VOLUME 84, NUMBER 18 P H Y S I C A L R E V I E W L E T T E R S 1 MAY 2000 Diluted Antiferromagnets in Exchange Bias: Proof of the Domain State Model P. Miltényi,* M. Gierlings, J. Keller, B. Beschoten, and G. Güntherodt 2.Physikalisches Institut, RWTH Aachen, 52056 Aachen, Germany U. Nowak and K. D. Usadel Theoretische Tieftemperaturphysik, Gerhard-Mercator-Universität-Duisburg, 47048 Duisburg, Germany (Received 23 December 1999) The exchange bias coupling at ferromagnetic/antiferromagnetic interfaces in epitaxially grown Co CoO layers can intentionally be increased by a factor of up to 3 if the antiferromagnetic CoO layer is diluted by nonmagnetic defects in its volume part away from the interface. Monte Carlo simulations of a simple model of a ferromagnetic layer on a diluted antiferromagnet show exchange bias and explain qualitatively its dilution and temperature dependence. These investigations reveal that diluting the antiferromagnet leads to the formation of volume domains, which cause and control exchange bias. PACS numbers: 75.70.Cn, 75.40.Mg, 75.50.Lk, 85.70.­w Exchange bias results from the exchange coupling at at the interface but rather to a domain state in the vol- interfaces of ferromagnetic(FM)/antiferromagnetic(AFM) ume part of the AFM which triggers the spin arrangement layers leading to a shift of the hysteresis loop along the and the FM/AFM exchange interaction at the interface. magnetic field axis. This shift occurs after cooling the These findings are an important new step in understand- system with the magnetized FM layer below the Néel tem- ing EB, explaining straightforwardly a number of puz- perature of the AFM or for layer deposition in an external zling experimental observations. Our main conclusions are magnetic field. Although this effect has been well known supported by Monte Carlo simulations performed at finite for many years [1,2] and is already intensively exploited in temperatures. magnetic sensor systems (spin valve [3] and magnetoresis- First we will describe the sample preparation by molecu- tance devices [4]), its microscopic origin is still discussed lar beam epitaxy (MBE) and characterization by reflec- controversially. tion high energy electron diffraction (RHEED), low energy In the approach of Malozemoff [5], exchange bias (EB) electron diffraction (LEED), and atomic force microscopy. is attributed to the formation of domain walls in the AFM We have chosen the AFM CoO for its experimentally con- below TN perpendicular to the FM/AFM interface due venient Néel temperature TN 291 K and because it to interface roughness. During cooling these AFM do- allows for two different ways to introduce nonmagnetic mains lead to a small net magnetization at the FM/AFM defects. The first type of defect can be formed with non- interface. This magnetization is then increasingly stabi- magnetic MgO since it has the same crystal structure as lized toward low temperatures, consequently shifting the CoO and only a 1.1% lattice mismatch. Second, Co can hysteresis loop. However, due to the lack of appropriate oxidize in any stoichiometry Co12yO ranging from CoO imaging methods, these domains have never been observed to Co3O4 y 0.25 [10]. Co3O4 has a Néel temperature directly. A recent micromagnetic model by Schulthess and of TN 33 K. This means that, by Co deficiency or, in Butler [6] yields EB only if uncompensated AFM spins are other words, overoxidation of CoO, defects can be created assumed at the interface, which were observed experimen- in the magnetic structure. tally [7]. Other EB models [8,9] assume the formation of As a substrate for film deposition we used (0001)- a domain wall in the AFM parallel to the interface during oriented single crystalline sapphire Al2O3 , which was the hysteresis loop. rinsed in methanol before transfer into the MBE chamber. In this Letter we show that it is possible to strongly Prior to film deposition the substrates were heated to influence (enhance or decrease) EB in Co CoO bilayers T 775 K for 1 h in order to outgas the substrate by diluting the antiferromagnetic CoO layer, i.e., by in- holder and then cooled to the Co growth temperature of serting nonmagnetic substitutions Co12xMgxO or defects T 575 K. 6 nm of Co were deposited by electron beam Co12yO not at the FM/AFM interface but rather through- evaporation at a rate of 0.2 nm min and annealed at a out the volume part of the AFM layer (see upper left temperature of T 775 K for 10 min. The pressure dur- inset of Fig. 2). A 0.4­nm-thick CoO layer with mini- ing evaporation was better than 5 3 1029 mbar. For all mum defect concentration was placed at the interface for samples a 0.4-nm-thick CoO film was grown at a tempera- all samples investigated. The strong dependence of