VOLUME 88, NUMBER 15 P H Y S I C A L R E V I E W L E T T E R S 15 APRIL 2002 Coarsening of Antiferromagnetic Domains in Multilayers: The Key Role of Magnetocrystalline Anisotropy D. L. Nagy,1 L. Bottyán,1 B. Croonenborghs,2 L. Deák,1 B. Degroote,2 J. Dekoster,2 H. J. Lauter,3 V. Lauter-Pasyuk,4,5 O. Leupold,6 M. Major,1,2 J. Meersschaut,2 O. Nikonov,3,4 A. Petrenko,4 R. Rüffer,6 H. Spiering,7 and E. Szilágyi1 1KFKI Research Institute for Particle and Nuclear Physics, P.O. Box 49, H-1525 Budapest, Hungary 2K.U. Leuven, Instituut voor Kern- en Stralingsfysica, Celestijnenlaan 200 D, B-3001 Leuven, Belgium 3Institut Laue-Langevin, BP 156, F-38042 Grenoble Cedex 9, France 4Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141 980 Dubna, Moscow Region, Russia 5Technische Universität München, James Franck Strasse 1, D-85747 Garching, Germany 6European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, France 7Institut für Anorganische Chemie und Analytische Chemie, Johannes Gutenberg Universität, D-55099 Mainz, Germany (Received 29 May 2001; published 29 March 2002) The domain structure of an antiferromagnetic superlattice is studied. Synchrotron Mössbauer and polarized neutron reflectometric maps show micrometer-size primary domain formation as the external field decreases from saturation to remanence. A secondary domain state consisting mainly of at least 1 order of magnitude larger domains is created when a small field along the layer magnetizations induces a bulk-spin-flop transition. The domain-size distribution is reproducibly dependent on the magnetic prehistory. The condition for domain coarsening is shown to be the equilibrium of the external field energy with the anisotropy energy. DOI: 10.1103/PhysRevLett.88.157202 PACS numbers: 75.70.Kw, 75.25.+z, 75.30.Gw Antiferromagnetically (AF) coupled metallic multi- samples showed j # 1 mm-size AF domains ["primary layers [1] have received much attention due to their domain state" (PDS)] when decreasing the external relevance in fundamental science and technology alike. field from saturation to zero. A PDS was invoked to The archetype Fe Cr system shows oscillatory interlayer describe the broad off-specular sheets in PNR at the coupling [2,3] and giant magnetoresistance (GMR) [4]. AF reflection of Fe Cr MLs in applied magnetic field Magnetic and transport behavior of coupled magnetic mul- [11]. The observations of the low-field behavior of the tilayers (MMLs) is affected by static and dynamic prop- domain structure of AF MLs are, nevertheless, contro- erties of the domain structure. Domain-size-dependent versial. A coarsening of the domains to an average size resistance noise may be as large as to limit GMR-sensor of j $ 10 mm ["secondary domain state" (SDS)] was applications [5]. Nevertheless, our direct knowledge on observed in a small decreasing or reverting field, in other the domain structure is limited to a few thick trilayer cases in small increasing external fields [5,6,8,9,14,15]. A studies [6,7]. This is related to the difficulties in visual- difference in the in-plane magnetic correlation length was izing in-plane AF domains in a multilayer (ML) of few found by soft-x-ray resonant magnetic diffuse scattering nm thickness. Therefore indirect methods such as resis- in a Co Cu ML when magnetized in the easy or hard tance noise [5] and magnetoresistance [8] measurements, direction [12]. Although the domain-wall energy is the off-specular nonpolarized [9] and polarized neutron reflec- driving force of the PDS ! SDS transition, this is, in the tometry (PNR) [10,11], and soft-x-ray resonant magnetic light of the above observations, not enough to explain diffuse scattering [12] have been used to estimate the their diversity. AF-domain-size distribution in MMLs. We investigated the PDS ! SDS transition by off- In remanence, a MML is in a multidomain state. In a specular synchrotron Mössbauer reflectometry (SMR) strongly AF-coupled ML the magnetic domain structure (grazing incident nuclear resonant reflection of synchro- of the individual ferromagnetic (FM) layers is strictly tron radiation) [16], and by PNR. For both methods, correlated through the ML stack from substrate to surface. the off-specular scattering width around an AF reflec- This results in zero net magnetization magnetic super- tion stems from the finiteness of j (domain structure, structure