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Physica B 397 (2007) 62–64

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Observation of difference in nuclear and magnetic roughnessin CoFe/TiZr multilayers by polarized neutron reflectometry

N.K. Pleshanova,�, B.G. Peskova, A.F. Schebetova, V.G. Syromyatnikova,B. Chenb, C.Q. Huangb, X.X. Lib

aPetersburg Nuclear Physics Institute, 188300 Gatchina, St. Petersburg, RussiabInstitute of Nuclear Physics and Chemistry, 621900 Mianyang, Sichuan, China

Abstract

A difference between nuclear and magnetic roughness in polycrystalline CoFe/TiZr multilayers was observed by polarized neutron

reflectometry. We infer from the neutron data that (a) the thickness of hardly magnetized regions with roughness induced magnetic

inhomogeneities at the interfaces of magnetic and non-magnetic layers is 0.5570.02 nm and (b) the magnetic roughness is less than the

nuclear (structural) roughness by 0.2270.02 nm. The difference between nuclear and magnetic roughness is a new factor, which was not

so far considered in theory of polarizing neutron coatings and which may play a significant role in defining their performance.

r 2007 Elsevier B.V. All rights reserved.

PACS: 61.12.Ha; 68.35.Ct; 75.70.�i

Keywords: Multilayers; Interfaces; Nuclear and magnetic roughness; Polarizing neutron supermirrors

The magnetic structure of the interfacial ‘‘magneticallydead’’ layers observed [1–6] in multilayers with alternatingmagnetic and non-magnetic layers is still poorly studied.As one may infer from magnetometry and neutronreflectometry (e.g., Ref. [6]), the magnetization in theinterfacial regions is close to 0. We shall use the term‘‘hardly magnetized’’ layers, supposing that the regionscontain unpaired electron spins with different orientations.The magnitudes of applied fields (o500Oe) are notsufficient to magnetize the interfacial regions with rough-ness induced magnetic inhomogeneities. Since specularneutron reflectivities are mainly defined by the potential,laterally averaged over many small domains, in calcula-tions the hardly magnetized regions will be represented (asbefore Refs. [3–6]) by non-magnetic layers. In CoFe(V)/TiZr multilayers, such layers of thickness d give rise toappearance of the potential barriers for spin-downneutrons and reflection of such neutrons is thus enhanced.

In Fig. 1, the experimental reflectivities of a CoFe/TiZrsupermirror on a Ti55Zr15Gd30 underlayer [7,8] for

front matter r 2007 Elsevier B.V. All rights reserved.

ysb.2007.02.045

ng author. Tel.: +781371 46973; fax: +7 81371 39053.

ss: pnk@pnpi.spb.ru (N.K. Pleshanov).

neutrons with the spin-up (R+) and spin-down (R�) theapplied field are represented, vs. the momentum transfer q.We have discerned three stages of the interfacial roughnessgrowth from layer to layer [7] in CoFe/TiZr multilayers.For the supermirror of given thickness, two stages of thelinear roughness growth,

sðzÞ ¼ s0 þ gðz� z0Þ, (1)

(z is the coordinate of an interface, z0 is the coordinate ofthe interface with a roughness s0), with s0 ¼ 1.0 nm,g ¼ 0.006 (stage I, so2.2 nm) and s0 ¼ 2.2 nm,g ¼ 0.0006 (stage II), allowed fitting [9] the spin-upreflectivity R+. However, attempts to fit R� at large q

with the model including interfacial roughness, surfaceoxide layer and hardly magnetized interfacial layers failed(e.g., see curves 1 and 2). The reason for a significantdifference in the findings for d obtained for a CoFeV/TiZrsupermirror (1.070.2 nm [10]) and for a periodic CoFe/TiZr multilayer (0.5170.02 nm [9]) was also not clear.The agreement between experiment and theory can

be achieved with an additional assumption that thenuclear (structural) and magnetic (induced by magnetic

