VOLUME 82, NUMBER 7 P H Y S I C A L R E V I E W L E T T E R S 15 FEBRUARY 1999 Quantifying Magnetic Domain Correlations in Multilayer Films Y. U. Idzerda, V. Chakarian, and J. W. Freeland* Naval Research Laboratory, Washington, D.C. 20375 (Received 20 July 1998) The vertical correlation of magnetic domains in a Co Cr Co trilayer is statistically quantified as a function of an applied magnetic field. These measurements, used with determinations of the individual layer magnetometry curves, identify the presence of both antiferromagnetic exchange coupling and ferromagnetic dipolar coupling for different regions within the trilayer. [S0031-9007(99)08427-6] PACS numbers: 75.70.Cn, 75.25.+z, 75.60.Ej With the explosive growth [1­4] in spin-polarized tically quantified by measuring the magnetic field depen- electron transport studies for spin-tunneling [5,6], spin- dence of the x-ray resonance magnetic scattering (XRMS) transistor [7], and magnetoresistive [8­10] device applica- [19­22]. X-ray resonance magnetic scattering is the angle tions, the importance of the correlation in the orientations dependent specular reflectance of circular polarized soft of magnetic domains is becoming increasingly apparent. x rays whose energy is tuned to the absorption energy The spin conductance of a magnetic heterostructure is con- of a magnetic element. It combines the element selectiv- trolled by the relative orientation of the magnetic moment ity of x-ray resonant scattering with the magnetic contrast directions of the component layers on a local scale (within of magnetic circular dichroism, and has been successfully a few spin mean-free paths) [11]. In real systems, local used to extract chemical and magnetic film thicknesses variations of the film and interface microstructure alter the with 0.05 Å sensitivity [23], identify the order of layer interlayer and intralayer coupling energies and therefore switching, and separately parametrize the magnetic and the field dependence of the relative orientation of the chemical roughness of interfaces [23­25]. layer magnetic moments. Any meaningful comparison The specular scattered intensity of a resonant soft x ray between the measured and calculated spin conductances is a function of the incident angle of the soft x-ray u requires a quantitative description of the field dependence and the magnetic configuration of the multilayer (which of the magnetic domain correlations. Furthermore, the is dependent on the applied magnetic field history). For a determination of the local domain alignments can be single film with magnetic domains large compared to the used to identify, and quantify, the possible interlayer and photon coherence length, the reflected intensity I u, B is intralayer coupling mechanisms present in these films, as given by well as elucidate modifications of magnetic behavior from X film lithography and device manufacture. I u, B Ik u xk B , (1a) Magnetic domain structure of a multilayer on this k appropriate length scale can be obtained by magnetic where k denotes a particular magnetic domain type within microscopy, in its many and varied forms [12], but the film, Ik is the scattered intensity from that domain, and the magnetic mapping is typically averaged by a depth xk is the fraction of the film in the kth domain type. (Note P weighting factor and does not isolate the relative moment that k xk B 1 at any field value.) For a film which directions of the component layers. One exception is exhibits a uniaxial magnetic anisotropy and therefore has magnetic imaging employing magnetic circular dichroism predominantly two possible magnetic domains (left and (MCD) [13]. (Magneto-optic techniques [14] also have right), Eq. (1a) becomes this capability with spatial resolution but for very particu- lar systems.) Magnetic circular dichroism is a powerful I u, B I! u x! B 1 I u x B . (1b) magnetic structure characterization tool and has been used Equation (1a) can also apply to a multilayer film, but now k for the determination of element-specific magnetometry denotes a particular configuration of the magnetic moment [15] and vector magnetometry [16] information, even orientations for each magnetic layer taken vertically along identifying the hysteretic behavior of an ultrathin buried the multilayer. Ik is the scattered intensity from that mo- magnetic layer sandwiched between two large ferromag- ment configuration and xk is the fraction of the multilayer netic sheets [17]. in that particular configuration [26]. Similarly, extending A statistical mapping of the correlations between mag- Eq. (1b) to a magnetic film system consisting of two lay- netic domains in different layers can be generated by MCD ers, each with two possible magnetic domain directions, imaging, but this is a laborious and lengthy task which the total scattered intensity becomes is difficult to perform in the presence of a significant ap- plied field (with the notable