JOURNAL OF APPLIED PHYSICS VOLUME 85, NUMBER 8 15 APRIL 1999

Lorentz transmission electron microscope study of ferromagnetic domainwalls in SrRuO 3: Statics, dynamics, and crystal structure correlation

A. F. Marshall, L. Klein, J. S. Dodge, C. H. Ahn, J. W. Reiner, L. Mieville, L. Antagonazza,A. Kapitulnik, T. H. Geballe, and M. R. BeasleyCenter for Materials Research, Stanford University, 435 Santa Teresa, Stanford, California 94305-4045

~Received 1 September 1998; accepted for publication 13 January 1999!

The magnetic microstructure of SrRuO3 thin films is studied using Lorentz transmission electronmicroscopy~TEM!. The zero-field-cooled magnetic stripe structure shows one-to-one correlationwith the crystal domain structure and is used to identify the uniaxial magnetic anisotropy of thesefilms, consistent with results on single domain films. The anisotropy is shown to be primarilymagnetocrystalline in nature with theb axis as the easy axis. Lorentz TEM also yields quantitativeinformation about the domain structure and domain wall resistivity, and allows forin situobservation of domain wall formation and dynamic response to an applied field. ©1999 AmericanInstitute of Physics.@S0021-8979~99!02908-4#

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I. INTRODUCTION

SrRuO3 is a metallic, perovskite-based oxide withmoderate carrier concentration, and a 4d itinerant ferromag-net (Tc5150 K). Early bulk studies of polycrystal and singcrystal SrRuO3 showed an orthorhombic structure, slightdistorted from cubic perovskite, with high magnetic anisropy and a reduced magnetic moment.1–3 Because of its me-tallic properties and structural compatibility with technologcally important oxide materials such as highTc

superconductors and ferroelectrics, SrRuO3 was recentlysynthesized in thin film form, leading to new investigatioof its fundamental properties.4–6 The magnetization, transport, and magnetoresistive behavior of single-crystal-likeitaxial thin films have been studied in detail; results are csistent with the bulk studies and furthermore show huniaxial magnetic anisotropy, strong magneto-optic cpling, anomalous transport behavior aboutTc and at lowtemperature, and strong irreversible magnetoresisbehavior.7–10

The crystalline and magnetic microstructure of theSrRuO3 films is of considerable interest both for correlatiowith the macroscopic magnetization measurements andfurther investigation of the magnetic properties. Lorentransmission electron microscopy~TEM! is well suited tosuch microstructural analysis as well as allowing forin situstudies of magnetodynamic behavior. We have previoureported on the use of low-temperature Lorentz TEM to iage the zero-field-cooled magnetic microstructure of SrR3films and to determine its relationship with crystorientation.11,12 In this article we report in detail on the TEMmagnetostatic results and extend the analysis to magnetnamic observations of domain wall motion in an applifield. Lorentz microscopy of films with multicrystal domai~twinned! structures gives quantitative information conceing the magnetic domain structure, and allows forin situobservations of domain wall motion and annihilation. Theresults are correlated with previously reported magnetizameasurements of highly aligned, single-crystal-like~un-

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twinned! films deposited on miscut substrates. The structof the single-crystal films is also characterized. We find tthe high uniaxial anisotropy of SrRuO3 thin films is largelymagnetocrystalline in origin and identify theb axis as theeasy axis, measure the resistivity of domain boundaries,relate the magnetostatics with the domain structure,characterize the response of the domain walls to appfields.

II. EXPERIMENT

SrRuO3 films were synthesized by laser ablation or ractive electron beam coevaporation onto a variety of oxsubstrates. The films reported on here were all depositedSrTiO3, because the latter can be removed by chemical eto provide large, uniformly thin TEM samples. The films a300–1000 Å in thickness, deposited on both standardmiscut substrates, and are removed with a chemical etcHF:HNO3:H2O diluted approximately 1:1:1. They are thesupported on standard carbon/formvar support films ongrids. The resulting TEM samples are large in extent~0.5mm or more!, uniformly thin, and robust, allowing for opti-mal Lorentz imaging and repeated cycling throughTc forcomprehensivein situ analysis. They are, however, extesively buckled, and consequently exhibit a great deal of rdom diffraction contrast~due to bend contours! which mustbe minimized by tilting in order to clearly observe the manetic domain walls.

