Direct extraction of exchange splittings from magnetic X-ray dichroism in photoelectron spectroscopy

surface s c i e n c e ELSEVIER

Surface Science 395 (1998) L227 L235

Surface Science Letters

Direct extraction of exchange splittings from magnetic X-ray dichroism in photoelectron spectroscopy J.G. Tobin a,,, K.W. Goodman a, F.O. Schumann b, R.F. Willis b J.B. Kortright c, J.D. Denlinger c, E. Rotenberg c, A. Warwick c, N.V. Smith c Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550, USA b Pennsylvania State University, Department of Physics, University Park, PA 16802, USA c Lawrenee Berkeley National Laboratoo'. Berkeley. CA 94720. USA Received 3 June 1997; accepted for publication 14 October 1997

Abstract

It will be demonstrated that core-level exchange splitting can be extracted directly from normalized difference curves in magnetic X-ray circular dichroism (MXCD) in angle-resolved photoelectron spectroscopy (PES). Although high resolution is a requirement for the method, this determination can be performed without resorting to time-consuming and difficult spectral simulations. For well-defined cases, it will be shown empirically that this method may also work for the analysis of magnetic X-ray linear dichroism (MXLD). Applying this approach, it will be possible to use MXCD and MXLD in PES for direct surface magnetometry with full elemental specificity. © 1998 Elsevier Science B.V. Keywords: Alloys; Angle resolved photoemission; Iron; Magnetic films; Magnetic phenomena; Magnetic surfaces; Nickel; Photoelectron spectroscopy; Semi-empirical models and model calculations; Soft X-ray photoelectron spectroscopy

I. Introduction

Direct surface magnetometry with full elemental specificity remains an important goal of synchrotron-radiation based investigations of ferromagnetic ultrathin films and surfaces. One avenue of approaching these problems is magnetic X-ray circular dichroism (MXCD) in X-ray absorption [ 1-17]. An appealing aspect of MXCD-ABS is the potential for application of the "sum rules" [1012], which directly relate the spin and orbital components to variations in the relative integrated peak intensities in spectra from localized and well-

* Corresponding author. Fax: (+ 1) 510 4237040. 0039-6028/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PH S0039-6028 ( 9 7 ) 0 0 8 3 1 - 5

defined systems. Unfortunately, significant limitations apply to this method [8,9, 17], including the impact of delocalization in the final state, multielectronic effects, and the presence of a surface magnetic dipole term. A potential alternative method would be to use magnetic X-ray dichroism, both circular [18-26] and linear [25 35], which has been observed in angle-resolved photoelectron spectroscopy (PES). In core-level photoemission, the transition is from an occupied core level into unoccupied states well above the strongly polarized states near the Fermi level. Thus the dichroism is generally not due to changes in integrated intensities, but is rather caused by variations of peak positions and peak shapes. These are induced by changing contributions from multiplet peaks inside

J, G. Tobin et al. / Sur[itce Science 395 (1998) L227 L235

tlae envelope of the overall core peak. It has been demonstrated previously that spectral simulations [24] (in this case a fully relativistic spin-specific multiple-scattering modeling) can be used to determine excl-~ange splittings from the magnetic X-ray dichroism observed in Fe 3p photoemission. Here, it will be ,~;hown that by extending a model similar to that proposed by Venus and co-workers [22,27 30,36 38], it is possible to directly extract exchange splittings from the MXCD difference spectra c,f Fe 3p at normal emission without recourse to sophisticated spectral simulation calculations. Furthermore, a comparison of our highresolution MXCD and MXLD spectra of Fe 3p in FeNi/Cu(001) and an analysis of MXLD theory will demonstrate empirically that this approach should also work for normal-emission MXLD photoemission, at least in the high-symmetry cases described below.