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153

2

100

10-1

10-2

10-3

10-4

0.05 0.1 0.5

q, nm-1

R±

1 R+

R-

V0, �

V1 V2±

d1 d2

4

� �

σm,j–1 σm,j σn,jσn,j–1 σm,j+1 σn,j+1

Fig. 1. The experimental spin-up (open circles) and spin-down (solid

circles) neutron reflectivities of a CoFe/TiZr (m ¼ 2.35) supermirror (142

bilayers) on a Ti55Zr15Gd30 (224 nm) underlayer are represented as

functions of q (both scales are logarithmic). Inset: the model of the

interfaces between magnetic and non-magnetic layers. Curves 1 (dashed)

and 2 (solid) are the reflectivities R� calculated with Dsnm ¼ 0 for dd equalto 1.0 nm [10] and 0.51 nm [9]. The theoretical reflectivities R7 (thick solid

curves) are obtained with the best-fit parameters: dox ¼ 3.470.2 nm, V1 ¼

�371 neV, V2�¼ �872 neV, d ¼ 0.5570.03 nm, s0 ¼ 1.170.2 nm and

g ¼ 0.00670.002 (stage I, so2.2 nm), s0 ¼ 2.270.1 nm and g ¼0.0007070.00005 (stage II), Dsnm ¼ 0.2270.02 nm, dox ¼ 3.470.2 nm,

Vox ¼ 126 neV. Solid curves 3 and 4 are the reflectivities R� calculated

with Dsnm ¼ 0.15 nm and Dsnm ¼ 0.3 nm. Curve 5 (dots) is calculated with

Dsnm ¼ 0.22 nm and V1 ¼ �18 neV.

101

10-1

10-3

10-5

0.1

q, nm-1

21

x100

R+

R-

Inte

nsity

Fig. 2. The reflectivities R+ (open circles) and R� (solid circles) for a

CoFe/TiZr multilayer (20 bilayers) on glass and the theoretical

reflectivities (solid curves) are represented as functions of q (both scales

are logarithmic). The fitting yields: dox ¼ 4.570.5 nm, Vox ¼ 85720 neV,

dp ¼ 85.571.5 nm, d1 ¼ 6.4570.02 nm, V1 ¼ �371 neV, d2 ¼ 7.1770.02 nm, V2

+¼ 23573 neV, V2

�¼ �871 neV, d ¼ 0.5570.02 nm,

Dsnm ¼ 0.2270.02 nm, V0 ¼ 120710 neV, ds ¼ 6078 nm, Vs0 ¼ 8272 neV, Vs ¼ 10372 neV, s0 ¼ 0.570.1 nm and g ¼ 0.006 (stage I).

N.K. Pleshanov et al. / Physica B 397 (2007) 62–64 63

inhomogeneities, domains, etc.) roughnesses differ. In ourmodel, the nuclear (sn;j) and magnetic (sm;j) roughnessparameters belonging to the jth interface characterize‘nuclear’ and ‘magnetic’ interfaces severed by a hardlymagnetized layer of mean thickness d (see the inset in Fig.1). A good fitting is achieved on the assumption that thedifference between sn;jand sm;j is the same for all interfaces(L is the total number of layers):

sn;j � sm;j ¼ Dsnm; j ¼ 1; 2; . . . ;L� 1. (2)

Fitting R�, we find Dsnm ¼ 0.2270.02 nm. As before,sn;j is supposed to linearly grow in two stages. The fitting ofR+ with Dsnm ¼ 0.22 nm yields values of s0 and g (see thecaption), which but slightly differ from those obtained withDsnm ¼ 0. To demonstrate the sensitivity of R� to Dsnm,calculations are also made with Dsnm equal to 0.15 nm(curve 3) and 0.3 nm (curve 4). A salient maximum of R�near q ¼ 0.14 nm�1 is due to interference of waves,reflected from the two boundaries of the thickest (70 nm)uppermost CoFe layer, which are enhanced by the oxidelayer and the hardly magnetized layer, formed on theboundaries. The thickness dox ¼ 3.470.2 nm of the oxidelayer coincides with that obtained for a single CoFeV layer[10]. The remaining discrepancy of experiment and theoryfor R� at q40.5 nm�1 is very likely to be due to diffusescattering.

