Sixth-order contribution to the cubic anisotropy in Fe(1 1 1) thin films on Si(1 1 1)

Surface Science 566–568 (2004) 278–284 www.elsevier.com/locate/susc

Sixth-order contribution to the cubic anisotropy in Fe(1 1 1) thin films on Si(1 1 1) M. Kak, R. Stephan, A. Mehdaoui, D. Berling, D. Bolmont, G. Gewinner, P. Wetzel * Facult
e des Sciences et Techniques, Laboratoire de Physique et de Spectroscopie Electronique, UMR CNRS 7014- 4 rue des Freres Lumiere, Mulhouse Cedex 68093, France Available online 20 June 2004

Abstract Combined transverse biased initial inverse susceptibility and torque measurements were performed on thin Fe(1 1 1) films epitaxially grown on Si(1 1 1), using a conventional magneto-optical Kerr effect magnetometer. This new method, called TBIIST, is a well suitable and sensitive technique for the study of magnetic anisotropies and in particular provides an accurate value of the anisotropy field strength in the sample and a precise determination of the anisotropy axes. For this purpose a 160 monolayer Fe film grown on Si(1 1 1) at normal incidence was investigated. A very small sixth-order contribution to the cubic anisotropy is readily detected, as expected for a Fe(1 1 1) film, corresponding to anisotropy fields as low as a few tenths of an Oersted.
2004 Elsevier B.V. All rights reserved. Keywords: Magnetic measurements; Epitaxy; Iron; Silicon; Silicide; Metal–semiconductor magnetic thin film structures

1. Introduction The magnetic properties of ferromagnetic thin films are largely determined by the symmetry, magnitudes and directions of the competing magnetic anisotropies (magnetocrystalline, dipolar, magnetoelastic, . . .) present in the film. Moreover, such low-dimensional magnetic systems are an exciting field of research and applications because they exhibit significantly different properties from those of corresponding bulk material. Thus, a careful control of the magnetic anisotropies of the layers allows to adjust the magnetic behaviour such *

Corresponding author. Tel.: +33-3-89-33-60-08; fax: +33-389-33-60-89. E-mail address: [email protected] (P. Wetzel).

as magnetization reversal of the system. Several works [1,3] have been devoted to the analysis of the magnetization behaviour in epitaxial Fe films deposited on Si(1 1 1). Most of these studies were dedicated to correlating the structure of the Fe film and the in-plane anisotropies resulting from various deposition conditions, film thickness, etc. We have shown in our previous work [4] that body centered cubic (bcc) Fe films grown on Si(0 0 1) plane, at normal incidence, are dominated by the classical in-plane fourfold anisotropy due to the cubic structure of Fe. The usual expression for the anisotropy energy of a cubic system is Ea ¼ K1 ða21 a22 þ a22 a23 þ a23 a21 Þ þ K2 a21 a22 a23

0039-6028/$ - see front matter
2004 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2004.06.124

þ K3 ða21 a22 þ a22 a23 þ a23 a21 Þ2 þ




ð1Þ

M. Kak et al. / Surface Science 566–568 (2004) 278–284

where K1 , K2 and K3 are the cubic anisotropy constants and a1 , a2 , and a3 the direction cosines of the magnetization vector with respect to the cubic axes. Let us consider the cubic (1 1 1) plane. The expression of the contributions to the bulk magnetocrystalline energy in this plane is given by Ea ¼