domains in a periodic ML of an even number "magnetic roughness"). In the present Letter, using SMR of equally thick FM layers. It is in this sense the term and PNR, we identify the key role of magnetocrystalline "AF domain" is used here [13]. Kerr microscopy on AF- anisotropy in the domain coarsening. We demonstrate that coupled Fe Cr Fe trilayers first revealed domains with the PDS ! SDS transition takes place when the system "sizes" of the order of a few mm arranged in a patchlike is passing a bulk-spin-flop (BSF) transition and that the pattern [6]. Let the lateral "size" of the AF domains field history is an important factor determining the actual (strictly speaking, the correlation length of the magne- domain structure. tization direction) be j. Electric transport data [5,8] The ML sample was grown on an MgO(001) sub- on coupled polycrystalline Co Cu sandwiches and ML strate at 450 K by molecular beam epitaxy alternately 157202-1 0031-9007 02 88(15) 157202(4)$20.00 © 2002 The American Physical Society 157202-1 VOLUME 88, NUMBER 15 P H Y S I C A L R E V I E W L E T T E R S 15 APRIL 2002 depositing 57Fe from a Knudsen cell and Cr from an All scans were taken at 290 6 2 K in zero magnetic field electron gun at a rate of 0.1 and 0.35 Å s, respectively, following a magnetic-field history as detailed below. The and base pressure of 4 3 10210 mbar. Using high- and off-specular scattering was measured on the first-order AF low-angle x-ray diffraction as well as Rutherford reflection at a fixed angle of 2Q 0.80± [18,19]. Photons backscattering an MgO 001 57Fe 26 Å Cr 13 Å 20 from both the electronic (prompt) and the resonant nuclear epitaxial superlattice structure was found with scattering (delayed, SMR) process were recorded as a MgO 001 110 k Fe 001 100 and root mean square function of the angle of incidence 0 , v , 2Q. interface roughness of 0.4 nm. Magneto-optical Kerr The PNR experiments were done at the SPN-1 polar- effect (MOKE) and vibrating-sample magnetometry both ized neutron reflectometer of Joint Institute for Nuclear indicated AF coupling with a saturation field Hs 0.9 T. Research, Dubna, Moscow, Russia [20] in in-plane static A schematic view of the chemical and magnetic structures magnetic fields parallel to the linear polarization of the in- of the sample is shown in the inset of Fig. 1A. coming neutrons at 286 6 2 K. Two spin flippers were The SMR experiments were performed at the ID18 operated to change the polarization of the incoming and beam line of the European Synchrotron Radiation Facility, the scattered neutrons. The spin of the scattered neutrons Grenoble, France [17]. The sample was placed in a super- was analyzed by a Soller-mirror polarizer. The neutrons conducting split-coil magnet mounted on a goniometer. reflected by the Soller mirror hit a position-sensitive de- tector so that the scattered neutron intensity was mapped onto the qz-qx plane in all (11, 12, 21, and 22) 100 channels. In remanence, the magnetization vectors of the Fe lay- ers in the AF superlattice with fourfold in-plane anisotropy 50 point parallel or antiparallel to either of the Fe[010] or A Fe[100] easy axes in the film plane. Releasing the mag- 0 netic field parallel to one of the easy axes from satura- 100 tion, the magnetizations settle solely in the perpendicular k easy direction. As recently observed with PNR [21] on [100] 50 an equivalent and with MOKE [18] and SMR [18,19] on B the same sample, an irreversible BSF transition takes place [010] when a moderate magnetic field is applied along the easy 0 axis in which the layer magnetizations actually lie. At a 100 [100] k critical BSF field of HSF 13 mT, where the magnetic k ("Zeeman") energy overcomes the fourfold in-plane mag- 50 10][0 [100] netocrystalline anisotropy, the layer magnetizations jump into the perpendicular easy axis [18,19,21]. The align- [010] C 0 ment is retained in remanence. In these samples since 100 [100] no uniaxial anisotropy was present, the surface-spin-flop transition previously observed in Fe Cr(211) superlattices reflected intensity (% of maximum) [22,23] played no role. 50 10] k [0 In the present SMR experiment, the sample was first D saturated along the Fe[100] easy direction in 4.07 T, a 0 field well above H -6 -4 -2 0 2 4 6 S. In Fig. 1, v scans are shown as a function of the longitudinal in-plane component qx q 