RAPID COMMUNICATIONS PHYSICAL REVIEW B VOLUME 57, NUMBER 14 1 APRIL 1998-II Superparamagnetic behavior of structural domains in epitaxial ultrathin magnetite films F. C. Voogt,* T. T. M. Palstra, L. Niesen, O. C. Rogojanu, M. A. James, and T. Hibma Materials Science Centre, University of Groningen, Nijenborgh 4, 9747 AG, Groningen, The Netherlands Received 31 October 1997 We provide evidence that thin films of magnetite Fe3O4 epitaxially grown on single-crystalline MgO 100 , form domains with unique magnetic properties. Strong 180° Fe-O-Fe superexchange paths at antiphase domain boundaries result in a frustration of the interdomain interactions. Probe-layer Mo¨ssbauer spectroscopy shows superparamagnetic behavior in the entire film, in spite of the nearly perfect layer-by-layer growth. Supercon- ducting quantum interference device magnetometry is used to determine the temperature and thickness depen- dence of the superparamagnetic blocking temperatures. S0163-1829 98 00914-X Thin-film systems of magnetic transition metal oxides are films are single crystalline, because of the completely lattice under intense investigation at present, for their unique mag- matched growth, they will inherently contain antiphase netic properties.1­3 The combination of full spin polarization boundaries.11 The lower symmetry and the larger unit cell of at the Fermi level and magnetic ordering temperatures above the inverse spinel crystal structure, compared to the rock-salt room temperature allow for the development of device con- structure, result in that an Fe3O4 island can nucleate on cepts. Much recent work focuses on spin-polarized current MgO 100 in eight unique ways. As shown in Fig. 1, an- injection.4,5 This way, one intends to control the resistance of tiphase boundaries are the result of the coalescence of is- magnetic materials or the critical current of superconducting lands, which are either rotated over 90° with respect to each materials. However, the charge transport in oxides is deter- other, or shifted, or both. Such antiphase boundaries have mined by short-range interactions, typically between nearest recently been made visible by scanning tunnel microscope or next-nearest neighbors. Therefore, the success of these STM imaging of molecular-beam epitaxy MBE grown concepts depends on the nature of the interfaces and surfaces Fe3O4 layers on MgO 100 .12 Consequently, the layer will of the materials. The structure in these regions can be differ- ent from the bulk by intrinsic effects, such as stress/strain, reconstructions, or by extrinsic effects, such as nonstoichi- ometry, interdiffusion, etc. Small variations can alter the magnetic behavior significantly. This makes a proper under- standing of the surface/interface magnetic state indispens- able. This state is not only critical for spin-polarized trans- port, but also for exchange biasing6,7 or for the magnetic properties of ultrasmall particles.8 Only a few materials combine full spin polarization with high Curie temperatures ( 300 K): the manganese perovs- kites, the spinel Fe3O4, CrO2, and several Heusler com- pounds such as PtMnSb. In this paper, we focus on Fe3O4, a highly correlated material with a TC of 858 K. There have been several reports of anomalous magnetic behavior. Stud- ies on thin-film saturation magnetizations at room tempera- ture showed a decrease, which was modeled with nonmag- netic or disordered, ``dead'' interface layers of 0.7 nm.9 Such layers would render this material impractical for spin- polarized transport or exchange biasing. However, this inter- pretation is in disagreement with earlier depth-selective Mo¨ssbauer spectra of 50.0 and 100 nm-thick bulklike films.10 The latter measurements indicated that the interface, surface, and bulk layers have the same magnetic properties, including the characteristic charge-ordering Verwey transition. FIG. 1. Schematic representation of the formation of an Fe In this paper, it is shown that for ultrathin layers also 3O4 film on MgO 100 . For clarity, only one monolayer, containing only ( 5 nm), the properties of the surface and interface layers octahedral Fe cations, is shown. The coalescence of islands 1 with are not different from the interior, i.e., the dead layer model 2, and 3 with 4, which are shifted with respect to each other, leads is invalidated. Instead, we will demonstrate that Fe3O4 films, to new antiferromagnetic 180° Fe-O-Fe superexchange paths at the in the ultrathin limit, behave superparamagnetically. The ori- antiphase boundaries, as indicated with solid lines. The same paths gin of this superparamagnetism lies in the nucleation process arise after coalescence of islands, which are rotated over 90° with of the Fe3O4 films on MgO 100 . Although these epitaxial respect to each other islands 1,2 with 3,4 . 