The application of Lorentz transmission electron microscopy ......Lorentz transmission electron microscopy has been used to study fine-scale exsolution micro structures in ilmenite-hematite,

American Mineralogist, Volume 94, pages 262–269, 2009

0003-004X/09/0203–262$05.00/DOI: 10.2138/am.2009.2989 262

The application of Lorentz transmission electron microscopy to the study of lamellar magnetism in hematite-ilmenite

Takeshi kasama,1,* Rafal e. Dunin-BoRkowski,2 ToRu asaka,3 RichaRD J. haRRison,4 Ryan k.k. chong,1 suzanne a. mcenRoe,5 eDwaRD T. simpson,1 yoshio maTsui,3 anD

anDRew puTnis6

1Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, U.K.2Center for Electron Nanoscopy, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark

3Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan4Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, U.K.

5Geological Survey of Norway, N-7491 Trondheim, Norway6Institut für Mineralogie, Universität Münster, Corrensstrasse 24, D-48149 Münster, Germany

aBsTRacTLorentz transmission electron microscopy has been used to study fine-scale exsolution micro-

structures in ilmenite-hematite, as part of a wider investigation of the lamellar magnetism hypothesis. Pronounced asymmetric contrast is visible in out-of-focus Lorentz images of ilmenite lamellae in hematite. The likelihood that lamellar magnetism may be responsible for this contrast is assessed us-ing simulations that incorporate interfacial magnetic moments on the (001) basal planes of hematite and ilmenite. The simulations suggest qualitatively that the asymmetric contrast is magnetic in origin. However, the magnitude of the experimental contrast is higher than that in the simulations, suggest-ing that an alternative origin for the observed asymmetry cannot be ruled out. Electron tomography was used to show that the lamellae have lens-like shapes and that (001) planes make up a significant proportion of the interfacial surface that they share with their host.

Keywords: Hematite, ilmenite, lamellar magnetism, Lorentz electron microscopy, electron to-mography, transmission electron microscopy

inTRoDucTionHematite-ilmenite (Fe2O3-FeTiO3) solid solutions occur abun-

dantly in nature as accessory minerals in igneous, metamorphic, and sedimentary rocks, and they play an important role in the acquisition of natural remanent magnetization (NRM). McEnroe et al. (2001a, 2001b, 2002, 2004a, 2007a) and Kasama et al. (2004) used transmission electron microscopy (TEM) to identify fine-scale exsolution microstructures of hematite and ilmenite in metamorphic and igneous rocks that exhibited significant NRMs. In all of these studies, the saturation magnetizations of the rocks were higher than would be estimated from their hematite contents, suggesting that the unusually large magnetic signals were associated with the interfaces between the coher-ently intergrown hematite and ilmenite phases (McEnroe et al. 2002). Kasama et al. (2004) studied the microstructures and compositions of magnetic minerals in metamorphic rocks with different magnetic properties and confirmed that the acquisition of stable NRM was likely to be related to the presence of fine exsolution lamellae.

Monte Carlo simulations have been used to relate the fer-rimagnetic moment of an intergrowth of hematite and ilmenite to the arrangement of cations and spins at interfaces between the two phases (Harrison and Becker 2001). Robinson et al. (2002, 2004) and Harrison (2006) used Monte Carlo simulations

to estimate that the saturation magnetization of an intergrowth of hematite and ilmenite lamellae can be stronger than that of end-member hematite if all of the interfacial moments are “in-phase,” i.e., oriented in the same direction. They defined this “lamellar magnetism” as being due to “contact layers,” i.e., cation layers at interfaces between hematite and ilmenite that do not correspond to the chemistry of either hematite or ilmenite. The lamellar magnetism hypothesis has been discussed in detail by Robinson et al. (2004). Kasama et al. (2003) used high-resolution TEM and energy-filtered TEM (EFTEM) to show that hematite and ilmenite can have coherent interfaces, with compositional transition widths of less than a few nanometers, which is a key requirement of the lamellar magnetism hypothesis.

