PHYSICAL REVIEW B VOLUME 57, NUMBER 13 1 APRIL 1998-I Micromagnetic structures and microscopic magnetization-reversal processes in epitaxial Fe/GaAs 001... elements E. Gu, E. Ahmad, J. A. C. Bland, and L. M. Brown Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, United Kingdom M. Ru¨hrig, A. J. McGibbon, and J. N. Chapman Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom Received 23 June 1997; revised manuscript received 20 November 1997 The in-plane size and orientation-dependent micromagnetic structures of thin epitaxial Fe 001 elements were studied by Lorentz electron microscopy. It is found that the single-domain remanent state supported by continuous epitaxial films with in-plane anisotropy decays into a multidomain configuration upon reducing the film lateral dimensions. For 150-Å-thick Fe 001 elements, such drastic changes in the remanent domain structure and reversal processes occur when the element size is reduced to 10 m. This transition can be explained as a consequence of the in-plane dipolar shape anisotropy contribution to the total energy becoming comparable with that of the magnetocrystalline anisotropy at this size. Due to the interplay between in-plane shape and magnetocrystalline anisotropies, novel micromagnetic phenomena were observed. Distinct micro- scopic reversal processes arise according to not only the crystallographic direction along which the field is applied but also the orientation of the element edges. For magnetization reversal along the in-plane 100 directions easy axes , domains nucleate at either element edges or corners depending on the orientation of element edges. For applied fields aligned along the in-plane 110 directions hard axes , a fine-scale stripe width 200 nm domain structure develops upon reducing the applied field from saturation. In addition to coherent rotation and domain-wall displacement, a 90° coherent jump reversal process has been observed for the elements with edges parallel to the 110 directions. The micromagnetic behavior of these epitaxial ele- ments is substantially different from those of either continuous epitaxial Fe 001 films E. Gu et al., Phys. Rev. B 51, 3596 1995 , C. Daboo et al., Phys. Rev. B 51, 15 964 1995 or polycrystalline elements in which the magnetocrystalline anisotropy is negligibly small. As the relative contributions of the in-plane shape and magnetocrystalline anisotropies can be modified by varying the element size, shape and orientation, these mesoscopic epitaxial elements not only offer an ideal model to study the roles of anisotropies in determining the micromagnetic structures but also allow the magnetic spin configuration to be controlled which could be useful for device applications, e.g., spin-polarized injection contacts and magnetic memory elements. G. A. Prinz, Physics Today 48 4 , 58 1995 . S0163-1829 98 04610-4 I. INTRODUCTION zero.6,7 Such a single-domain state has been observed in ul- trathin Fe/Ag 001 Ref. 8 and Co/Cu 001 films9 and in The art of growing epitaxial magnetic thin films has en- 35­450 Å thick epitaxial Fe/GaAs 001 films.10­12 On the gendered fascinating new topics in fundamental magnetism other hand, if a thin-film structure has a lateral size which is research and has also offered possibilities for a range of tech- comparable to or even smaller than a domain-wall thickness, nical applications. Epitaxial magnetic films with controllable a single-domain state will be again preferred regardless of magnetic anisotropies provide the experimentalist with an the large stray field energy since no domain wall can form. opportunity to study the interplay between dipolar shape However, between these two extreme cases, whether do- and magnetocrystalline or interface anisotropies. In the case mains exist in epitaxial thin films and how the domain struc- of ultrathin Fe/Cu 001 1 and Co/Au 111 2,3 films for ex- tures evolve with film in-plane dimensions and orientation ample, the perpendicular spin orientation favored by the in- are not clear. It is expected that novel micromagnetic phe- terface anisotropy is overwhelmed by the dipolar energy as nomena may be observed by changing the film's lateral di- the film thickness is increased. The question of how the mi- mensions and orientation, i.e., making artificial mesoscopic epitaxial structures elements . In this case, the micromag- cromagnetic structure evolves with thickness is important in netic structure will be determined by the interplay between gaining an understanding of how this transition occurs, and in-plane shape and magnetocrystalline anisotropies, and the the domain structure which forms in the vicinity of the re- former is expected to become important when the film's lat- orientation transition has therefore received much attention eral dimensions are reduced. Furthermore, since