0163-1829/98/57 14 /8107 4 /$15.00 57 R8107 © 1998 The American Physical Society RAPID COMMUNICATIONS R8108 F. C. VOOGT et al. 57 FIG. 2. Room-temperature conversion electron Mo¨ssbauer spectra CEMS of 100 Fe3O4 /MgO multilayers, as a function of Fe3O4 layer thickness indicated above each spectrum , and 57Fe probe position: a in the center of the Fe3O4 layer, and b at the Fe3O4 /MgO interface. have a continuous O2 sublattice, but a fragmented cation research from several other groups see Ref. 15 . Therefore, sublattice. Fe3O4 thin films should, therefore, be regarded as we stress that the films are not poly, but single crystalline, a patchwork of domains. with atomically flat interfaces. We will provide evidence that this domain structure leads The structural quality of the multilayers was checked with to a unique form of superparamagnetism. The bulklike ex- x-ray specular reflectivity measurements. Apart from the change interactions are interrupted at the antiphase bound- bulk Bragg peaks, the spectra clearly show superlattice aries, which causes the crystallographic domains to act like peaks, due to the Fe3O4 /MgO bilayer repeat unit, and smaller magnetic domains. These domains can change their magne- secondary maxima, due to the total multilayer thickness. The tization direction with thermal activation energies. Fe3O4 layer thicknesses mentioned in this paper have been To investigate the magnetic properties of ultrathin Fe3O4 obtained from fits to these spectra. For the interface rough- films, we have adopted the technique from Ref. 10. nesses, we find values of 0.3 nm, which correspond to Multilayer samples were made consisting of 5 Fe3O4 layers, only 1­2 monolayers. separated and capped by 2.0 nm-thick MgO layers. Three Figure 2 shows room-temperature conversion electron different Fe3O4 layer thicknesses were studied, i.e., 1.8, 3.5, Mo¨ssbauer spectra CEMS as a function of the Fe3O4 layer and 5.3 nm. Each Fe3O4 layer consisted of a probe layer of thickness and 57Fe probe position. Two features of the spec- 0.42 nm 2 monolayers grown with the Mo¨ssbauer active tra directly catch the eye. First, as the layer thickness de- isotope 57Fe, positioned in a matrix grown with natural Fe. creases, there is a transition from a static configuration to a By locating this probe layer either at the Fe3O4 /MgO inter- phase where the magnetic spins are fluctuating very rapidly. face or in the center of the Fe3O4 layer, position-specific For the two 5.3 nm samples, the spectra show two hyperfine- information concerning the magnetic properties could be ob- split sextets, originating from the long-range ferrimagnetic tained. We point out that the function of the multilayer struc- order in Fe3O4.10 The hyperfine fields are smaller than those ture is merely to enhance the Fe3O4 signal. The MgO spacer of the bulk, already indicating enhanced fluctuations for this thickness is large enough to exclude exchange coupling be- thickness. In the case of the thinnest layers 1.8 nm , the tween successive Fe3O4 layers via ferrimagnetic bridges.13 spectra are completely motionally narrowed, showing only The multilayers have been grown epitaxially on ex situ one single line. Here, the Fe magnetic spins are fluctuating at cleaved single crystalline MgO 100 substrates, by means of least two orders of magnitude faster than the Larmor preces- NO2-assisted MBE. Details concerning this growth technique sion frequency of the nuclear spins ( 108 Hz). Typical re- can be found in Ref. 14. Both oxides grow perfectly lattice laxation behavior is found for the two 3.5 nm samples. In matched on top of each other, with 100 orientations and a this intermediate case, the spins are fluctuating on the same parallel alignment of the 100 cubic crystal axes. Moreover, time scale as the Larmor period. we always observe strong and persistent reflection high- Second, probe layers at the interface and in the interior energy electron diffraction intensity oscillations during depo- have similar magnetic properties. As can be seen in Fig. 2, sition, which is a fingerprint of layer-by-layer growth. This the shape of the spectra only depends on the layer thickness, conclusion is not only reached from our work, but also by and not on the probe position. This observation, together RAPID COMMUNICATIONS 57 SUPERPARAMAGNETIC BEHAVIOR OF STRUCTURAL . . . R8109 K, MR rapidly vanishes for the thin films. The monotonous decrease of MR with temperature indicates superparamag- netic relaxation. The point where the MR curves level off can be identified as the maximum blocking temperature, TB . This gives values of 40, 140, and 250 K for the 1.8, 3.5, and 5.3 nm thick films, respectively. The decay of MR is governed by the relaxation time , the time to reverse the