PHYSICAL REVIEW B, VOLUME 65, 224417 Ferromagnetic domain distribution in thin films during magnetization reversal W.-T. Lee,1 S. G. E. te Velthuis,2 G. P. Felcher,2 F. Klose,1 T. Gredig,3 and E. D. Dahlberg3 1Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 2Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 3Department of Physics, University of Minnesota, Minneapolis, Minnesota 55455 Received 20 December 2001; revised manuscript received 8 April 2002; published 3 June 2002 It is shown that polarized neutron reflectometry can determine in a model-free way not only the mean magnetization of a ferromagnetic thin film at any point of a hysteresis cycle, but also the mean-square dispersion of the magnetization vectors of its lateral domains. This technique is applied to elucidate the mechanism of magnetization reversal of an exchange-biased Co/CoO bilayer. The reversal process above the blocking temperature Tb is governed by uniaxial domain switching, while below Tb the reversal of magneti- zation for the trained sample takes place with substantial domain rotation. DOI: 10.1103/PhysRevB.65.224417 PACS number s : 75.25. z, 75.60.Jk, 75.70. i Polarized neutron reflectometry PNR was introduced in Conventionally, a fitting procedure allows a model mag- the beginning of the 1980s to map the magnetic profiles of netic profile to be obtained from the spin-dependent reflec- thin films and multilayers.1­3 This technique has been ap- tivities. However, simple and transparent relations are avail- plied to study systems in which the magnetic structure con- able, linking the magnetization to the reflectivities. When the sists of a stack of laterally uniform magnetic layers. The direction of magnetization M and the applied field are in the experiments reveal the depth dependence of the magnetiza- film's plane, and M is at an angle with H, then,5 tion, in size as well as in direction: this is the information needed to characterize magnetic interactions between differ- R R R R cos , 1 ent layers. Polarized neutron reflectometry can also be instru- R s 0° Rs 0° Rs 0° Rs 0° mental in understanding a different, but still outstanding problem in magnetism: the breakdown into domains of a R ferromagnet during the hysteresis cycle.4 While neutron re- sin2 . 2 R 90° flectivity studies are limited to samples in the form of thin s flat films, this is the form of many magnetic systems created These relations are valid at all values of qz above the critical in recent years for diverse applications, from magnetic re- edge for total reflection, provided that the direction of M is cording to magnetic memory to sensors. Magnetic domains constant along the thickness of the film. The normalizing significantly impact the performance of these devices. In quantities Rs(0°) and Rs(90°) refer to reflectivities mea- most applications the ferromagnetic layers are so thin that sured with M aligned parallel and perpendicular to the neu- only a single magnetic domain can be energetically stable tron polarization, respectively. The single-superscript reflec- through the thickness. While passing through a hysteresis tivities are those measured without polarization analysis, i.e., loop, however, the film may break down into a collection of R R R and R R R for this configura- magnetic domains within the film plane i.e., lateral do- tion of fields, R R . mains , each characterized by a size and a direction of mag- When a film breaks down into lateral domains, the effect netization. In spite of the progress made in the use of micro- on the reflectivity will depend on the size of the domains. scopic and scattering probes, the problem of observing these Infinitely large domains specularly reflect plane waves. For domains-especially at some distance below the surface- finite domains the reflected beam has some divergence, remains difficult. Yet, as demonstrated in this paper, a statis- which is inversely proportional to the domain size. Since the tical measure of the domain distribution can be obtained di- incident beam itself has some divergence, for each instru- rectly from PNR. ment there is a minimum size of the domains for which there In a PNR experiment, the intensity of the neutrons re- is a recognizable broadening. For domains larger than this flected from a surface is measured as a function of the com- length, the intensities reflected from different domains super- ponent of the momentum transfer that is perpendicular to the impose incoherently in the specular beam. In this case, the surface, qz 4 sin / , where is the angle of incidence terms in of Eqs. 1 and 2 can now be interpreted as and reflection and the neutron wavelength. Since qz is a averages across the sample plane. While the term cos variable conjugate of the depth z from the surface of the film, may be measured as well by conventional magnetometery, a scan over a suitable range of qz provides excellent infor- sin2 provides information leading to the mean-square dis- mation on the chemical and magnetic depth profile of the persion of the domain orientations 2: film. When the incident neutrons are polarized along an ap- plied magnetic field H, and the polarization after reflection is 2 cos2 cos 2 analyzed along the same axis, four reflectivities are recorded: R , R , R , R . The first second sign refers to the R 1 R R 2. 