the mag- recently.1­5 However, so far, the related question of how netic anisotropy properties in these artificial structures can be in-plane dipolar fields compete with in-plane anisotropies in controllably modified, it is expected these mesoscopic epi- determining the magnetic domain structure in epitaxial films taxial structures will offer a range of applications. Various has not been addressed. For a continuous two-dimensional device applications of ferromagnetic metal-semiconductor 2D epitaxial film with in-plane anisotropy, a single-domain epitaxial systems, such as spin-polarized injection contacts, state is predicted as the demagnetizing constant approaches have been suggested recently.13 0163-1829/98/57 13 /7814 9 /$15.00 57 7814 © 1998 The American Physical Society 57 MICROMAGNETIC STRUCTURES AND MICROSCOPIC . . . 7815 Although a number of experimental investigations have been carried out on the micromagnetic structure supported by regular thin polycrystalline Permalloy elements,14­18 to our knowledge no micromagnetic studies have been reported for thin epitaxial elements. The micromagnetic studies of epitaxial elements are substantially different from the size- dependent magnetic domain investigations of polycrystalline elements in which the magnetocrystalline anisotropies are negligibly small. In the present work, the in-plane dimension and orientation dependence of the domain structures and mi- croscopic reversal processes in 150-Å-thick epitaxial Fe 001 elements were studied by Lorentz transmission electron mi- croscopy TEM . By comparing the domain structures and microscopic reversal behavior of continuous epitaxial Fe films of the same thickness which were studied extensively in our recent work,10,11 the present work shows that the size, edge, and orientation of epitaxial Fe elements play an impor- tant role in determining their domain structures and micro- scopic reversal processes. A transition from single domain to multidomain remanent states has been observed by reducing the film dimension to 10 m. At this size range, the do- main structures and microscopic reversal processes of the epitaxial Fe elements are significantly different from those of larger elements and continuous films. Due to the interplay between in-plane shape and magnetocrystalline anisotropies, these epitaxial Fe elements show novel and controllable mi- cromagnetic behavior. FIG. 1. a Cross-section schematic diagram of a Lorentz TEM specimen of epitaxial Fe elements prepared by optical lithography II. SPECIMEN PREPARATION AND OBSERVATION and selective chemical etching techniques, b Plane view TEM TECHNIQUES image of an epitaxial Fe 001 element supported on a GaAs single- crystal membrane. Lorentz TEM specimens must be sufficiently thin so as to permit the transmission of electrons. Furthermore, for mag- epitaxial bcc Fe film. Furthermore, from MOKE measure- netic domain studies, it is desirable to form such an electron ments, a weak uniaxial anisotropy (Ku /K1 0.1) with its transparent window far from the sample edge so that the easy axis parallel to one of the hard axes ( 1¯10 direction influence of stray fields arising from the edges is greatly of the fourfold anisotropy has also been observed. Recent reduced. In this work, we used a selective chemical etching studies showed that this uniaxial anisotropy exists in other technique developed recently to prepare suitable window epitaxial Fe/GaAs 001 films21 and the origin of this uniaxial specimens.10 anisotropy has been attributed to the surface atomic structure Arsenic-capped GaAs 001 substrates with a Ga of the GaAs 001 surface.22,23 0.7Al0.3As etch stop layer supporting an molecular-beam epitaxy grown Epitaxial square Fe elements with different size were fab- GaAs 001 epilayer membrane were used for epitaxial Fe ricated utilizing optical lithography, ion milling and reactive film growth. The As cap layer on the GaAs 001 epilayer etching techniques. The edges of these elements are parallel surface was desorbed in UHV before the film growth by to either 100 easy or 110 hard directions. The thin GaAs 001 membrane which supports these epitaxial ele- annealing at 550 °C so as to get a clean and ordered GaAs ments and is suitable for Lorentz TEM observation was surface.19 During Fe growth, the pressure was less than 5 formed by selective chemical wet etching from the back sur- 10 10 mbar and the film thickness was monitored by a face of GaAs 001 substrates. After fabrication, the structure quartz microbalance calibrated by a Dektak profilometer. and chemical composition of the elements were character- The substrate temperature of 150 °C and a deposition rate of ized by scanning electron microscopy SEM , TEM, and 1 Åmin 1 were used for the Fe growth. The epitaxial growth energy-dispersive x-ray analysis EDX . A