domain magnetization over a barrier with a height W. In a simple activated model, we can write18 1 0 exp(W/kT), where 0 is the attempt frequency ( 1011 Hz). It follows that the observed TB depends on the timescale of the measurement, m . If m , the system FIG. 3. Remanent magnetization MR , in units of B per for- behaves superparamagnetically, and if it is the other way mula unit Fe3O4, of Fe3O4 /MgO multilayers, after saturation in an around, we observe the blocked state. By definition, m at external field of 1 T at 5 K, as a function of temperature and Fe3O4 T layer thickness. B . Given the difference in m for CEMS and SQUID mag- netometry, i.e., 10 8 vs 102 s, TB observed with CEMS with similar observations reported for 50.0 and 100.0 nm- should be 175, 600, and 1080 K, for the three films. This is thick bulklike layers,10 rules out the idea of magnetically in reasonable agreement with our data, i.e., the 1.8 nm films inactive, dead layers, sandwiching a ferrimagnetic interior. behave fully paramagnetic, the 3.5 nm films are approaching Instead, the Fe3O4 layer behaves as a single magnetic entity TB , and the 5.3 nm films are in the blocked state. Note, that for all thicknesses. We point out that the broad parabolic with SQUID we have determined the maximum values of background in the case of probe layers situated at the inter- TB . These have to be considered as the upper limit of a face corresponds to the outermost atomic plane in the Fe3O4 broad distribution. layer. The Fe2 and Fe3 ions in this monolayer have a We attribute the superparamagnetic behavior to thermal reduced number of nearest neighbors, resulting in a weak- fluctuations of the magnetic moments of structural domains. ened ferrimagnetic ordering. The parabolic shape of this To demonstrate that these domains can indeed change the background probably arises from a broad distribution of re- orientation of their magnetization with thermal activation en- duced hyperfine fields.10 ergies, we will evaluate the various barrier heights for fluc- In bulk Fe3O4, the dominant superexchange interaction tuation. These depend on intrinsic properties of the domains, between nearest-neighbor A-B ions is quite strong, i.e., JAB and also on the interaction between them.18 We will consider 23.4 K,16 leading to a high ferrimagnetic ordering tem- domains in the thinnest film, assuming a columnar, rectan- perature T gular shape with lateral dimensions of roughly 10 nm.12 C of 858 K.17 This excludes a description in terms of individually fluctuating spins, i.e., paramagnetism. There- The following three barriers are considered: fore, the observed fluctuations must be collective spin fluc- i Magneto-crystalline anisotropy energy. The barrier in tuations of entire domains, i.e., the thin films are superpara- the film plane is given by Wa K1V/4, with K1 13 kJ/m3 magnetic. Ref. 9 and V the volume of the domain. This leads to Wa Complementary evidence was obtained with supercon- 4 meV. ducting quantum interference device SQUID magnetom- ii Magnetic dipole-dipole interactions between domains. etry measurements MPMS-7, Quantum Design . In the in- Following the model of Dormann et al.18 for interacting fer- verse spinel structure of Fe3O4, the antiparallel coupling of rimagnetic particles, we estimate this contribution to be Wd the A- and B-site sublattices yields formally one uncompen- 0M2V jnjaj kT jnj , where the summation is over sated Fe2 spin per formula unit Fe 3 3O4, with a magnetic all neighboring domains. Here, aj (3 cos2 i 1)V/di , with moment of 4.1 B .17 At 25 K, all multilayers can be magne- i and di the polar angle and length of the position vector of tized to saturation in external fields of 0.5 T, yielding mag- domain i with respect to the origin domain, taking the do- netic moments of 4.9, 5.2, and 4.5 B /Fe3O4 for thicknesses main magnetization M as the z axis M 497 kA/m, Ref. 9 . of 1.8, 3.5, and 5.3 nm, respectively. This indicates that the Considering arrangements of four up to eight nearest and local coordination in the thin films is the same as in the bulk, next-nearest-neighbor domains, we find that Wd 0.15 eV at preserving the magnetic moments of all Fe ions. Again, this TB 40 K. contradicts the dead layer model. It is not clear why the From i and ii , it follows that the volume of the do- moments are larger than the bulk value of 4.1 B . Most mains is indeed small enough to induce superparamagnetism. likely, it is related to the large uncertainties that arise when The resultant barrier is comparable to the maximum barrier the relatively large diamagnetic and paramagnetic contribu- height of 0.10 eV, as derived from SQUID magnetometry. tions of the substrate are subtracted from the small signal of However, since the films are single crystalline, we must