VOLUME 78, NUMBER 6 P H Y S I C A L R E V I E W L E T T E R S 10 FEBRUARY 1997 Micromagnetism of Epitaxial Fe(001) Elements on the Mesoscale E. Gu, E. Ahmad, S. J. Gray, C. Daboo, J. A. C. Bland, and L. M. Brown Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, United Kingdom M. Rührig, A. J. McGibbon, and J. N. Chapman Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom (Received 5 January 1996) The size and orientation dependent micromagnetic structures of epitaxial Fe(001) thin film elements with in-plane anisotropy are reported. A transition from single domain to multidomain remanent states is observed upon reducing the element size beneath 50 mm, indicating that the in-plane dipolar field becomes competitive with the magnetocrystalline anisotropy at this size. Because of this competition, distinct micromagnetic structures arise according to the orientation of the element edges. The epitaxial elements are of high structural quality allowing the micromagnetic behavior to be controllably modified. [S0031-9007(97)02363-6] PACS numbers: 75.70.Kw, 68.55.­a, 75.30.Gw, 75.50.Tt Epitaxial magnetic thin films with controllable mag- controllable magnetic properties may also offer a range of netic anisotropies provide the experimentalist with an applications [13]. opportunity to study the interplay between dipolar (shape) Although a number of experimental investigations have and magnetocrystalline or interface anisotropies. In the been carried out on the micromagnetic structure of thin case of ultrathin Fe Cu(001) [1], Fe Ag(001) [2], and polycrystalline elements [14­18], to our knowledge no Co Au(111) [3,4] films, for example, the perpendicular micromagnetic studies have yet been reported for epi- spin orientation favored by the interface anisotropy is taxial thin film elements. The micromagnetic structures of overwhelmed by the dipolar energy as the film thickness epitaxial elements are expected to be substantially differ- is increased, i.e., the spin reorientation transition (SRT) ent from the magnetic domain structures of polycrystalline occurs. The question of how the micromagnetic struc- elements in which the magnetocrystalline anisotropy is ture evolves with thickness, i.e., how it is determined negligibly small. Furthermore, it has been found that the by the competition between interface anisotropy and domain structure in polycrystalline elements is greatly in- dipolar interactions, is important in gaining an under- fluenced by defects [14]. Thus epitaxial single crystal standing of how this transition occurs, and the domain thin elements with high structural quality are necessary structure which forms in the vicinity of the SRT has there- for studying how the micromagnetic structures are deter- fore received much attention recently [1­6]. However, mined by the interplay between in-plane inhomogeneous so far, the related question of whether in-plane dipolar dipolar fields and magnetocrystalline anisotropy. fields can (and if so how) compete with strong magne- In this work the in-plane dimension and orientation de- tocrystalline anisotropy in determining the magnetic pendence of domain structures and microscopic reversal domain structure in epitaxial thin films has not processes in 150 Å thick epitaxial Fe(001) elements was been addressed. For a continuous epitaxial thin studied for the first time by Lorentz transmission electron film with in-plane magnetization, a single domain microscopy (TEM). The high spatial resolution of Lorentz state is predicted as the demagnetizing constant ap- TEM makes it a desirable technique for studying domain proaches zero [7,8]. Such a single domain state has structures in small magnetic elements. However, due to been observed in epitaxial Fe Ag(001) films [9], the difficulties of preparing Lorentz TEM specimens of Co Cu(001) films [10], and Fe GaAs(001) films [11,12]. epitaxial elements, this technique has not been used so far However, for an epitaxial thin film with in-plane to characterize magnetic epitaxial elements. In this work anisotropy, can magnetic domains be created by de- we used a selective chemical etching technique developed creasing the film in-plane dimensions? Also, and more recently to prepare electron-transparent window specimens importantly, how do the micromagnetic structures and suitable for Lorentz TEM [11]. The procedure for epitaxi- microscopic reversal processes evolve with film in-plane al Fe film growth can be found in