cross-section of bcc Fe was confirmed by in situ low-energy electron- schematic diagram of a completed Lorentz TEM specimen is diffraction and ex situ transmission electron diffraction. Fi- shown in Fig. 1 a . Figure 1 b shows a plane view TEM nally, the completed Fe film was covered by a 15 Å Cr cap image of a 30 30 m2 epitaxial Fe element. The dark bands layer which can effectively prevent oxidation of the Fe film, shown in this image are bend contours arising from the as confirmed by electron energy-loss spectroscopy single-crystal GaAs membrane. It can be seen that the edges measurements.20 Prior to element fabrication, the magnetic of the element are relatively straight and smooth. EDX mea- anisotropy properties of the continuous Fe film were charac- surements confirmed that the Fe in the gaps between ele- terized by magneto-optical Kerr effect MOKE vector mag- ments has been completely removed and that the thin Fe netometry. MOKE measurements show the film has a pre- elements are well protected by the Cr cap layer. dominant in-plane fourfold anisotropy with its easy axes Lorentz TEM is a desirable technique for the study of parallel to the in-plane 100 directions as expected for an micromagnetic structures in micron or submicron size mag- 7816 E. GU et al. 57 netic elements.24,25 However, due to the difficulties of pre- paring Lorentz TEM specimens of epitaxial elements, this high-resolution technique has not been previously used to characterize their micromagnetic properties. In this work, us- ing the specimen preparation technique described above, the magnetic domain structure and microscopic reversal pro- cesses in the epitaxial Fe elements were studied by using both a modified Philips CM20 and a JEOL 2000 FX Lorentz electron microscope. In both microscopes the specimen can be rotated in-plane by a driver and its orientation is deter- mined by the electron-diffraction pattern. A magnetic field in the microscope thus can be applied in any in-plane direction with respect to the specimen to carry out in situ magnetizing experiments. III. RESULTS AND DISCUSSION FIG. 2. Demagnetizing field distributions within 150 Å epitaxial A. Remanent domain structure elements of different size. Element edges are parallel to the 100 directions and the elements are assumed to be magnetized uni- The studies of the remanent domain structures in these formly along one of in-plane 100 easy directions. epitaxial Fe elements have been recently published elsewhere.26 Here the main results are briefly summarized elements is determined by the competition between dipolar and further analyses are given, which will be helpful in order interactions and magnetocrystalline anisotropy.26 to analyze and explain the microscopic reversal processes of these epitaxial elements shown in the following sections. B. Microscopic reversal processes along the S100 The most important finding from these remanent domain easy directions structures is that thin epitaxial films with in-plane anisotropy To carry out reproducible micromagnetic studies, it is im- transform into a multidomain state at remanence upon reduc- portant that the initial magnetic state is well defined. For ing their in-plane size and that for the 150-Å-thick film this reversal along the 100 easy directions, a ``single-domain'' transition occurs at a size of a few tens of microns. These state of elements was induced first by applying an initial results indicate that with decreasing element size, the in- magnetic field Hi (Hi 120 Oe) parallel to one of the 100 plane demagnetizing field, which has been considered to be easy axes. After removing the field, the microscopic reversal negligibly small for a thin epitaxial film,7 becomes important processes were studied by applying a reverse field Hr and in determining the domain structures. The demagnetizing simultaneously monitoring and recording the domain struc- field arises from the magnetic charges formed at element ture in the electron microscope. Figure 3 shows a series of edges or domain walls. In the case that the elements with Fresnel domain images of a 55 55 m2 element taken dur- edges parallel to the 100 directions were initially magne- ing reversal along the 1¯00 easy direction. The correspond- tized along one of the 100 easy directions, the magnetiza- ing magnetization distributions in these images are shown in tion vector tends to remain in that direction upon reducing Fig. 4. It should be noted that most dark lines and bands the applied field due to the magnetocrystalline anisotropy. shown in the images are bend contours coming from the Hence, magnetic charges would be uniformly distributed on single-crystal GaAs substrate. Minor tilting of the specimen the edges perpendicular to the magnetization vector. The de- allows these features to be distinguished unambiguously