Ultramicroscopy 3 (1978) 203-214 0 North-Holland Publishing Company

THE DIRECT DETERMINATION OF MAGNETIC DOMAIN WALL PROFILES BY DIFFERENTIAL PHASE CONTRAST ELECTRON MICROSCOPY

J.N. CHAPMAN, P.E. BATSON, E.M. WADDELL and R.P. FERRIER Department of Natural Philosophy, University of Glasgow, Glasgow G12 SQQ, Scotland

Received 18 January 1978

A new technique for the quantitative investigation of magnetic structures in ferromagnetic thin films is proposed. Unlike previous techniques the detected signal is simply related to the magnetic induction in the film, and as such the direct deter- mination of domain wall profiles is possible. The technique utilizes a differential phase contrast mode of scanning transmis- sion electron microscopy in which the normal bright field detector is replaced by a split-detector lying symmetrically about the optic axis of the system. The difference signal from the two halves of the detector provides the required magnetic infor- mation.

Analysis of the image formation mechanism shows that, using a commercially available scanning transmission electron microscope equipped with a field emission gun, wall profiles should be obtainable directly from most structures of interest in Lorentz microscopy. Furthermore, signal-to-noise considerations indicate that these results can be obtained in accept- ably short recording times. Finally, experimental results using both polycrystalline and single crystal specimens are presen- ted, which confirm the theoretical predictions.

1. Introduction

To understand many properties of ferromagnetic elements and alloys, a knowledge of their domain and domain wall structure is essential. Depending on the material, domains vary in size from <lOO nm to >lO mm, whilst domain wall widths range from 1 atomic repeat to Z 100 nm. A particularly useful technique for investigating domains of small size and, domain wall profiles is that of transmission electron micros- copy, provided that the structures of interest exist in sufficiently thin foils to permit the passage of, typic- ally, 100 kV electrons without significant energy loss. In the electron microscope an electron wave passing through a region of magnetic field suffers a phase shift proportional to the flux linked [ 11.

Thus, in the vicinity of the domain wall illustrated in fig. 1, the phase shift, $J(x), is given by

qb(x) = e/fi j J B,(x, z)dz dx , 0 --

(1)

where B,(x, z) is the y-component of magnetic induc-

tion. (The co-ordinate system shown in fig. 1 is used throughout the paper.) In general, for an untilted foil of thickness r with magnetization distribution indepen- dent of y, there is no y-component of induction beyond the surfaces of the foil, and we may define an average m-plane induction,

By(X) = l/t s By(X, z)dz . --oo

It is the determination of the spatial variation of this quantity, the domain wall profile, with which we are primarily concerned here.

The only effect of a spatially varying magnetic induction distribution is to phase-shift the electron wave, and an in-focus image in a Eonventional trans- mission electron microscope (CTEM) shows no con- trast variations. To reveal the presence of such mag- netic inhomogeneities as domain walls, the electron microscope must then be used in a phase contrast mode. In section 2 a summary of the most commonly used methods is given, together with comments on their main advantages and disadvantages. Common

204 JN. Chupnmn et al. /Direct determination of magnetic domuir? wall profiles

Incitknl plane wave

Domain wall

0 OEo

m * x

k I

,;A,>

x

Fig. 1. The phase shift suffered by an incident plane wave in the vicinity of a domain wall.

to all of them is a difficulty in interpreting the observed contrast variations, but this is clearly necessary if we are to determine domain wall profdes, rather than simply the distribution of domain walls. In section 3 a new mode of phase contrast electron microscopy, introduced by Dekkers and de Lang [2,3] and using a scanning transmission electron microscope (STEM), is described and its suitability for quantitative mag- netic studies assessed. Its signal-to-noise characteris- tics are derived in section 4 and are compared with those of a more familiar STEM technique. A suitable experimental system is described in section 5, and examples of domain wall profiles directly recorded from different magnetic samples are given. Finally, conclusions derived from the existing system and further improvements to the technique are considered in section 6.

2. Modes of phase contrast Lorentz microscopy

In this section we consider the two most common techniques used for revealing the existence of mag- netic domains: the Fresnel or defocus method and that involving insertion of an aperture or phase plate in the back focal plane of the objective lens. Other methods which have been used include electron inter- ferometry [4], techniques peculiar to single crystal specimens [ 51, and use of the low angle diffraction pattern [6]. The first two have not been used for domain wall profile determination, whilst the third is only generally of use in this role when periodic mag- netic structures are under consideration.

2.1. The Fresnel or defocus method

Domain walls are delineated in defocused images, generally as narrow dark or bright bands on a uniform background (e.g. [S]) and as long as the illumination in a CTEM is sufficiently coherent, examination of the bright band, a converging domain wall image, reveals it to be a set of interference fringes. For a given domain wall structure it is a straightforward matter to synthe- size on a computer both converging and diverging do- main wall images. This is generally carried out by image transfer theory [7]. Using this it is easy to show that although a linear relation exists between the com- plex image disturbance, f’(x), and the specimen trans- mittance, f(x) = exp[ir$(x)] , there is no such relation between the image intensity, If( and f(x), for non-weak phase objects. That most magnetic objects fall under the category of strong phase objects can be seen by insertion of typical values into eq. (l), which yields phase shifts Z 1 rad on traversing a domain wall.