3 incident reflected neutron polarization with respect to H. R s 90° Rs 0° Rs 0° 0163-1829/2002/65 22 /224417 6 /$20.00 65 224417-1 ©2002 The American Physical Society W.-T. LEE et al. PHYSICAL REVIEW B 65 224417 These quantities are constant, and independent of qz , if the domains extend through the entire thickness of the film. As a comparison with transverse magneto-optic Kerr effect MOKE , one can measure cos and sin , but not sin2 . Recapitulating the universality of the method, it can be stated that PNR can be applied to measure the mean magne- tization and the mean-square dispersion of domains on thin films, provided that the following hold. 1 The film is flat and smooth enough to reflect neutrons. 2 The reflectivity with neutrons polarized perpendicu- larly to the film's magnetization in the saturated state can be obtained. In the case in which a direct measurement is not possible, the reflectivity curve can, in principle, be calculated from a model of the saturated film that has been derived through other means, for instance, reflectivity measurement FIG. 1. Polarized neutron reflectivity of a Co/CoO bilayer on Si with the film saturated parallel to the neutron polarization. in a saturating field of 5 kOe. Both measured points and calculated The two quantities M and 2 that have been extracted lines are presented for incident neutrons polarized parallel (R ) and from the data are valid provided that: antiparallel (R ) to the applied field. The inset shows the scattering length density profile calculated for the two spin states. The layer 1 cos and sin2 are independent of qz. thickness for Co and CoO were found to be 130 and 45 Å, respec- 2 The reflected beam is not appreciably broader than the tively, with a half-width roughness of 15 Å between the two and 15 incident beam. Å at the film surface. Although a robust analysis of the limits of validity has not been devised yet, some rules of thumb are provided below coercive field and a characteristic temperature below TN .11 If for a practical example. the sample is field cooled to below the ``blocking tempera- These ideas have been applied in the study of the mag- ture'' Tb ,12 exchange bias appears-the hysteresis loop is no netic behavior of a partially oxidized Co film6,7 that exhibits longer symmetric with respect to the applied field. Figure 2 exchange bias.8 A nominal 120-Å-thick polycrystalline Co shows the hysteresis loops of our film above and below Tb film was deposited on a silicon substrate by magnetron sput- 130 K, at 140 and 10 K, respectively, after field cooling in tering. Its surface was then oxidized in ambient atmosphere 5 kOe from room temperature. The cooling and measure- to form an 30-Å-thick CoO top layer. Since the Co layer ment fields were along the same axis, parallel to an arbitrary was thinner than a domain wall 500 Å ,4 only one domain direction in the film surface. At 140 K, the hysteresis loop is was expected along the sample's thickness. At the same time, symmetric with a coercive field HC 100 Oe. At 10 K, the the shape anisotropy constrained the magnetization to be in initial reversal after field cooling (A2 B2) has a sharply the plane of the film. The neutron measurements were carried squared shape and a large reversal field (Ha 1.1 kOe). out at the POSY I reflectometer at the Intense Pulsed Neu- Subsequent loops through C2, D2, etc. exhibit a more tron Source of Argonne National Laboratory. POSY I is a gradual S shape, with Ha 300 Oe at one side and Ha time-of-flight reflectometer, utilizing neutron wavelengths comprised between 2 and 14 Å.9 It is equipped with an ana- lyzer consisting of a polarization splitter.10 For the evaluation of sin2 in relation 2 , we use R from measurements with the analyzer. For the evaluation of cos in relation 1 , we use R and R measured without the analyzer. Fig- ure 1 shows the R and R reflectivity pattern of the film at saturation. The reflectivity was taken at 10 K. The fitted pro- file of the scattering amplitude densities gives the thickness of the layers, the interface roughness between the ferromag- netic FM Co and the antiferromagnetic AF CoO layers, and the ferromagnetic contribution from Co. The AF order of CoO is not considered in the analysis, because for this range of qz the scattering properties are averaged over a length scale that well exceeds the antiferromagnetic period of CoO. Films of this type have been found to have three magnetic phases. At temperatures higher than the Ne´el temperature FIG. 2. Hysteresis curves a above Tb at 140 K and b below TN , the magnetization follows a square hysteresis loop. As Tb at 10 K. The labels A2 at M saturation, others at M 0 the temperature is lowered, the hysteresis loop becomes S indicate locations where neutron reflectivities are measured. The shaped and exhibits a scaling behavior as a function of the inset shows the temperature dependence of the bias field H(T) . 