magnetizing fields arising from such uniformly distributed from the magnetic contrast of interest. Some defects have magnetic charges in square Fe elements with thickness 150 also been observed. These defects were induced during the Å and different sizes were calculated and are shown in the process of fabricating elements. During reversal processes, Fig. 2. Our previous work showed that the coercive field, the detailed local domain structures in the element may be determined by the nucleation and unpinning of 90° domain perturbed by these defects as they act as pinning points. walls of a continuous epitaxial Fe film of the same thickness, As before, at remanence the element is almost in a single- is about 8 Oe.10 From Fig. 2 it can be seen that if an element domain state with small spike domains at the element edges. has a size smaller than about 20 20 m2, the demagnetiz- With respect to the reversal field, these edge domains have ing field within almost whole element becomes larger than lower Zeeman energy. Therefore, upon increasing the rever- the value of this nucleation field and for all the elements the sal field, these edge domains expand quickly through 90° demagnetizing field at the element edge is much larger than domain-wall displacements as shown in Figs. 4 a ­4 e . It is this nucleation field. Furthermore, there are always some im- noticed that during the above processes, a new edge domain perfections at the element edges which may serve as nucle- in which the magnetization is oriented parallel to the reversal ation centers. Thus, upon reducing the applied field, domain field direction is nucleated. Upon increasing the reversal nucleation occurs at the element edges. Our studies show field, this reversed domain grew again through domain-wall that for smaller elements these edge domains will develop to displacements until the whole element was reversed see form a multidomain remanent structure and the configuration Figs. 4 d ­4 h . The above reversal processes are similar to of the remanent domain structures in these epitaxial thin Fe those observed in continuous epitaxial Fe films.10,11 How- 57 MICROMAGNETIC STRUCTURES AND MICROSCOPIC . . . 7817 FIG. 3. Magnetic domain images of a 55 55 m2 Fe element with edges parallel to the 100 directions during reversal along the 100 easy axis. ever, some important differences due to the element edges board domain formation in the continuous Fe films is mainly were observed. Firstly the process of domain nucleation is due to the in-plane fourfold symmetry in the magnetocrys- influenced by the element edges, e.g., in order to reduce the talline energy. The ratio Ku /K1 of the continuous epitaxial magnetostatic energy, new domains nucleate only at those Fe film from which the elements were fabricated was deter- element edges where the magnetization is not originally par- mined to be about 10%. This uniaxial anisotropy makes the allel to the edges. Secondly, an irregular flux closure check- real easy axes depart slightly from the crystalline cubic 100 erboard domain pattern was observed during the reversal directions as shown by the dashed lines in Fig. 4 a and processes. This checkerboard domain pattern is constructed therefore causes the magnetization to jump during reversal by domains in which the magnetizations are oriented along from the initial 100 direction to the 01¯0 direction rather the four easy directions of the fourfold anisotropy, respec- than to both the 01¯0 and 010 directions to form a check- tively. For continuous epitaxial Fe films, our earlier work erboard domain structure. The formation of the local flux showed that the checkerboard domain structures were only closure checkerboard domain pattern in the element is observed for epitaxial films with a predominant fourfold an- caused by edge effects. In order to reduce the magnetostatic isotropy, i.e., the ratio of uniaxial to the fourfold anisotropies energy, the magnetization within the edge domains tends to Ku /K1 should be smaller than 1%. Therefore the checker- orient parallel to the element edges. As the element edges are FIG. 4. The magnetization schematics of the domain images shown in Fig. 3. 