Journal of Magnetism and Magnetic Materials 192 (1999) 297-304 Study of antiferromagnetic NiO using grazing incidence reflectivity and soft X-ray absorption Gerrit van der Laan* Magnetic Spectroscopy, Daresbury Laboratory, Warrington WA4 4AD, UK Received 27 March 1998; received in revised form 7 October 1998 Abstract High-resolution grazing incidence X-ray absorption and reflection spectra near the critical angle for total reflection provide a useful means to refine the analysis of multiplet and charge-transfer satellite structure at the absorption edges for core level excitation. An optical oscillator model can adequately explain the strong spectral changes observed in the region of the Ni 2p edge of NiO epitaxially grown on Mg(1 0 0). The results confirm that NiO is a charge-transfer-type insulator with parameters that relate to the effective superexchange interaction. 1999 Elsevier Science B.V. All rights reserved. PACS: 78.70.Dm; 75.50.Ee; 71.70.!d Keywords: Antiferromagnets; X-ray spectroscopy; Superexchange; Reflectivity; Electron yield 1. Introduction [4,5,47] the large on-site d-d Coulomb repulsion suppresses high-energy charge fluctuations, dL# The electronic structure of the late 3d transition dLPdL\#dL>, which describe the hopping of metal monoxides has been a controversial subject a d electron between two metal sites. It is important ever since the discovery that these oxides are insu- to note that this excitation involves an effective lators [1], which is in sharp contrast with one- parameter U for the repulsion energy, which is electron band structure theory [2,3] that predicts strongly reduced from its atomic value due to the them to be metallic. The insulating behaviour is influence of screening and covalence in the solid. thought to be caused by strong electron correlation For example, U is 6.7 eV in bulk NiO, while the effects, resulting in a breakdown of the one-electron atomic value would be 18 eV. Although the Mott- picture. According to the Mott-Hubbard model Hubbard model explains correctly the existence of a wide optical gap, it fails to give a quantitative account of the optical gap [6] and X-ray spectra * Tel.: #0-1925-603-448; fax: #0-1925-603-124; e-mail: [7] of 3d transition metal oxides, halides and chal- g.vanderlaan@dl.ac.uk. Invited Paper presented at the "International Workshop on cogenides. The optical gap in these materials is Soft X-ray Magneto-Optics", Institut fu¨r Angewandte Physik, determined by the charge-transfer energy, , which Heinrich-Heine-Universita¨t Du¨sseldorf, 13 November 1997. is the energy cost to transfer an electron from 0304-8853/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 5 4 1 - 1 298 G. van der Laan / Journal of Magnetism and Magnetic Materials 192 (1999) 297-304 a ligand to a metal ion, i.e. dLPdL>¸, where ¸ guished corresponding to the four possible [1,1,1] denotes a hole in the ligand band M [8]. M Although directions which can be further divided into three NiO was originally believed to be a Mott-Hubbard S domains corresponding to the three possible insulator, i.e. with a gap determined by U, Fujimori [1,1,2] directions with two different spin directions. et al. [9] showed by a cluster model calculation for The exchange biasing is attributed to the interfacial the valence band photoemission that this material exchange interaction between FM and AFM spins is actually a charge-transfer insulator. The combi- of the antiferromagnetic domains. AFM materials nation of photoemission and inverse photoemis- in contact with FM materials can give rise to hys- sion gives an experimental value for the band gap teresis loop shifts away from the zero-field axis. of 4.3 eV, [10,11] while density functional theory Originally, it was thought that the AFM spins predicts only a gap of 0.3 eV [12]. The electron order in a single domain with all interfacial AFM transport properties are rather well described by spins perfectly aligned in a single direction parallel impurity model calculations as a function of the to the FM spins, resulting in a net moment due to ligand p-band width, w, and the p-d hybridisation the uncompensated AFM spins at the interface. with hopping matrix element, t. The virtual charge However, measurements show that biasing fields excitations which couple the spins on the different are typically two orders of magnitude smaller than metal ions can be described by an Anderson super- expected. Recent theoretical work, supported by exchange model [13]. In terms of the ground state neutron diffraction, suggests domain formation re- parameters t, , and º, the effective superexchange sulting from a 90° coupling between the AFM and interaction J can be written as [14] FM moments [21]. 