the ture of T 350 K and at a rate of 0.3 nm min by evapo- EB on the dilution of the AFM layer will be argued to rating Co in an oxygen atmosphere of 3.3 3 1027 mbar. have its origin in the formation of a domain state in the This ensures that all samples have an identical FM/AFM volume part of the AFM. We demonstrate that in our interface independent of the dilution of the following AFM systems EB is primarily due not to disorder or defects layer. Then for one set of samples a 20 nm Co12xMgxO 4224 0031-9007 00 84(18) 4224(4)$15.00 © 2000 The American Physical Society VOLUME 84, NUMBER 18 P H Y S I C A L R E V I E W L E T T E R S 1 MAY 2000 layer was grown by electron beam evaporation of Co In order to explain the observed RHEED patterns, a and MgO at a temperature of T 350 K, a rate of (111) orientation of the Co12yO layer is assumed, where 0.3 nm min and an oxygen pressure of 3.3 3 1027 mbar. twins with 60± in-plane rotation relative to each other are The Mg concentration was varied between 0% and 100%. present. The expected diffraction patterns are shown in For a second set of samples, 20 nm of Co12yO were grown Fig. 1(c). The solid and open circles are both recipro- at a temperature of T 350 K and with variable cobalt cal lattice points; however, only the solid circles fulfill deficiency y by choosing the oxygen pressure between the diffraction condition for an fcc lattice. For both di- 3.3 3 1027 mbar and 1.0 3 1025 mbar. All thicknesses rections of 0± and 30± the pattern of full circles fits very of the different layers were controlled by a calibrated well to image Fig. 1(a), while, for explaining the im- microbalance and ex situ atomic force microscopy. age of Fig. 1(b), all reciprocal lattice points have to be In situ RHEED studies of the Co layer indicate taken into account. We conclude that at an oxygen pres- diffraction from a two-dimensional surface. LEED inves- sure of p O2 3.3 3 1027 mbar, practically defect-free tigations reveal a clear sixfold symmetry indicating that CoO is deposited, while, for p O2 1.0 3 1025 mbar, presumably a mixture of hcp (0001) and fcc (111) phases Co12yO is formed. For the Co12yO the destructive inter- is present due to stacking faults. In Fig. 1, RHEED ference from the fcc lattice is suppressed because of some images are shown for a Co12yO layer grown at an oxy- empty lattice sites, and more diffraction spots become vis- gen pressure of (a) p O2 3.3 3 1027 mbar and (b) ible. Without the assumption of twins the symmetrical p O2 1.0 3 1025 mbar. For each Co12yO layer, two RHEED patterns in the right panel 30± of Figs. 1(a) and in-plane orientations denoted as direction 0± and 30± of 1(b) cannot be explained. Atomic force microscope im- the incident electron beam relative to the sapphire ¯1¯120 ages (not shown) reveal crystallites with a size of approxi- axis were chosen (see two vertical panels in Fig. 1). mately 50 nm. This growth mode corresponds to that The diffraction patterns from the Co12yO layer show a reported in Ref. [12]. Hence, we conclude that on epi- transmission image, i.e., diffraction from a rough surface taxial Co(111) layers grown on sapphire(0001) the 0.4 nm with islands [11]. CoO and 20 nm Co12yO or 20 nm Co12xMgxO were de- posited with 60± twins. The magnetic characterization of the samples was performed with a superconducting quantum interference device (SQUID) magnetometer. The EB field was deter- mined from hysteresis loops measured at temperatures between 5 and 320 K. Figure 2 shows hysteresis loops at T 5 and T 320 K of the sample with the Co12yO layer grown at p O2 3.0 3 1026 mbar. The tempera- ture dependence of the EB field of this sample is shown in the inset at the lower right. The blocking temperature is close to TN CoO 291 K. 4 Co1-xMgxO 3 or Co1-yO 320 K 2 CoO Co 5 K 1 Al2O3 2 ] Am 0 -7 -1 80 60 m[10 -2 40 TN -3 20 [mT] 0 -4 0 100 200 300 B EB T[K] -600 -400 -200 0 200 400 600 B[mT] FIG. 1. RHEED images of the Co12yO layer prepared at (a) p O2 3.3 3 1027 mbar y 0 and (b) p O2 FIG. 2. Hysteresis loops of Co12yO CoO Co Al2O3 (0001) 1.0 3 1025 mbar. (c) Calculated reflections of the diffraction at T 5 and 320 K with the Co12yO prepared at p O2 pattern of CoO(111) with 60± twins but only the solid dots fulfill 3.0 3 1026 mbar. The lines are a guide to the eye. The up- the diffraction condition for an fcc lattice. The two vertical per left inset shows schematically the layer structure of the panels show the patterns for 0± and 30± in plane orientation of sample. The lower right inset shows the EB field as a function of the incident electron beam relative to the sapphire ¯1¯120 axis. temperature. 