exception of MCD transmis- I u, B INxN 1 I:x: 1 I-x- 1 IMxM, (2) sion [18] and magneto-optical [14] microscopy). Instead, where xN and xM are the fractions of the film with the the correlation between magnetic domains can be statis- magnetic domains of the top and bottom film aligned 1562 0031-9007 99 82(7) 1562(4)$15.00 © 1999 The American Physical Society VOLUME 82, NUMBER 7 P H Y S I C A L R E V I E W L E T T E R S 15 FEBRUARY 1999 with each other and x: and x- are the fractions of the This latter angular dependence is demonstrated in the top film antialigned to each other. It is these four magnetic panel of Fig. 2, where the log of the specular scattered in- field dependent fractions which will ultimately express the tensities for negative helicity light and the resulting asym- vertical correlation of magnetic domains in the trilayer, metry I1 2 I2 I1 1 I2 are shown for the sample and it is the extraction of these terms from the measured fully magnetized by an applied field of 1120 Oe I1 and scattered intensities which is the subject of this Letter. 2120 Oe I2 . Displayed with these angle dependent re- To experimentally realize only these four magnetic flectance curves is a subset of the field dependent reflected domain configurations, a magnetic structure with a strong intensity curves recorded at the reported incidence angles uniaxial magnetic anisotropy is utilized. To accomplish (shown in the eight curves at the bottom of Fig. 2). Be- this, a single crystal Co(50 Å) Cr(35 Å) Co(50 Å) cause of the changing contribution of the scattering inten- trilayer is deposited at 175 ±C at a vacuum of sities Ik u , these curves are markedly different. ,5 3 10210 Torr, on an epitaxially grown ZnSe(001) The obvious variation in these curves belies a hidden substrate (shown in Fig. 1). To stabilize the bcc Co similarity. In Eq. (2), the dependence on the applied mag- structure, a seed layer of 5 Å of bcc Fe is first deposited netic field is contained only in the four configuration frac- on the ZnSe. The growth of the second Co layer on the tions xk B , whereas the angular dependence is derived bcc Cr also produces a single crystal bcc structure [27,28]. solely from the four prefactor terms IN u , I: u , I- u , The multilayer is then capped with a 30-Å Al layer to and IM u which each remain constant for a fixed inci- prevent oxidation. dent angle. The large variations observed in the field Vibrating sample magnetometry (VSM) confirmed that scans taken at different incidence angles (Fig. 2) result this system displayed a strong uniaxial anisotropy, super- only from a variation of these multiplicative constants and imposed on the cubic magnetic anisotropy inherent to the allow for a separate determination of the four configura- fourfold surface and identified the easy-easy axis of mag- tion fractions xN B , x: B , x- B , and xM B which are netization to be in the [110] direction. Magnetic force independent of the incidence angle. microscopy (MFM) measurements taken for the trilayer Actually, only two of these prefactors are unknown. showed only two magnetic domain configurations, with In the top panel of Fig. 2, we show the experimentally the net magnetization direction along the [110] axis. The MFM measurement could not isolate the moment direction of each individual Co layer but, as previously noted, repre- sents some depth-weighted average of the entire magnetic structure. As shown in Fig. 1, the soft x ray is incident at an angle u, and the specular reflected intensity is measured using a Si photodiode located at an angle 2u to the incident beam direction (u to the film plane). The circular polarized soft x ray (degree of polarization is set to 75%) is tuned to the Co L3 edge (778 eV), corresponding to the maximum in the Co absorption curve (imaginary part of the complex Co dielectric tensor). To quantify the magnetic domain configuration fractions xk B , the applied field dependence of the scattered inten- sity is measured. But, as indicated in Eq. (1a), the con- tributions to the total scattered intensity depend separately on the applied magnetic field and on the incidence angle. FIG. 2. Top panel: Scattered intensity and a normalized asymmetry for circular polarized soft x rays near the Co L3 edge (778 eV) for a trilayer fully magnetized in either direction. FIG. 1. XRMS scattering geometry for a Co Cr Co single Bottom panel: Eight magnetic field dependent specular intensity crystal trilayer with the field applied along the magnetically spectra acquired at the indicated incidence angle for circular easy-easy [110] axis. polarized soft x rays near the Co L3 edge (778 eV). 