The films were examined in a Philips CM20FEG~fieldemission gun! fitted with a special lens for magnetic imaging, the twin 2 or Lorentz lens. For normal high resolutioimaging the specimen is situated in the middle of the hmagnetic field, approximately 2 T, of the objective imagilens; this will significantly alter most magnetic microstrutures. For Lorentz imaging this lens is switched off and tLorentz lens, just below the objective lens, is used asimaging lens. The advantage of the Lorentz lens, overmore traditional use of the intermediate projector lens asmagnetic imaging lens, is improved resolution and range

1 © 1999 American Institute of Physics

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4132 J. Appl. Phys., Vol. 85, No. 8, 15 April 1999 Marshall et al.

magnification. In order to compensate for any residual firemaining at the specimen with the objective lens turnedand the Lorentz lens on, the current in the twin~minicon-denser! lens above the specimen is reversed; calibrationobserving domain wall motion with tilt in a Co film indicatea cancellation current of about21700 mA. Exact field can-cellation is difficult to reproduce with precisely the same lesettings, probably due to hysteresis in the various lensessmall variations in lens currents as imaging conditionsvaried; however when the twin lens current is not reversobservation of magnetic microstructures indicate that thera residual field on the order of 1 kG which is reducedorder of magnitude or greater by the current reversal.

The films are observed both in Lorentz mode~LLM ! andby conventional imaging with the objective lens~OLM!. Theferromagnetic transition is observed by cooling the spemens in a Gatan liquid nitrogen cold stage. Using LLmagnetic domain walls become visible in a defocused imas alternating black and white lines due to alternating cvergence and divergence of the electron beam at theposition as it is deflected by the magnetic moment ofdomains. This is described by the Lorentz force,F5ev3B. Using OLM allows for conventional diffraction analysis; a comparison between crystalline and magnetic mistructure is thus carried out over large areas of the specimTo study domain wall motion, the objective lens is turnedThe field of the lens is normal to the untilted specimen plathe specimen is tilted~630° allowed tilt! to achieve an in-plane component of field in the desired direction. In this wdomain wall motion can be studied under a variety of applfield directions. The specimen is warmed and cooled repedly to achieve the same approximate starting domain stture.

III. RESULTS AND DISCUSSION

A. Relationship between crystal structure andmagnetic microstructure

As a multicrystal domain SrRuO3 film is cooled throughTc in approximately zero field, a stripe magnetic microstruture of alternating black and white domain walls is observ~Fig. 1!. Sets of stripes are at 45° to each other and varyspacing. We will demonstrate, using a combination oflected area electron diffraction and Lorentz imaging charteristics, that the stripe structure shows the presence infilm of all six of the possible crystallographic domains, athe existence of a single magnetic easy axis whose orietion is close to theb axis. The magnetic and crystalline domain structures are shown schematically in Fig. 2. The crelation of the uniaxial anisotropy with a specific crysaxis, shows that this anisotropy is primarily magnetocrysline in nature and not a substrate effect.

We first describe the formation of the observed crysdomain structure; this structure occurs because the orrhombic SrRuO3, having lower symmetry than the cubsubstrate, aligns in several symmetry-related orientationsthe substrate: The orthorhombic structure is based on a cperovskite subcell~a>3.93 Å!, with the c axis doubled andthe closely spaceda and b axes rotated 45° with respect t

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the subcell~a55.53, b55.57, c57.82 Å!. The relationshipbetween the orthorhombic and subcell axes is also showFig. 2. During film deposition, the approximately cubic sucell aligns with the cubic axes of the substrate resultingthe six crystal domain orientations shown.

1. The orthogonal c-axis orientations

Since thec axis is readily distinguished by electron difraction and remains parallel to the substrate axes, a conient way to consider the crystal domain structure is as thorthogonal6orientations of thec axis, parallel to the sub-strate axes. Thea andb axes of the film are then rotated witrespect to the substrate axes as shown in Fig. 2. Selectedelectron diffraction confirms the three orthogonalc-axis ori-entations as shown in Fig. 1, and determines the correlawith the stripe orientation as shown in the schematic. Forwidely spaced walls at645° to the substrate axes, thec axisis perpendicular to the substrate and thea andb axes are inthe plane of the film with the walls parallel tob. For thenarrowly spaced walls parallel to the substrate axes, thcaxis is in the plane of the film, perpendicular to the stri

FIG. 1. The zero-field-cooled stripe magnetic domain structure of a SrR3

thin film and diffraction patterns showing the orthogonalc-axis directions inregions with different stripe orientation.

FIG. 2. Schematic showing the six crystal domain orientations of ortrhombic SrRuO3 on cubic SrTiO3 and the corresponding magnetic striporientations.