1 Core level spectroscopy studies using synchro- J+! 2t # tron radiation can provide important element-spe-  1º , (1) cific information about the electronic and magnetic where for simplicity multiplet effects have been ground state of composite materials. Magnetic X- neglected. Neutron scattering gives a value of J" ray dichroism (MXD) and X-ray resonant magnetic 19 meV for NiO, [15,16] which agrees very well with scattering have found wide application in the study the values of º"6.7 eV, "6.2 eV and t"0.5 eV of magnetic properties of ferro-, ferri- and antifer- obtained from the analysis of X-ray core level spec- romagnetic systems [22-25,48]. Sum rules allow troscopies with impurity model calculations [17,18]. the separation of the total magnetic moment into Thin film structures containing transition metal an orbital and spin contribution [26-28]. However, oxides have sought-after magnetic properties, such in X-ray absorption the true line shape can be as exchange biasing [19]. Considerable experi- strongly distorted depending on the specific detec- mental effort has been put into this phenomenon tion technique [29-31]. Saturation effects occur because of its technological significance in domain near the absorption edge if the mean escape depth stabilisation of magnetoresistive devices, such as of the detected particles, such as electrons in the spin valves [20]. The bulk magnetic structure of case of total electron yield or photons in the case of NiO below the Ne´el temperature of 520 K consists fluorescence detection, cannot be neglected with of ferromagnetically (FM) aligned spins in the respect to the X-ray attenuation length [32]. For (1 1 1) planes, which are antiferromagnetically strong absorption structures, such as the 3dP4f in (AFM) stacked with respect to each other. There rare earths, these effects can even show up at nor- are 24 different magnetic domains in total. Four mal incidence [29]. Sometimes, additional informa- principle, so-called ¹, domains can be distin- tion can be obtained about the underlying decay mechanism that causes the strong absorption. By analysing the total electron yield as a function of  The parameters U and in this paper are defined with respect to the lowest level of the configuration, whilst in Refs. incidence angle, van der Laan and Thole [30] ob- [17,18] they are defined to the average, E tained the La 3d autoionisation lifetime width and "E(F)#1.3 eV. Furthermore, the six neighbours in NiO result in an effective Vogel et al. [33,49] assessed the mean electron transfer integral of ¹"t(6. escape depth. G. van der Laan / Journal of Magnetism and Magnetic Materials 192 (1999) 297-304 299 In this paper, we will compare grazing incidence complex refractive index of the medium is n"( , reflectivity and total electron yield measurements where the permittivity tensor "D/E and per- using linearly polarised light. In Refs. [34,35] it was meability tensor "B/H connect the electric field shown that the strong spectral distortions at gra- E and magnetic field B to the electric displacement zing incidence make it possible to reveal the weaker vector D and magnetic induction H, respectively. structures in the absorption spectrum. In the case The complex refractive index can be written as of NiO this provides an important verification for n"n#in with (n,n)3+R,, where the spectral the charge transfer model. The Ni 2p absorption refractive index, n, and extinction coefficient, n, structure is ideally suited since it displays an are connected by a Kramers-Kronig (KK) trans- atomic-like multiplet structure which is dominated formation. by a small number of intense peaks, while weaker Eq. (2) shows that the intensity is exponentially structures are unresolved. These weaker structures damped with an attenuation factor contain important information concerning the de- tails of the ground state electronic structure. E(z)/E(0)"e\L)X,e\IX, (3) A study of the absorption and reflection near gra- zing incidence makes it possible to observe these where z is the length in the medium and hidden transitions. A straightforward optical anal- ysis is sufficient to extract the information concern- 2 "2K n" n (4) ing the peaks positions and