K1 K2 K3 þ sin2 ð3hÞ þ þ


4 54 6

ð2Þ

where h is the angle between the magnetization and the [)1 1 0] axis. It is noteworthy that the first dominant term (fourth-order in spin) of cubic anisotropy energy does not vary in this plane, only the higher order K2 term (sixth-order in spin) has an angular dependence and contributes to the anisotropy energy. So, on the Fe(1 1 1) plane the magnetocrystalline anisotropy energy exhibits a sixfold symmetry only related to the weak (103 – 104 erg/cm3 [5]) K2 term. Note that the order of magnitude of K1 measured at room temperature (RT) is typically 5 · 105 erg/cm3 which is considerably larger than K2 . Hence, since in epitaxial Fe films on Si(1 1 1) the dipolar interaction tends to confine the magnetization to the (1 1 1) plane, this system offers an excellent opportunity to investigate the weak higher-order K2 term. If K2 is positive, there are six energy minima along the equivalent Æ1 )1 0æ directions. Such axes are the easy axes that correspond to possible equivalent directions of the spontaneous magnetization. However, as shown in Refs. [1–3], small structural modifications are sufficient to reduce the sixfold symmetry to twofold symmetry as a result of the contributions from other anisotropy mechanisms. In this paper we present a new method capable of determining the components of any combination of magnetic anisotropies in ferromagnetic films using conventional ex situ magneto-optic Kerr effect (MOKE). The magnetic anisotropy energy is determined in two distinct ways by means of combined transverse biased initial inverse susoH ceptibility v1 ¼ oM ðM ¼ 0Þ and torque (field offset) DH ¼ H (M ¼ 0) measurements. To demonstrate the power of this method, called TBIIST, we present the results obtained on a 160 monolayers (ML) thick Fe film epitaxially grown on Si(1 1 1) at RT and at normal incidence.

279

2. Experimental The structural and chemical quality of the samples was checked in situ using low-energy electron diffraction (LEED), inelastic medium energy electron diffraction (IMEED) and X-ray photoelectron diffraction (XPD). The crystallographic directions have been unambiguously identified from IMEED and XPD. The XPD measurements were performed with a 150 mm radius Leybold EA200 hemispherical analyser with a total acceptance angle of 2. The measurements of the photoelectron diffraction modulations of the Fe2p3=2 and Si2p core lines at kinetic energies of 779 and 1388 eV, respectively, were performed with an AlKa radiation (hm ¼ 1486:6 eV). Polar scans were recorded by rotating (angle h) the sample around its surface normal. IMEED maps were collected by means of the conventional LEED optics. The magnetic properties were investigated by ex situ MOKE measurements at RT in the longitudinal geometry. A detailed description of the measuring MOKE equipment is given elsewhere [4]. The Si(1 1 1)-7 · 7 surface is prepared by cycles of argon ion sputtering followed by annealing to 850 C. A 160 ML Fe film was deposited in a two  thick FeSi2 seed layer, step process. First, a 10 A grown on Si(1 1 1) by deposition of 2 ML of Fe followed by heating to 500 C, was inserted between the substrate and the Fe-film in order to prevent the diffusion of Si into the Fe layer and to ensure epitaxial growth. This procedure gives a highly ordered (2 · 2) periodic structure. Then, Fe was deposited at RT and at normal incidence. Normal incidence is adopted here because oblique incidence breaks the threefold symmetry of the film normal direction and is found to induce a strong in-plane uniaxial anisotropy, that actually obscures the detection of the tiny sixth-order magnetocrystalline contribution. Finally, on top of the Fe-layer a 20 ML Au cover layer was grown at normal incidence to serve as an anticorrosion coating for ex situ investigations. Both Fe and Au films were deposited at a rate of one ML per minute from Al2 O3 crucibles. Here, we define one ML as the atomic density of the Si(1 1 1) surface.