There have been several attempts to prove the lamellar magnetism hypothesis experimentally. It has been shown from the relationship between crystallographic orientations and NRM directions that NRM vectors appear to be parallel to the a-axes of hematite and ilmenite, as predicted by the lamellar magnetism hypothesis (Robinson et al. 2006). Although these measurements can be related to the sublattice magnetization direction of he-matite, they cannot be linked directly to the lamellar interfaces. Some of the measured moments may be associated in part with spin canting.

Mössbauer spectroscopy studies have suggested the presence of a minor ferrimagnetic component, which could originate from a cation arrangement of Fe2+ and Fe3+ at lamellar interfaces (Dyar et al. 2004; Frandsen et al. 2007).

McEnroe et al. (2000, 2001a, 2001b, 2002, 2004a, 2004b,

* Present address: Center for Electron Nanoscopy, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark. E-mail: [email protected]

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2007a) showed that samples containing ilmenite lamellae in hematite have higher coercivities and thermal stabilities than those containing hematite lamellae in ilmenite. Monte Carlo simulations were used to show that the magnetic moment of an ilmenite lamella in a hematite host depends on its physical position and that a reversal of the moments in the hematite host may be required to reverse the moments associated with each lamella (Robinson et al. 2004).

Recently, a giant exchange bias of >1 T at temperatures below 57 K, which is the ordering temperature of ilmenite, was discovered in samples containing fine ilmenite lamellae in hematite hosts (McEnroe et al. 2007b). Fabian et al. (2008) reported that the spins that are responsible for the large exchange bias are also responsible for the NRM of the sample. Since ex-change bias is inherently an interface phenomenon, the NRM is therefore also associated directly with the interface spins. Monte Carlo simulations suggested that contact-layer spins, which are coupled antiferromagnetically to neighboring Fe2+ spins in the ilmenite lamellae, are tilted out of the (001) plane and may explain the origin and magnitude of the exchange bias (Harrison et al. 2007).

Although the presence of fine hematite and ilmenite lamellae in rocks that exhibit stable NRM appears to be consistent with the lamellar magnetism hypothesis, the magnetic properties of individual interfaces between hematite and ilmenite have been difficult to measure due to their small size. Previous studies only measured bulk magnetic properties of the samples. Here, we attempt to examine the magnetic properties of individual fine ilmenite lamellae within a hematite host at high spatial resolution using Lorentz electron microscopy (LEM), conventional TEM, and electron tomography, to investigate the lamellar magnetism hypothesis experimentally.

expeRimenTal meThoDsThe sample examined here is an igneous rock from Rogaland, Norway, of

which approximately 80% consists of an ilmenite host with multiple generations of hematite and ilmenite exsolution lamellae. Plagioclase, biotite, and a small quantity of quartz and chlorite are also present. The details of the constituent minerals and the chemistry and texture of the igneous rock have been described previously by McEnroe et al. (2001a, 2002). The sample exhibited coercivities of 40–70 mT, an average NRM of 25 A/m and an average saturation magnetization of 1055 A/m (McEnroe et al. 2001a, 2002), four times higher than the value expected for the end-member hematite.

For TEM examination, approximately 30 µm thick slices were removed from thin sections of the rock, polished mechanically, and thinned to electron transpar-ency by Ar ion milling. The thinned specimens were coated lightly with C before they were examined by TEM.

A Hitachi HF3000L TEM, equipped with a field emission gun (FEG) and oper-ated at 300 kV in Lorentz mode, was used to image magnetic structure out-of-focus using Fresnel imaging. The image contrast recorded using this technique results from the deflection of the incident electron beam by the Lorentz force associated with the in-plane component of the magnetization in the specimen, as illustrated schematically in Figure 1. By analyzing the contrast in such images, which usually gives rise to bands of bright or dark intensity at the positions of magnetic domain walls, information about the local direction of the magnetic moment in the speci-men can be inferred. In the present study, Lorentz images were always acquired in magnetic-field-free conditions with an objective aperture inserted, and recorded on negatives without energy-filtering, after magnetizing the sample parallel to the lamella direction using a 5 T magnetic field in a superconducting quantum interfer-ence device (SQUID) magnetometer at the National Institute for Materials Science. The negatives were digitized, and the experimental contrast was interpreted from undersaturated regions in which the intensity could be obtained with confidence from the measured optical density after subtracting the intensity of unexposed

