Element-specific magnetometry with photoelectron dichroism: FeCo and FeNi

Surface Science 478 (2001) 211±228

www.elsevier.nl/locate/susc

Element-speci®c magnetometry with photoelectron dichroism: FeCo and FeNi J.G. Tobin *, F.O. Schumann 1 Lawrence Livermore National Laboratory, Department of Chemistry and Material Science, P.O. Box 808, L357 Livermore, CA 94551, USA Received 14 December 2000; accepted for publication 12 February 2001

Abstract We have investigated fcc Fex Co1 x and Fex Ni1 x alloys grown on Cu(1 0 0) with X-ray magnetic linear dichroism angular distributions in photoemission (XMLDAD). To achieve this end, a simple model has been developed, which accurately describes the experimental spectra and supports our application of XMLDAD as a form of elementally speci®c magnetometry. This model combines the simplicity and physical insight of a single-electron picture with multielectronic e€ects, via the utilization of ``Doniach±Sunjic'' lineshapes for each component within the Fe 3p multiplet. We will also brie¯y discuss the observed ®ne structure in the emission of the Fe 3p core level, which was previously predicted but lacking experimental con®rmation. We have found di€erent behavior for the dichroism of the Fe 3p level at high and low Fe concentrations upon alloying with Co, compared to alloying with Ni. These contrasting observations can be explained in part by the di€erent behavior of the atomic volume. Both systems show also a change of the in-plane easy axis upon increasing the Fe content. For small concentrations the easy axis is along the f0 1 1g direction, which changes to the f0 0 1g direction at a higher Fe content. Interestingly the actual transition occurs in both instances at roughly the same electron/atom count. Published by Elsevier Science B.V. Keywords: Semi-empirical models and model calculations; Magnetic measurements; Synchrotron radiation photoelectron spectroscopy; Epitaxy; Cobalt; Iron; Nickel; Single crystal surfaces

1. Introduction Core-level spectroscopies are by de®nition element-speci®c and it is now well established that magnetic contrast can be achieved in absorption and photoemission experiments [1±3]. This ap-

* Corresponding author. Tel.: +1-925-422-7247; fax: +1-925423-7040. E-mail address: [email protected] (J.G. Tobin). 1 Present address: Frei Universitaet-Berlin, SFB 290, Arnimallee 14, 14195 Berlin, Germany.

0039-6028/01/$ - see front matter Published by Elsevier Science B.V. PII: S 0 0 3 9 - 6 0 2 8 ( 0 1 ) 0 0 9 5 5 - 4

proach presents a unique opportunity to study element-speci®c magnetic properties and has been employed in several studies so far [4±10]. Ultimately, it is important to move from the qualitative (observation of an e€ect) to the quantitative (element-speci®c magnetometry). (For an empirical calibration and comparison to more ``classical'' magnetometry, please see Ref. [7].) To this end, a simpli®ed theoretical model of the photoemission dichroism will be introduced, tested and utilized. In fact, the model will be tested against the best Fe 3p data available to date. For the ®rst time, incontrovertible experimental evidence of the

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internal component structure within the Fe 3p photoemission peak will be presented. The materials focus of this work is Fe-based alloys, which can be prepared in a fcc phase throughout the whole concentration regime [11, 12]. This is in contrast to the behavior of the bulk, where a bcc phase is adopted for Fe-rich alloys. In this work we will use X-ray magnetic linear dichroism angular distributions in angle-resolved photoelectron spectroscopy (XMLDAD), which has been shown by Roth et al. to yield strong effects when studying 3p levels [3]. We will show that the magnitude of the Fe 3p dichroism is very different for Fex Ni1 x and Fex Co1 x alloys at high Fe concentrations. In the case of Fex Ni1 x , we observed a strong reduction of the dichroism near 65% Fe related to a magnetic moment±atomic volume instability [6,7]. However, Fex Co1 x alloys maintain a large dichroism indicative of a highspin state, which seems to contradict the predictions by James et al. [13]. Nevertheless, the experiments of Zharnikov et al. reveal a di€erent behavior with respect to the atomic volume when compared to Fex Ni1 x [11]. There is also a di€erent behavior for alloys with a small Fe content. In contrast to Fex Co1 x alloys, Fex Ni1 x shows a decrease upon reducing the Fe concentration. The latter point has also been observed by Schellenberg et al. who used the 2p level for magnetic contrast [8,9]. Finally, another result we present is the change of the easy axis for both alloy systems from a f0 1 1g to a f0 0 1g orientation upon increasing the Fe content. Interestingly this transition occurs in both instances at almost the same electron count/atom.

has been demonstrated that fcc Fex Co1 x alloys can be stabilized via growth on a Cu(1 0 0) surface [11]. The same approach has been shown to work for fcc Fex Ni1 x alloys [12,16±18]. All ®lms investigated have an in-plane magnetization. Magnetization reversal was achieved by applying ®eld pulses with a Helmholtz coil without the need of any sample movement. It is possible to vary the sample azimuth inside the coil, allowing a quick change of the chirality of the experiment. Corelevel photoemission spectra were recorded in normal emission with an photon incidence of 35° and 7° angular resolution. The energy resolution was in general better than 0.15 eV for spin-integrated work and the photon energy of the p-polarized light was in general 190 eV unless otherwise stated. The magnetic ®eld was applied along the easy axis, which we determined to be either along the f0 0 1g or f0 1 1g direction depending on the concentration. For spin-resolved work on the Fe 3p corelevel we employed an energy resolution of 0.35 eV and used a photon energy of 190 eV. It has been demonstrated that dichroism in photoemission can be observed when studying 3p

2. Experimental The experiments were performed using a novel electron spectrometer with spin analysis capability at the Spectromicroscopy Facility [14] of the Advanced Light Source, Berkeley [15]. Using standard procedures, a clean and well-ordered Cu(1 0 0) surface was obtained and alloys were grown by simultaneous evaporation with two e-beam sources at 300 K. Unless speci®ed otherwise, typical alloy ®lm thicknesses were about 7 ML. It

Fig. 1. Diagram of dichroism experiment, with photoelectron emission along the surface normal ( z). Here the magnetization is in the surface plane but perpendicular to the yz plane containing the electron emission direction and the Poynting vector and linear polarization vector (E) of the X-rays. a is the grazing angle of incidence between the incoming photon and the surface plane. The magnetization (M) de®nes the sign of the ‡x axis. The ‡y axis is determined by the right hand rule from ‡z and ‡x. Magnetization reversal does not a€ect z but rather ¯ips ‡x and thus ‡y.