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4133J. Appl. Phys., Vol. 85, No. 8, 15 April 1999 Marshall et al.

direction and thea andb axes are out of the plane at 45°, i.ethese domains are in a@110# orientation. Electron diffractioncannot easily distinguish the6c-axis twin orientationsshown in the schematic, which also correspond to reversathe closely spaceda andb axes; we will use characteristicof the magnetic images to identify these twins as describelow. We refer to the in-plane orientations of thec axis asci , and to the normal orientation asc' . As shown in Fig. 2there are fourci orientations~two sets of twins at 90° to eacother! and two twin-relatedc' regions.

2. The magnetization direction

Lorentz microscopy then shows that the stripe oriention also indicates the magnetization direction, i.e., for thzero-field-cooled conditions, the easy magnetic axis. Thidone by observing the direction of beam deflection bymagnetic domains. The Lorentz lens is defocused to obsthe back focal plane of the lens where the diffraction pattis formed. The deflection of the beam by the different dmains is observed as a splitting of the transmitted beamthe diffraction pattern; the direction of the spot splittingcorrelated with different stripe directions by the use ofselected area aperture~in this case, the objective apertursince the normal image and diffraction modes of the micscope are reversed!. As shown in Fig. 3, it is observed thathe spot splitting is always normal to the stripe directioconfirming that the magnetization of the domains is parato the domain walls.13 This is expected, since the wall energis minimized for a parallel configuration. The magnetizatiis therefore in theac or bc plane forc' and in theab planefor ci , indicating an easy axis alonga and/orb ~assuming

FIG. 3. Selected area Lorentz diffraction patterns from differently orienstripe domain regions:~a! a c' twin, ~b! ci domains. The splitting perpendicular to the walls confirms the in-plane direction of magnetizationparallel to the domain walls~deflection of the beam by the Lorentz force!.Also the split is larger forc' regions which have their magnetization completely in-plane. A peculiar feature of theci splitting is the occurrence of thecenter spot, indicating regions of no magnetization, or magnetization plel to the electron beam.

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the same easy axis for both orientations!. The magnitude ofthe spot splitting from thec' regions is greater than that otheci domains, indicating that the magnetization is closeror in the film plane for the former~greater Lorentz forceresulting in greater beam deflection!, confirming that theeasy axis is approximatelya and/orb for both types of do-mains.

3. Identifying 6c domains, b as the easy axis

The stripe structure therefore indicates both the directof the magnetic easy axis and the presence of three orthnal crystal orientations of the SrRuO3 structure. From detailsof the magnetic images, one can further determine the pence of the twin-related6c-axis crystal domains, confirmingthe presence of all six crystallographic domains in thefilms. Forc' regions we observe that there are two 90° oentations of the domain walls~the more widely spaced walls!and that, for a given area, these walls always return insame orientation during temperature cycling throughTc .This indicates that there is, in fact, a unique easy axis aleithera or b, and that there are twin-relatedc' regions of thefilm wherea andb reverse direction. It is difficult to distin-guish a and b by absolute measurements, as they are vclose in magnitude. However selected area diffractiontwinnedc' regions~those with widely spaced domain walat 90° to each other! exhibit spot splitting which allows formeasurement of the relative magnitude of the in-plane ctal axes.~This splitting effect is due to the small differencein lattice spacing and is distinct from the central spot spting of Fig. 3 which is due to magnetic deflection.! We usethis to determine thatb is the easy axis as follows: Sposplitting in a selected area diffraction pattern of a twinnedc'

region is shown in Fig. 4. Each of a set of split spots canassigned to one of the twin regions by shifting the selecarea aperture from one twin to the other. The closer sporeciprocal space, i.e., the largerb axis in real space, is parallel to the wall direction, indicating that theb axis is themagnetization direction and therefore the easy axis. Notethedirectionof the spot splitting is at 45° to thea andb axes,as is the plane of the boundary. That is, the boundary plan~110!, which allows for atomic matching at the interface aa coherent boundary. Thea andb axes tilt slightly across thisboundary leading to the spot splitting along@110#. These tiltsand the lattice mismatch with the substrate lead to sevbuckling of the film which is evident in the curved blackand-white bend contours visible in the images.

