher / Magnetic depth profiling studies by polarized neutron reflection 143

ordering temperature, and a concurrent change
of the perpendicular anisotropy for thicknesses
~6 A; however, the ferromagnetic moment at
saturation remains (2.2:!: 0.2)JLB/Fe down to the
thinnest sample ( figs. 4, 5) .Finally, films of Cr
(down to sub monolayer thickness) [33], depo-
sited on Ag(OO 1) , did not show any measurable
induced magnetization, in fields up to 0.83 kOe.
Table 1 shows a compendium of the ex-
perimental results hitherto obtained and com-
pares them with theore~ical predictions. The
magnetic moments, as determined by PNR at
different laboratories, are entirely consistent:
however, they are very close to the bulk value
and do not show the enhancement predicted for
thin film materials. For Cr, the calculation is in
the limit of the single atomic plane and the
moments of a second plane are thought to be
coupled antiferromagnetically to the first. How-
ever, the discrepancy between theory and experi-
ment is clear and strong in the casc of BCC iron,
which should have enhanced magnetic moment
in thin films on a number of different substrates.
It is to he hoped that future experiments clarify
this important point. Looking farther in the
future, good ferromagnetic thin films may be-

I:e
~
" 6
"
tlJ I Fig. 5. Polarization functions for (bottom) 4 A. (middle) 6 A
" and (top) sA Fe films at T=40K and H=5kOe. All fits
used the same parameters except for the iron thickness (see
MgO
~- ---1 ref. [35]).

~ !1 ? Fe come useful to test in detail the properties of the
phase transition in truly two-dirnensional sys-
u If~~
0) 10
!;: 1 terns.
0) Surface
~

4. Magnetic coupling in multilayers
10'~ The development of reliable and controlled
deposition techniques has made possible the
, ,
IO.'L-- fabrication of metallic multilayers formed by
000 001 002 003 004 005 006 007 008 interleaving ferromagnetic films with nonmag-
q(A-I)
Fig. 4. Spin-dependent reflectivity of a }6 A thick Fe film. netic spacers. The original goal of this research
The data were obtained at room temperature in a magnetic was to manufacture materials with novel mag-
field of 200 Oe. Solid dots indicate data for neutron spin netic properties just stacking conventional metals
parallel to the applied field ( + ); open circles for spins in layers of controlled thickness. First for very
anti parallel to the field ( -) .The insert is the schematic selected couples, then for a rapidly expanding
diagram of the neutron potential for + and -spin neutrons
through the sample (see ref. [35]). host of combinations it was found that the