J.G. Tobin, F.O. Schumann / Surface Science 478 (2001) 211±228

levels [3]. Necessary for observing the lineshape di€erences upon magnetization reversal is a chiral geometry (Fig. 1). The electron emission and propagation direction of the light determine a plane, in which the polarization vector of the synchrotron light lies. If the magnetization is perpendicular to this plane, maximum contrast upon magnetization reversal is observed [19±21]. A schematic representation of this case is shown in Fig. 1. Unless stated otherwise, this will be the geometry of the experiment. If the magnetization has an angle b from the perpendicular direction, the dichroism signal varies with cos …b† according to an atomic model, which has been experimentally observed previously [19±21]. This makes it possible to determine the easy axis. In the following we will compare measurements with either the f0 0 1g or f0 1 1g axis perpendicular to the scattering plane. Here the assumption is made that the in-plane easy axis is along a high symmetry direction of the fourfold (1 0 0) surface: it will be shown this assumption is essentially correct. Finally, we would like to de®ne the dichroism ratio as the ratio of the dichroism measurements along the f0 0 1g and f0 1 1g directions. Following the atomic model we would expect a value of 0.71 if the f0 1 1g is the easy axis, whereas a value of 1.41 should be observed if f0 0 1g is the easy axis. This

213

will be discussed in more detail in the sections below. 3. Theory and application of simpli®ed model The goal of our simpli®ed theoretical model is modest: to capture the essential physics in an easily tractable form and then apply it to the problem of element-speci®c magnetometry. The model is based upon more sophisticated approaches developed earlier by Tamura et al. [22] and van der Laan [23]. In our spectral simulations, there will be several key energies: the exchange splitting (Hs), spin orbit splitting (f), lifetime broadening, Gaussian broadening and Doniach±Sunjic (DS) asymmetric broadening [24]. However, the underlying e€ect will be the overlap of the two pure spin states …‰3=2; 3=2i† with opposite signs in the dichroism. To demonstrate the validity of our approach, our simulations will be compared to experimental data and the e€ect of varying Hs tested. An example of our experimental data in shown in Fig. 2. The model is quite simple. The initial p states are quantized along M, with M de®ning x. The ®nal state, which is plane-wave-like, is quantized along z. Transitions are electrical dipole …E
r†

Fig. 2. Displayed are core-level photoemission spectra for a Fe81 Co19 sample. Upper curve is the di€erence curve derived from the two spectra obtained with magnetization ÔupÕ (solid line) and ÔdownÕ (dashed line). Despite the high Fe concentration of 81% a clear signal from the Co 3p can be obtained.

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J.G. Tobin, F.O. Schumann / Surface Science 478 (2001) 211±228

and the dichroism arises from the coordinate axis reversal which occurs when M (and x) are reversed and z remains constant (Fig. 1). E is the linear polarization of the X-rays and r is the position vector in real space. a is the grazing angle of incidence of the X-rays. (Here we assume b ˆ 0.) Let us begin with the initial states quantized along M. The Hamiltonian contains two parts: a spin±orbit splitting and an exchange splitting. While this means that j is no longer a ``good'' quantum number (j ˆ 3=2 and j ˆ 1=2 states mix), mj is still valid. Following Tamura et al. [22] and van der Laan [23], we can de®ne six orthogonal states and then solve for their composition and energy positions by diagonalizing the matrix. The results of this are shown in Fig. 3 and Table 1. The tan 2h and tan 2/ equations are the relations which ensure the orthogonality of the ``mixed'' states, i.e., 2, 3, 5 and 6. States 1 and 4 are the pure spin states. Here we have adopted the identical nomenclature as van der Laan (b), using Hs for the exchange splitting or spin ®eld (the separation of states 1 and 4) and f as the spin orbit splitting parameter. Fig. 3 reproduces the previous result of van der Laan [23] and Ebert [25]. Fig. 3 and Table 1 also corrects the errors of an earlier, incorrect parameterization [26,27]. Thus, we have analytically solved for the properly orthogonalized states of the Hamiltonian, shown in Table 1. It should be

noted that care must be taken with inverse tan functions. The ®nal state needs to be an outgoing wave with momentum parallel to z. The natural candidate is a plane wave along z, which can be expressed as a summation of spherical harmonics with m ˆ 0, i.e. Yl;mˆ0 . In our case, using an electric dipole excitation and an initial p state, only the s (l ˆ 0, m ˆ 0) and d3z2 r2 (l ˆ 2, m ˆ 0) are accessible. However, as will be seen below, the plane wave ®nal state is too simple and rigid. An illustration of this is that neither the s state nor the d3z2 r2 state is sensitive to a coordinate reversal, the essence of the XMLDAD experiment. So, we will use a slightly more sophisticated ®nal state, with the plane wave state as a guide. Wf ˆ Ad Wd ‡ As Ws

…1†

Here Ad and As are complex and not necessarily equal. The axis of quantization for the ®nal state remains z. Because the quantization axes of the initial and ®nal states are not equal, the d transitions were calculated in two steps: (1) using electric dipole selection rules …Dml ˆ 1; Dms ˆ 0†, the initial p states were connected to d…x† states quantized along x; and (2) the projections of the d…x† states are then made onto the d3z2 r2 state (quantized along z) using angular momentum rotation rules. For the s state, spherical symmetry allows any quantization axis and rotation. To calculate the average matrix element (M) and dichroic di€erence (D) for each component, one can simply work through the two cases shown associated with magnetization reversal. Here M ˆ …1=2†…M‡ ‡ M † and D ˆ …M‡ M †, or M‡ ˆ M ‡ …1=2†D and M ˆ M …1=2†D. Of course, asymmetry ˆ A ˆ …M‡ M †=…M‡ ‡ M † ˆ D= 2M. 2

Fig. 3. Calculation of the energies of the six orthogonalized component states within the p manifold, as a function of the exchange splitting (Hs) versus the spin±orbit splitting parameter (f).