The presence of twin-relatedci regions, due to6c-axisorientation, is not shown by the stripe orientation becaushas the same direction for such regions~see Fig. 2!. Thepresence of this twinning can be determined by more suobservations of variations in contrast and wall dynamics ding tilting. We assume an out-of-plane magnetizationthese regions approximately along theb axis, as indicated bythe previous results. If aci region is tilted about thec axis,then theb axis will be tilted either closer to the electrobeam direction or farther away from it, depending on the6sense of the crystal domain~see schematic of Fig. 5 whereci region is viewed sideways along thec axis!. Tilting de-creases or increases the magnetic domain wall contrast

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4134 J. Appl. Phys., Vol. 85, No. 8, 15 April 1999 Marshall et al.

spectively, because the contrast depends on the LorentzF5ev3B, i.e., the angle between the electron beam andmagnetization. A givenci region will reverse its contrasbehavior~stronger versus weaker contrast! with reverse tilt,and twin-related regions will show opposite contrast chanwhen tilted in one direction. Such twin-relatedci domainsare shown in Fig. 5 for630° tilt about thec axis. Domainsthat decrease in contrast for one tilt direction, e.g., regimarked ‘‘X’’ in Fig. 5~a!, show an increase in contrast for thopposite tilt, Fig. 5~b!, and both twin orientations, distinguished by ‘‘X’’ and ‘‘ Y’’ in Fig. 5, are apparent in the areobserved. When a field is applied~to be discussed in mordetail later! parallel to the beam, the low contrast magnedomains, having their magnetization tilted toward the beaare the first to grow, and the domain walls of these regionlow contrast are therefore the first to annihilate@Figs. 5~c!and 5~d!#. For the same tilt, the twin-related regions of strocontrast have their magnetization almost perpendicular tofield, requiring rotation to align with the field and thereforesisting domain wall motion.

B. The emerging picture

The TEM analysis shows one-to-one correlation betwthe local film orientation and the magnetic stripe structwhich, by itself, is sufficient to indicate uniaxial magnet

FIG. 4. The split spots of the diffraction pattern result from the twin-relac' regions and each can be assigned to a specific twin by selecteddiffraction; thea andb axes are then identified by the relative position of tsplit spots.b is always parallel to the walls/magnetization direction.

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anisotropy. Furthermore, it shows that the easy magnettion axis is very close to the filmb axis. Forci regions thisimplies an easy axis which is tilted out of the plane of tfilm at about 45°, while forc' regions the easy axis is in thplane of the film at 45° relative to the substrate unit axes

These conclusions are consistent with global magnettion measurements of fully aligned films grown on miscSrTiO3 substrates which have theirc axis predominantly inthe plane of the film~perpendicular to the miscut direction!.These measurements indicated an easy axis out-of-planabout 45° along eithera or b. The significance of the presenresults is not only in identifying the easy axis as theb axisbut, by showing the correlation between the magnetic eaxis and the crystallographic axis, which holds irrespectof the relative orientation of the film with respect to thsubstrate, we have substantiated the intrinsic magnetocryline nature of the magnetic anisotropy and excluded the psibility of a dominant substrate-induced strain effect.

C. Crystal domain morphology and crystal defects

In addition to showing us magnetization behavior, tmagnetic microstructure is a more effective way to imagecrystal domain morphology than conventional diffractiocontrast imaging. This is because diffraction contrasttween crystal domains is small, highly sensitive to smchanges in orientation, and overshadowed by that fromfilm buckling, whereas the magnetic contrast is not sensito small tilt variations. The magnetic microstructure furthe

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FIG. 5. Twin-relatedci regions are identified by contrast changes and dmain wall motion with6 tilt. The direction of tilt is as shown in the schematic. The specimen has been warmed and cooled between images,wall structures are not identical between~a! and ~c!. Regions markedXshow low contrast in~a! and high contrast in~b!; the same regions lose theidomain walls in~c! and retain them in~d!. The region markedY shows theopposite behavior.

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4135J. Appl. Phys., Vol. 85, No. 8, 15 April 1999 Marshall et al.

FIG. 6. ~a! Lorentz image of an aligned film on miscut SrTiO3. While most of the film isci aligned, somec' regions are observed~markedX!, possiblyformed after removing the film from the substrate.~b! and ~c! Films on nonmiscut substrates. The Lorentz images are effective in delineating the cdomain structure by changes in the stripe orientation.~d! Higher magnification OLM image of the same film as~c! showing crystal domain boundaries anend-on dislocations~black dots!.

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more directly indicates individual domainorientationover alarge field of view, allowing the degree of film alignmentbe measured. This orientation distribution is not easilyserved in conventional dark-field or high resolution imagdue to the film buckling and small field of view, respectiveHowever quantification of the film alignment by the Lorenimages requires caution as there are indications that scrystal domain reorientation occurs when the specimenremoved from the substrate.14 Figure 6~a! shows the mag-netic microstructure of a film, deposited on a miscut sustrate, estimated to be greater than 95%ci aligned from mag-netization measurements. Large areas of the film are indci aligned, as shown in Fig. 6~a! and untwinned, as confirmed by the contrast changes with tilting described preously. However, a number ofc' domains are observed, aindicated by the striped wall orientation. Overall, about 15of the film appears misaligned, confirming some reoriention of the film upon removal from the substrate.