7818 E. GU et al. 57 FIG. 5. Magnetic domain structures of a 12 12 m2 epitaxial Fe element with edges parallel to the 100 directions during reversal along the 100 easy axis. parallel to the 100 easy directions, the configuration with From the above images and analyses, it can be seen that the magnetization parallel to the edges also decreases the for reversal along the 100 easy direction the 55 55 m2 magnetocrystalline anisotropy energy. On the other hand, the and 12 12 m2 elements with edges parallel to the 100 magnetization orientation adopted should also minimize the directions show very different remanent domain structures formation of magnetic charges at domain walls by keeping and reversal behavior. For the 55 55 m2 large element, the perpendicular components of magnetization approxi- the reversal takes place via a combination of two 90° mag- mately continuous across the domain walls. To satisfy these netization reorientations. This process is similar to that ob- conditions, when the edge domains expand and come into served in continuous epitaxial Fe films10 although the de- contact with each other, the checkerboard domain pattern tailed domain configuration is perturbed by the element develops in the Fe element. Thus, although the checkerboard edges. For the 12 12 m2 element, the reversal proceeds domain patterns were observed for both continuous epitaxial mainly via 180° domain-wall reorientation and displace- Fe films and Fe elements, their origins differ. ments. Since the remanent domain structures of the 55 By applying the field along the 100 directions, the mi- 55 m2 and 12 12 m2 elements are significantly croscopic reversal processes of the epitaxial elements with edges parallel to the 110 directions have also been studied. different,26 it is expected that they will show different rever- The domain images and corresponding magnetization distri- sal behavior. Figure 5 shows the domain structures and mag- butions of such a 12 12 m2 element during reversal is netization distributions of a 12 12 m2 element with edges shown in Fig. 6. At remanence the element supports a stripe parallel to the 100 directions during reversal along the multidomain structure with magnetization oriented parallel 100 direction. On the application of a reverse field, the to either the 100 or 01¯0 easy directions. Increasing the domains in which the magnetization was antiparallel to the reversal field results in the 100 oriented domains which reverse field shrank. This continued until a critical field, de- have a lower Zeeman energy growing through 90° domain- noted Hc1 (Hc1 16.4 Oe), was attained whereupon the un- wall displacements. Further increasing the applied field favorably oriented domains disappeared and an irreversible forces domain walls into contact in the middle of element as change took place between Figs. 5 b and 5 c . At this tran- shown in Fig. 6 c . In this image, almost the whole element sition field, a domain with the magnetization oriented along was oriented along the 100 direction and only the two ele- the reverse field direction nucleated at the bottom edge and ment corners remained oriented parallel to the 01¯0 direc- expanded rapidly. As this favorably oriented domain grew, tion in order to minimize the magnetostatic energy. Again a the original vertical 180° domain wall parallel to the 010 strong field (H direction in Fig. 5 b became shorter and finally disappeared r 32 Oe) is needed to drive these corner do- and immediately a 180° domain wall parallel to the 100 direction appeared as shown in Fig. 5 c . Although the actual transition was too rapid to record, the key to this transition was that the orientation of the 180° wall changed by 90° to facilitate an increase in size of the favorably oriented do- main. A further increase in the reverse field caused the movement of the 180° domain wall towards the element edge and only by applying a strong reverse field (Hr 35 Oe) could the 180° wall be driven into the side of the element. Furthermore, it was found that after the 180° domain wall was driven into the side of the element, on reduction of the field, the domain structure with the 180° wall parallel to the 100 direction could regenerate. Decreasing the field further to Hc2 which satisfies 0 Hc2 Hc1 resulted in a transition back to a domain structure similar to that shown in Fig. 5 a . FIG. 6. Magnetic domain structures of a 12 12 m2 Fe ele- Not much change in the domain configuration was observed ment with edges parallel to the 110 directions during reversal when further decreasing the field from Hc2 to zero. along the 010 easy axis. 57 MICROMAGNETIC STRUCTURES AND MICROSCOPIC . . . 7819 FIG. 8. Magnetization reversal process of continuous epitaxial Fe films for applied fields near the 110 hard direction. From these patterns, the overall magnetization reversal pro- cess can now be explained with reference to Fig. 8. While 110 lies midway between the easy 100 and 010 direc- tions, in practice, the applied field will not be exactly along the intended direction. Thus, as the field strength is reduced from a high value along a direction close to the 110 axis, the magnetization will coherently rotate towards the nearest FIG. 7. Magnetization schematics of a 55 55 m2 Fe element easy axis 010 in Figs. 7 and 8 . It is found that after re- with edges parallel to the 100 directions during reversal near the moval of the initial field small spike domains formed at the 110 hard