2

M ˆ 2E2 RM f sin2 ajhiŠy‰fij ‡ cos2 ajhiŠz‰fij g

…2†

D ˆ 4E2 RD sin a cosa RefhiŠy‰fihfŠz‰iig

…3†

Here RM and RD are proportionality factors and E is the magnitude of the linear polarization. Eq. (3) is consistent with derivations following the approach of Venus [28±30] and with Eq. (19) of van der Laan [23]. This includes the sin 2a dependence:

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215

Table 1 Orthogonalized initial states within the p manifold ‰l ˆ 1, ml , s ˆ 1=2, ms i ˆ ‰ml , ms i

Sp. Spin Cont.

Relative intensity D

M

‰1i ˆ ‰1; 1=2i ‰2i ˆ cosh‰0; 1=2i ‡ sin h‰1; 1=2i ‰3i ˆ cos/‰ 1; 1=2i ‡ sin/‰0; 1=2i ‰4i ˆ ‰ 1; 1=2i ‰5i ˆ sin /‰ 1; 1=2i ‡ cos/‰0; 1=2i ‰6i ˆ sin h‰0; 1=2i ‡ cosh‰1; 1=2i

" # " # " #

1 sin2 h cos2 / 1 sin2 / cos2 h

1 sin2 h cos2 / 1 sin2 / cos2 h

H ˆ Hspinorbit ‡ Hexchange Hex‰ms i ˆ ms Hs‰ms i, ms ˆ 1=2 Hso‰mj i ˆ …f=2†‰mj i for mj ˆ 3=2 and 0 6 sin h; sin /; cosh; cos/ 6 1

f‰mj i for mj ˆ 1=2

0 6 h 6 35:3° …2=3†1=2 6 cosh 6 1 …1=3†1=2 6 cos/ 6 1 0 6 / 6 54:8° p tan2h ˆ …2 2†=‰…2Hs=f† ‡ 1Š p tan2/ ˆ …2 2†=‰…2Hs=f† 1Š h1ŠH‰1i ˆ Hs=2 ‡ f=2 p h2ŠH‰2i ˆ Hsf cos2 h 1=2g ‡ …f=2†f2 2 cosh sinh sin2 hg p h3ŠH‰3i ˆ Hsf cos2 / 1=2g ‡ …f=2†f2 2 cos/ sin / cos2 /g h4ŠH‰4i ˆ Hs=2 ‡ f=2 p h5ŠH‰5i ˆ Hsf cos2 / 1=2g …f=2†f2 2 cos/ sin / ‡ sin2 /g p 2 h6ŠH‰6i ˆ Hsf cos h 1=2g …f=2†f2 2 cosh sinh ‡ cos2 hg Binding energy shift ˆ

hiŠH‰ii

the broad maximum is centered at 45°. 2 In our case, a ˆ 35°, with only a small (6%) reduction in D. Also seen in Table 1 are the predictions of the relative intensity of the dichroism di€erence (D) and the relative intensity of the average spectrum (M), across the six component initial states. (Sp. Spin Cont. is the spectroscopic spin contribution, which will be used later.) It should be noted that both sets of the y matrix elements, hY0;0 Šy‰ii and hY2;0 Šy‰ii, are pure reals with the same relative magnitude and signs, with the magnitude pattern following the square root of the dependences in

2 Eq. (3) also corrects a small error in the XMLDAD equations of Ref. [23]. Here, the sin dependence had been improperly imbedded in the equation for the XMLDAD dichroism as a factor of 1=2. (a ˆ 30° in that case and sin 30° ˆ 1=2.) However, substitution of 0.866 for cos 30° into the equations for XMLDAD and XMCDAD corrects the error and demonstrates the strong similarity of XMLDAD and XMCDAD for the a ˆ 30° case.

Table 1. Similarly, the z matrix element sets, hY0;0 Šz‰ii and hY2;0 Šz‰ii, are pure imaginary and follow the same magnitude pattern (again, the square root of the pattern in Table 1), but di€er between groups by a negative sign. These characteristics are also consistent with the work of van der Laan [23]. Pure s …hiŠy‰Y0;0 ihY0;0 Šz‰ii† or pure d …hiŠy‰Y2;0 ihY2;0 Šz‰ii† terms will vanish, since each will be a pure imaginary and Eq. (3) requires a real part to be non-zero. Similarly, if a plane wave ®nal state were used, even cross teams such as those containing …hiŠy‰Y0;0 ihY2;0 Šz‰ii† would also vanish, since the coecients which one would derive from the spherical Bessel functions of the plane wave would not provide sucient non-canceling complexity, i.e., the cross terms would also vanish. It is only with the addition of complex coecients such as those shown in Eq. (1) that the cross terms would be non-zero. (Even with the complex coef®cients of Eq. (1), the square terms would still be 2 2 zero, since jAd j and jAs j would each be real.) Finally, it is the cross terms which drive the energy

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Fig. 4. Comparison of the circular (XMCDAD) and linear (XMLDAD) photoemission dichroism for 6 ML of Fe50% Ni50% =Cu(0 0 1), with x along [1 0 0], 45° from the easy axis along [1 1 0]. The photon energy was 95 eV. Backgrounds have been subtracted from the experimental curves. Note that both peak asymmetries are 11.4%, where asymmetry is A ˆ …I ‡ I †=…I ‡ ‡ I †. See Refs. [26,27] for details.