Despite the indications of some reorientation, the TEsamples do indicate a high degree of alignment for SrRu3

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on miscut substrates and are expected to give a reasonindication of crystal domain structure variations from sustrate to substrate. Figures 6~b! and 6~c! compare the mag-netic microstructure of two other films, deposited on~100!SrTiO3 ~not miscut! with the aligned film; Fig. 6~b! showsmany small ci domains and a few, largec' domains,whereas Fig. 6~c! shows fewerci domains and many, smac' domains. We have also previously observed variationdomain size between SrTiO3 and LaAlO3 substrates.7 Thecrystal domain boundaries tend to follow~110! planes, asshown in Fig. 6~d!, an OLM, higher magnification image othe film in Fig. 6~c!. A high density of end-on dislocation~black dots! is also visible in Fig. 6~d!.

D. Analysis of the domain wall spacing

Lorentz microscopy gives direct measurement of themain wall spacing. We observe that the striped walls ofci

andc' domains differ both in spacing and in the dependenof spacing on crystal domain size. Theci domain walls are

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more closely spaced, having an average spacing of a2000 Å, independent of either crystal domain size or thiness for film thicknesses of about 300–1000 Å. Thec' re-gions, on the other hand, are on the order of a micronmore in spacing and the spacing varies considerably. Thobservations correlate with the anisotropy and the shapependence of the demagnetizing factor. The magnetostaticergy of ci regions, with the magnetization out-of-plane,higher than that ofc' regions, and the domain wall spacingare correspondingly smaller. They also show little depdence on crystal domain size since the demagnetizing fafor this out-of-plane flat-plate geometry is about 1/2p andcorrelates with the aspect ratio of domain size to film thicness which is always very large. When the magnetizatioin-plane, as forc' regions, the demagnetizing factorsmaller. It also depends on the domain dimension in therection of magnetization which now corresponds to themain size. The striped spacing ofc' regions therefore showa strong dependence on the size of the domains, increasithe domains become larger~Fig. 1!.

In principle, the domain wall spacing represents a bance between the magnetostatic energy, which is reducedomain formation, and the domain wall energy. Therefomagnetization constants such as the domain wall energythe anisotropy constant should be obtainable from themain wall spacing measured by TEM combined with tsaturation magnetization and exchange stiffness measurethe aligned films. An expression for single crystals wuniaxial magnetic anisotropy is given by Cullity:15

D5(gL/1.7Ms2)1/2, whereD is the domain wall spacing,g is

the wall energy,Ms is the saturation magnetization, andL isthe dimension parallel to the magnetization direction, iapproximately the film thickness forci regions and the crystal domain dimension parallel to the walls forc' regions.g is then related to the anisotropy constant byg52(JS2p2K/a)1/2, whereJ is the exchange constant,S is thespin, and K is the anisotropy constant. UsingMs

5213 emu/cm3, J526.33kB , and S51, we have the rela-tionship for the anisotropy constant, K51.6231015(D4/L2) ergs/cm3. Forc' regions, withD52 mm and1 mm, L535 mm and 11mm as typical values for large ansmall crystal domains we obtainK on the order of 1 – 23105 ergs/cm3, two orders of magnitude lower than that epected from magnetization measurements on the aligfilms. The latter indicateK.107 ergs/cm3. However, thevariation of D with L is reasonably consistent forc' do-mains. Forci grains, usingMs5151 emu/cm3, D52000 Åand L51000 Å, we obtain a slightly higher value,K56.73105 ergs/cm3. Cullity’s description assumesL.D andtherefore negligible interaction between surfaces, which dnot strictly hold forci regions. A more precise expression fthe magnetostatic energy by Malek and Kambersky16 ac-counts for this interaction with a prefactor summation tedepending onL/D; for ci regions inclusion of this factodecreasesK further so that the values for both types of rgions are approximately the same, also giving internal csistence. However, since theci regions do not show an obvious dependence onL/D for the film thicknesses observehere~300–1000 Å!, and since the calculated values ofK are

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much lower than indicated by other measurements, it is cthat the relationship of the domain wall spacing to the mnetization parameters requires clarification beyond thstandard models.