oscillator strengths. n" c The outline of this paper is as follows. In Section 2 we discuss how the optical constants and oscil- is the absorption or attenuation coefficient. lator strengths can be extracted from the X-ray In principal, n can be determined from the de- absorption spectrum measured in total electron crease in X-ray intensity as a function of sample yield and reflection. The origin of the peak struc- penetration z. Therefore, measurement of the at- ture in the Ni 2p absorption spectrum is described tenuation of the beam through the sample appears in Section 3. Experimental details about the to be the most obvious way to determine the ab- measurements are given in Section 4. Results of the sorption coefficient. Although measurements in total electron yield and reflectivity measurements transmission mode are indeed standard in the hard are presented in Section 5. Conclusions are drawn X-ray region, they are strenuous to perform in the in Section 6. soft X-ray region. In order to avoid saturation effects caused by the small absorption length, the samples need to be very thin ((100 As). The preparation of 2. Optical constants extremely thin samples without pinholes suitable for transmission mode measurements is a difficult task. First we discuss how we can extract the optical Therefore, alternative methods based on monitoring constants from the absorption spectra. the flux of decay products, such as electrons, photo- ns or ions, upon core hole de-excitation are more 2.1. Attenuation coefficient conceivable. In this case the signal is not necessarily proportional to the absorption cross section. The electric field of the X-rays propagating in a medium can be written as 2.2. Electron yield detection E(r,t)"Ee Kr\SR The probability that an electron excited at depth "E z will reach the detector is given by Ce\XB, where e\LKre LYKr\SR (2) the factor C takes into account the detector efficien- with wave vector K" n/c"2 n/ "Kn, angu- cy. The mean electron escape depth d is indepen- lar velocity , frequency , wavelength , and velo- dent of z but depends weakly on the kinetic energy city c. K is the wave vector in vacuum. The of the electron. 300 G. van der Laan / Journal of Magnetism and Magnetic Materials 192 (1999) 297-304 The quantum yield as a function of depth can be state with oscillator strength f written as GH. The latter is a di- mensionless quantity which represents the effective ½(z)"C number of electrons per atom for a transition at Fe\XIFe\XB, (5) frequency where GH. In the spectral region near the ab- F" /sin is the effective absorption depth sorption edge we can make the approximations at a grazing angle of the incident X-rays with  respect to the surface. For a film of thickness t the GH! P2 GH( GH! ) and P GH , so that quantum yield per incident photon is given by N f nJ1# Ge GH( GH! ) , (11) m  H ( GH! )# GH ½"C(1!R)R½(z)dz N f  nJ Ge GH GH . (12) m  H ( GH! )# GH "C(1!R) Fd [1!e\ >IFB RB] (6) 1# Thus the spectral distribution of n is a sum over Fd lines with a dispersive shape, whereas that of n is where also the correction for reflection of the X- given by a sum over Lorentzians with energy posi- rays at the sample surface is taken into account. tions For s-polarised light the reflectivity is given by the GH and half-widths GH. The imaginary and real part of the spectral re- Fresnel equation [36] fractive index in Eqs. (11) and (12) which are mu- tually related by KK transformation, provide R" cos !(n!sin . (7) directly the spectra in which we are interested. The cos #(n!sin absorption coefficient is proportional to the imagi- nary part, cf. Eq. (4). The angular-dependent reflec- 2.3. Classical oscillator model tivity is a function of both imaginary and real part, cf. Eq. (7). Applying these equations avoids the A simple way to represent the interaction of the explicit use of KK transformations, which are core electrons with the X-rays is provided by using known to suffer from problems of slow convergence a classical oscillator model. The equation of motion and the necessity of choosing high cutoff values for for an oscillator with resonance frequency  and the energy [37,38]. damping constant m is given by Hooke's law as [36] e r]# r#  3. Origin of the peak structure r"! E m e SR, (8) which gives the solution The 2p absorption spectrum of NiO is shown in Fig. 1. Its structure has been explained in detail in e (  Ref. [17], so that it is only briefly touched here. The ! #i )r"! E(t). (9) m ¸ main structure (peak a and b) is due to The scalar polarisation (dipole moment per unit transitions into 2p3d final states and the volume) is P"!Ner" ¸ E, so that  main structure (peak f and g) is due to transitions into 2p ,1# 3d states. Both edges display a multiplet splitting into roughly two peaks. For Ner a large part this splitting is due to the 2p-3d ex- "1# change interaction [38-40]. The weak structures E Ne 1 between the two edges (peak c and d) are due to "1# . (10) excitations into 2p m 3d¸ final states. The broad  ! #i structure around 866 eV (peak e) is caused by the The transition from classical oscillators to atoms onset of the 2p is accomplished by replacing N by N 3d¸ k final states. Compared G fGH and  by with the main ¸  peak, these final states contain an GH, where NG is the density of atoms in the ground extra ligand hole and a continuum electron. This G. van der Laan / Journal of Magnetism and Magnetic Materials 192 (1999) 297-304 301 (SRS) at Daresbury Laboratory using beamline 3.4 equipped with a double beryl crystal mono- chromator [43]. The sample was a cleaved NiO single crystal measured with total electron yield and the X-ray beam at normal incidence. Total yield and reflectivity measurements at grazing incidence (Fig. 2) were done at the SRS undulator beam line 5U.1, which is equipped with a variable-included-angle plane-grating mono- chromator [44]. The vertical entrance aperture of the monochromator was restricted to give a high linear polarisation ('90%). Angular measure- ments were performed using a -2 reflectometer operated under high vacuum conditions. In this apparatus the sample deflects the beam vertically while the rotation axis is horizontal and parallel to the electric vector of the X-rays. The beam reflected Fig. 1. Ni 2p absorption spectrum of NiO measured in total from the sample was detected by a slitted GaAsP/ electron yield with the X-rays at normal incidence. See text for Au photodiode. The total electron yield was peak assignment. monitored using a high current channeltron posi- tioned directly above the sample. A grid over the results in a relative energy at the onset of *#Q, front of the channeltron was biased at #200 V to where * is the ionisation energy of a ligand 2p ensure a good collection efficiency. The sample and electron (&6 eV) and Q is the screened 2p-3d the photodiode could be independently rotated us- Coulomb interaction (&7 eV). ing high precision rotary tables with 0.001° resolu- The peak ratio in the ¸ structure is very sensi- tion. The angular position of these tables was tive to the orientation of the linear polarisation controlled via stepping motors under computer vector of the X-rays with respect to the spin ori- control. The photon energy was scanned at differ- entation. This makes it interesting to study NiO ent and the reflectivity and electron yield was with magnetic X-ray linear dichroism (MXD) as recorded simultaneously. In order to avoid MXD was demonstrated by Kappert et al. [41] and Al- effects, the direction of the electric vector was kept ders et al. [42]. A preferred spin orientation can be horizontally by using s-polarised light and only the imposed by thin film epitaxial growth on grazing angle was changed. a MgO(1 0 0) single crystal substrate, which due to For the experiments on line 5U.1 the sample the interface anisotropy results in a preferential consisted of 27 monolayers NiO epitaxially grown spin in the [$2,$1,$1] directions. In the isot- in a layer-by-layer fashion on a single crystal of ropic spectrum (cf. Fig. 1) the low-energy peak (f) MgO(1 0 0) as monitored by reflection high-energy has the highest intensity. However, for ordered electron diffraction [45]. NiO and MgO exhibit samples on MgO the relative ratio of the two peaks a face-centered-cubic rocksalt (NaCl) structure changes strongly with the direction of the linear with lattice constants of 4.176 and 4.212 As, respec- polarisation and the intensity of the two peaks can tively, resulting in a lattice mismatch of 0.85%. be interchanged. 