dependence predicted in Fig. 4 of Ref. [23], as can be surmised from an examination of the energy dependencies of the total [31] and d-wave only [32] 3p cross-section calculations. Obviously, nonvanishing and roughly equivalent magnitudes of s and d wave contributions will tend to maximize the magnitude of D in Eq. (3). Let us turn now to a consideration of Eqs. (2) and (3) and the relative magnitude for each component state, shown in Table 1. The relative magnitudes in Table 1 are correct within each group, i.e., within the dichroism (D) set or within the M set. However, scaling the dichroism D to M in some sort of absolute way is problematic for this simple model of XMLDAD. This is because we are not using a true plane wave state but instead the plane-wave-like state shown in Eq. (1). To get around this, the D:M scaling from a XMCDAD (circular) analysis has been used. Empirically, this is justi®ed based upon the apparent identicality of XMCDAD (circular) and XMLDAD (linear) under the present con®guration, as demonstrated in Fig. 4 [26,27,33]. Here, the XMLDAD and XMCDAD of the Fe 3p from Fe1=2 Ni1=2 =Cu(0 0 1) at a photon energy of 95 eV can be seen to be essentially identical. Using a plane wave ®nal state, assuming that the Y2;0 component is dominant,

and neglecting terms of 0.3% or less, we have found a scaling factor of 16/19 between the dichroism D and M for an XMCDAD arrangement analogous to the XMLDAD experiment [26,27]. The choice of Y2;0 ®nal state is supported by a consideration of the cross-section calculations in Fig. 4 of Ref. [23] as well as those in Refs. [31,32]. It appears that for kinetic energies above 20 eV (photon energies above 80 eV for the Fe 3p), the d component of the ®nal state should dominate. At this point, the positions and intensities of each component peak, both within D and M, have been speci®ed as a function of Hs and f. However, looking at the experimental data in Figs. 2 and 4, it is clear that a histogrammatic approach will fail. Consider the histogram shown at the top of Fig. 5, for Hs ˆ 0:95 eV, f ˆ 0:7 eV, which is approximately the case for the Fe 3p states [22,23]. The experimental data, which is subject to various forms of broadenings, only vaguely resembles the histogram. Hence, in order to reconstruct the experimental data from the histogrammatic positions and intensities, the various broadenings must be properly taken into account. The foundation for inclusion of broadening effects is the DS lineshape (Fig. 5), a convolution of lifetime broadening and peak asymmetry caused by multielectronic Fermi surface excitations in connection with the primary core-level excitation [24]. The lifetime broadening is principally seen on the low binding energy (high kinetic energy) side of the peak. On the high binding energy (low kinetic energy side), the peak is broadened by both the lifetime broadening and an exponential tailing function. This type of asymmetric tailing can be seen in the ``raw'' data shown in Fig. 2: clearly, a type of step-function or tailing occurs under the Fe 3p peak. At lower photon energies (and kinetic energies), the rising low energy background can mask this e€ect, but at high photon (kinetic) energies, a clear step-like e€ect is consistently observable. In our case, each individual component will have its own lifetime broadening and exponential tailing. It is also expected that lifetime broadening should increase with binding energy [22,23]. There are other sources of broadening as well. One type which must be dealt with is instrumental broadening. Generally, the strategy here is to

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217

Fig. 5. (a) Histogrammatic diagram of the component state dichroic intensities (D) versus energy position, with Hs ˆ 0:95 eV and f ˆ 0:7 eV. Binding energy shift ˆ hiŠH‰ii. (b) DS lineshape, for 2c ˆ 0:5 eV and a series of DS asymmetries, following Ref. [24]. (c) Exponential asymmetric tail of the DS lineshape, for c ˆ 0 eV and DS asymmetry ˆ 0:2 eV, again following Ref. [24]. In the ®gure, a0 is the DS asymmetry parameter.

perform the experiments with high enough resolution that the instrumental broadening is negligible. To that end, our spin-integrated experiments are typically done with a total energy band pass of 0.1±0.2 eV. Because of the large lifetime broadening of core levels, to a ®rst approximation, it is fairly justi®able to simply neglect the Gaussian

broadening from the instrumental band pass, using solely the DS lineshape. However, for exact comparisons, a convolution of the DS lineshape with a Gaussian is utilized. Another cause of effective broadening is crystal ®eld (CF) splitting [34±36]. While in some respects, this is more dicult to handle, in our case the analysis is saved

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Table 2 E€ect of CF splitting Double groups point symmetry (no magnetization) Using [j; mj i nomenclature with j ˆ 3=2 and 1=2 No CF

D3=2 ‰3=2; 3=2i ‰3=2; 1=2i

D1=2 ‰1=2; 1=2i

Octahedral CF

C8 ‰3=2; 3=2i ‰3=2; 1=2i

C6 ‰1=2; 1=2i

Lower symmetry CF

Ca ‰3=2; 3=2i

Cb ‰3=2; 1=2i

Cc ‰1=2; 1=2i

‰j ˆ 3=2; mj ˆ 3=2i ˆ ‰ml ˆ 1; ms ˆ 1=2i and ‰j ˆ 3=2; mj ˆ 3=2i ˆ ‰ml ˆ 1; ms ˆ 1=2i: Therefore the exchange splitting (Hs) is una€ected.

by the high symmetry of the pure spin states, as can be seen from examination of Table 2. Using double point groups [37±39], under the absence of CF splitting and exchange splitting, the p states split into the j ˆ 3=2 and j ˆ 1=2 doublet. Under an octahedral CF, appropriate for a bulk fcc lattice, the representations remain the same, with the major e€ect being a CF perturbation of the apparent or e€ective spin±orbit splitting. If a lower CF symmetry is applied, e.g., a surface or distorted fcc structure, then the representations split, with the ‰3=2; 3=2i, ‰3=2; 1=2i, and ‰3=2; 1=2i separated. Interestingly, the ‰3=2; 3=2i are the pure spin states separated only by the exchange splitting, Hs. Thus while the CF splitting may shift the pair of states …‰3=2; 3=2i† together, it will not perturb the crucial exchange splitting of states 1 and 4. (We will return to this discussion below.) However, the CF perturbation can have the e€ect of mixing the other states. That is because states ‰2i and ‰3i are ‰3=2; 1=2i and states ‰5i and ‰6i are ‰1=2; 1=2i only under the condition that Hs ˆ 0. When Hs is on the scale of f and the manifold is split into six components, the e€ect of the residual CF perturbation should be to mix and shift the non-pure spin states, i.e., ‰2i with ‰6i and ‰3i with ‰5i. The e€ect of these site speci®c (®rst, second, third layers) shifts will be to broaden the peaks. In fact, one could argue that over many sites, the CF would tend to average out di€erences in D, except those due to Hs. Operationally, the