con- the multilayer. sider a third barrier: The superparamagnetic nature becomes evident from the iii Superexchange interactions at antiphase boundaries. behavior of the remanent magnetization, MR . In Fig. 3, MR This barrier arises because the domains are fully intergrown. is shown as a function of temperature for the three film thick- In order to estimate its importance, we have analyzed the nesses. These data were obtained by monitoring MR while structure and properties of all possible antiphase boundaries. heating the samples, after saturating the magnetization in a During the layer-by-layer growth of Fe3O4 on MgO 100 , field of 1 T at 5 K. Whereas bulk Fe3O4 has a high TC of 858 stacking faults will appear in the first monolayer, with 110 RAPID COMMUNICATIONS R8110 F. C. VOOGT et al. 57 directions. The STM images of Ref. 12 indicate that these Uij 2JijSi Sj , with S 2 or 52 , and an average number of are the preferred orientations of the step edges. In the spinel 3 1019 m 2 superexchange interactions between neighbor- structure, the orientation of the subsequent monolayers is ing domains, this leads to Wex 3 101 eV per 10 nm length determined by the orientation of the first monolayer. There- of antiphase boundary. fore, the stacking faults will extend in all subsequent mono- Comparing this estimate with the experimental data, we layers, resulting in planar antiphase boundaries with 110 conclude that the influence of the huge superexchange barri- orientations. The domains will have a rectangular and colum- ers must be largely suppressed in the thin films. This can be nar shape, and a volume that increases linear with the film explained by domain frustration. The new 180° Fe-O-Fe in- thickness. We point out that, in a multilayer structure, layer- teractions play a crucial role in this, because they lead to by-layer growth on MgO and the accompanying stacking antiferromagnetic coupling between domains. If all cou- fault formation will occur in every Fe plings were ferromagnetic, a domain would be rigidly 3O4 layer. Therefore, all layers will have similar domain structures. However, the locked, and superparamagnetism would not be observed at intermediate MgO layers are single domain, like the sub- all. Antiferromagnetic coupling, however, unavoidably leads strate. Therefore, antiphase boundaries in one Fe to frustration, similar to the situation in a spin glass. The 3O4 layer superexchange barriers effectively cancel each other out, en- cannot extend into the other layers, i.e., they are not corre- abling the domains to fluctuate much more freely. Thus, the lated. single crystalline film becomes superparamagnetic. Most important, we find that the network of exchange To conclude, it was shown that the Fe interactions in Fe 3O4 layer behaves as 3O4 is altered at the antiphase boundaries. one magnetic entity for all thicknesses, without dead or non- There are new, strong 180° Fe-O-Fe superexchange paths magnetic interface layers. The anomalous magnetic behav- between octahedral cations, across the boundary plane. ior, generally observed for ultrathin Fe These 180° paths, not present in bulk Fe 3O4 100 films, is 3O4, originate from caused by a superparamagnetic state of the film. This finding an intertwining of 110 octahedral cation chains from two is essential for the interpretation of studies on exchange bi- domains, which do not match at the antiphase boundary see asing, magnetic interlayer coupling, and magnetic interface Fig. 1 . They are present in every monolayer, all over the anisotropy. Furthermore, it will open up again the large po- boundary plane. Also normal JAB couplings are present, but tential of this material for application in spin electronics de- they are usually outnumbered by the new 180° couplings. vices. Since similar arguments apply, the superparamagnetic Therefore, the resultant coupling between two domains turns behavior is also expected to occur in epitaxial films with out to be either frustrated or, in most cases, antiferromag- other orientations, such as 110 and 111 . Furthermore, it is netic. Only when two islands with matching orientations not restricted to Fe meet, the resultant coupling between the two domains is fer- 3O4, but can occur in all spinel ferrite films grown on rocksalt-type substrates such as MgO, NiO, romagnetic. However, this event, with a probability of only or CoO, depending on the strength of the 180° superex- 18 , is equivalent to the formation of 1 larger domain out of change interactions. two smaller ones, without an internal boundary. The estimated exchange constant J of the 180° Fe-O-Fe We thank G. A. Sawatzky and T. Fujii for valuable com- interaction is 25 K,19 which is of the same magnitude as ments, and J. 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