5. Results 4. Experimental The reflectivity and total electron yield spectra at The high-resolution spectrum shown in Fig. the Ni 2p absorption edges are shown in Fig. 2 as 1 was obtained at the synchrotron radiation source a function of the angle between the (1 0 0) plane 302 G. van der Laan / Journal of Magnetism and Magnetic Materials 192 (1999) 297-304 Fig. 2. Glancing angle ( ) dependence at the Ni 2p absorption edge of 27 ML NiO on MgO(1 0 0) single crystal using s-polarised light. (a) measured total electron yield; (b) measured reflectivity; (c) theoretical total electron yield; and (d) theoretical reflectivity using the Lorentzian lines indicated by the sticks under the bottom spectrum. All spectra have been normalised. and the direction of the incident s-polarised X-rays. angles a dip evolves in the pre-edge, preceded by The top panels show the experimental results and a bump with its maximum shifting towards higher the bottom panels show the simulations computed photon energy for reduced angles of incidence. This using the optical model. The observed spectra ex- bump reveals the critical angle for total reflection. hibit a strong distortion compared to the spectrum When the photon energy is scanned towards the in Fig. 1, which was measured at normal incidence. ¸ In the electron yield spectra (Fig. 2a) the most  edge, the absorption coefficient increases and at sufficiently small grazing angles the condition for intense peak is suppressed at grazing angles due to total reflection can be reached. Then, apart from the influence of saturation and all features tend to the evanescent wave, no light will penetrate inside reach comparable heights. At very low grazing the sample. Thus the total electron yield will be G. van der Laan / Journal of Magnetism and Magnetic Materials 192 (1999) 297-304 303 reduced, even though the absorption coefficient is line shape which requires also an asymmetry para- increased for energies closer to the ¸ edge. This meter [46]. Fig. 2c shows a comparison of the best effect suppresses the strongest multiplet lines and as theoretical fit using Eq. (6) to the angular-depen- a result the weaker ones, which are normally dent electron yield data, where the escape depth of eclipsed, are now distinguishable. This is nicely the electrons was somewhat arbitrarily set to 50 As demonstrated for the charge-transfer satellite struc- [35]. The overall agreement with experiment, as tures above the ¸ edge. shown in Fig. 2, is very good. Simulations using Fig. 2b shows the measured reflectivity as a func- a Fano line shape did not significantly improve the tion of the grazing angle. At large glancing angles fitting, suggesting that the coupling of the final state ( '6°) the reflectivity spectrum displays only the multiplet with the continuum states is small. Fig. 2d most intense feature of the electron yield ¸ spec- shows the theoretical reflectivity spectra as ob- trum at 852 eV. At smaller angles an extra peak in tained from fitting of the electron yield spectra, the pre-edge of the ¸ evolves. It is interesting to where again a good agreement is reached. note that at low glancing angles ( (2°) the reflec- tivity spectrum resembles the electron yield spec- trum but with its shape upside down. This is because 6. Conclusions the sum of absorbed and reflected light is constant with energy. Grazing incidence absorption and reflection Only a few oscillators, which are shown at the measurements in the soft X-ray region display dra- bottom of Fig. 2c and Fig. 2d, were included in the matic changes the spectral line shape which can be calculation. This covers globally in Fig. 1 the main explained using a simple optical model based on structures a and b of the ¸ edge and the structures Fresnel's equation. The results provide detailed in- f and g of the ¸ edge, as well as the feature e. Thus, formation about the underlying multiplet structure weak satellite features, such as c and d, were not at the X-ray absorption edges. The critical angle included. This leads to some prominent differences behaviour of the multiplet structure has been ex- in the region between the ¸ and ¸ peaks, namely ploited to study low-intensity satellite structures. the calculated spectra are smooth while the experi- The method provides a novel way to study the mental spectra show quite a lot of weak structure, magnetic ground state of transition metal com- especially at smaller angles. It clearly demonstrates pounds. that low-intensity features become more distinct at smaller angles. The origin of the features between the ¸ and ¸ peaks can be traced to the Acknowledgements 2p3d¸ final states, which have higher photon energies than the 2p3d final states due to the I would like to acknowledge the collaboration core-valence Coulomb interaction. Also the shapes with K.C. 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