CF e€ect will be dealt with by the utilization of a lattice dependent f and additional broadening of the peaks of the component states, particularly ‰2i, ‰3i, ‰5i, and ‰6i, via the DS lineshape parameters. An example of our simulation (and comparison to experimental data) is shown in Fig. 6 and Table 3. Our goal was to use physically justi®able parameters. Here, the Hs and f were chosen to be consistent with previous analyses [22,23]. Both the DS asymmetry (a0i ) and lifetime broadening (ci ) are increased with binding energy, i.e., from i ˆ 1±6. The concept of increasing lifetime broadening with binding energy is well accepted [22,23,40] and by implication would also seem to apply to the DS asymmetric tailing parameter as well. Empirically, we have found that without an increase in a0i with binding energy, a second oscillation in D near states 5 and 6 persists. While this type of double oscillation is observed in systems with large spin orbit splittings, e.g., the Fe 2pÕs [8,9], it is not observed in the Fe 3pÕs [22,23,26,27]. It also seems that using larger lifetime broadenings alone is insucient to completely eliminate the second oscillation [23]. Final re®nement of these parameters was made via visual inspection: the multiplicity and inter-relation of the parameters militated against an automated ®t. As might be expected based upon more sophisticated analyses [22,23,40] which include e€ects such as photoelectron diffraction, the raw spectral pairs exhibit a photon energy dependence, as can be seen in Fig. 7. (Here,

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219

lope of the dichroism appears to be independent of the photon energy, providing us with a measure of dichroism which is independent of e€ects which distort the ``raw'' spectral lineshapes. The robust nature of the dichroism lineshape and the good agreement between our experimental data and the simulation using physically reasonable parameters encouraged us to investigate a key question: ``Does the dichroism depend linearly upon the core-level exchange splitting?'' In Fig. 8, the result of a numerical analysis using f ˆ 0:73 eV and varying the value of Hs is shown. It is important that the magnitude of the predicted dichroism in Fig. 8 agrees well with the experimental values in Fig. 7, both being about 15% at Hs of about 1 eV and a photon energy of 190 eV, respectively. (Di€erences in lifetime and DS broadening within each ``j'' manifold were collapsed as Hs went to zero. That is, of course, physically reasonable.) Within the 1% error bars typical of XMLDAD analyses of asymmetry (or height of the dichroism), the relationship is not only linear but proportional over the range of Hs ˆ 0 to Hs  f. This linear and proportional relationship will even hold over a wider range, albeit with larger error bars. When Hs reaches a value near 2f (or Eso), the curve levels o€ and there is no dependence upon Hs, as is expected from our model and earlier work [23]. So it would seem that even for the Fe 3p, with Hs  1 eV and f  0:7 eV, the linear and proportional relationship will hold approximately. For Ni and Co, with larger fÕs and smaller HsÕs, the accuracy should improve correspondingly. Previously, it had been suggested that the energy separation of the positive and negative lobes of the dichroism lineshape could be used as a measure of the exchange splitting [20,21]. Using this numerical approach and

Fig. 6. Comparison of the simulation results and the Fe 3p experimental XMLDAD data from Fe55 Co35 =Cu(0 0 1). Top panel: magnetization up, raw spectra; lower panel: magnetization down, raw spectra.

rather than arti®cially manipulate the parameters to match the variation with photon energy, a representative pair of spectra have been chosen, i.e. Fig. 6.) Consistent with earlier measurements [20,21], the magnitude of the dichroism also varies with photon energy. Most importantly, the enve-

Table 3 Fe

f

Eso

Hs

r

a01

a02

a03

a04

a05

a06

c1

c2

c3

c4

c5

c6

0.7

1.05

0.95

0.15

0.2

0.242

0.261

0.291

0.325

0.325

0.26

0.45

0.5

0.47

1.2

1.2

f is the spin orbit splitting parameter. Eso is the spin orbit splitting, or actual separation of the 3=2 and 1=2 peaks, if the exchange splitting is zero …Eso ˆ 1:5f†. Hs is the exchange splitting in the p manifold, i.e. the separation of the 3=2, 3=2 and 3=2, 3=2 components. r is the magnitude of the width (sigma) of the Gaussian convolution. ci is the lifetime width (gamma) of the Lorentzian part of the DS lineshape of the ith component. All of the above are in eV. a0i is the asymmetry parameter of the DS lineshape of the ith component.

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Fig. 7. (a) The photon energy dependence of the Fe 3p experimental XMLDAD spectra, for 8 ML of Fe77% Co23% =Cu(0 0 1), is shown here. The top three panels show raw spectra at three photon energies: 145, 155 and 190 eV. The two curves in each panel are the two spectra for magnetization up and magnetization down, respectively, following Figs. 2 and 6. The bottom three panels show the corresponding spectral di€erences at each of the three photon energies. (b) Plot of the photon energy dependence of the Fe 3p dichroism magnitude for FeCo/Cu(0 0 1).