The experiment unambiguously shows that Dsnm40, i.e.the magnetic roughness is smaller than the nuclear(chemical) roughness. For most bilayers in the supermirror,the barriers are almost equidistant. The asymmetry of theneighboring barrier profiles (due to Dsnm6¼0) leads to adeviation of the potential profiles (for groups of layers)from 1

2structure period profiles and enhances R� . Since the

roughness is comparable to the thickness of the layers, thesmoothed profiles of the neighboring barriers overlap.Thus, nuclear and magnetic roughness increases theaverage potential for spin-down neutrons of non-magneticand magnetic layers, respectively. It means that, in ourcase, (V2

�oV1) the neutron optical contrast of layers isincreased and the reflectivity R� is additionally enhanced.The polarizing efficiency of the supermirror can beimproved if we increase the content of Ti in TiZr so thatV2�4V1 (curve 5). Note that, when the difference Dsnm 6¼0

is ignored, the fitting is improved by increasing d [10].The new model was also used to fit R7 (Fig. 2) for a

periodic CoFe/TiZr multilayer with an additional TiZrlayer protecting the structure against oxidation in air.Many parameters were fitted with a good reliability due tomeasurement of the reflectivities in a wide range of q. TheBragg peak positions yield the structure periodD ¼ d1(TiZr)+d2(CoFe). The total reflection edge for R+

and intensities of odd Bragg peaks give d1/d2, V1 and V27.

The Kiessig fringes in R+ are not resolved, but the periodand the amplitude of their modulation are defined by thethickness of the protective layer (dp) and the oxide layer(dox), respectively. The Bragg peak intensities yields0 ¼ 0.570.1 nm, which agrees with the data on roughnessof our glass substrates. Only stage I of the roughnessgrowth (g ¼ 0.006) is effective for the multilayer of given

ARTICLE IN PRESSN.K. Pleshanov et al. / Physica B 397 (2007) 62–6464

total thickness. The Bragg peaks in R� are sensitive to thestate of the interfaces (d and Dsnm). The sharp drop in R�near q ¼ 0.14 nm�1 can be fitted only with an additionaltransition layer (see also Refs. [11,12]) of thicknessds ¼ 60 nm at the surface of the glass substrate, with thepotential growing linearly from Vs0 ¼ 82 neV (surface) toVs ¼ 103 neV (bulk).

Note that the reflectivities of the multilayer (unlike thoseof the supermirror) can be fitted with Dsnm ¼ 0 [9]. Mostparameters obtained from the new fitting, started withdd ¼ 0.55 nm, Dsnm ¼ 0.22 nm, remained practically thesame. Yet, we should mention a change in findings for V2

�

from 2neV (Dsnm ¼ 0) to �8 neV (Dsnm ¼ 0.22 nm). Thelatter coincides with the value found for the supermirror,which is in favor of the new model of the interfaces. Atthe final stage of the fitting we varied d, Dsnm and thecoincidence of the values obtained with those for thesupermirror is also quite remarkable.

The version that the interfacial regions are originatedfrom interdiffusion does not comply with the fact that themagnetic roughness is smaller than the structural rough-ness. Indeed, the concentration gradient in the interdiffu-sion region would tend to produce the magnetic roughnessexceeding the structural roughness. The smaller roughnesssm indicates that the magnetic disorder is more likely to becaused by the surface charges, present due to roughness,which increase the dipolar energy competing with theexchange and anisotropy to determine the lowest energyconfiguration of the interfacial spins [13]. It implies that themagnetic disorder is orientational. The dominant exchangeinteraction tends to decrease the orientational spindisorder. In Ref. [13] the difference between the structural(chemical) and magnetic roughness was found to linearlygrow with the structural roughness. In CoFe/TiZr multi-layers the structural roughness changed from 1 to 4.5 nm,

yet the fitting was satisfactory with a constant Dsnm ¼

0.22 nm. More detailed studies, both experimental andtheoretical, are required to understand the cause of thisdiscrepancy. In conclusion, note that magnetic interfacesdefine, e.g., GMR and exchange bias, which have attractedgreat interest due to their important applications.

The work was supported by the Grant INTAS 03-51-6426.

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