In situ Lorentz TEM gives valuable insight into the situation, allowing direct observation of additional factors cotrolling the domain wall spacing. We find that the domawall distribution that forms during cooling does not represemagnetostatic equilibrium, even for the minimum cold statemperature of 100 K, as will be discussed in more debelow. Also, since both the saturation magnetization andanisotropy constant are temperature dependent, we mustinto account the different temperature ranges in whichmeasurements are made. The magnetization constantsrived from macroscopic magnetization measurementsaligned films are made at 4.2 K, whereas the TEM obsertions are in the range fromTc to 100 K. The saturation magnetization and anisotropy constant are changing rapidlythe temperature decreases belowTc , the effects of which weobserve by TEM, and have values quite different from thomeasured at low temperature. Finally, the domain wall sping does not depend on the film thickness, as the abovepressions predict, for films in the range of 300–1000 Å.

Using Lorentz microscopy, we observe directly the prcess of domain formation and the qualitative variation ofmagnetization parameters during cooling. Figure 7 showseries of video frames during cooling of aci grain. As thegrain is cooled throughTc a very regular, faint stripe structure begins to form with a wall spacing of about 1000 Å@Fig.7~a!#. The specimen is cooling at a rate of about 7°/min.Fig. 7~b!, one degree cooler, the stripe structure is mustronger in contrast, but still very regular with about tsame spacing. As the cooling progresses, both the wall ctrast and the average wall spacing increase, the latter becing more irregular due to annihilation of pairs of black-anwhite walls@Figs. 7~c! and 7~d!#. Both the magnetization andanisotropy, which have opposite influence on domain sare increasing rapidly with decreasing temperature, the cpetition between them clearly favoring an increase indomain wall spacing, i.e., the anisotropy energy containethe wall is increasing faster than the reduction of magnestatic energy due to the presence of domains. However othe walls have formed, their average spacing can onlycrease by annihilation of a pair of walls as opposed to invidual wall movement, since the latter enlarges one domat the expense of another. Furthermore, the energeticswall formation is also influenced by the energy requiredmove a wall: it is observed that following wall pair annihlation, the adjacent walls tend to keep their position ratthan adjusting to a more regular spacing, indicating thatwalls are already immobile, relative to these magnetostenergy changes, a few degrees belowTc . Wall motionand/or annihilation ceases about 15° belowTc and the re-maining stripe structure has a distribution of domain spings with an average spacing of about 2000 Å forci do-mains. This final spacing of the domain walls clearly donot represent magnetostatic equilibrium, but dependsmagnetodynamic energetics of domain wall motion, and abecomes frozen in at temperatures fairly nearTc where mag-

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4137J. Appl. Phys., Vol. 85, No. 8, 15 April 1999 Marshall et al.

FIG. 7. Sequence of video images during cooling of SrRuO3 ci aligned film. The initial faint stripe structure~a! increases rapidly in contrast as thmagnetization increases~b!. Pairs of black-and-white domain walls annihilate to increase the average wall spacing~c!. This process continues for about 15below Tc ~d! and the wall structure remains unchanged with further cooling down to about 100 K.

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netization parameters are more difficult to measure thatemperatures well belowTc .

The fact thatD does not vary significantly with filmthickness forci regions further indicates that the wall enerper area for these regions is not a constant as assumecalculatingK, but likely contains a magnetostatic term duethe intersection of the wall with the surface. For the rangefilm thicknesses studied here, the wall energy may depsignificantly on the surface term and the energy per areabe therefore both variable and underestimated. We plathe future to examine ultrathin films, 100 Å or less, as was thicker films,;2000 Å being an upper limit for TEMtransparency, to investigate further the effects of film thicness onci domain spacing.

Quantitative information about the domain wall resistity is available from theci domain wall spacing. A zerofield-cooled, aligned film exhibits large irreversible magntoresistance with an applied field of about 2 kG, as shownFig. 8. This corresponds to a resistivity of approximate10215Vm2/unit area.10 Due to the high anisotropy, the domain walls are expected to be Bloch walls. Calculation ofdomain wall width usingd5(0.3kTcp

2/4Ka)1/2 ~see Ref.15, p. 291!, where d is the wall width, k is Boltzmann’sconstant, andK is the anisotropy constant, is assumed to107 ergs/cm3, indicates a very narrow domain wall width oabout 20 Å. This is again due to the large anisotropy consestimated at 4.2 K; the walls are expected to be wider atTEM observation temperatures.