1563 VOLUME 82, NUMBER 7 P H Y S I C A L R E V I E W L E T T E R S 15 FEBRUARY 1999 determined values for the angle dependence of the scat- tablish the bcc growth of Co. (Element-specific magnetic tered intensity when the film is completely magnetized to hysteresis measurements of a single 50-Å Co layer de- saturation in the positive [xN 1 and I1 u IN u ] posited on a 5-Å Fe seed layer showed the Fe and Co or negative [xM 1 and I2 u IM u ] field direction. hysteretic behavior to be identical.) Superimposed over Utilizing the many field dependent scans, an itera- these curves are the calculated hysteresis loops as deter- tive, least-squares, best-fit procedure can be applied to mined from the four extracted configuration fractions and determine the two remaining unknown intensity factors, Eq. (3). The agreement is nearly exact, giving confidence which are different constants for each scan, and the in the extraction of the film fractions. four configuration fractions, which must be the same for Rather than display the four configuration fractions all scans. In this way, the fraction of the film with a separately, a more meaningful and compact presentation particular magnetic domain configuration can be uniquely is plotted in the bottom panel of Fig. 3. For spin- determined. conductance applications, it is the relative orientation of The validity of this procedure can be checked by com- the magnetic moments within a domain which gives rise paring measured magnetometry loops with calculated mag- to the resistance variation (aligned for low resistance, netometry loops derived from the four extracted domain antialigned for high resistance). Therefore, the correlation configuration fractions by noting that the moment of the function x"" 2 x"# representing the fraction of the film bottom layer, Mbottom, is given by which is aligned, x"" xN 1 xM, minus the fraction of M the film antialigned, x"# x: 1 x-, is a more useful bottom M0 x! 1 2 x 1 , (3) quantity to examine. This quantity is simply the average where x! 1 x 1 is the fraction of the bottom magnetic layer deviation from ferromagnetic-type alignment of the mag- with moment along (opposed to) the applied field direction. netization of the two layers, where a value of 11 21 This can be rewritten in terms of the four configuration represents complete alignment (antialignment) of the two fractions by noting that x! 1 2 xN 1 x- and x 1 x: 1 film moments. xM (and similarly for the top magnetic layer). At high fields, the two Co films are aligned with each The top panel of Fig. 3 shows both the normalized total other and both essentially single magnetic domains. As moment hysteresis curve (measured by vibrating sample the field is increased or decreased from these extremes, magnetometry) as well as the normalized hysteresis curve domains form (first in the top Co film) and the correlation of just the bottom layer. We have directly measured function is reduced from unity. The correlation function the hysteresis behavior of the bottom film by measuring drops to a minimum value and returns to unity at the op- the element-specific hysteresis curve in absorption of the posite extreme. From Fig. 3, it is clear that the Co Cr Co strongly coupled Fe seed layer used as a template to es- film never reaches a fully antialigned configuration, but achieves a maximum negative value of 255%. This field value corresponds to the peak in the magnetoresistance since it is at this point that the two magnetic layers are most antialigned and the trilayer has the highest resistance. This correlation function can be used in conjunction with mea- sured transport curves to extract the coefficient of magne- toresistance [29] or for a detailed comparison with theory. It can also be used to identify and quantify the interlayer coupling mechanisms present in this multilayer. In the absence of any type of interactions between the magnetic layers, the purely random distribution of mag- netic domains will still result in a statistical probability that two vertically offset regions of different magnetic layers within the multilayer are aligned with each other. For two noninteracting independent films, the predicted fraction of the film in a particular configuration, XNI B , can be calculated as simply the product of the individual domain fractions of each layer (i.e., keeping with the pre- vious notation x- NI x 1 3 x! 2 , and similarly for each of the other configurations). Since, as shown in Fig. 3, the individual layer fractions can be extracted from ei- FIG. 3. Top panel: Normalized magnetometry loops for the ther the magnetometry data or the measured two-layer total moment and only the bottom film (the Fe hysteresis configuration fractions themselves, a correlation function loop). Superimposed is the calculated hysteresis loops from the configuration fractions (see text). Bottom panel: The extracted for two noninteracting films can be separately constructed correlation function (as defined in the text) for increasing and for comparison with the derived correlation function of decreasing field. Fig. 3. By comparing the calculated noninteracting films 1564 VOLUME 82, NUMBER 7 P H Y S I C A L R E V I E W L E T T E R S 15 FEBRUARY 1999 derived