varying Hs, we found that while the apparent splitting and Hs values sometimes tracked each other, the values were not proportional, required an o€set for agreement and diverged badly at low Hs values. The underlying principle which drives the proportionality for 0 6 Hs 6 f is shown in Fig. 9. Here we use a simpli®ed triangular lineshape to illustrate the overlap of the plus and minus dichroic intensities of the pure spin states, ‰1i and ‰4i. As described above, states ‰1i and ‰4i are separated by only the exchange splitting, Hs. Because we are working in a high instrumental resolution mode, the DS lineshape is appropriate. The front, or lower binding energy side of each peak is ap-

proximately linear, owing to the Lorentzian character of the low binding energy side of the DS lineshape. The overlap of the triangular peaks gives rise to a plateau (ac) whose height is proportional to Hs. Intriguingly, even this very naive picture gives us a qualitative agreement in lineshape with the experimentally derived quantities, with a narrower, larger de¯ection at low binding energy and a broadened, smaller de¯ection of reversed sign at high binding energies. What is crucial here is the interplay of three energies: The exchange splitting (Hs), the spin±orbit splitting parameter (f) and the lifetime broadening (c). A non-zero f is necessary for XMLDAD. If Hs gets too big, there is no dependence of the XMLDAD

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Fig. 8. Variation of the dichroic asymmetry as a function of the exchange splitting (Ð). Error bars indicate uncertainty of experiment (around 1%). Dashed line is a linear ®t of the solid line with exchange ranging from 0 to 0.8 eV. Using the model and simulated spectra similar to those in Fig. 6, the dichroic peak asymmetry is calculated as a function of Hs. Here, f ˆ 0:73 eV and parameters similar to those shown in Table 3 were used, with the Lorentzian and DS broadenings collapsing to identical values within each j (3=2 and 1=2) manifold at Hs ˆ 0. Within the 1% error bars, the curve is a approximately linear out to Hs ˆ 0:8 eV and has an intercept at zero.

on Hs. While the large lifetime broadening of core levels is what makes it so dicult to isolate the components, it is the same Lorentzian character

221

which gives rise to the linear overlap of peaks associated with ‰1i and ‰4i. There remains the issue of the non-pure spin states …‰2i; ‰3i; ‰5i and ‰6i† and their impact upon the dichroism measurements. It appears that the combination of lifetime and DS asymmetry broadenings which increase with binding energies, plus the possibility of CF induced broadening from multiple sites, has the tendency to ``smear out'' the contributions from states ‰2i, ‰3i, ‰5i and ‰6i. A strong empirical argument which supports this is that the second oscillation (associated with states ‰5i and ‰6i) is not observed experimentally in the 3p spectra. Finally, to con®rm the spin assignment of the features in the spin-integrated spectra and dichroisms, spin-resolved spectroscopy has also been performed. Shown in Fig. 10 is a series of spinresolved Fe 3p photoelectron spectra taken under dichroic conditions, albeit with poorer resolution. These results agree with a previous study done at lower photon energy [3]. Also, shown is the spinresolved result of our model. (Interestingly, owing to the strong selection rules for this con®guration, each component state generates a pure spin contribution, as shown under Spectroscopic Spin Contribution (Sp. Spin Cont.) in Table 1.) Although the experimental features remain broadened relative to our modelÕs predictions, the

Fig. 9. An example of spectral overlap in the Fe 3p multiplet, using skewed peaks with elongated tails (lower kinetic energy) and linear shapes on the leading edge of each peak as an approximation of DS lineshape. It is the overlap of the peaks 1 and 4 which is proportional to the exchange splitting. Top: dichroic peaks 1 and 4 only. Bottom: the sum of peaks 1 and 4.

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may have been underestimated in the analysis of the spin-integrated spectra. Another possibility is more extensive electron correlation e€ects [41]. 4. Fine structure in the emission of the Fe 3p core level

Fig. 10. Spin-resolved XMLD Fe 3p spectra for FeCo/ Cu(0 0 1), both experimental and simulated using our model. The upper (lower) panel shows magnetization up (down). The dashed (solid) curves are for ``spin up'' (``spin down''). The photon energy was 190 eV and the resolution was 0.35 eV in the experiment. Both the experimental and simulated spin-resolved spectra are shown with a Shirley background removed. The simulated spectra include convolution with a 0.35 eV Gaussian, to mimic the instrumental resolution. The instrumental Sherman function used was 0.15.

correct relationships are reconstructed by the modelÕs simulated spectra. In fact, summing the spin-resolved spectra for a given magnetization allows us to recapture the dichroism result, albeit with poorer resolution (not shown). Moreover, the experimentally observed broadenings may re¯ect the CF-driven e€ect described above, which

One of the predictions of the earlier, more sophisticated models was that more spectral structure should be observable in the Fe 3p dichroic spectra [22,42]. It is known experimentally that the Fe 3p lineshapes are virtual identical upon excitation with either circular or linear polarized light [26,27,33]. Therefore we should expect the observation of such a ``double-peak'' structure in XMLDAD. Up to now this was not experimentally observed, thus calling into question the theoretical analysis. Here, we report for the ®rst time conclusive observation of this spectral structure. In Figs. 6 and 7, we can see the ®ne structure on the Fe 3p level. The key observation is a clearly resolved double-peak structure in the spectrum with the magnetization ÔupÕ. For the other magnetization direction the peak at higher binding energy appears only as a shoulder. The doublepeak structure could be observed throughout the whole concentration range and over a wide photon energy range: this will be discussed in detail in a forthcoming article [43]. It is tempting to identify these two peaks with the pure spin states, since we obtain a result which is qualitatively reminiscent of Fig. 23 in Ref. [42]. The logical extrapolation of this assignment is to then assume that the separation of the ``double peaks'' is the core-level exchange splitting. But this is incorrect and misleading. Strictly speaking the double-peak energy separation is not the true exchange splitting, since overlapping contributions of the component peaks will a€ect not only the energy position of the double peaks, but also the amount of the observed splitting. This will also be true of the spectral differences generated by subtracting one member of a spectral pair from the other. (This issue was discussed in Section 3.) Splitting determinations are further complicated by the photon energy dependence of these spectral structures. As an example of this, changing the photon energy moves the

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spectral weight between these two peaks as demonstrated for a Fe77 Co23 sample in Fig. 7. (Concurrently we observe an increase in the dichroism signal upon decreasing the photon energy.) Finally, it is known that the calculations tend to overestimate the splitting signi®cantly. Consequently in a comparison with experimental work one often scales the exchange splitting [22,40].