2. Experimental

The photoemission measurements [34,35] were made at the Spectromicroscopy Facility (Beamline 7) of the Advanced Light Source at the Lawrence Berkeley Laboratory [39]. Extraordinarily bright, linearly polarized X-rays were generated by the U 5.0 undulator, and wavelength selection was achieved using the spherical grating monochromator, with a resolving power of over 8000. Circularly polarized beams at hv=95 eV were obtained via the use of a novel soft X-ray phase retarder [40,41]. The soft X-ray "quarter wave plate" was composed of a multilayer used in transmission mode, operated near a Bragg angle. The photoelectrons were detected using the angle-resolving multi-channel (5.4 in radius) Perkin-Elmer hemispherical deflector system. Sample alignment (including pseudomorphic growth), cleanliness and composition were measured using the hemispherical deflector and a separate MgK~ (photon energy=1254eV) source, thus freeing up the beamline for other uses during our periods of sample preparation. The actual MXCD and MXLD measurements used highly polarized (94% linear, 83% circular) synchrotron radiation, and were performed with a total instrumental energy

resolution of less than 100 meV and an angular resolution of 2" or less. The angle of incidence of the X-rays was 30 '~ relative to the surface plane. The electrons were collected along the Cu(001) surface normal (i.e. "normal emission"). For MXCD, the magnetic alloy was magnetized in the plane of the surface but perpendicularly to the plane containing the emission direction (surface normal n) and the Poynting vector (q) and electric polarization vector (E) of the X-rays. Thus, the "transverse-chiral" condition necessary for MXLD was achieved: reversing the magnetic field causes two mirror-image configurations which are equivalent but totally non-superimposable. For MXCD, the magnetic alloy was again magnetized in the surface plane, but M was now rotated into the plane containing the surface normal and the X-ray Poynting vector. The samples were magnetized along the [100] direction of Cu(001). Thus, the plane containing the X-ray Poynting vector and the surface normal (and linear polarization in MXLD) was always a member of the { 100} family of planes. Fe and Ni were simultaneously coevaporated onto Cu(001) at room temperature, giving rise to a pseudomorphic alloy overlayer with a high degree of crystalline order and presumably complete chemical disorder [34,35]. The samples were magnetized using a 3 kOe pulse generated via a Cu coil. All measurements were made at room temperature. Photoelectron spectroscopy was performed using remanently magnetized samples in the absence of applied fields. Magnetization reversal was achieved by rotating the sample about the normal by 180c'.

3. Discussion and results

One very important, elementally specific measure of the state of magnetization is the exchange splitting in a core level. Moreover, exchange splittings should scale directly with the magnetic moment [42]. In Fe 3p, the exchange splitting AEEx is the energy separation of the Fe ~=3/2, m~= +3/2) and [/'=3/2, mj= - 3 / 2 ) states (Fig. 1). However, a determination of this separation is complicated by the presence of state-mixing, lifetime and instrumental broadenings, peak tailing

J. G. Tobin et al.

SurIktce Science 395 (1998) L227 L235

mj

| = a / 2 ~

mI

-1/2

--

Spin up m= = 1/2

)-----r---I

------

! t

ASso

~EEx

->

--1

-1/2

m

J=1/2~ Spin orbit only

0

1/2

~ S p t norbit

/

i

Spi.n down m= =-1/2

Exchange onq

Exchange with spin orbit perturbation

exchange perturbation

8

~

/

AEEx

q

KINETIC ENERGY BINOING ENERGY Fig. I. Top panel: the effect of spin orbit and exchange splitting on a p core-level. Two perturbative approaches are shown: large spin orbit and small exchange splitting (left) and small spin-orbit and large exchange splitting (right). Middle and bottom panels: an example of spectral overlap in the Fe 3p multiplet, using skewed peaks with elongated tails (lower kinetic energy) and linear peak shapes on the leading edge of each peak as an approximation of the Lorentzian lineshape. It is the overlap of the 3/2 and - 3/2 peaks which is proportional to the exchange splitting. Mid panel: dichroic peaks 1 and 4 only. Bottom panel: the sum of peaks ] and 4. a s y m m e t r i e s a n d the o t h e r m e m b e r s o f the m u l t i p l e t besides mj = _ 3/2. W i t h i n the f r a m e w o r k o f a s i n g l e - e l e c t r o n picture, w h i c h has b e e n d e m o n -

strated to w o r k very well for Fe [23 25], it will be s h o w n t h a t the e x c h a n g e splitting c a n be e x t r a c t e d directly f r o m n o r m a l i z e d difference curves in the