2kQ v 2 Q of the scattering vector q, where k jkj x (10-4 Å-1) and k is the photon wave vector. When the field was re- FIG. 1. Off-specular v scans. Reflected intensity vs scat- leased, the layer magnetizations lay in the perpendicular tering vector component qx 2kQ v 2 Q of a MgO 001 Fe[010] easy direction, parallel or antiparallel to k (inset 57Fe 26 Å Cr 13 Å 20 ML at the AF Bragg-reflection (Q of Fig. 1B). While a sharp specular reflection was ob- 0.4±) measured in zero external magnetic field: (A) prompt served in the prompt reflectivity (Fig. 1A), only a broad reflectivity, not being dependent on magnetic field prehistory, (B)­(D) delayed reflectivity, (B) following saturation in 4.07 T, diffuse shoulder appeared in the SMR v scan (Fig. 1B). (C) following exposure to 13 mT parallel to the magnetizations On rotating the sample by 90±, the magnetizations turned (open circles: nonflipped domains; full circles: flipped do- perpendicular to k, and the AF reflections disappeared mains), (D) following exposure to a field of 35 mT. The inset since for k-perpendicular hyperfine field no AF reflec- in (A) is a schematic side view of the chemical and magnetic tions are expected in Q 2 2Q SMR scans [16]. The structure of the sample in the vicinity of a domain wall (dot- intensity of the AF reflections recovered, when a field ted line). The insets in (B)­(D) are schematic top views of the orientation of the crystallographic axes and of the top-layer of 12 to 16 mT was applied along the Fe[010] direction magnetizations (short and long arrows represent small and large perpendicular to the photon wave vector k and the ML domains, respectively) relative to the photon wave vector k. passed the BSF [19]. Figure 1C shows two v scans of 157202-2 157202-2 VOLUME 88, NUMBER 15 P H Y S I C A L R E V I E W L E T T E R S 15 APRIL 2002 considerably different width, taken in two mutually per- pendicular orientations of the sample relative to k follow- ing an exposure of the ML to 13 mT, halfway in the BSF transition. At this point, the flipped regions of the ML (left inset of Fig. 1C) mainly give rise to a narrow specu- lar peak, whereas the not-yet-flipped regions (right inset of Fig. 1C) stay to show a broad diffuse shoulder in the de- layed intensity. By exposing the sample to 35 mT, the BSF transition is completely passed (inset of Fig. 1D) and the v scan is dominated by a specular peak (Fig. 1D). No fur- ther change in the shape of the v scan could be induced by any field cycle including repeated generation of BSF transitions, until the system was fully saturated. However, exposing the sample to a 4.07 T field again, the v scans became identical with that shown in Fig. 1B; i.e., the spec- ular peak disappeared from the SMR v scan. The pure diffuse delayed reflectivity in Fig. 1B shows that the PDS is retained in zero field. The magnetic corre- lation length j of the AF domains can be calculated from the shape of the diffuse shoulders. Supposing an expo- nential autocorrelation function for the in-plane magne- FIG. 2. Normalized neutron reflectivity maps. Polarized tization in the PDS, j 2.6 mm is estimated from the neutron intensity scattered specularly and off-specularly by a SMR peak width. The narrow specular peak following the MgO 001 57Fe 26 Å Cr 13 Å 20 ML in a magnetic field of (A) 7 mT, (B) 14.2 mT, and (C) 35 mT in R22 (left side) BSF (Fig. 1D) is indicative of large domains. In this SDS, and in R21 (right side) channels as a function of the scattering large and small flipped domains coexist, giving rise to nar- vector components qx and qz. row and broad components in the v scan, respectively. Because of the finite experimental resolution in 2Q, only a lower limit of j . 