regions. Simulations of Lorentz image contrast were carried out in Semper image processing software using a continuum approach (Ross and Stobbs 1991a) that does not take into account dynamical diffraction, the unknown atomic arrangement at the interfaces between the two phases, or interface roughness.

Conventional TEM imaging and electron tomography were carried out at 300 kV using a Philips CM300ST FEG TEM and at 200 kV using an FEI Tecnai F20 FEG TEM, respectively, at the University of Cambridge. Electron tomography involved the acquisition of ultra-high-tilt series of EFTEM images (Midgley and Weyland 2003) to examine the morphologies and positions of the ilmenite lamellae, using a specimen tilt increment of 4° and a tilt range of –72 to +76°. An objective aperture of semi-angle ~4 mrad was used to provide a close-to-optimal spatial resolution for energy-filtered imaging. At each specimen tilt angle, three energy loss images were acquired using an energy window width of 20 eV, one just above the 456 eV onset of the Ti L edge (centered at 471 eV) and two below the edge (centered at 416 and 441 eV). Each image was obtained using an acquisition time of 45 s, resulting in a total acquisition time for each electron tomographic data set of over three hours. Three-window background-subtracted elemental mapping (Egerton 1996) was used at each tilt angle to obtain images of the projected Ti intensity, which were used as input to tomographic reconstruction algorithms. The simultaneous iterative reconstruction technique (SIRT) was used to reconstruct the three-dimensional Ti signal from the tilt series of Ti maps using IDL image processing software.

ResulTs

MicrostructurePrevious TEM observations have revealed the presence of

fine hematite lamellae in ilmenite and, conversely, fine ilmenite lamellae in hematite (Kasama et al. 2003; McEnroe et al. 2002). Here, we focus solely on large hematite lamellae that are a few micrometers in thickness, which contain fine ilmenite lamellae. Figure 2a shows a bright-field (BF) TEM image of a region of the specimen that contains fine ilmenite lamellae (5–10 nm in thick-ness) in a hematite host, alongside a corresponding Ti elemental map (Fig. 2b). Hematite and ilmenite both have hexagonal crystal structures, with space groups R3c and R3, respectively. The fine lamellae lie on (001) planes and are often surrounded by strain contrast, suggesting that they have coherent interfaces with their host (e.g., Kasama et al. 2003). The ilmenite lamellae appear to have lens-like or kinked shapes in Figure 2b. The Ti map shown in Figure 2b can be used to determine—in projection—the sizes, shapes, and distributions of the lamellae, which are difficult to discern from the BF image. The chemical compositions of the lamellae are known, from previous TEM energy dispersive X-ray spectroscopy studies, to correspond to Ilm13–19Hem87–81 for hema-

figuRe 1. Schematic diagram illustrating image contrast formation in the Fresnel mode of Lorentz electron microscopy, for an in-plane-magnetized specimen that contains three 180° magnetic domain walls.

KASAMA ET AL.: TEM STUDy FOR LAMELLAR MAGNETISM264

tite and Ilm97–99Hem3–1 for ilmenite (Kasama et al. 2003; McEnroe et al. 2002). It should be noted that the “ilmenite” composition contains up to ~20% MgTiO3, both in ilmenite lamellae in large hematite lamellae, and in ilmenite hosts.