224417-2 FERROMAGNETIC DOMAIN DISTRIBUTION IN THIN . . . PHYSICAL REVIEW B 65 224417 FIG. 3. Contour plots of the specularly reflected beam state at T 10 K, at saturation, the reversal point B2 of the untrained film, and the reversal point C2 of the trained film. The reflected beam is reflected, at all wavelengths, at an angle f equal to the angle of incidence. While the specular peak width has not increased significantly, Yoneda scattering emerges in B2 and C2. 500 Oe at the other side, giving a bias field He 100 Oe. The inset of Fig. 2 shows the temperature de- pendence of the bias field of the trained sample, for which Tb 130 K. To elucidate the mechanism of reversal of the magnetiza- FIG. 4. The spin-flip reflectivities R a at 140 K, at the reversal points B1 and C1 ; b at 10 K, at reversal points of the tion, PNR measurements were taken close to the reversal untrained film (B2) and the trained film C2 and D2 , compared to points where M 0, as marked in Fig. 2, as well as at satu- those measured with the magnetization saturated along the field ration. The width of the reflection lines in all cases was not R (0°) (A2) and perpendicular to the field R (90°) (E2). appreciably broader than expected on the basis of the instru- s s mental resolution, as it can be seen in Fig. 3. The instrumen- tal width of the reflection line is such to make difficult the the reflectivities at saturation, Rs (0°) and Rs (0°), with the evaluation of domain sizes exceeding 20 m. In addition to neutron quantization axis parallel to the magnetization. To the specular beam, a faint off-specular scattering, of the within measurement error, R and R at the reversal points Yoneda type,13 was found when the sample was not in a are identical, giving cos 0 over the entire q range. The saturated state.7 While the details of this scattering are the qz dependence of 2 Fig. 6 was obtained by processing the subject of a separate investigation, its size is such, never spin-flip intensities R according to Eq. 3 and correcting exceeding a few percent of the reflected beam, that neglect- for the efficiencies of the instrument. ing it does not affect the conclusions reached here. The spin-flip reflectivity Fig. 4 and consequently 2 The spin-flip reflectivities R before correcting for in- Fig. 6 is very dependent on temperature and training. To strument efficiency are presented in Fig. 4. They are ob- put in perspective the results, let us consider the extreme tained from measurements at both the ascending and de- cases Fig. 7 for M 0 ( cos 0). 2 0 means that scending reversal points. The spin-flip reflectivity measured sin2 1, so all the moments are oriented perpendicular to at saturation R s (0°) ideally equal to 0 is indicative of the H, implying that the reversal occurs through magnetic do- polarizing efficiency of polarizer and analyzer. In order to main rotation. In contrast 2 1 means sin2 0 so that obtain the normalizing reflectivity R s (90°), the sample half of the moments are parallel and half antiparallel to the was field cooled in H 2000 Oe to 10 K. Then the field was field: the reversal occurs by uniaxial domain switching. For brought to zero a guide field of a few oerateds in a perpen- an isotropic distribution of the domains, 2 0.5. While a 2 dicular direction was sufficient to orient the neutron spins, value between 0 and 1 does not uniquely identify a particular but too weak to affect the magnetization . The procedure was distribution, it indicates an angular spread of the domains. As made possible because for this sample the remnant magneti- seen in Fig. 6 a , 2 measured at the reversal points at 140 K zation after field cooling is close to the saturated value. B1 and C1 deviates only slightly from unity: above Tb , R s (90°) obtained was used to normalize the measurements the magnetization reversal occurs primarily through uniaxial at the reversal points at both temperatures, as the reflectivi- domain switching. Similarly, in Fig. 6 b reversal of the un- ties from a saturated film as such do not change between 10 trained film at 10 K (B2) gives 2 close to unity. In contrast, and 140 K. The reflectivities R and R measured at the the 2 values are much smaller for the trained film at the two reversal points are presented in Fig. 5. It was trivial to obtain reversal points C2 and D2. The pertinent 2 values, ranging 224417-3 W.-T. LEE et al. PHYSICAL REVIEW B 65 224417 FIG. 5. Reflectivities R and R at 140 K, at the reversal points B1 and C1 ; and at 10 K, at reversal points of the untrained film (B2) and the trained film C2 and D2 . The reflectivities are dis- placed by factors of 10 for clarity. FIG. 6. Mean-square dispersion of lateral domain orientation 2 a at 140 K, at the reversal points B1 and C1 ; b at 10 K, at from 0.50 to 0.65, indicate a breakdown in domains with a reversal points of the untrained film (B2) and the trained film C2 substantial angular spread of their magnetic orientations. and D2 . The present results substantiate a model recently proposed11 for the magnetic behavior of Co/CoO. Above the formed with their sublattice magnetization rigidly aligned blocking temperature, the S-shaped hysteresis loop has been along two perpendicular axes. Consequently the orientation interpreted in terms of a modified Ising model. The FM Co of the ferromagnetic domains of polycrystalline Fe, grown layer is