5. Case studies: FeNi and FeCo 5.1. Concentration dependence of the dichroism in Fex Co1 x alloys In Fig. 2 we show the spectra for di€erent magnetization directions together with the di€erence spectrum for an Fe81 Co19 =Cu(1 0 0) ®lm. We can see a strong e€ect for the Fe 3p level, but there is also a clear di€erence visible for the Co 3p level. We also observe a double-peak structure in the emission from the Fe 3p level in the case of magnetization up, as discussed in Section 4. Before we proceed we would like to explain how we derived the actual values for the dichroism. In a ®rst step we determined the di€erence between the positive and negative peaks in the di€erence spectrum in

Fig. 11. Co 3p peak for magnetization up of a Co/Cu(1 0 0) sample. The arrows ÔaÕ and ÔbÕ measure the peak height with respect to the background.

223

the spectral range of the 3p level in question. It is clear that one has to take into the account the fact the individual peak height will change as a function of the concentration. One way of dealing with this is to measure the peak height of the core-level of interest for magnetization ÔupÕ and ÔdownÕ as shown in Fig. 11. As an example the spectrum of a Co/Cu(1 0 0) ®lm with magnetization ÔupÕ is displayed. The length of arrow ÔaÕ in this ®gure is the quantity of interest, which is equivalent to the removal of a constant background. The same has to be done for the other magnetization direction. Therefore we can write Asymmetry ˆ ‰I…up† I…down†Š =‰I…up† ‡ I…down†Š

…4†

Our procedure is essentially identical to the one reported by Schellenberg et al. [8,9]. Following this procedure we can plot now the dichroism of the Fe and Co 3p level as a function of the concentration, as is done in Fig. 12. As mentioned in the experimental section, we measured the dichroism along the f0 0 1g and f0 1 1g direction. Therefore we plotted the larger of these values in Fig. 12. We notice that upon approaching 30±40% Fe both the Fe and Co show a decrease in the dichroism when compared with smaller Fe concentrations. At around 50% Fe the dichroism values have increased again and stay fairly constant for Fe. However the Co dichroism shows a clear linear increase. A closer inspection however reveals that this result is an e€ect of the tailing of the Fe 3p peak into the Co 3p region. In Fig. 11 we have shown the Co 3p peak for magnetization ÔupÕ. As mentioned above, the arrow ÔaÕ re¯ects the peak height. If there is no interference we would expect that the ratio of arrow ÔaÕ and ÔbÕ is a constant upon changing the concentration, which has a value of 1.4 in the case of Co/Cu(1 0 0). However evaluating this number for all alloys, in particular on the Fe-rich side, reveals that this number is signi®cantly reduced. This is obviously caused by the tailing of the Fe 3p peak, which becomes more important for Fe-rich alloys. This has the e€ect that one e€ectively underestimates the Co 3p peak height, which in turn leads to an overestimate of the ÔtrueÕ Co 3p dichroism when Eq. (4) is used.

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Fig. 13. Concentration dependence of the dichroism ratio ‰0 0 1Š=‰0 1 1Š for the Co 3p (m) and Fe 3p (d) peak, see text. The horizontal lines indicate the ÔperfectÕ behavior 0.707 and 1.414 if ‰0 0 1Š is hard or easy axis. For both elements we notice that a change in the easy axis at around 50% Fe.

Fig. 12. Concentration dependence of the 3p dichroism of Fe (d) and Co (4). Plotted is the larger of the values measured along f0 1 1g and f0 0 1g. (a) Uncorrected values, (b) as in (a), but with a corrected Co peak height, see text.

Therefore it is justi®ed to correct the values for the Co 3p dichroism, which we have done the following way. Rather than using the length of arrow ÔaÕ

we use the length of arrow ÔbÕ, which we measure at a binding energy 5 eV larger than the Co 3p peak. Assuming that the ÔcorrectÕ ratio between them is 1.4 we calculate a new value for ÔaÕ. This should now give a better measure of the actual peak height. We are then able to replot Fig. 12a, which we show in Fig. 12b. We notice that now the Co 3p dichroism essentially follows the behavior of the Fe 3p dichroism, remaining constant at Fe concentrations greater than 50%. In both cases the dichroism displays a minimum at around 40% Fe content. It is now interesting to plot the ratio of the dichroism measured along the f0 0 1g and f0 1 1g directions, which is shown Fig. 13. We observe for both elements a ratio near 0.71 for Fe concentrations up to 50%. For higher concentrations we observe values near 1.41. Using the arguments in the experimental section, we can state that we observe a change of the easy axis from f0 1 1g at Fe concentrations up to 50% followed by an f0 0 1g orientation at higher Fe content. A f0 1 1g orientation of the Co-rich alloy does not come as a surprise since it is now well established that this is the easy axis for ultrathin Co/Cu(1 0 0) ®lms [44± 46]. However to our knowledge there do not exist data on anisotropy constants of bulk fcc Fex Co1 x alloys.

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5.2. Concentration dependence of the dichroism in Fex Ni1 x alloys and comparison with Fex Co1 x alloys In a previous publication we have discussed the motivation of investigating fcc Fex Ni1 x alloy ®lms [6,7]. The focus was to investigate the region near the invar concentration (65%) and we found a correlation of the atomic volume and the Fe 3p dichroism. These measurements were done along the f0 0 1g axis, which according to bulk values should be the easy axis in the concentration regime of interest. However as it turns out this is not true for ultrathin alloy ®lms and will be discussed in the following. Nevertheless the conclusion drawn from the previous paper remain valid. In Fig. 14 we show the result of the new measurements near the invar concentration. Here the larger of the dichroism values measured along f0 0 1g and f0 1 1g is displayed. In agreement with the previous publication we ®nd a sharp decrease of the magnitude of the dichroism signal at around 65% Fe. However compared to the previous results, the data show signi®cantly less scatter and due to the ®ner mesh near the critical concentration, the very sharp transition becomes more apparent. This we can attribute to the better experimental setup where magnetization reversal does not require any sample movement. Coming back to the easy axis change of the two alloy systems it is now appealing to translate the concentration into an average number of elec-

Fig. 14. Fe (d) and Ni (h) dichroism versus Fe concentration in FeNi/Cu(0 0 1).