J. G Tobin et al. / Surjace Science 395 (1998) L227-L235

disrupt the approximations used here. Finally, in calculating the dichroic intensity contribution from each component of the multiplet, the degree of state mixing must be included. Generalized states, which apply for any ratio of exchange (AEEx) to spin-orbit (AEso) splitting, are shown in Table 1. It is the separation of the pure spin states (mj= +_3/2) which do not mix, which is the AEEx parameter which we seek to determine. Below, we will present the following. (i) The close relationship between the theoretical prediction of the MXCD and MXLD dichroisms for normal emission from a system with in-plane magnetization and four-fold symmetry will be established. (ii) A simple model utilizing the overlap of component dichroic peaks will be shown to be applicable for the extraction of the exchange splitting from the MXCD data. (iii) An empirical comparison of MXCD and MXLD results from a four-fold symmetric system will demonstrate the equivalence of MXCD and MXLD for such cases. First, it is necessary to derive equations for the linear and circular dichroisms for the Fe 3p states, This can be done by constructing a coordinate system with the electron emitted along the surface

magnetic X-ray dichroism of normal-emission photoelectron spectroscopy of in-plane magnetized surfaces or ultrathin films. Interestingly, while spin-orbit splitting and lifetime broadening can be viewed as causing difficulties such as state-mixing and peak broadening, respectively, it will be shown that they are also essential to the solution of the problem. The magnetic X-ray dichroic effects would not be seen without the spin-orbit splitting, and the triangular front edges which are associated with lifetime-broadened (Lorentzian) peaks are the means of dealing quantitatively with peak overlap, which in turn is proportional to the exchange splitting. The problem of peak tailing asymmetries (i.e. the elongated tail structures associated with multi-electronic effects [23-30]) is rendered moot: by concentrating on the overlap of following peaks with the leading (lowest binding energy, highest kinetic energy) peak (the mj= 3/2 peak), only the well-defined, high kinetic-energy side of each multiplet component is allowed to contribute. This is illustrated in Fig. 1. In order to obtain a nicely defined linear overlap function, it is essential that the spectra are collected under high-resolution conditions. Otherwise, a Gaussian lineshape would Table 1 Fe 3p multiplet states Component

Peak intensity

Peak position

II= I,mt,s = 1/2,s) I/) = ll½) 12) = 710½)+~/I --c~211-½)

(Mlzlk>(klYlM> iR

0

i(1 -cd)R

(c~2- 2)AEso+ ( 1--:z2)AEEx

13> = V I -,:~21- 1½) +~t0-½)

-(1

(~2- ])AEso+:tZAEEx

14) = l - l - ½ ) 15>= - V I - cd 10½)+all -½>

-iR

AEEx

+icdR

(5- cz2)AEso÷ ~2AEEx

16)~

-i~2R

(5--~2)AEso + ( ' - o~2)AEEx

~l 1 ½ > + ~ 1 0 - ½ >

c~2)R

R is a weighted sum of radial matrix elements and is real and photon-energy dependent. "~/~
- - ( A E 4 / ' ~ ' 4 ) 2 q-

l

1 "

(3)

In the limit of triangular peak shapes, the intensity at the peak 1 maximum and across the flat top of the total spectrum would be given by

AE4"]

AEEx)

(4)

i (c)

1

I

56

55

i

I

I

i

I

54

53

52

51

50

419

Binding Energy (eV)

Again, assuming a triangular line shape, the width of the flat top (hF) would be 2 X - A E E x . This illustrates an important point: lifetime broadening is necessary for the utilization of this approach. If Y~drops below ½AEEx, no overlap would occur in the triangular model. Complications or deviations from the desired result of Eq. (4) can arise due to intensity from components 2, 3, 5 and 6. Consider the limit ~2=2/3, AEEx< ( 2 / 3 ) R ) and increases a s (x2 increases. As peak 6 approaches peak 4, the higher binding-energy side of plateau ac becomes diminished. The lower

Fig. 3. C o m p a r i s o n of the computational results of T a m u r a et al. [25] with the results of Table 1. The calculation from