144 G.P. Felcher Magnetic depth profiling studies by polarized neutron reflection

coupling between subsequent ferromagnetic
layers oscillates from ferromagnetic to antiferro-
magnetic to ferromagnetic again as the thickness
of the nonmagnetic spacers is increased. The
nature of the coupling, inferred from the mag-
netization measurements, was first directly ob-
served by neutron reflection. In all recorded
cases the alignment of the magnetization of the
subsequent layer was either ferromagnetic (F) or
antiferromagnetic (AF) of the type + -+ -,
with a simple doubling of the chemical period-
icity.
The first material to exhibit oscillatory mag-
netic interaction was a gadolinium/yttrium
superlattice, epitaxialy grown on tungsten with
the hexagonal c-axis perpendicular to the sur-
face. When the yttrium spacer is ten atomic
layers thick the superlattice is AF, as confirmed
by polarized neutron diffraction [36]. A weak
magnetic field in the surface plane has the effect
of slightly canting the AF structure, with the
main AF component perpendicular to the field.
When the yttrium thickness is increased to twen-
ty atomic planes, or decreased to six, the materi-
al becomes ferromagnetic. The oscillatory be-
havior has been well explained in terms of
a Ruderman-Kittel-Kasuya-Yosida (RKKY) Co/Ru [44], Ni/Ag [45], Co/Cu [46] and Fe/Nb
model [37] .The basic assumption is that the [47]. In the case of Fe/Si, F to AF oscillations
conduction electrons of Y provide an indirect were found to be present only for short Si
coupling between the gadolinium layers. Since thicknesses, when silicon forms a crystalline .
those first experiments, the studies have greatly metallic silicide. For thicknesses larger than :?0 A
expanded to cover other rare earths and other silicon is deposited as an amorphous semicon-
spacers [38]. ductor which, unless excited, does not pro\'ide
The magnetic coupling is oscillatory also in magnetic coupling to the adjacent iron layers.
multilayers of Fe. Co, Ni interleaved by most of In retrospect, polarized neutron reflection had
the 3,4.5 d nonmagnetic metals. Among these. only a marginal role in the study of the magnetic
the first to be studied were multilayers of iron/ multilayers formed by transition metals. Actually
chromium [39,40,41 ]. The magnetic fields the presence of an AF or an F state is no\\'
needed to saturate the samples were found to observable in direct space by means of scanning
vary periodically with the chromium thickness. electron microscopy with polarization analysis
The presence of an AF ground state for multi- [49] as well as by magnetooptic Kerr effect
layers with high saturating fields was quickly microscopy. However, neutron measurements
confirmed [42,43] by PNR. The only magnetic contain a wealth of information that reaches far
structures found up to now in this system are of beyond proving the nature of the ground state.
the F and the AF kind: the latter configuration is From the intensities of the series of superlattice
destroyed by applying a sufficiently large mag- peaks up to large scattering angle, and of their
netic field (see fig. 6). Similar findings were spin dependence, one can obtain a detailed
found for other kind of multilayers, such as profile of the magnetization within the single

G.P. Felcher / Magnetic depth profiling studies by polarized neutron reflection

magnetic layer, with a resolution that might parallel to the field. Since the magnetic coupling
approach the interatomic spacing [38]. While is weaker for the surface layer, it has been
experiments at large kz are considered more suggested that the phase transformation in a
properly in the area of conventional polarized magnetic field should initiate at the surface, and
neutron diffraction, even observations at small its character should depend on the nature of the
kz, i.e. in the region where the mean refractive surface layer [52]. Experiments now in progress
index of the material cannot be neglected, yield [53,54] tend to confirm in real samples the main
information that is far beyond the mere de- features of the mean field model.
termination of the F or AF state. Up to now it was implicitly assumed that the
As already discussed the analysis of the polari- sample is composed of a single domain. In this
zation of the reflected neutrons can be used to case the reflected neutrons are not depolarized
determine the direction of the magnetization at (even from nonuniaxial samples) but at most the
any depth in the sample. The simplest arrange- direction of their spins change from the initial
ment consists in analyzing the neutron spin in polarization axis. In principle the reference field
reference to the quantization axis of the neutrons for polarization analysis can be rotated until
before hitting the surface. The non-spin-flip parallel to the quantization axis of the exiting
reflectivity is due to the projection of the sam- neutrons: the spin-flip components of the reflec-
pie's magnetization on the quantization axis, tivity become identically zero. If a device ca-
while the spin-flip reflectivity is due to the pable of pro\riding 'flexible' polarization analysis
perpendicular component of the magnetization. were constructed [ 55] , it would also discriminate
In this way the presence of a canted arrangement the case discussed above from that, in which
of spins has been observed first in Gd/Y [36] and more than one magnetic domain is present in the
later in Fe/Cr [42]. A more quantitative com- sample. Here, since different neutrons ex-
parison of IR++12, IR+-12, IR-+12 and IR--12 has perience different magnetic pathways, the re-
been done for Co/Cu [46]. Polarization analysis flected beam is truly depolarized. Magnetic do-
is also been used [50] to search for direct mains have an additional effect: the magnetism is
evidence of a magnetic state where two magnetic no longer uniform in the plane of the film, and
layers of a sandwich are magnetized at a 90° the finite size of the domains gives rise to
angle, rather than at 0° or 180°. The presence of scattering around the direction of the reflected
such a state has been inferred from magnetic beam.
measurements, and it is justified if biquadratic
terms in the magnetic exchange become impor-
tant [51]. s. Forward magnetic scattering
Polarization analysis becomes important to
sort out the structures of more complex artificial In order to measure the reflected beam suffices
superlattices, as those made by the alternation of a single counter, poised at an angle 0 with the
two magnetic metals. Prototype of this class is a reflecting surface, and 20 with the primary beam.
Gd/Fe multilayer, a material for which model However, in several instruments a one-dimen-
properties have been proposed [52] and pres- sional, position sensitive detector is used, with
ently tested. This material is made of two the geometry sketched in fig. 7. Such detectors
magnetic components, Gd and Fe, which are offer several practical advantages: the reflected
anti parallel to each other but have in general beam is easily localized and both signal and
different sizes. In an applied magnetic field the background are measured at the same time .
magnetic structure is predicted to transform from More important, these detectors measure not
a ferrimagnetic to a 'twisted' configuration. This only reflected neutrons, but also those scattered
is composed of an antiferromagnetic component at grazing incidence. Notice that in the geometry
perpendicular to the field and a ferromagnetic shown in fig. 7 a one-dimensional detector dis-
component, unequal for the two components, criminates only neutrons leaving the surface at