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3. Theoretical basis

steady bias field H? oriented perpendicular to the sweep field H longitudinal direction of the magneto-optical set-up. Both H? and H fields are applied in the film plane. Magnetization component M along H is measured versus sweep field H along

Let us consider the experimental configuration shown schematically in Fig. 1a. The TBIIST measurements consist in the application of a

ϕ H⊥

M H

(a)

α [1-10]

-10

0.9

-8

-6

-4

-2

0

2

4

0.2

χ

0.1

0.6

0.0

m l= M / M s

0.3

∆Η

-0.1

-0.2

0.0

-0.3

-0.6

-0.9 -60

-40

-20

(b)

0

20

40

60

H (Oe) 300

250

150

χ

-1

(O e )

200

100

50

0

(c)

0

50

100

150

200

250

300

H ⊥ (Oe) Fig. 1. (a) Representation of the applied fields and the magnetization vector in plane of the sample; (b) experimental determination of v1 and DH ; and (c) the dependence of v1 versus the applied H? field for a 160 ML Fe film.

M. Kak et al. / Surface Science 566–568 (2004) 278–284

different directions in the substrate plane specified by the angle a. Actually, for a given a, precise data on the MðH Þ relationship are only collected in the region near M ¼ 0 as shown in Fig. 1b and two quantities are calculated by the data acquisition program namely the transversely biased initial inoH verse susceptibility v1 ðaÞ ¼ om ðml ¼ 0Þ and the l field offset DH ðaÞ ¼ H (ml ¼ 0), where ml ¼ MMs and Ms is the magnetization at saturation. Note that we concentrate on the data around ml ¼ 0 rather than H ¼ 0. This is the specific feature of the present method that distinguishes it from standard TBIS [6] or transversely biased initial susceptibility measurements, where the initial susceptibility om ðH ¼ 0Þ is actually determined. As shown beoH low, our approach has the specific advantage to probe simultaneously the second and first derivative of the anisotropy energy function Ea exactly at a þ p=2. TBIS instead probes only the second derivative of Ea and at an angle that deviates generally from a þ p=2 by an unknown quantity unless the first derivative vanishes, i.e., along easy or hard axes. Note that the latter are generally not known a priori and our method permits to determine them with a high degree of accuracy. Within a single domain model (Stoner Wohlfarth) and magnetization in film plane, the energy per unit volume can be written as   p Et ¼ Ea a þ þ u  Ms H? cos u  Ms H sin u 2 ð3Þ where a þ p=2 þ u is the angle between [1 )1 0] and magnetization direction (see Fig. 1a). Ea corresponds to the in-plane anisotropy energy and the second and third terms to the Zeeman energies due to the applied H and H? magnetic fields. Minimizing the total energy in Eq. (3) with respect to u yields for small uðM ffi 0Þ   1 o2 Eða þ p=2Þ M H ¼ H? þ Ms oa2 Ms 1 oEða þ p=2Þ ð4Þ þ Ms oa Actually, applying the second derivative crite2 rion: oouE2t P 0, we obtain minimum solutions around M ¼ 0 if H? is large enough so that

H? þ

281

1 oEða þ p=2Þ P0 Ms oa

Thus we obtain 1 o2 Eða þ p=2Þ v1 ¼ H? þ Ms oa2

ð5Þ

1 oEða þ p=2Þ ð6Þ Ms oa i.e. measurement of v1 ðaÞ and DH ðaÞ provides two independent determinations of Ea ðaÞ. Note that the field offset DH ðaÞ measures actually the torque exerted by the sample on the magnetization vector. This is why we propose to coin our method TBIIST for transversely biased initial inverse susceptibility and torque measurements. Pure linear relationship between the longitudinal Kerr rotation or ellipticity and the longitudinal magnetization component is generally not observed in Kerr measurements. Thus, linear and quadratic terms (mixing of transverse and longitudinal magnetization components) of the longitudinal Kerr response have been separated using a method based on in-plane magnetic field rotation similar to the one described in Ref. [7]. Taking into account the second-order magneto-optic effect, the longitudinal Kerr signal can be described by the equation

DH ¼

s ¼ a0 ml þ 2b0 ml mt þ c0 ðm2l  m2t Þ

ð7Þ

where ml and mt are the longitudinal and transversal components of the magnetization, a0 describes the linear Kerr effect and b0 and c0 describe the contributions due to the quadratic effect. This method enables the determination of a0 , b0 and c0 coefficients and allows the extraction of ml from s data by a simple iteration method since b0 , c0  a0 . In this way, we have carried out measurements of v1 and DH as a function of in-plane polar angle a in the whole 0–360 range. Finally, the different symmetry contributions to the magnetic anisotropy have been extracted by a Fourier analysis of v1 ðaÞ and DH ðaÞ.