Ref. [11]. The film dimensions and orientation, i.e., how are they determined thickness was selected at 150 Å since for 150 Å thick epi- by the competition between in-plane dipolar interactions taxial Fe films, the fourfold magnetocrystalline anisotropy and magnetocrystalline anisotropy? In analogy to the is well developed and their micromagnetic structures are studies of the SRT, it is expected that novel micromag- well understood from our earlier studies [11,12]. Be- netic phenomena may be observed by decreasing the fore fabricating the elements, the magnetic anisotropies film lateral dimensions, i.e., making mesoscopic epitaxial of the continuous Fe film were determined by magneto- structures (elements). These epitaxial elements with optical Kerr effect (MOKE) vector magnetometry. MOKE 1158 0031-9007 97 78(6) 1158(4)$10.00 © 1997 The American Physical Society VOLUME 78, NUMBER 6 P H Y S I C A L R E V I E W L E T T E R S 10 FEBRUARY 1997 measurements show that the original Fe(001) film has a main state much the same as for a continuous epitaxial Fe predominant in-plane fourfold anisotropy with its easy film [11]. However, fine spike domains are observed to axes parallel to the in-plane 100 directions as expected form at the element edges perpendicular to the initial ap- for an epitaxial bcc Fe film. Epitaxial square Fe elements plied field. Figure 2(b) shows that as the size of the ele- with their edges parallel to the 100 or 110 directions and ment decreases the edge domains extend. For the element different size were fabricated using a combination of opti- with a 12 mm the edge domains extend throughout the cal lithography, metallization, ion milling, and reactive ion whole element forming a multidomain configuration as etching techniques. Through optical lithography the de- shown in Fig. 2(c). For these epitaxial Fe elements, the sign patterns were transferred from an optical mask to the magnetic field has also been applied along the 110 hard resist layer, spun on the sample prior to the lithography. directions to induce an initial single domain state. Lorentz Then metallization and lift-off were performed. In these TEM images show that at remanence, again a multido- processes a Ti(500 Å) Cr(20 Å) bilayer was deposited on main structure forms in the 12 3 12 mm2 element and the patterned resist layer, and then the resist was dissolved the 55 3 55 mm2 element is almost in a single domain away, leaving only the patterns of Ti Cr on the Fe film. configuration. We used ion milling to remove the Fe film surrounding The most remarkable new finding from these images is the Ti Cr masks to obtain square Ti Cr Fe elements. Fi- that the magnetic structure of an epitaxial thin film with nally, the Ti was removed by reactive ion etching using in-plane anisotropy changes into a multidomain state at a combination of CF4 and O2 gases. A TEM bright field remanence upon reducing its in-plane size and that for the image of an epitaxial Fe element is shown in Fig. 1. The 150 Å thick film this transition occurs at a size of a few tens dark bands shown in this image are the bend contours aris- of microns. These results indicate that upon decreasing ing from the single crystal GaAs membrane. It can be seen element size the in-plane demagnetizing field, which has that the edges of the element are straight and smooth. been considered to be negligibly small for an epitaxial thin In this study both the Foucault and Fresnel modes of film [7,8], becomes important in determining the domain Lorentz electron microscopy were used [19]. The rema- structures. In the case that the elements were initially nent domain states of Fe elements with their edges parallel magnetized along one of the 100 easy directions, due to the 100 easy directions were investigated firstly. In to the magnetocrystalline anisotropy, the magnetization the Lorentz electron microscope, an initial magnetic field vector tends to remain in that direction upon reducing Hi 120 Oe was applied along one of the 100 directions as the field. Hence "magnetic charges" would be uniformly determined from the diffraction pattern. In this field, all distributed on the edges perpendicular to the magnetization the elements of different size supported a single domain vector. However, our previous work showed that the configuration. In the remanent state, it was found, how- coercive field, determined by the nucleation and unpinning ever, that for elements of different size