4225 VOLUME 84, NUMBER 18 P H Y S I C A L R E V I E W L E T T E R S 1 MAY 2000 sical Heisenberg model (exchange constant J). The dipo- lar interaction is approximated by including an anisotropy term (shape anisotropy) leading to an in-plane magnetiza- tion. Also, we introduce an easy axis in the FM (anisotropy constant 0.1J) in order to obtain well-defined hysteresis loops. In view of the rather strong anisotropy in CoO we assume an Ising Hamiltonian for the DAFF (see Ref. [14] and references therein; exchange constant JAF 2J 2), where the easy axis is parallel to that of the FM. For the coupling between AFM and FM we assume the same cou- pling constant JINT JAF as for the AFM. In order to model the same interface structure for all calculations the interface monolayer of the AFM was fixed at a dilution of 50%, while we vary the dilution in the volume of the AFM film (8 layers), in analogy to what was done in the experiments. The system is cooled in zero field from above to below the ordering temperature of the DAFF. While the FM is long-range ordered during the cooling procedure the AFM develops due to its coupling to the FM layer a domain state with a surplus magnetization similar to a DAFF when FIG. 3. (a) EB field as function of the Mg concentration x in cooled in an external field. Then hysteresis loops were the Co simulated with the field B almost parallel to the easy axis 12xMgxO layer for various temperatures. ( b) EB field as a function of the oxygen pressure during deposition of the of the system. Co12yO layer for various temperatures. Lines are guides to A typical hysteresis loop is shown in Fig. 4(a). Note the eye. that the interface magnetization of the AFM is shifted to negative values since the exchange coupling to the FM In Fig. 3(a) the EB field is shown as a function of the Mg is negative. This shift of the magnetization of the AFM concentration x for different temperatures. In Fig. 3(b) the is responsible for the EB. Figure 4(b) shows the depen- EB field is shown at different temperatures as a function dence of the EB on the dilution. The overall qualitative of the oxygen pressure p O2 during the preparation of the Co12yO layer. In both cases it can clearly be seen that defects in the AFM layer increase the EB field by a factor of 2­3. At very high dilution the EB starts to drop (a) since the AFM order is destroyed. These results can be explained within the framework of the physics of diluted antiferromagnets. It is by now well known that a diluted antiferromagnet in an external magnetic field (DAFF) develops a domain state when cooled below its Néel temperature [13]. The driving force for the domain formation is a statistical im- balance of the number of impurities of the two sublattices in a finite region of the DAFF. This leads to a net mag- netization which couples to the external field. The neces- (b) sary energy increase due to the formation of domain walls can be minimized if the domain walls pass preferentially through nonmagnetic defects at no cost of exchange energy [14]. Hence, defects substantially favor the formation of domains in the DAFF. Applying this to the present system the domains in the volume of the AFM layer alter the spin structure at the FM/AFM interface leading to a small net magnetization, which results in EB. To support this picture we performed Monte Carlo simu- FIG. 4. (a) Simulated hysteresis loop of the model explained lations of a model consisting of a FM monolayer (size in the text at kBT 0.2J. Shown is the magnetization per spins of the FM monolayer and of the interface AFM monolayer. 128 3 128 sites) exchange coupled to a diluted AFM film (b) EB field as a function of the dilution of the AFM volume consisting of 9 layers. The FM layer is described by a clas- for kBT 0.2J, 0.3J, and 0.5J. 4226 VOLUME 84, NUMBER 18 P H Y S I C A L R E V I E W L E T T E R S 1 MAY 2000 agreement with the experimental finding is clearly given. Since disorder in the AFM layer of exchange bias systems Especially, we observe a strong increase of the EB with the is rather common, our model yields a general understand- dilution before it drops again for larger dilution due to ing of the microscopic origin of exchange bias. Consid- the loss of connectivity of the AFM spin lattice. Since ering the physical properties of diluted antiferromagnets, the thus appearing isolated spin clusters do not contribute important features of EB systems can be explained such as to the AFM domain structure on longer time scales this the differences in EB using thin film or single crystal anti- leads to a decrease of EB for very high dilution. We ferromagnets, positive EB as well as temperature and time would like to emphasize that the maximum strength of the dependence of EB, and others. Further work following simulated EB is of the order of a few percent of the inter- these lines is in progress