remainder of the correlation function associated with interacting films which probes the fundamentally sig- nificant behavior of the magnetic films by identifying and quantifying the type and strength of the interlayer cou- pling mechanisms. Although the correlation function and the two-layer domain configuration fractions themselves are tremendously useful for understanding spin-transport behavior, the coupling-derived remainder of the correla- tion function provides the physical insight, and becomes even more useful when investigating coupling mecha- nisms as functions of changing temperature, interlayer thickness, or after film lithography and device processing. FIG. 4. The bottom layer hysteresis behavior (solid line), the This work was supported by the Office of Naval extracted correlation function (dashed line), and the coupling- Research. NSLS is supported by DOE. derived remainder of the correlation function (dots) of the Co Cr Co trilayer as a function of increasing field. *Permanent address: Adv. Photon Source, Argonne, IL 60439. correlation function to the extracted correlation function, [1] G. A. Prinz, Phys. Today 48, 58 (1995). we can imply the presence of coupling between the mag- [2] G. A. Prinz, Science 250, 1092 (1990). netic layers and even ascertain the sign of the coupling. [3] L. M. Falicov et al., J. Mater. Res. 5, 1299 (1990). This comparison is performed in Fig. 4, where is shown [4] B. Heinrich and J. F. Cochran, Adv. Phys. 42, 523 (1993). the bottom film hysteresis curve, the extracted correla- [5] R. Meservey et al., Phys. Rev. Lett. 25, 1270 (1970). tion function, and the difference between the extracted [6] P. M. Tedrow and R. Meservey, Phys. Rev. B 7, 318 correlation function and the calculated correlation func- (1973). tion for noninteracting films, each for only the increasing [7] D. J. Monsma et al., Phys. Rev. Lett. 74, 5260 (1995). [8] P. Grunberg et al., Phys. Rev. Lett. 57, 2442 (1986). field leg of the hysteresis loop. This difference is just [9] M. N. Baibich et al., Phys. Rev. Lett. 61, 2472 (1988). the remainder of the correlation function caused by cou- [10] B. Dieny et al., Phys. Rev. B 43, 1297 (1991). pling between the films [30]. As the field is increased [11] P. Bruno and C. Chappert, Phys. Rev. Lett. 67, 1602 in the data of Fig. 4, the extracted correlation function (1991). is reduced while the bottom film hysteresis loop shows [12] P. Grutter et al., in Scanning Tunnelling Microscopy, that the bottom film is still near saturation. Since the edited by R. Weisendanger and H.-J. Guntherodt coupling-derived remainder of the correlation function re- (Springer, Berlin, 1992), Vol. II, p. 151. mains zero, as it must if either film is at saturation, the ini- [13] J. Stohr et al., Science 259, 658 (1993). tial reduction in the extracted correlation function would [14] M. Ruhrig et al., Phys. Status Solidi (a) 125, 635 (1991). occur regardless of the presence or absence of any inter- [15] C. T. Chen et al., Phys. Rev. B 48, 642 (1993). action between the films. As the field is increased farther, [16] V. Chakarian et al., Appl. Phys. Lett. 66, 3368 (1995). [17] V. Chakarian et al., Phys. Rev. B 53, 11 313 (1996). the coupling-derived remainder of the correlation function [18] P. Fischer et al., J. Phys. D 31, 645 (1998). remains near zero until a significant number of magnetic [19] K. Namikawa et al., J. Phys. Soc. Jpn. 54, 4099 (1985). domains have begun to form in the bottom film. At this [20] C.-C. Kao et al., Phys. Rev. B 50, 9599 (1994). point, the coupling-derived remainder of the correlation [21] J. M. Tonnerre et al., Phys. Rev. Lett. 75, 740 (1995). function becomes nonzero and positive, indicating that a [22] V. Chakarian et al., J. Magn. Magn. Mater. 165, 52 (1997). significant fraction of the film is interacting and that the [23] Y. U. Idzerda et al., Synch. Radiat. News 10, 6 (1997). magnetic domains are preferentially aligned to those do- [24] J. F. Mackay et al., Phys. Rev. Lett. 77, 3925 (1996). mains directly opposite them in the adjacent layer, prob- [25] J. W. Freeland et al., J. Appl. Phys. 83, 6290 (1998). ably from dipolar coupling. At higher applied fields, this [26] Here we have ignored intradomain scattering or scattering predominant ferromagnetic interaction is replaced by an from domain walls. [27] F. Scheurer et al., Surf. Sci. Lett. 245, L175 (1991). antiferromagnetic coupling, indicating that the majority of [28] S. Folsch et al., Phys. Rev. B 57, R4293 (1998). the sample is now dominated by an antiferromagnetic in- [29] Y. U. Idzerda et al., J. Appl. Phys. 76, 6525 (1994). terlayer coupling mechanism. [30] Domain correlations may occur for noninteracting films Of the various formulations for describing the magnetic if growth nonuniformities propagate vertically through the domains with this trilayer system, it is the final coupling- structure, acting as magnetic domain nucleation sites. 1565