225

trons. With Fe having 26, Ni 28 electrons, and Co 27 electrons per atom, one derives 26:7  0:1 electrons and 26:5  0:1 electrons per atom for the Fe63 Ni37 and Fe49 Co51 alloys (the transition points), respectively. The error in the electron count re¯ects the uncertainty of the exact concentration, where the easy axis changes. These two values are very close to each other and this would suggest the importance of band-®lling for the anisotropy energy. James et al. emphasize band ®lling in their work, but do not discuss magnetic anisotropy [13]. The very small value of the dichroism above 70% Fe content for Fex Ni1 x alloys is strikingly di€erent from the observation of fcc Fex Co1 x alloys as discussed in Section 5.1. A possible reduction of Tc appears not to be the reason for this if one recalls the results of SMOKE experiments [12,18]. However in the light of the limited cooling (Tmin 250 K) available at the time, one might ®nd the experimental evidence not convincing enough. Therefore we have investigated the behavior of the dichroism at lower temperatures. Speci®cally we did not observe an increase of dichroism at 100 K compared to the value measured at 300 K. This conclusively proves that the small dichroism is not related to a Curie temperature e€ect. Another piece of evidence con®rming the different magnetic properties of Fe-rich Fex Co1 x and Fex Ni1 x alloys comes from spin-resolved valence band spectroscopy. Exciting with hm ˆ 190 eV and collecting electrons which are emitted along the surface normal, one essentially probes the C-point. In Fig. 15 we show the spin-resolved spectra for Fe72 Co28 and Fe75 Ni25 alloy ®lms. It becomes clear that the behavior is again very di€erent. In the case of Fe72 Co28 , well-separated spin-up and spin-down distribution curves are visible. This is in contrast with the observation for Fe75 Ni25 alloy: here the distribution curves look almost identical. Finally, in an extension to our previous work on FeNi [6,7], we have included points on the Ni-rich side. In Fig. 14, we plot the complete concentration dependence of the Fe 3p dichroism. A striking di€erence between the results for Fex Ni1 x and the results for Fex Co1 x alloys (shown in Fig. 12) is the strong decrease at low Fe concentration, i.e. x below 30%. An equivalent observation has been

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5.3. Atomic volume and magnetic e€ects

Fig. 15. Spin-resolved valence band spectra showing the presence (a) and absence (b) magnetization. See text for details.

made by Schellenberg et al., who investigated the Fe 2p dichroism [8,9]. This diminishment of the Fe dichroism at low x is a bit of a surprise. The low concentrations are far away from the magnetic instability. Measurements of bulk or thick ®lms point to a large Fe moment [47,48]. It has also been possible to obtain agreement with SQUID measurements on ultrathin Fex Ni1 x =Cu(1 1 1) multilayers by Freeland et al. [49], without resorting to a diminished Fe dichroism at low Fe concentrations [7]. Further work will be necessary to explain the origin of this e€ect at low Fe concentrations.

The magnetic properties of fcc Fe/Cu(1 0 0) are now well documented and a complex behavior has been observed [50±60]. Speci®cally it has been shown that fcc Fe/Cu(1 0 0) is structurally very unstable. This translates into complex magnetic behavior. The complex behavior is caused by the near degeneracy of magnetic con®gurations at the lattice constant of Cu, which can also be described as a atomic volume±magnetic moment instability [61±64]. Recent experimental results of the properties of fcc Fe/Cu(1 0 0) have stressed the importance of the correlation between magnetic properties and the atomic volume [56±58,60]. The origin of these e€ects can be found in the form of the density of states (DOS) curve. In the paramagnetic case, the Fermi level is positioned in a valley between two maxima. Depending on the actual lattice constant the DOS will ful®ll the Stoner criterion and ferromagnetism is possible. More precisely, at a larger lattice constant the overlap of the 3d wave functions is reduced. This reduces the band width and therefore an increase of the DOS is to be expected. Naively, it seems that in the limit of pure fcc Fe/Cu(1 0 0), the magnetic properties of Fex Ni1 x and Fex Co1 x alloys should be identical and in both cases the structural instability should be observed. However the alloying of fcc Fe with Ni or Co stabilizes states with signi®cantly di€erent atomic volumes: Fex Ni1 x alloys with Fe contents above 80% have a small atomic volume [6,7]; Fex Co1 x =Cu(1 0 0) alloys have a larger atomic volume, as measured by Zharnikov et al. [11]. Consequently the magnetic properties of the pure Fe limit for each alloy are di€erent as described above. 6. Summary A simple yet e€ective quantitative model for XMLDAD has been developed and utilized. It establishes the proportional relationship between dichroism asymmetry and the core-level exchange splitting. Core-level exchange splitting is assumed to be directly dependent upon the valence state exchange splitting and the magnetic moment [65].

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Fine structure in the Fe 3p core-level spectra has been observed and analyzed. The concentration dependence of FeCo/Cu(0 0 1) magnetic ultrathin ®lms has been measured and compared to that of FeNi/Cu(0 0 1). The change of the easy axis from in these systems has been observed and correlated with electron number per atom [66]. Contrasts in the FeCo and FeNi behavior at high Fe concentrations has been attributed to volume di€erences due to stabilization by the alloy partner and the magnetic/volume instability of Fe/Cu(0 0 1).

Acknowledgements This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48. Experiments were carried out at the Spectromicroscopy Facility (Beamline 7.0) at the Advance Light Source, built and supported by the US Department of Energy. JGT wishes to thank G. van der Laan for pointing out the error in the earlier parametrization of the initial state.

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