axis. edges parallel to the 100 direction see Fig. 7 a . This domain structure shows that at remanence the element is al- main walls into the element edge to realize a 100 -oriented most in a single-domain state with magnetization vector par- single-domain state. After the element was driven into the allel to the 010 direction and only in the small edge do- single-domain state, further increase of the reversal field did mains the magnetization is parallel to the element edges. not cause the element to split into a multidomain structure Application of a field of the opposite polarity i.e., parallel to again. However, it is found that at a high critical reversal 1¯ 1¯0 ) causes the edge domains in which the magnetization field, one dark band along an element edge jumped suddenly is oriented along 1¯00 , the easy direction near to that of the to the opposite edge compare Fig. 6 c with Fig. 6 d . applied field, to grow. Increasing the field strength by only a These dark bands arise from the electron deflection occurring fraction of 1 Oe allows at the element edges due to the Lorentz force. The deflection 1¯00 -oriented domains to grow through Barkhausen-like jumps which were observed di- direction is determined by the orientation of the magnetiza- rectly on the microscope screen. The observed domain-wall tion vector at the edge. If the electrons are deflected at an jumps are due to wall unpinning. The jump direction is along edge towards the element, a dark band appears at this edge. Thus, from Fig. 6 c and Fig. 6 d which show that the dark 1¯10 , that is, perpendicular to the field direction. When it is band jumps to the opposite edge, we can deduce that further complete the whole of the film is once again almost uni- reversal at the high reversal field took place by the magneti- formly magnetized but the direction of magnetization has zation coherently jumping 90° from being parallel to the changed from being along 010 to lying along 1¯00 . In- 100 to the 010 direction. Such a 90° coherent jumping creasing the reverse field strength to the second critical value reversal process has never been observed for continuous ep- leads to the nucleation and expansion of new domains in itaxial Fe films. Clearly, the reversal process shown in Fig. 6 which the magnetization is now oriented close to the 01¯0 is remarkably different from that of the element with the direction. It is important to note that the domain walls at this same size but with edges parallel to the 100 directions. stage are oriented almost along the 1¯10 direction rather than the 110 direction as was the case in the first domain process. These new domains grow quickly again through C. Microscopic reversal processes along the S110 hard Barkhausen-like jumps until the element reaches the third directions single-domain state Fig. 7 f in which the magnetization is To investigate the magnetization reversal processes along oriented close to the 01¯0 direction. Increasing the field the 110 hard directions, the epitaxial Fe elements were ro- strength further leads to a coherent rotation of the magneti- tated through 45° in the microscope so that one of the 110 zation away from the 01¯0 direction towards that of the directions, say the 110 direction, lay parallel to the field applied field until the element is saturated. The description direction. Following a similar procedure to that used for the given above is in accord with the magnetization distributions 100 directions, a single-domain state was induced by ap- shown in Figs. 7 a ­7 f . If the applied field was initially plying an initial field Hi along 110 . Magnetization reversal closer to 100 rather than to 010 similar processes would was then studied by applying successively greater fields par- be involved although the magnetization vector would now allel to 1¯1¯0 . change in a clockwise sense during reversal. Coherent rota- Figure 7 shows the domain structures and magnetization tion would be responsible for the initial and final stages as distributions of a 55 55 m2 element during reversal. The before. In general, the above reversal processes are similar to edges of this element are parallel to the 100 easy directions. the reversal behavior observed in continuous epitaxial thin 7820 E. GU et al. 57 FIG. 9. Magnetization schematics of a 12 12 m2 Fe element with edges parallel to the 100 directions during reversal near the 110 hard axis. Fe films.10,11 However, the detailed domain configuration is sector direction hard axis , one domain orientation was al- perturbed by the element edges. For example, when domains ways more favorable than the another. Therefore, at very expand to touch the element edges, spike domain walls ap- high reverse field, the favorable domains would nucleate and pear in order to avoid the formation of magnetic charges at