4. Results and discussion Structural information concerning the growth of Fe can be quickly obtained by IMEED [8].

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Fig. 2a shows an IMEED pattern measured on 160 ML Fe deposited at RT onto the FeSi2 template layer. The pattern is taken for the electron beam at normal incidence with respect to the surface, and at a primary energy Ep ¼ 900 eV. A well contrasted pattern is observed, which clearly shows a threefold symmetry. This immediately indicates that a well-ordered film grows on FeSi2 , which adopts a cubic or nearly cubic structure. In order to get more specific-site structural information about the structure of Fe film, we have used XPD [9]. Fig. 2b shows the intensity angular dependence of Si2p and Fe2p3=2 core levels recorded along the substrate [1 )2 1]Si azimuth for the clean Si(1 1 1) substrate and the 160 ML Fe layer, respectively. For the clean Si substrate, the Si2p profile exhibits structures characteristic of a well-ordered diamond structure. The three major

Fig. 2. Structural characterization: (a) IMEED pattern for 160 ML Fe/Si(1 1 1) and (b) intensity angular dependence of Si2p (d) and Fe2p3=2 (s) core levels recorded along the substrate [1 )2 1]Si azimuth for the clean Si(1 1 1) substrate and the 160 ML Fe layer, respectively.

peaks identified at polar angle around 0, 35 and 70 correspond to emission along the [1 1 1], [0 1 1] and [1 1 )1] atomic rows, respectively. After deposition 160 ML of Fe, major features are now visible at around 0, 30 and 54. The relevant intensity maxima correspond to the [1 1 1], [3 1 1] and [1 0 0] atomic rows of a bcc phase. The corresponding azimuth is [)1 2 )1]Fe . Thus, it is immediately apparent from these results that Fe grows in an essentially bcc structure on Si(1 1 1) with B-type orientation, i.e., the film is rotated by 180 around the surface normal. Let us now consider the magnetic properties. Fig. 1c shows the experimental curve of v1 versus the applied H? field for a 160 ML Fe film on Si(1 1 1) recorded for a ¼ 90. As can be seen, v1 increases linearly with H? , and this behaviour is in agreement with the coherent rotation process of the simple Stoner–Wohlfarth model presented above. These results indicate that by applying perpendicular field H? of the order of 30 Oe or more, guarantees a true single domain behaviour of the sample. Fig. 3a shows the initial inverse susceptibility v1 ðaÞ and field offset DH ðaÞ versus in-plane polar angle a measured with a transverse bias field H? of 30 Oe. It can be seen that both v1 and DH exhibit prominent oscillations congruent with the structural sixfold symmetry, which reflects the magnetocrystalline anisotropy expected for the cubic structure. It is interesting to note that the two signal are in quadrature of phase, as expected in our model, since the initial inverse susceptibility is expected to vary as the derivative of the shift field. Here, the maxima of the v1 curve correspond to the in-plane equivalent Æ1 )1 0æ directions of the Fe layer, which are the magnetically easy directions. The minima of the v1 curve correspond to the in-plane Æ1 )2 1æ directions, which are the magnetically hard directions. This behaviour indicates that the sixth-order cubic anisotropy constant K2 is positive. As mentioned previously, the different orders of the anisotropy energy with respect to a can be directly derived from both v1 ðþp=2Þ and DH ða þ p=2Þ by using a Fourier transform. The parameters extracted from the Fourier analysis are summarized in Table 1. Excellent quantitative agreement is found between the anisotropies extracted from the two sets of

M. Kak et al. / Surface Science 566–568 (2004) 278–284

283 -10

H -1

35

30

-12

-13

-1

25

-14 20

H ( + 9 0 ˚ ) (O e )

( + 9 0 ˚ ) (O e )

-11

-15 15 0

60

(a)

120

180

240

POLAR ANGLE =120˚

-60

360

(deg.)