the domain struc- of 90± domain walls in an epitaxial Fe film of the same tures are very different. Figure 2 shows remanent Fresnel domain images and corresponding magnetization schemat- ics of three square Fe elements with side length a 55, 30, and 12 mm. From Fig. 2 it can be seen that the 55 3 55 mm2 element at remanence is almost in a single do- FIG. 2. Remanent domain images and corresponding magneti- zation schematics of the epitaxial Fe elements with edges paral- lel to the 100 directions. The field was initially applied along FIG. 1. Bright field TEM image of an epitaxial Fe(001) the 010 direction. The element sizes are (a) 55 3 55 mm2, element supported on a GaAs single crystal membrane. (b) 30 3 30 mm2, and (c) 12 3 12 mm2. 1159 VOLUME 78, NUMBER 6 P H Y S I C A L R E V I E W L E T T E R S 10 FEBRUARY 1997 thickness, is about 8 Oe [11]. The in-plane demagnetizing and anisotropy energies. For a square epitaxial Fe element field near the element edges is much larger than this with edges parallel to the 110 hard axes, the in-plane nucleation field. Thus, upon reducing the applied field, dipolar fields will compete with the magnetocrystalline domain nucleation occurs at the element edges as shown anisotropy whose easy axes are now oriented along the in Fig. 2(a). Since the magnetization within these spike diagonal directions of the elements. Such elements edge domains is parallel to the edges, the magnetic charges with a larger size are found again to be almost in a at the edges and in turn the demagnetizing fields and single domain state at remanence. Here, only smaller magnetostatic energy arising from these charges are greatly elements are considered. Again, a single domain state reduced. However, since the normal components of the of a 12 3 12 mm2 epitaxial element was first induced by magnetization cannot be continuous across these spike applying a field along the 010 easy direction. Reducing domain walls, volume magnetic charges will develop at the the applied field results in domain nucleation and growth walls and produce a demagnetizing field in the elements. at the element corners as shown in the image [Fig. 3(a)] The magnetic charges formed at the edge domain walls taken at Hi 6.0 Oe. The image of the remanent domain are oppositely charged for the two opposing edges, and structure and corresponding magnetization schematic is therefore the demagnetizing field due to the charges at the shown in Fig. 3(b).This remanent domain configuration domain walls along one edge acts to unpin the domains is significantly different from those observed for the on the opposite edge. In the larger elements, such a elements of the same size but with edges parallel to the demagnetizing field is smaller than the unpinning field 100 directions. As the field was initially applied along since the element edges are well separated. The small edge the 010 easy axis, the maximum demagnetizing field domains thus cannot expand and the element is maintained occurs at the two element corners [corners A and B in almost in the original single domain state. Fig. 3(a)]. Upon reducing the applied field, new domains With decreasing element size, the charged edge domain nucleate and grow at these two corners. As the corners of walls approach each other. At a critical size, the demagne- the elements are always rounded off, the corner domains tizing fields arising from these charged domain walls be- with the local magnetization oriented along the [100] come strong enough to cause the edge domains to unpin easy direction [see Fig. 3(a)] reduce greatly the magnetic and expand throughout the whole element so that a mul- charges at the corners and in turn the magnetostatic tidomain remanent structure is formed. We have calcu- energy. By further decreasing the applied field, these lated the size at which the demagnetizing field approaches corner domains grow by domain wall displacement. For the unpinning field. The estimated size is about 15 mm this element, whereas the magnetocrysalline anisotropy and therefore is consistent with the experimental measure- favors alignment of the magnetization parallel to the 100 ments. From an energy point of view, for the epitaxial ele- easy axes, the in-plane dipolar field tends to form domain ments with edges parallel to the 100 easy directions, the standard Kittel-type flux closure multidomain structure as shown by the dashed lines in Fig. 2(a) has a lower energy than the "single