comprised of a number of domains for which the on the top of FeF applied field determines the direction of the magnetization.14 2 , had to be more constrained at the M 0 points of the hysteresis loop, as it was confirmed by Their reversal takes place over a finite interval of fields be- comparing the experimental reflectivities with those calcu- cause of a range of coupling strengths with different antifer- lated for a model structure with appropriate distributions of romagnetic CoO domains.15 The orientation of the sublattice domains. magnetization of the AF domains is not fully locked by the We have shown that a model-free analysis of reflectivity crystalline anisotropy and the coupling between different AF measurements on a thin film composed of a collage of mag- domains. Below Tb , however, the AF domains are stabilized. The orientation of the sublattice magnetization of CoO now strongly influences the direction of the FM domains. Unless a strong external magnetic field is present, the FM domains turn their magnetization in the direction optimizing both the coupling with the AF domains and the Zeeman energy,16,17 giving rise to the rotation of domains we observed. The results obtained for T Tb may be compared with those obtained on a different exchange-bias system: ferro- magnetic Fe coupled with antiferromagnetic FeF2 .18 The type of neutron measurements carried out in the two cases is similar: the four spin-dependent reflectivities have been mea- sured close to the M 0 points of the hysteresis loop. The results reflect the inherent difference of the two physical sys- FIG. 7. Schematic diagrams illustrating some possible magnetic tems. In the polycrystalline Co/CoO bilayer, a fairly isotropic configurations in the thin film and the corresponding values of ferromagnetic domain distribution of Co implies that the AF sin2 and 2 all have cos 0 : a single domain, b collin- domain distribution of CoO is equally isotropic. In FeF2 ear domains with magnetization along the applied field H, c do- grown semiepitaxially on MgO 100 , AF domains are mains with a dispersion of magnetic orientations. 224417-4 FERROMAGNETIC DOMAIN DISTRIBUTION IN THIN . . . PHYSICAL REVIEW B 65 224417 that the reversal mechanisms are different above and below the blocking temperature. The applicability of this method partly relies on the possibility to obtain the normalizing quantity appearing in Eq. 2 , R s (90°). Furthermore, with respect to the domain size issues, it may be possible to apply the method for small domains, provided that all neutrons scattered in a broader reflectivity line are properly counted and correlation effects between the magnetization of adjacent domains are taken into account.19 The weak, but nonzero dependence of 2 on qz that is observed for Co/CoO could indicate that the direction of magnetization is not completely uniform throughout the thickness. The simulations shown in Fig. 8 give a measure of the sensitivity of reflectivity to a magnetic structure in which the direction of magnetization is depth dependent. Although a general theoretical basis for in- terpreting all reflectivity patterns is not available yet, the experiment itself seems to offer a number of checks on the validity of the procedure. If used as described above, PNR does not need detail structural modeling to obtain cos and 2 at any point of a hysteresis cycle. Technically it is becoming feasible to mea- sure a reflectivity curve in a matter of minutes, a data- acquisition rate comparable to that of conventional magneti- zation measurements. Both cos and 2 measured by PNR can then be compared with the results of micromagnetic calculations.20 Even more desirable is the development of a theoretical framework along the lines of the work done to extract information from the magnetization-as obtained by passing with minor hysteresis loops through different paths FIG. 8. Reflectivity calculated for a 140-Å thin film of Co on of metastable states.21,22 If not only the average magnetiza- silicon of which the surface layer 10 Å is magnetized at an angle tion but also 2, the mean-square dispersion of the domain with the applied field. The bottom picture shows how the misalign- orientations, is available, how much easier or more realistic ment of magnetization of a small region may affect the determina- becomes the analysis of the magnetization process? tion of 2. The crossing point of the envelope of calculated 2 is at q 0.035 Å 1, at a value 2 /d given by approximately i.e., in the Work done at the Argonne National Laboratory was sup- first Born approximation the thickness d of the magnetic layer. ported by U.S. DOE, Office of Science Contract No. W-31- 109-ENG-38 and by Oak Ridge National Laboratory, man- netic domains provides not only the average magnetization, aged for the U.S. DOE by UT-Battelle, LLC under Contract but also the mean-square dispersion of the domain orienta- No. DE-AC05-00OR22725. Work done at the University of tions. Applying this analysis to the M 0 points of the hys- Minnesota was supported by the NSF MRSEC NSF/DMR- teresis cycle in an exchange-biased Co/CoO sample revealed 9809364. 1 J. F. 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