Ref. [25] is lbr a four-fold symmetric Fe(001 ) structure, with normal emission and the magnetization in a C4v mirror plane and the plane of the surface. Here the photon energy was 90 eV and 0 - 16. AEEx~ AEso~ 1 eg. Curve b is the differencecurve from Tamura's calculation, and the overlap model of this work is shown in curve c. An asymmetric triangular function was used. On the leading edges, X= 1/2 eV in order to be consistent with Tamura et al. The following tail is four times wider, in part to offset the internal peak splinings in peaks 2, 3, 5 and 6 used by Tamura et al.

binding-energy side, nearer c, should remain the maximum and reflect the dependence on ALEx shown in Eq.(4). Nevertheless, once peak 6 reaches peak 4, the plateau is sheared off and the dependence is lost. Thus we see that within the triangular model, our operating limits are ALEx -< AEso (2/3 _<~2 < 5 / 6 ) and AEEx < 2X. Another approach is to calculate the error within the framework of the assumption that all AEis are less than or equal to 1.5X. To be exact, one can sum the Lorentzian contribution from each component at the maximum of the first peak

J. G. Tobin et al. .; SloJhce Science 39~ (1998) L ~ 7 L~3~

( 1 or m~ = 3/2 ). I+R

1

(1

- + (AEa/X4) 2 + 1 [(AEz/X2) 2 + 1

~2 )

~(2 +

(AE3,/~3) 2 + l

(AE5./-~5) 2 + 1

~2

(AE6/_Y'6)2+]I }"

(5)

Here, AEi is the energy separation of peaks 2 6 from the leading peak 1 (AEEx=AE4). ~'i is the lifetime broadening. We will assume that all Xs are the same within a given manifold. The intensities reflect the magnitudes from Table 1. The sum of the terms in the first bracket is the quantity which we seek. The following bracket contains error contributions from peaks 2, 3, 5 and 6. If we use the energy positions from Table 1 and a linear approximation for the Lorentzian lineshape (good to 20% for AE/X<< 1.5), we obtain the following result: I + R ( ~ A;Ex ) [1 +(2~2 -- 1 )2].

(6)

The linear relationship between AE~,x and intensity, due to the overlap of the 3/2 and - 3 / 2 peaks, can be seen here. The (2~ 2 - 1 ) term is the "error" or non-linear perturbation from the components 2, 3, 5 and 6. For ~2=2/3, the pure j states case, (2,~2 - 1 )2 = 11%. For ~2 = 5/6 (AEEx ~ AEso, appropriate for Fe) (2~ 2 - 1)2=44%. Over narrow ranges, where ~2 varies slowly, the linear relationship would hold quite well. Furthermore, using an iterative approach, one can always correct for varying ~2. In fact, for the range 2/3 _<~2_< 5/6, the following is a very good approximation (within 3%) for Eq. (6) [43]:

1

Eqs. (6) and (7) represent the interplay of the exchange splitting (AEEx), the lifetime broadening (S) and the spin--orbit splitting (through ~2: see

Table 1). One needs to operate in the high-resolution limit, so that the Lorentzian lineshape is retained on the high kinetic-energy side of the peaks. As the AEs increase beyond 1.5£, the linear approximation will start to break down, but typically X ~ I eV, and thus one should be able to measure AEEx out to about 1.5 eV, a fairly large value. In the limit of large spin-orbit splitting, terms 5 and 6 will tend to cancel in any case. (In this limit, one can drop the last two terms from Eq. (5) and show that the error will reverse in sign, this time with a maximum magnitude of 22%.) Beyond the triangular lineshape zeros, remnants from the Lorentzian peak shapes can exist. Nevertheless, these are very small, with a maximum possible error of 20%. Also, it is reasonable to expect that X should be fairly constant for a given element and core level. Thus, within reasonable constraints, it is possible to extract directly the exchange splitting from the normalized MXCD difference curves. The relationship is approximately linear, with corrections due to varying 3( 2 possible. Relative changes in AEL~x will be simple to follow, so long as other effects such as photoelectron diffraction can be kept constant or minimized. Finally, it would be beneficial if the results of this model could be extended to include magnetic X-ray linear dichroism. Our arguments here are primarily empirical. (i) The experimental results for MXCD and M X L D of 6 ML (Feso% Ni5o%) on Cu(001) are essentially identical. (ii) We can obtain near-quantitative agreement with previous calculations [25] for Fe(001 ). In the spectra shown in Fig. 2, the similarities are in both the original spectra and in the difference spectra. The calculated asymmetry ( A S Y M = ( I + - I )/(1 + + I )) is 11.4% in both cases. Qualitatively, the difference spectra resemble the lowest panel of Fig. l, albeit with a narrowed or rounded plateau. In Fe, we are probably at the limit of the model: AEEx ~ AEso ~ 1 eV and the lifetime broadening is probably 1 eV or less. Nevertheless, the empirical comparison of the M X C D and M X L D results remains valid. Another test of this model would be to compare its predictions for the MXCD dichroism to the calculations of Tamura et al. [25] for the M X L D dichroism in Fe(001). This is