Lorentz observationsLEM images, acquired at nominal defocus values of –50

µm (underfocus) and +50 µm (overfocus) after the application of a 5 T field parallel to hematite or ilmenite [100], are shown in Figures 3b and 3c, respectively. The images were acquired from the region marked in Figure 3a, in which fine ~5 nm thick ilmenite lamellae are present within a large hematite lamella. The specimen was tilted by a few degrees from hematite [120], while keeping the interfaces between the lamellae and their host paral-lel to the electron beam direction to reduce diffraction contrast. Significantly, asymmetric contrast appears at the position of each lamella and inverts between the images obtained underfocus and overfocus. On the assumption that this behavior is associated primarily with phase contrast and not diffraction contrast, the images suggest qualitatively that the asymmetric contrast may be associated with the magnetic properties of each lamella, as conventional (compositional) Fresnel fringe contrast would be expected to be symmetrical, while diffraction contrast would not be expected to change sign with focus (see, for example, the regions marked by a circle in Figs. 3b and 3c).

The asymmetric contrast observed in Figures 3b and 3c is parallel to the direction of each lamella. If its origin is magnetic, then the images suggest that the lamellae contain magnetic mo-ments that are in the plane of the specimen and parallel to their

interfaces with their host [i.e., that the moments lie on the (001) planes]. It should be noted that the Lorentz images provide little or no information about the possible presence of magnetic mo-ments oriented in the electron beam direction. Therefore, it is difficult to determine the directions in which the moments may point within the (001) planes. Although some of the lamellae appear to have symmetrical contrast, this may result either from

figuRe 2. (a) Bright-field TEM image of a region containing fine ilmenite lamellae (f-ilm) in a large hematite lamella. The ilmenite lamellae are surrounded by strain contrast. (b) Background-subtracted three-window Ti elemental map obtained from the region marked in a. The ilmenite lamellae lie on (001) planes of the hematite host.

figuRe 3. (a) In focus bright-field TEM image of a region containing fine ilmenite lamellae (f-ilm) in a large hematite lamella (hem) in an ilmenite host (ilm host), showing strong diffraction contrast. The beam direction is close to hematite [120]. (b and c) LEM images of ilmenite lamellae acquired from the region marked in a, recorded in magnetic-field-free conditions at nominal defocus values of –50 µm (underfocus) and +50 µm (overfocus), respectively, after the application of a 5 T field parallel to hematite or ilmenite [100]. The direction of the applied-field H is shown with a large arrow in a. The presence of strong diffraction contrast precludes interpretation of the magnetic contrast in the region marked by circles.

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a combination of asymmetric contrast from two lamellae that are very close to one another or from the presence of local strong diffraction contrast.

The asymmetric contrast visible in Figure 3 was only observed within ~2 µm of the sample edge, possibly because thicker regions of the specimen exhibited stronger diffraction contrast and greater inelastic scattering contributions to the image intensity. Conversely, the signal from thinner regions of the TEM sample may have been affected by ion milling during sample preparation (Kasama et al. 2006).

Image simulations To investigate whether the asymmetric contrast observed in

the LEM images (Fig. 3) may be associated with the presence of magnetic moments at the interfaces of the lamellae, image

simulations that incorporated parameters derived from the Monte Carlo results of Robinson et al. (2002) were performed. The top part of Figure 4 shows the specimen geometry used for LEM im-age simulation. A plate-like lamella with parallel, flat interfaces was assumed. One-dimensional magnetic and electrostatic [i.e., mean inner potential (MIP)] contributions to the phase shift were calculated by using the expressions:

φMIP(x) = CEV0(x)t(x) (1)

φMAG t( ) ( ) ( )xe B x x dx=−

⊥∫ (2)

φTOT(x) = φMIP(x) + φMAG(x) (3)

where x is a direction in the plane of the sample, V0 is the mean

figuRe 4. Illustration of the procedure used to simulate LEM image contrast, incorporating the effects of lamellar magnetism, and predicted phase shifts calculated using Equations 1–3, incorporating magnetic parameters obtained from the Monte Carlo simulations of Robinson et al. (2002). Parameters used in the simulations include: an accelerating voltage of 300 kV, a lamella width of 5 nm, contact layer widths of 0.23 nm, an induction of 0.485 T in each contact layer, MIPs of 19.34 V for the “hematite” component and 19.41 V for the “ilmenite” component, a specimen thickness of 150 nm and defocus values of ±50 µm. The dotted line shows the expected magnetic phase shift for a lens-shaped lamella with curved surfaces.