grow from the element edge as shown in Fig. 9 i and when the edges. it finished, the element reached a single-domain structure For a field applied along the hard axis, again, strikingly with its magnetization oriented near the 1¯00 direction different magnetization reversal behavior was observed for which is the easy axis closest to the field direction. Increas- the 12 12 m2 epitaxial elements. Figures 9 a ­9 j show ing the field further would result in the magnetization rotat- schematically the domain structures and magnetization dis- ing coherently to the field direction. tributions of a 12 12 m2 element with edges parallel to For reversal along the 110 hard direction, the 12 12 the 100 directions during reversal along the 110 hard m2 epitaxial elements with edges parallel to the 110 di- axis. In the remanent state Fig. 9 a , this element shows a rections show distinct and relatively simple reversal behav- flux closure multidomain structure. On the application of a ior. In this case, a magnetic field was again first applied reversal field, the favorably oriented two domains in which along the 110 direction to induce the initial single-domain magnetizations were parallel to the 01¯0 and 1¯00 direc- state. At remanence, the element supported a stripe multido- tions, respectively, grew at the expense of those less favor- main structure as shown in Fig. 10 a . As discussed in Ref. ably oriented through domain-wall displacements. An in- 26, such a stripe domain structure can reduce greatly the crease in the reversal field caused further movement of the magnetostatic energy. Upon reversing the field and increas- domain walls and the domain pattern became very distorted. ing the reverse field strength, the 1¯00 -oriented domains It can be seen that as the domain walls were driven close to which have lower Zeeman energy grew and became pre- the element edges, they became more bowed and parallel to dominant as shown in Fig. 10 b . In this domain structure, the edges as shown in Fig. 9 f . At the same time, the length of the 180° domain wall became shorter and finally disap- peared. When the reversal field is higher than 34 Oe, only one domain wall remained and the rest had been driven into the element edges as shown in Fig. 9 h . At this stage, it can be seen that the remaining domain wall became an almost straight line oriented along the diagonal direction of the ele- ment. This domain configuration was maintained in a large reversal field range until the reversal field was increased to 50 Oe. The reason why this domain structure is stable is because the angles between the magnetization vectors in the two domains and the reversal field are almost the same. It should be noted that at the high reversal fields, the magneti- zation vectors which were originally aligned along the 100 easy axes would rotate from the easy axes towards the field FIG. 10. Magnetization schematics of a 12 12 m2 Fe element direction as shown by the dashed arrows in Fig. 9 h . Since with edges parallel to the 110 directions during reversal along the in practice the field cannot be exactly aligned along the bi- 110 hard axis. 57 MICROMAGNETIC STRUCTURES AND MICROSCOPIC . . . 7821 small domains with magnetization oriented along the 010 directions remained only at the two corners in order to mini- mize the magnetostatic energy. These small corner domains shrank upon further increasing the reverse field. After the element reached a 1¯00 -oriented single-domain state, further increasing the reversal field caused the magnetization to ro- tate coherently towards the field direction. During the above reversal processes, we deliberately re- duced the magnetic field in several stages. Lorentz micros- copy measurements revealed that the domain structures shown in Figs. 9 and 10 were reversible. It is found that upon decreasing the field from the value sufficient to drive all the domain walls into the element edge, the whole domain pat- terns shown in Fig. 9 can still be regenerated. This behavior is different from the reported reversal behavior occurring in the polycrystalline permalloy elements where once the do- main walls were driven into contact with the edges of the elements, very complex domain structures would appear as the applied field was reduced.15 It has been pointed out that FIG. 11. The fine-scale stripe domain structures of a 12 these complex domain structures were caused by the imper- 12 m2 epitaxial Fe element with edges parallel to the 100 fections at the element edges. The fact that the same domain directions. These domain structures develop upon decreasing the patterns can be regenerated in these epitaxial Fe elements initial applied field Hi Hi in image a Hi in b Hi in c suggests that the edges of these elements are smooth and which is well aligned along the 110 hard axis. have