16.5 mm can be deduced for the large following consideration. A lateral variation of the cou- domains. The deduced minority small flipped domain size pling strength due to layer thickness fluctuations is un- is j 2.6 mm, i.e., equal to that in the PDS. Midway into avoidable. Consequently, the saturation field HS is also the BSF transition (Fig. 1C), the nonflipped regions are in subject to a finite lateral distribution characterized by a the PDS, whereas the flipped regions are in the SDS. correlation length jS close to the terrace length of the The domain coarsening can be monitored by polarized ML (typically a few tens of nm). Gradually releasing neutron diffuse scattering, without rotating the sample. the field applied along the [100] direction from full satu- Prior to the PNR experiment the sample was ex situ satu- ration, first the strongest-coupled regions have the freedom rated in 2.1 T, i.e., well above HS and mounted in zero "to decide" whether their odd and even layers start ro- field with magnetization parallel antiparallel to the inci- tating clockwise and counterclockwise, respectively, or dent neutron polarization. PNR maps taken in increasing vice versa [14]. Upon further decreasing the field, the external field are shown in Fig. 2. Left and right columns layer magnetization direction of the neighboring regions in Fig. 2 represent non-spin-flip and spin-flip reflectivi- becomes unstable. The minute AF domain-wall energy ties (here R22 and R21 , corresponding to magnetization becomes decisive in this state and the neighboring regions components parallel antiparallel and perpendicular to the nucleate on the already rotated regions, so that the sense neutron spin, respectively. In a field below HSF (Fig. 2A) of rotation of the individual layers is preserved. The nu- the AF reflection appears only in the non-spin-flip chan- cleation goes on until the individual layer magnetizations nels and consists of a broad diffuse sheet. In contrast, settle in either the [010] or the 0¯10 direction, giving rise in Fig. 2C, in a field above the transition, the AF reflec- to the observed patch structure [6] consisting of two types tion is observed only in the spin-flip channels. While the of domains in remanence that differ only in the order of non-spin-flip channels consist only of off-specular diffuse the FM sheets (180± domain walls). Nevertheless, in the sheets, the spin-flip channels show mainly specular scat- PDS j . jS, since with decreasing field the domain-wall tering. Midway into the transition (Fig. 2B), the AF re- angle and, consequently, the domain-wall energy per unit flection shows up in both channels, in full accordance with area increases. Therefore, also j increases beyond jS to the SMR results. decrease the domain-wall density and, thereby, to mini- The experiments show that the BSF transition in an an- mize the domain-wall energy. This spontaneous growth of tiferromagnetically coupled multilayer results in a sudden the domains is limited by the domain-wall pinning (coer- coarsening of the primary domain size by at least 1 order civity), and the gain in domain-wall energy is not enough of magnitude. The formation of the PDS and the sudden to increase the average domain size beyond a certain limit. coarsening on BSF can be understood qualitatively by the Using literature values of the Fe exchange and anisotropy 157202-3 157202-3 VOLUME 88, NUMBER 15 P H Y S I C A L R E V I E W L E T T E R S 15 APRIL 2002 constants, the Fe saturation magnetization and measured in the literature by showing that the condition for domain values of the interlayer-coupling constant, and estimated coarsening is not the equilibrium of the Zeeman energy values of the coercivity [24], the critical size of the patch with the domain-wall energy, but the equilibrium of the domains in the PDS jc 0.6 8.4 mm was predicted [25], Zeeman energy with the anisotropy energy. It is only this in accordance with the observed value of 2.6 mm. The do- equilibrium that permits the minute AF domain-wall en- mains are bound to their original sense of rotation as long ergy to radically shape the domain structure. Out of this as the magnetic field remains parallel to the [100] or to the equilibrium the Zeeman energy and the anisotropy energy, ¯100 direction, since the domain orientation is stabilized whichever is greater, assist the coercivity in stabilizing the by the Zeeman energy in high fields and by the magneto- actual domain structure. crystalline anisotropy energy in low fields. This work was partly supported by the Hungarian The mechanism of BSF-induced coarsening basi- Scientific Research Fund (OTKA) under Contract cally differs from that of the PDS formation. In- No. T029409, the Flemish-Hungarian bilateral Project deed, when an increasing magnetic field is applied in (20/98), and the European Communities (Contract the magnetization-parallel ([010] or 0¯10 ) direction, the No. ICA1-CT-2000-70029). The authors acknowledge anisotropy energy preserves the primary domain structure helpful discussions with Dr. E. Kunnen, Dr. Yu. V. only for H , HSF. At H HSF, the system becomes Nikitenko, and Dr. K. Temst. B. D. and J. M. thank the energetically unstable and the layer magnetizations flip Belgian Science Foundation (F.W.O.