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inner potential of each material, t is the specimen thickness, B⊥ is the component of the magnetic induction perpendicular to both x and z (the incident electron beam direction), and CE is an energy-dependent constant that takes a value of 6.53 × 106 rad/(V·m) at a microscope accelerating voltage of 300 kV (Dunin-Borkowski et al. 2004). The image simulations assumed a lamella width of 5 nm, contact layer widths of 0.23 nm, a specimen thickness of 150 nm, an induction of 0.485 T in each contact layer (converted from the magnetic moment of a single lamella of 4.168 µB per formula unit given by Robinson et al. 2002) and MIPs of 19.34 V for the “hematite” component (85% Fe2O3·15% FeTiO3) and 19.41 V for the “ilmenite” component (71% FeTiO3·22% MgTiO3·7% Fe2O3) (McEnroe et al. 2002; Robinson et al. 2002). The MIPs were calculated using the neutral free atom electron scattering factors of Doyle and Turner (1968) (Gajdardziska-Josifovska and Carim 1998). The simulations were performed by assuming that the specimen is a phase object and then propagating the exit-plane wavefunction in free space to the desired defocus values, for an accelerating voltage of 300 kV, a spherical aberration coefficient (CS) of 38.6 mm and defocus values of ±50 µm.

The simulated MIP images in the left-hand column of Figure 4 illustrate the contrast that would be observed from non-magnetic lamellae, whereas the “total” images in the right-hand column incorporate both MIP and magnetic contributions to the contrast. The magnetic contribution to the contrast was calculated for the magnetization that would be predicted according to the lamel-lar magnetism hypothesis. In the “total” images, asymmetric contrast appears clearly and reverses with defocus, in qualita-tive agreement with the experimental results. The simulations are almost unchanged if the magnetic phase shift is smoothed to form a single step (the dotted line in the simulated magnetic phase shift in Fig. 4), as would be expected for a lens-shaped lamella with curved surfaces (see below). Figure 5 shows that the positions of the contrast features are almost unchanged with specimen thickness.

Figure 6 shows a qualitative comparison between the experi-mental image contrast features across the lamella marked by an arrow in Figures 3b and 3c and the simulations. Line profiles of the contrast measured across the middle of the lamella are shown in Figure 7, alongside simulated profiles for a lamella width of 3 nm, a specimen thickness of 200 nm and defocus values of ±50 µm. The agreement between the widths of the experimental and simulated profiles suggests that the experimental defocus values are approximately correct. The experimental profiles shown in Figures 7c and 7d exhibit features in their lower intensity regions (arrowed) that are not reproduced in the simulations. These additional contrast features may be associated either with the experimental contrast reaching its minimum possible level and then broadening, or with the presence of dynamical diffraction contrast that is not included in the simulations and moves with defocus with respect to the true position of the lamella. Most significantly, it should be noted that the simulated contrast is lower than the experimental contrast by more than an order-of-magnitude.

Electron tomographyEFTEM electron tomography was used to investigate the

three-dimensional morphologies of the ilmenite lamellae, which

figuRe 5. Illustration of the effect of specimen thickness on image contrast calculated for a defocus of +50 µm. The parameters used are the same as those used in Figure 4. “B” and “W” denote the minimum and maximum contrast levels, respectively.

figuRe 6. (a and b) Simulated images, shown alongside (c and d) observed LEM image contrast recorded from the 3 nm thick lamella marked by an arrow in Figures 3b and 3c. Images c and d were acquired at nominal defocus values of –50 and +50 µm, respectively. The simulations were carried out for a lamella width of 3 nm, a specimen thickness of 200 nm and defocus values of (a) –50 µm and (b) +50 µm. The other parameters are the same as those used to acquire the images shown in Figure 3. “B” and “W” denote the minimum and maximum contrast levels, respectively.