J. G. Tobin et al. / Sur[ctce Science 395 (1998) L227 L235

shown in Fig. 3. The calculated spectra from Ref. [25] are shown in panel a of Fig. 3, while the difference curves are shown in panels b and c. Here, we have used Z = I / 2 e V in order to be consistent with Tamura et al. Note the fairly good agreement for the lead positive peak. The disagreement at binding energies near 51 eV stems from the failure of the triangular lineshapes to mimic the Lorentzians far from the peak centroids. Tamura et al. [25] utilized peak splitting within peaks 2, 3, 5 and 6. To match this, we have used a skewed triangular lineshape with the tail four times wider than the front edge. Although the agreement is not that good for binding energies of 53 eV and above, this is irrelevant because our model and analysis method is predicated on using the front or lead dichroic difference peak. Also, it may be that the peak splittings in peaks 2, 3, 5 and 6 may mask the underestimation of lifetime broadening as 1/2 eV. A larger lifetime broadening, nearer to 1 eV, may in fact be more reasonable.

4. Summary We have demonstrated that core-level exchange splittings can be extracted directly from the difference spectra of photoemission magnetic X-ray dichroism data (both circular and linear cases). The combination of normal photoelectron emission with in-plane magnetization within a C4v mirror plane sets up a near-ideal case for our demonstration. Since exchange splittings correlate with magnetic moments, this technique thus provides for elementally specific surface magnetometry.

Acknowledgements This work was performed under the auspices of the US Department of Energy by the Lawrence Livermore National Laboratory under Contract No. W-7405-ENG-48. The Spectromicroscopy Facility and the Advanced Light Source were constructed and are operated with support from the US Department of Energy. We also wish to thank Karen Sitzberger for her clerical support.

This work was based in part on work supported at the Pennsylvania State University by the National Science Foundation under Grant Number DMR-95-21196.

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[35] J.G. Tobin, K.W. Goodman, G.J. Mankey, R.F. Willis, J.D. Denlinger, E. Rotenberg, A. Warwick, J. Vac. Sci. Technol. B 14 (1996) 3171. [36] D. Venus, Phys. Rev. B 49 (1994) 8821. [37] D. Venus, Phys. Rev. B 48 (1993) 6144. [38] D. Venus, L. Baumgarten, C.M. Schneider, C. Boeglin, J. Kirschner, J. Phys. Condens. Matter 5 (1993) 1239. [39] J.D. Denlinger, E. Rotenberg, T. Warwick, G. Visser, J. Nordgren, J.H. Guo, P. Skytt, S.D. Kevan, K.S. McCutcheon, D. Shuh, J. Bucher, N. Edelstein, J.G. Tobin. B.P. Tonner, Rev. Sci. lnstrum. 66 (1995) 1342. [40] J.B. Kortright, Appl. Phys. Lett. 60 (1992) 2963. [41] J.B. Kortright, J.H. Underwood, Nucl. lnstrum. Methods A 291 (1990) 272. [42] F.J. Himpsel, Phys. Rev. Lett. 67 ( 1991 ) 2363. [43] Eq. (7) is predicated upon the expression in Table 1 for ~, relating AEEx and AEso. Eqs. (1)-(6) are essentially independent of this expression. Even the error estimates given for the (2~ 2 - 1 )2 term, etc., are fairly independent of this expression for ~, since it is known that ~2 = 2/3 in the small AE~x limit, ~2=1 in the small AEso limit and ~:=5/6 for AE~x- AEso in the middle of the range.