-Vlaanderen) for to either the [100] or ¯100 direction. There is again a financial support. freedom in the sense of rotation and, similar to HS, also HSF obeys a distribution. However, at H HSF the system is close to an energy maximum and behaves like an explosive material: it may jump to an energy minimum [1] P. Grünberg et al., Phys. Rev. Lett. 57, 2442 (1986). by 90± or 290± rotation of the magnetization. Once [2] S. S. P. Parkin, N. More, and K. P. Roche, Phys. Rev. Lett. the first region with the lowest value of HSF "decides" 64, 2304 (1990). between a 90± or 290± flop, it will "ignite" the neighbor [3] J. Unguris, R. J. Celotta, and D. T. Pierce, Phys. Rev. Lett. regions, which will choose the same direction of magne- 67, 140 (1991). tization to avoid creating new domain walls. In contrast [4] M. N. Baibich et al., Phys. Rev. Lett. 61, 2472 (1988). to primary domain formation, secondary domains on BSF [5] H. T. Hardner, M. B. Weissmann, and S. S. P. Parkin, Appl. may grow without any long-range domain-wall motion, Phys. Lett. 67, 1938 (1995). and this growth is, therefore, not limited by coercivity. [6] M. Rührig et al., Phys. Status Solidi A 125, 635 (1991). [7] R. Schäfer, J. Magn. Magn. Mater. 148, 226 (1995). BSF-induced domain coarsening is an explosionlike 90± [8] N. Persat, H. A. M. van den Berg, and K. Cherifi- flop of the magnetization annihilating primary 180± walls Khodjaoui, J. Appl. Phys. 81, 4748 (1997). (and also the temporary 90± walls created during the [9] S. Langridge et al., Phys. Rev. Lett. 85, 4964 (2000). BSF). Consequently, the secondary patch domain size [10] G. P. Felcher, Physica (Amsterdam) 192B, 137 (1993). may become comparable with the sample size. [11] V. Lauter-Pasyuk et al., Physica (Amsterdam) 283B, 194 The details of the PDS ! SDS transition and the mor- (2000). phology of the resulting SDS depend on the correlation [12] T. P. A. Hase et al., Phys. Rev. B 61, R3792 (2000). length j [13] Unless otherwise stated, all domain properties (size, orien- SF of HSF and also on how the domain-wall den- sity scales with j. During the BSF, new nucleation centers tation, etc.) will be meant for the remanent state. may be formed beyond j [14] N. Persat et al., J. Magn. Magn. Mater. 165, 446 (1997). SF. If the "explosion" of a new center is fast enough so that the flopped domain becomes [15] L. J. Heyderman, J. N. Chapman, and S. S. P. Parkin, J. Appl. Phys. 76, 6613 (1994). larger than jc before it will be surrounded by a domain of [16] D. L. Nagy et al., Hyperfine Interact. 126, 353 (2000). opposite layer magnetization, it survives as an inclusion; [17] R. Rüffer and A. I. Chumakov, Hyperfine Interact. 97/98, otherwise it disappears. In fact, such inclusions are stable 589 (1996). only for j . jc [25]. This qualitatively explains the ob- [18] L. Bottyán et al., J. Magn. Magn. Mater. 240, 514 (2002). served coexistence of small and large domains in the SDS [19] L. Bottyán et al., in ESRF Highlights 1999 (European but a detailed model calculation is not yet available. Synchrotron Radiation Facility, Grenoble, 2000), p. 62, In conclusion, off-specular SMR and PNR evidenced a available through http://www.esrf.fr/. field-history dependent AF domain structure in a coupled [20] http://nfdfn.jinr.ru/fks/spn.html Fe Cr superlattice. Leaving the saturation region, a pri- [21] K. Temst et al., Physica (Amsterdam) 276B­278B, 684 mary small-domain state is created in remanence. From (2000). this, when the system passes a BSF transition, a secondary [22] R. W. Wang et al., Phys. Rev. Lett. 72, 920 (1994). [23] R. W. Wang and D. L. Mills, Phys. Rev. B 50, 3931 (1994). domain state is formed that predominantly consists of large [24] The coercivity of a fully compensated AF-coupled ML domains. The presented model gives a new insight into the cannot be measured directly. Therefore, data measured on nature of the domain transformation (with obvious impli- similar ferromagnetically coupled samples were used. cations on the transport noise) and lifts the controversy [25] D. L. Nagy et al., Phys. Status Solidi A 189, 591 (2002). 157202-4 157202-4