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can affect both phase contrast and diffraction contrast in conven-tional TEM images. A Ti elemental map, which was taken from the ultra-high-tilt series of images used for tomographic recon-struction, is shown in Figure 8a, while an isosurface visualization showing the morphologies of the three reconstructed ilmenite lamellae is shown in Figure 8b. The reconstruction shows that the lamellae have lens-like shapes, as suggested by previous studies (Kasama et al. 2003; McEnroe et al. 2002). The reconstruction also shows that the selected lamellae have been cut by TEM sample preparation, with approximately 40 nm of their full size preserved in the electron beam direction. Although finer lamellae were observed abundantly between the three lamellae visible in the reconstruction, they have been omitted from Figure 8b be-cause of the presence of artifacts in the reconstruction resulting from diffraction contrast and the effect of the tomographic point spread function on the results. The detailed surface structures of the lamellae are difficult to determine using electron tomography because of the presence of artifacts resulting from diffraction contrast and electron beam damage. The lamella surfaces are likely to be smoother than suggested by the reconstructions shown in Figure 8 (Kasama at al. 2003).

Figure 9 shows an extrapolation of the dimensions of lamella 2 in Figure 8 to its probable full size. The lamella sizes that are measured from the original Ti elemental map and estimated from the reconstruction in the manner shown in Figure 9 are summarized in Table 1. Although there is no significant differ-

ence between the sizes of the lamellae measured using the two approaches in this case, in general, electron tomography provides a valuable check of the “true” lamella size and morphology, and its possible modification by TEM sample preparation.

Discussion

Ratio of lamellae with opposite signs of asymmetric contrast

Monte Carlo simulations predict that the direction of the mo-ment of an ilmenite lamella in a hematite host should be related to its physical position, and that the directions of the observed moments should be random if there is no significant field pres-ent when the sample acquires its magnetization (Robinson et al. 2002, 2004). The number of lamellae that exhibited opposite signs of asymmetric contrast in Figure 3 is summarized in Table 2 and is in the ratio 34:31. [Although some lamellae with oppo-site moments are close to one another, simulations based on the equations of Beleggia and Zhu (2003) (not shown) were used to confirm that magnetic interactions between adjacent lamellae are negligible]. According to Monte Carlo simulations, the moments carrying NRM may be deviated by up to 20° from the a-axis of hematite and by 10° on average as a result of a combination of lamellar magnetism and the spin-canted antiferromagnetism of hematite (Robinson et al. 2006), and the proportion of “in-phase” lamellae should be 0.03–0.07 (Robinson et al. 2006). The ratio

figuRe 7. (a and b) Simulated intensity profiles calculated for a lamella width of 3 nm, a specimen thickness of 200 nm, and defocus values of ±50 µm. The other parameters are the same as those used to acquire the images shown in Figure 3. (c and d) Experimental intensity profiles taken from the images shown in Figures 6b and 6d, shown after division by their mean intensities. The arrows in c and d indicate inconsistencies with the simulations. It should be noted that the simulated contrast levels are lower than the experimental values by more than an order of magnitude. This difference might be attributed to unknown values of defocus, specimen thickness and magnetization, or to possible effects of dynamical diffraction that are not considered in the simulations.

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Table 2. Number of measurements and ratio of ilmenite lamellae showing asymmetric contrast in each direction

Direction 1 Direction 2

Number of measurements 34 31Ratio* 52 (±12)% 48 (±12)%

* The maximum margin of error at 95% confidence level was calculated statistically.

figuRe 9. Illustration of the procedure used to estimate the dimensions of lamella 2 shown in Figure 8 from the tomographic reconstruction, on the assumption that its true shape is an ellipsoid, only part of which remains following TEM sample preparation. The estimated sizes of the three lamellae shown in Figure 8 are summarized in Table 1.

figuRe 8. (a) Titanium elemental map taken from the ultra-high-tilt series of images used for EFTEM electron tomography. (b) Isosurface visualization of a tomographic reconstruction of the three lamellae marked in a. The thicknesses of the lamellae in the electron beam direction are approximately 40 nm.

that we measure experimentally is 0.05 ± 0.24. Although the directions of the moments of individual lamellae are predicted to be determined by the number of atomic layers between them, it is difficult to use electron microscopy to measure this number because of the similarities of the crystallographic structures and

atomic numbers of hematite and ilmenite, the presence of strain contrast, and the lens-like morphologies of the lamellae.