=60˚

-30

(b)

300

0

30

60 -60

-30

0

30

60

M AGNETIC FIELD (Oe)

M AGNETIC FIELD (Oe)

Fig. 3. (a) Initial inverse susceptibility v1 ða þ p=2Þ (s) and field offset DHða þ p=2Þ (d) versus in-plane polar angle a measured with a transverse bias field H? of 30 Oe and (b) hysteresis loops measured on the 160 ML Fe film with H applied along along a ¼ 125 and a ¼ 60.

Table 1 Anisotropy fields and directions corresponding to the ith contribution to the anisotropy energy extracted from the Fourier analysis from both v1 ðaÞ and DH ðaÞ ith-order

i¼2 i¼4 i¼6

v1

DH

Ki (Oe) Ms

Angle a (deg.)

Ki (Oe) Ms

Angle a (deg.)

1.55 0.20 0.36

)50.12 12.69 )59.77

1.57 0.19 0.35

)41.05 15.31 0

data which confirms the validity of the TBIIST method. The anisotropy is a superposition of an in-plane sixfold and an in-plane uniaxial contribution, i.e., magnetocrystalline term with magnetic easy axes along the equivalent Æ1 )1 0æ directions, and a uniaxial term with an easy axis not related to

a specific crystallographic direction of the film. are 0.7 The corresponding anisotropy fields 2K Ms and 3 Oe, respectively. Assuming the RT bulk saturation magnetization value for Fe (Ms ¼ 1708 emu/cm3 ), we obtain a value of the cubic anisotropy constant K2 ¼ 3  104 erg/cm3 which is comparable with those previously reported data for bulk bcc Fe [5]. This result indicates that this is consistent with a sixth cubic contribution. Yet, let us point out here that the measured constant should be interpreted as an effective constant that includes a contribution from fourth-order cubic term of similar magnitude due to the fact that at the finite applied field H? used in the present experiment the magnetization vector does not stay exactly in the (1 1 1) plane [10]. The origin of the weak twofold anisotropy is not totally understood

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at present, but it is not correlated to the geometry of the deposition system. The surface morphology in particular the presence of oriented steps is the most probable source for the uniaxial anisotropy. It is remarkable to note that it is possible to extract a very small sixth-order contribution to the cubic anisotropy of Fe which corresponds to anisotropy fields as low as 0.70 Oe. On the other hand, it is also possible to separate very small in-plane anisotropy contributions of different symmetry. Finally, Fig. 3b presents hysteresis loops with coercive fields Hc around 6–7 Oe measured on the Fe film with sweep field H applied along two sixfold anisotropy easy axes. For H applied along a ¼ 125 the hysteresis loop exhibits a nearly squared-shaped loop. When the field is applied along a ¼ 60, the longitudinal magnetization switches in two clear jumps. This means that the existence of the small uniaxial anisotropy superimposed over the sixfold crystalline anisotropy, leads to the inequivalency of the six cubic easy axes.

5. Conclusions The symmetry, the magnitude and the direction of in-plane magnetic anisotropies present in thin Fe(1 1 1) films grown on Si(1 1 1) at normal incidence have been quantitatively described by using a new method based on transverse biased initial

inverse susceptibility and torque measurements. By taking into account the contribution of the second-order magneto-optic effect, a small sixfold in-plane magnetic anisotropy has been readily detected and measured. Finally, this method is well adapted to separate any mixture of in-plane fourfold, sixfold as well as uniaxial anisotropy contributions present in thin magnetic layers.

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