less defects. The other possible reasons for regenerating the same domain structures in these epitaxial Fe elements zation vector coherently rotates towards one easy axis, say may be that they have a a strong magnetocrystalline anisot- 100 due to a small misalignment between applied field and ropy which favors a well-defined domain structure and b a the hard axis, the demagnetizing field which is oriented large magnetic moment which increases the energy penalty along the direction opposite to the magnetization vector will for disordered domain structures. rotate towards the 1¯00 direction. The resultant field of this Furthermore, the above measurements show that for a demagnetizing field and the applied field will make the mag- field applied along the hard axis, a small misalignment be- netization rotate towards the 010 direction in the areas tween the applied field and hard axis will make the magne- where the local hard axes deviate slightly from the 110 tization first rotate coherently towards the nearest easy axis towards the 100 direction due to the local structural inho- upon reducing the initial field. However, it is found that if mogeneity. Thus, the initial fine-scale stripe domain structure the applied field and the hard axis are carefully aligned, re- can still be formed. For the continuous epitaxial films, as the ducing the field resulted in a fine-scale stripe domain struc- demagnetizing field is negligibly small, the fine stripe do- ture developing first as shown in Fig. 11. The fine stripes in main structure only occurs when the applied field and the the images correspond to the areas of clockwise towards the hard axis are well aligned. 100 easy direction and anticlockwise towards the 010 These measurements show that due to the in-plane mag- easy direction rotated magnetization vectors apart from the netocrystalline anisotropy, the reversal processes of the epi- hard axis. Initially, the width of stripes was only a few hun- taxial elements along the 110 hard axes are significantly dred nanometers and the magnetic contrast was lower. Upon different from the reversal behavior along the 100 easy decreasing the field, the width of the stripes broadens and axes. Again, striking differences in the microscopic reversal magnetic contrast increases as shown in Fig. 11 c . The cor- processes were observed for the elements with different size. responding magnetization schematic of this image is shown For the small elements with the same 12 12 m2 size, the in Fig. 11 d . For continuous epitaxial Fe films, such fine- element orientation plays an important role in determining scale stripe domain structures have also been observed but their reversal behavior. they occur only when the angle between the 110 hard axis and applied field is smaller than 0.1°.27 Outside this angular IV. SUMMARY range, upon decreasing the field, the magnetization vector rotates coherently towards the nearest easy axis. For the con- In summary, we have investigated the in-plane size and tinuous epitaxial Fe films, the fine-scale stripe domain struc- orientation dependence of micromagnetic structures and mi- tures were attributed to be a consequence of a domain split- croscopic reversal processes in epitaxial Fe elements by Lor- ting process arising from local film structural entz electron microscopy. Upon reducing the element lateral inhomogeneity.27 Our experiments showed that for the 12 dimensions, a transition from a single-domain to a multido- 12 m2 epitaxial elements such fine-scale stripe domain main remanent state has been observed. For 150-Å-thick ep- structures can occur for the field applied within about 1° of itaxial Fe elements such dramatic changes in the remanent the hard axis. The reason why for small epitaxial elements domain structure and microscopic reversal behavior occur the initial fine-scale stripe domain structure could be ob- when the element size is reduced to 10 m. The transition served within a larger angular range is again due to the role can be explained as a consequence of the in-plane dipolar of the in-plane demagnetizing field. If initially the magneti- contribution to the total energy becoming comparable to that 7822 E. GU et al. 57 of the magnetocrystalline anisotropy at this size. Due to the information on the microscopic magnetization process within interplay between in-plane shape and magnetocrystalline small epitaxial elements. Such information is extremely use- anisotropies, distinct micromagnetic structures arise accord- ful for understanding the macroscopic magnetic behavior of ing to not only the crystallographic direction along which the these epitaxial elements and is relevant to practical device field is applied but also the orientation of the element edges. applications. 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