Origin of the asymmetric contrastThe comparisons between the experimental and simulated

LEM images shown in Figures 6 and 7 suggest, qualitatively, that the asymmetric contrast observed at the position of each lamella is consistent with a combination of magnetic and MIP contri-butions to the phase shift experienced by the incident electron beam. If this explanation for the origin of the observed contrast is correct, then it provides the first direct local evidence that the stable magnetization examined by bulk measurements in these materials is related to the presence of such fine lamellae. No other magnetic signals, such as magnetic domain walls, were observed in this sample. However, the fact that the magnitude of the ex-perimental contrast is much higher than that in the simulations (Fig. 7) indicates that, if the asymmetric contrast is magnetic in origin, then it must be much larger than that associated with the interfacial moments predicted by the Monte Carlo simulations of Robinson et al. (2002) and Harrison (2006) alone. If it is not magnetic in origin, then it may be associated with diffraction contrast due to strain (Scheerschmidt et al. 1989) and/or local tilts of the lamellae (Ross and Stobbs 1991b).

Ross and Stobbs (1991b) showed that tilted interfaces could produce asymmetrical phase contrast even at small tilt angles. The sign of the contrast can change between images acquired overfocus and underfocus. In the present sample, many lamel-lae have interfaces that are not exactly parallel to the electron beam direction since the sample was tilted slightly away from a zone-axis orientation to reduce unwanted diffraction contrast. However, asymmetric contrast is visible in both directions, and the inconsistency between the observed and simulated contrast levels could not be explained even assuming non-vertical in-terfaces.

Strain in the vicinity of lamellae can also affect their con-trast. Computer simulations of diffraction contrast associated with strain fields suggest that significant contrast modification can occur with tilt angle, defocus, and specimen thickness (Scheerschmidt et al. 1989). The sign of the contrast is not ex-pected to change with defocus according to the simulations of Scheerschmidt et al. (1989), suggesting that this effect may not be present in our sample.

Table 1. Dimensions of lamellae measured both in projection from a conventional Ti elemental map and from a tomographic reconstruction

Lamella* Measured from Ti map Measured from tomographic reconstruction

Diameter (nm) Thickness (nm) Diameter (nm) Thickness (nm)

1 75 (±2) 22 (±2) 81 (±5) 20 (±5)2 73 (±2) 19 (±2) 80 (±5) 18 (±5)3 66 (±2) 18 (±2) 69 (±5) 16 (±5)

* Lamellae 1, 2, and 3 correspond to those marked in Figure 8.

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However, we cannot rule out these alternative effects in the present experimental measurements. Therefore, we regard our results as preliminary and suggestive, and will address these is-sues in greater depth in a future study that considers the effect of specimen thickness, specimen tilt, and dynamical diffraction on the observed contrast and includes atomistic image simulations (e.g., Bursill and Barry 1978).

acknowleDgmenTsWe thank Eiji Takayama-Muromachi of the National Institute for Materials

Science (Japan) for SQUID assistance and Ken Harada of Hitachi Ltd. (Japan) for valuable discussion, and the Nanotechnology Support Project of MEXT (Japan), the Royal Society (U.K.), and the Deutsche Forschungsgemeinschaft (Germany) for support. This work was supported in part by NERC grant NE/D002036/1.

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Manuscript received March 27, 2008Manuscript accepted septeMber 8, 2008Manuscript handled by Joshua Feinberg