146

"""" important difference between the two cases, and
~ detect thus to avoid confusion I will name the scattering
,~ in the plane of reflection as 'for}1'ard scattering.
+ to distinguish it from the lateral scattering at
/V grazing incidence.
In both cases the scattering is due to dis-
homogeneities in the plane of the film, which
might be represented by a vector '7' with planar
" projections 7x and 7\1 (fig. 8). In the for'vard
~ scattering ~t is obtained from the separation ~O
/ between the scattered and the reflected beam. In
9--\.-- sample the lateral scattering 7y is obtained from the
angle ~<1> between the scattered beam and the
reflection plane. When '7' is small in comparison
Fig. 7. Geometry of forward and lateral scattering of neu. with the incoming wavevector, the laws of con-
trons at grazing incidence. servation of energy and momentum in plane
reduce to:
an angle Of different from Oi; however, the Tx = Ikl sin (J .lfJ
scattering always takes place in the plane of (6)
reflection. In contrast, in the most common Tv = Ikl.lcp (lkl = 21T/A)
geometry of scattering at grazing incidence [56],
the observations are focussed on the neutrons For comparable elements ~(J. ~<1> the regions of
scattered out of the reflection plane. There is an T, .T, are entirely different. For instance. if ~f) =

01 =02
a) I~ ,

r-- I~ ~
rosrnoN
SENSmVE ~
Dt":=R ~

J ~

~
<D=-
to
9"""
;
O~

I
'-"" """"
<-< - I -' n ~
-;, ~.~
"'-- ~ 0-.: -~---
II) ::c '.

(') I. I
I.
--,-
3.1 2.9 2.7 2.5 2.3

01 +02
Fig. 8. Intensity contour of a Co/Ru multilayer (from ref. [44]). The locus of the reflected beam is a vertical line at 81 = 82. The
forward scattering ridge is at Iql = 'T" centered around the AF peak.