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E. Domain wall motion in an applied field

Domain wall motion is observed by turning on the fieof the objective imaging lens. This field is normal to thuntitled specimen plane; an in-plane component of fieldachieved by tilting the specimen. As the field is appliepairs of black-and-white stripe domain walls move togethand annihilate. An example is shown in Fig. 9 where tin-plane component of the field is parallel to the right-ha

FIG. 8. Large initial magnetoresistive behavior of zero-field-cooled SrRu3

is due to the removal of domain walls as demonstrated in Lorentz TEM

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4138 J. Appl. Phys., Vol. 85, No. 8, 15 April 1999 Marshall et al.

set of c' domain walls as shown. As the favorably aligndomains grow, pairs of walls move together and annihil@Fig. 9~b!#. Observedin situ, the wall motion is discontinu-ous, both jerky in time and spatially segmented, demonsing the Barkhausen effect, i.e., the existence of pinning swithin the SrRuO3. As seen in Fig. 9~b!, walls that havemoved are no longer as straight as when formed and tenshow kinks, also indicating pinning. As mentioned, the filmcontain a high density of end on dislocations@Fig. 6~d!#,which are likely pinning sites. Their density is an ordermagnitude greater than that of the domain walls, and theynot clearly visible in Lorentz images, so their influencepinning requires more detailed correlation between convtional and magnetic image modes, which will be left to fture experiments. The boundaries between crystal domare also apparent in Fig. 6~d!; some of these domains form avery small regions within larger crystal domains and habeen observed to act as pinning sites during magnetizareversal.

The stripe domain walls disappear gradually as the fiis increased and are completely annihilated at a field emated to be about 2 kG from the objective lens current~500mA!, consistent with the magnetoresistance measuremAlthough we cannot reverse the objective lens field, wereverse the in-plane field component by tilting the specimin the opposite direction; this affects only thec' regions. We

FIG. 9. When a field is applied, the domains aligned with the field arefirst to grow as evidenced by comparing the domain wall structures in~a!zero field and~b! H'0.2 kG with an in-plane direction as marked. Thec'

domain walls parallel to the field, such as those marked 1, 2, 3, 4, anhave moved and/or partially annihilated in~b!. The black walls are movingup and the white walls down as aligned domains grow. It is seen thatwalls become crooked, with bowed and kinked segments, as they moveshorter white arrows show two points where black and white walls jotheir segments having annihilated to the left of these points. Thec' domainwalls which are oriented at 90° to the applied field, such as those marke7, 8, and 9, remain unchanged.

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observe no reformation of the stripe structure, again content with the magnetoresistance behavior. Rather, asspecimen tilt is reversed, the magnetization ofc' regionsreverses by the movement of individual domain walls acrthe film. However the stripe structure can be reproducwith the precise wall positions varying somewhat, by waring and cooling the film throughTc . In this way, the sameregion can be studied with the field applied in different drections ~different specimen tilt direction!. The stripe do-mains are observed to annihilate in a sequence that issistent with the direction of tilt, or field. The most alignedomains are the first to grow and lose their striped wastarting with an applied field of about 0.2 kG; the leaaligned are last. For example, thec' domain walls on theright-hand side of Fig. 9, have moved together and paannihilated in a field of about 0.3 kG~90 mA!, while thoseon the left-hand side, which remain perpendicular to the fiduring tilting, have not changed position. For this tilt somof theci domains will also be favorably oriented in the fiedirection which will be indicated by a loss of contrast~aspreviously demonstrated in Fig. 5!. Most of theci walls vis-ible in Fig. 9 show strong contrast and resist the field. Hoever careful examination of theci walls just to the left ofcenter shows that this area has weaker contrast in Fig.~a!and some movement of the walls toward each other in F9~b!. The remainingci walls show strong contrast and resimovement until higher fields.

As the field continues to increase all of the stripe waeventually annihilate. Above about 2 kG, when the strwalls have completely disappeared, magnetic domain wremain between crytallographic domains. This indicates tdomain rotation has not occurred; for such a region, whneither set of domains is macroscopically aligned towardfield direction, it is likely that one set has a small magnezation component along the field which favors its growover the other set, leading to domain wall annihilation. Tfinal structure of domain walls at crystallographic boundarpersists even after the objective lens is increased to its mmum value of about 2 T, and then back to zero fieldimaging. This is shown in Fig. 10 which compares the saregion of the specimen by conventional and high resolutimaging of crystal boundaries, with the zero-field-cooled amagnetized~to 2 T! Lorentz images. The high crystallinanisotropy either prevents the crystal domains from rotattheir magnetization from the easy axis, or returns the mnetization to that state when the field is removed. Wetempted to observe domain rotation by Lorentz microscowhich requires that the full field of the objective lens bapplied. However such an image could not be obtainedcause the necessary microscope alignments were beyoninstrument capabilities with both imaging lenses turnedNote that the domain walls observed in Fig. 10 are no lon180° walls but are approximately 60° and 90° walls, tformer occurring between two orthogonal~c axis! ci do-mains or aci and c' domain, and the latter between twinrelated~6c axis! ci grains orc' domains. The tip of thesmall ci twin just to the left of center in Fig. 10~c! does notshow domain boundary contrast because the magnetic

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4139J. Appl. Phys., Vol. 85, No. 8, 15 April 1999 Marshall et al.