and will be published elsewhere. face coupling constant in agreement with typical measure- This work has been supported by the Deutsche ments [2]. For small dilution our model does not show any Forschungsgemeinschaft through SFB 341 and 491. EB in contrast to our experimental findings. This can be explained by grain boundaries in the twinned AFM layer which reduce the domain wall energy, thus leading to EB without intentional dilution. On the other hand, in EB sys- tems as, for instance, permalloy on a single crystal of CoO *Email address: peter.miltenyi@physik.rwth-aachen.de [15] and Fe on a single crystal of FeF Email address: uli@thp.uni-duisburg.de 2 [16] only very small EB fields are found in agreement with our model calcula- [1] W. H. Meiklejohn and C. P. Bean, Phys. Rev. 102, 1413 (1956); 105, 904 (1957). tions. For epitaxial NiO layers half the EB field was found [2] J. Nogués and Ivan K. Schuller, J. Magn. Magn. Mater. in comparison to polycrystalline NiO layers [17]. Our find- 192, 203 (1999). ings concerning the role of defects in the volume of the [3] B. Dieny et al., Phys. Rev. B 43, 1297 (1991). AFM layer complement the ideas of Malozemoff [5] who [4] C. Tsang, J. Appl. Phys. 55, 2226 (1984). assumed exclusively an interface roughness as the cause of [5] A. P. Malozemoff, Phys. Rev. B 35, 3679 (1987); J. Appl. domains in the AFM. Phys. 63, 3874 (1988); Phys. Rev. B 37, 7673 (1988). Assuming that the AFM used in EB systems is in a do- [6] T. C. Schulthess and W. H. Butler, Phys. Rev. Lett. 81, 4516 main state similar to that of a DAFF, further experimental (1998); J. Appl. Phys. 85, 5510 (1999). findings can be understood straightforwardly. First, it is [7] K. Takano et al., Phys. Rev. Lett. 79, 1130 (1997); J. Appl. the positive EB [18] or reduced EB [19] observed experi- Phys. 83, 6888 (1998). mentally in strong cooling fields. During the cooling in [8] D. Mauri et al., J. Appl. Phys. 62, 3047 (1987). [9] M. D. Stiles and R. D. McMichael, Phys. Rev. B 59, 3722 a strong field the AFM forms domains with the surplus (1999). magnetization being parallel to the external field and also [10] R. Dieckmann, Z. Phys. Chem. 107, 189 (1977). to the magnetization of the FM. If the coupling between [11] M. G. Lagally, D. E. Savage, and M. C. Tringides, in Re- AFM and FM is negative as assumed in Ref. [18], this will flection High-Energy Electron Diffraction and Reflection yield positive EB. Second, the time dependence of EB in Electron Imaging of Surfaces, edited by P. K. Larsen and Ni66Co18Fe16 NiO and Ni66Co18Fe16 FeMn [20] after the P. J. Dobson (Plenum Press, New York, 1987), p. 139. FM layer is reversed from its cooling field direction can [12] M. J. Carey et al., J. Mater. Res. 6, 2680 (1991). be understood in the framework of the dynamics of the [13] For a review, see W. Kleemann, Int. J. Mod. Phys. B 7, DAFF. Here it is known that the remanent magnetization 2469 (1993); D. P. Belanger in Spin Glasses and Random of the domain state relaxes nonexponentially on extremely Fields, edited by A. P. Young (World Scientific, Singapore, long time scales after the field is switched off [21,22]. This 1998). [14] U. Nowak and K. D. Usadel, Phys. Rev. B 46, 8329 (1992); relaxation of the magnetization of the DAFF is linked di- J. Esser, U. Nowak, and K. D. Usadel, Phys. Rev. B 55, rectly to the relaxation of the EB, if one assumes that the 5866 (1997). domains in the AFM are responsible for EB. Third, the [15] T. J. Moran, J. M. Gallego, and Ivan K. Schuller, J. Appl. reason for the so-called training effect can be understood Phys. 78, 1887 (1995). from Fig. 4(a), where it is shown that the hysteresis loop of [16] J. Nogués et al., Phys. Rev. B 59, 6984 (1999). the AFM is not closed on the right-hand side. This implies [17] R. P. Michel, A. Chaiken, and C. T. Wang, J. Appl. Phys. that the magnetization of the AFM is lost partly during the 81, 5374 (1997). hysteresis loops due to a rearrangement of the AFM do- [18] J. Nogués et al., Phys. Rev. Lett. 76, 4624 (1996). main structure. [19] T. J. Moran and Ivan K. Schuller, J. Appl. Phys. 79, 5109 In conclusion, we have shown both by experiments and (1996). by Monte Carlo simulations that diluting the AFM layer in [20] P. A. A. van der Heijden et al., Appl. Phys. Lett. 72, 492 (1998); J. Appl. Phys. 83, 7207 (1998). the volume part away from the FM/AFM interface signifi- [21] S-J. Han et al., Phys. Rev. B 45, 9728 (1992). cantly enhances EB. This dilution induced by nonmagnetic [22] U. Nowak, J. Esser, and K. D. Usadel, Physica (Amster- defects supports the formation of volume domains in the dam) 323A, 40 (1996); M. Staats, U. Nowak, and K. D. AFM which are crucial for the existence of exchange bias. Usadel, Phase Transit. 65, 159 (1998). 4227