G.P. Felcher "'lognetic depth profi/ing stlldies b>' po/arized nelltron reflection 147

e = ~<1> = 1°, and a neutron wavelength A = 10 A, has the form of a ridge centered around a value
4 A -1 2 ° -I
'Tx = 1.9 x 10- , while 'Ty = 1.1 x 10- A . of jql equal to the value of the maximum of the
The difference is about of two ordcrs of mag- AF peak, i.e. where qz = Tz, Tz being the propa-
nitude. This means that, if the lateral fluctua- gation vector of the antiferromagnetic structure.
tions 'T are isotropic in the plane of the film In contrast, at the first Bragg reflection due to
{'Tx = 'Ty) scattering might be present at a detect- chemical modulation of the multilayer no corre-
able ~(} even when ~<1> is negligibly small. The sponding broadening is present. The forward
size of the objects that give rise to lateral scattering is of magnetic origin: it is as if the
scattering is the same as that giving rise to small antiferromagnetic domains had finite size. It is
angle scattering in transmission geometry: it is of easy to form a picture of the configuration, by
order of 100 A. The fluctuations that give rise to assigning to each domain a magnetization axis,
observable forward scattering are instead of the which may point along a local crystallographic
order of one micron . ax IS.
Sizeable forward scattering has been observed It is easy to calculate the lateral dimensions of
in several instances, when reflectivity measure- the domains observed for Co/Ru \\'ith the help
ments were taken on magnetic multilayers. In of a simple formula. In the kinematic approxi-
fig. 8 is shown an intensity contour pattern mation the intensity of the antiferromagnetic
obtained for a Co/Ru multilayer [44], and in fig. peak [57] may he \\'ritten as
9 that for a Fe/Nb multilayer [47]. The measure-
ments were done at a pulsed neutron source, sin2(N"ak sin (} cas a)
= J. J, =
where the intensity reflected at a given angle sin2(ak sin (} cas a)
with respect to the primary beam, (}i + et' are
measured for all neutron wavelengths. In this sin2(N,ak sin (j sin a) . 7
pattern, the reflected heam appears as a vertical sin~(ak sin (j sin a)
line of intensity at e, = (}t. The visible scattering
\\hcre we have neglected tluctuations along y. In
eq. (7), a is the (Intiferromagnetic spacing and N=
C!
~ is the numbcr of laycrs composing thc film. In
-w !, .(1 is in reality a dummy parameter: what is of
~ intcrest is the total length IJx = N,(1 in the .r
.:;; ---
"':;b dircction. a is the (mgle between the sc(lttering
~ vcctor and the z-direction: (It the Br(lgg reflec-
- tion a = O (lnd the arguments in J = are multiples
0 of 20. When the incident \Vavevector k = 21T / A is
ch(lnged (but the (lngle of incidence O remains
< ~ constant) the m(lximum of J = occurs for finite a :
;:;E it is easy to see that under this condition q =
q=O.IO6A-l remains constant. At finite a, !, rapidly de-
crcases; Lx m(ly be chosen by finding the value
of a at which !t = 0. From fig. 8 it may be
deduced that, for Co/Ru, L., = 4 fJ.m. In the case
of Fe/Nb (fig. 9) the counter used is too limited
to give an estimate of the size of Lt and only an
~I, -' I - , , I
4.4 4.2 4.0 3.8 3.6 upper limit can be given: L.1: < 0.6 fJ.m.
In conclusion, in the past ten years PNR has
ei +ef(degree)
been developed into a mature technique which is
Fig. 9. Forward scattering of a Fe/Nb multilayer (from ref. being employed to study a variety of magnetic
[47]). The forward scattering is much broader than the
dimension of the counter (2.5 cm, at 90 cm from the sample). phenomena in samples having lamellar geome-

148 G.P. Felcher I Magnetic depth profiling studies by polarized neutron reflection

try. At the same time, the development of
(lateral) scattering at grazing incidence, as well
as that of forward scattering, may open new and
exciting areas of research.

Acknowledgements

The present work was supported by the US
Department of Energy, BES-Material Sciences,
under contract W-31-109-ENG-38. The author
would like to thank Prof. W.G. Stirling for giving
him the opportunity to present this work at the
ILL-ESRF Workshop on Neutrons and X-rays in
Magnetism. The author is also grateful to R.
Goyette and Y.Y. Huang for their help in prepar-
ing the figures, and to Hong Lin for a critical
reading of the manuscript.

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