FIG. 10. The same area of the film is shown for~a! zero-field-cooled before applying field,~b! conventional OLM imaging, and~c! magnetized to 2 T~fieldremoved!; these images are all at the same magnification. Short, black arrows mark approximately the same region in each image.~d! and ~e! are highresolution images of the crystal domain boundaries marked by white arrows. The boundary in~d! is between twin-relatedci regions~the c axis changesdirection across the boundary by 180°! and corresponds to the broadened light region down the center of the image. Because of the 180° orientationthere is no obvious difference in the lattice image across the boundary. The boundary in~e! is betweenci andc' regions and the lattice image shows a clechange across the boundary. Both boundaries become visible under the magnetized condition of~c! where the black and white magnetic domain boundarmark the crystal domain boundaries. However the boundary in~d! is not visible in the zero-field-cooled structure of~a! because the stripe domains are in thsame direction on either side of the crystal domains. The boundary in~e! is visible in ~a! due to the change in direction of the stripe domains acrossboundary. Note that tip of theci twin ~arrow! in ~c! is not visible because the magnetization is perpendicular to the boundary in this region giving no Lcontrast.

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flection of the beam is parallel to the boundary in this regrather than perpendicular to it.

There are several features of the domain walls thatunusual and indicate directions for future analysis. One iscentral spot observed in theci Lorentz diffraction pattern,suggesting a stable state of perpendicular magnetizationcurring in some fraction of the domains or domain wstructure. Another is the response of the domain walls asapplied field is increased: the walls first move together ifairly continuous way with increasing field, but some threach a state where they remain ‘‘stuck’’ on each other,close together~estimated as 900 Å or less!, but failing toanihilate until noticeably higher fields are reached. A psible explanation for such behavior is the concept of 3walls, i.e., a state of a pair of walls where the magnetizatrotation across both walls varies continuously by 360°. Tis in contrast to rotation of1180° across one wall an2180° across the adjacent one. Annihilation of the formstate would be expected to require more energy thanlatter. A third feature of the domain wall anihilation somtimes observed is a fading of wall segments just priorannihilation, also indicating an intermediate or transient sin the anihilation process. All of the above suggest compdomain wall structures, perhaps metastable states, notdicted by basic models. Finally when a magnetized film

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warmed throughTc , the domain walls are observed to retujust belowTc and~in a apparent reversal of the cooling prcess! to become more finely spaced with the increasing teperature untilTc is reached and they disappear. Althoughis not clear if this latter effect, which is again due to magntization parameters changing with temperature, will revany new physics of the domain walls, there is the potentiausing the initial few domains as a starting point for studyireversal effects.

IV. CONCLUSIONS

Lorentz TEM is a powerful tool for analyzing the magnetic microstructure, crystal structure, andin situ magneto-dynamic behavior of these SrRuO3 films. Furthermore, theirhighly organized crystal structure and uniaxial magneticisotropy make these films ideal for such studies. Using ttechnique we have:~1! independently confirmed the uniaxiaanisotropy found for aligned films and found it to be largemagnetocrystalline in nature;~2! identified the easy axis athe orthorhombicb axis; ~3! compared the crystal domaistructure of films on conventional and miscut substrates;~4!analyzed the domain wall spacing and observed details oformation relative to the ferromagnetic energy state;~5! mea-sured the domain wall resistivity, and~6! characterized the

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4140 J. Appl. Phys., Vol. 85, No. 8, 15 April 1999 Marshall et al.

magnetodynamic behavior of wall anihilation. The resualso indicate future directions for using Lorentz microscoto study magnetodynamics and details of domain wall strtures in these films.

ACKNOWLEDGMENT

This work was supported by the NSF-MRSEC prograthrough the Center for Materials Research at Stanford Uversity.

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13That the center of the pattern lies between the split spots in Fig. 4~a! wasconfirmed by overlapping the patterns from the two areas. A peculiarconsistent feature ofci regions is the occurrence of a central spot betwethe split spots. This suggests regions of magnetization parallel to the b~or possibly unmagnetized regions!, and is believed related to the domawall structure. Attempts to further identify the source of this spotobserving changes with tilting and applied field have been ambiguouswill be pursued in more detail in future experiments.

14C. B. Eom~private communication!.15B. D. Cullity, in Introduction to Magnetic Materials~Addison-Wesley,

Reading MA, 1972!, p. 301.16Z. Malek and V. Kambersky, Czech. J. Phys.8, 416 ~1958!.