domain" structure with many small spike edge domains as shown in Fig. 2(a). The reasons for this are (i) the domain wall length in the Kittel multidomain structure is shorter than that in the single domain struc- ture with small spike edge domains, hence the multidomain structure has a lower wall energy, (ii) whereas magnetic charges develop in the spike domain walls, in the multido- main structure, the domain walls are moved to positions where they are free of magnetic charges greatly decreas- ing the magnetostatic energy. However, for the continuous epitaxial films and larger elements the demagnetizing field is not strong enough to overcome the energy barrier arising from domain wall pinning to realize the low energy mul- tidomain state. It is found that the remanent multidomain configurations in the smaller epitaxial elements are strongly influenced by several factors such as initial magnetizing direction and element orientation. It can be seen that each remanent domain pattern shown in Fig. 2 attempts to achieve flux FIG. 3. Domain images and corresponding magnetization closure with the magnetizations lying parallel to the schematics of a 12 3 12 mm2 epitaxial Fe element with edges element edges. Since the edges of these elements are parallel to the 110 directions. The field was initially applied along the 010 easy direction. (a) Corner domain nucleation parallel to the 100 easy directions of bcc Fe, such domain and growth upon reducing the applied field Hi 6.0 Oe , (b) configurations obviously minimize both the magnetostatic Remanent domain structure. 1160 VOLUME 78, NUMBER 6 P H Y S I C A L R E V I E W L E T T E R S 10 FEBRUARY 1997 FIG. 4. Domain structures of the 12 3 12 mm2 epitaxial Fe element with edges parallel to the 100 directions during reversal along the [100] easy axis. structures with magnetization vectors parallel to the ele- film have also been observed for reversal along the hard ment edges in order to reduce the magnetostatic en- axes. The 12 3 12 mm2 element with edges parallel to ergy. As a compromise, the element splits into an the 110 directions also shows distinct reversal behavior. irregular stripe domain structure at remanence as shown These results will be reported elsewhere [20]. in Fig. 3(b). In this structure, the magnetization vec- In summary, this study shows that magnetic domains tor in each domain remains parallel to the easy axes can be created in the epitaxial Fe thin films with a strong of the fourfold magnetocrysalline anisotropy at the cost magnetocrysalline anisotropy by reducing their in-plane of inducing magnetic charges at the element edges. size beneath 50 mm. The drastic changes in the rema- However, the stripe domain structure brings the posi- nent state and microscopic reversal processes indicate that tive and negative magnetic charges closer, thus decreas- the in-plane dipolar field becomes competitive with the ing greatly the spatial extent of the stray field and in magnetocrystalline anisotropy at this size, and distinct mi- turn the magnetostatic energy in comparison with the cromagnetic structures arise controllably according to the single domain structure. A similar stripe remanent do- orientation of the element edges. main structure has also been observed when the element We thank Dr. D. A. Ritchie, Dr. M. England, and was initially magnetized along the 110 hard axes. Professor H. Ahmed for their help with the work. The By recording domain images during field reversal, the financial support of the EPSRC, the Newton Trust, microscopic reversal processes of these epitaxial elements Cambridge and the EC (HCM program) for this work is have also been studied. Whereas the 55 3 55 mm2 ele- greatly acknowledged. ments are found to have reversal processes similar to those of continuous Fe films, the smaller elements show signif- icantly different reversal behavior. For a 12 3 12 mm2 [1] R. Allenspach and A. Bischof, Phys. Rev. Lett. 69, 3385 element with edges parallel to the 100 directions, the (1992). domain structures during reversal along the [100] direc- [2] A. Berger and H. Hopster, Phys. Rev. Lett. 76, 519 (1996). tion are shown schematically in Fig. 4. On applying a [3] R. Allenspach, M. Stampanoni, and A. Bischof, Phys. Rev. reverse field, the domains with magnetization oriented op- Lett. 65, 3344 (1990). posite to the reverse field shrank. This continued until a [4] M. Soeckmann, H. P. 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