Thus, the main problem encountered with the Fresnel mode of Lorentz microscopy is: given If(x)12, how may f(x) and hence the wall profile be deter- mined? Reimer and Kappert [8] have used a series of diverging wall images to extract a wall width param- eter, but Marti and Lewis [9] have demonstrated that errors can arise when analysing complex wall profiles. Hothersall [lo] has used a technique of comparison of computer synthesis with experiment, but such a method requires good physical insight as to the likely wall profile and very accurate knowledge of defocus distance and the product of saturation induction and specimen thickness. A further technique [ 111, using a geometrical theory to interpret a series of diverging wall images from tilted foils, yields much information about the symmetry, rather than the detailed profile, of domain walls.

We therefore conclude that the Fresnel mode of Lorentz microscopy is not ideally suited to the deter- mination of domain wall profiles. Furthermore, when investigations are carried out in a CTEM equipped with a normal heated tungsten filament the current density on the fmal viewing screen is insufficient to pemlit direct observation of the fine detail in images of domain walls, so that little information on a par- ticular domain wall may be gleaned until after develop- ment of the photographic emulsion. Even then, quan- titative electron intensity data required for any analy-

Jfl. Chapman et al. /Direct determination of magnetic domain wall profiles 205

sis procedure is not available until the plate has been subjected to microdensitometry. These latter disadvan- tages may both be overcome by utilization of a STEM equipped with a field emission gun. Details of an experi. mental technique using such an instrument have been given by Chapman et al. [ 121 and involve the use of a small detector aperture so that only a small fraction of the electrons in the probe incident on the specimen are actually used to form the image. This has a serious effect when noise is considered, and we return to this point in section 4 where we compare the effect of noise in the Fresnel mode with that in the differential phase contrast mode of Dekkers and de Lang.

2.2. Foucault and related methods

In the Foucault mode of Lorentz microscopy (e.g. [5]) an opaque aperture is inserted to obstruct one- half of the back focal plane of the objective lens so that only those electrons passing through the other half con- tribute to the final image. In this way domains in which the magnetization lies alternately parallel and anti- parallel to the y-axis appear alternately bright and dark. Using the transfer theory of imaging, it is once again straightforward to calculate the image which would result from any given domain wall structure; but as before, given the image intensity ]f(x)12, there is no direct inversion procedure which enablesf(x), and hence the wall profile, to be deduced. Further- more, as the positioning of the aperture has a marked effect on the image intensity distribution in the vici- nity of the domain wall, even qualitative information on the domain wall profile is difficult to obtain.

Similar criticisms apply when, instead of an opaque, aperture, a thin foil is positioned in the back focal plane of the objective lens [ 131. This phase-shifts that part of the diffraction pattern it intersects, with the result that the presence of the domain wall is revealed in the final image, but unless the magnitude of the phase shift is accurately known no accurate quantita- tive data may be derived. Thus, whilst both the Fres- nel and Foucault modes of Lorentz microscopy enable the existence of domain walls to be revealed readily, only the former appears at all suitable for the deter- mination of domain wall profiles. Even then extrac- tion of the required information is both difficult and laborious, and no universally applicable analysis pro-

cedure has been developed. Thus, there is an incen- tive to seek new phase contrast modes of Lorentz microscopy which overcome some of the disadvan- tages described above. A description and evaluation of such a technique, together with a comparison with the Fresnel mode, is given in the remainder of this paper.

3. Differential phase contrast Lorentz microscopy

Dekkers and de Lang [2] have described how the difference signal from two semi-circular detectors in a STEM is related to one component of the deri- vative of the phase variation of transmittance of the specimen.The diameters of the two semi-circles are adjacent and lie symmetrically about the optic axis of the STEM, and it is the phase gradient perpendicu- lar to the split between the semi-circles which is detec- ted. Unfortunately, this result is not true for all spe- cimens, although its application is not restricted to those which only modulate the beam weakly. In this section we derive a general expression for the difference signal from a detector system comprising two semi- infinite detectors and investigate the conditions under which the signal obtained, as the probe is scanned perpendicular to a domain wall, is a good measure of the domain wall profile. For this purpose we consider a single straight domain wall parallel to the split, and for simplicity we carry out the analysis in one dimen- sion only. Clearly, in any real system the scanning probe must be described by a two-dimensional func- tion, and the effect this has on the analysis is con- sidered in this section.

With the geometric arrangement as defined in fig. 2, let the wave function of the probe, initially assumed to be coherent, just before the specimen be $e(x) and the specimen transmittance be f(x) = a(x) exp [i@(x)], Thus, when the probe is centred on a point x0 of the specimen, the waye function at the bottom surface of the specimen is 9(x, x0) = J(x) tio(x - x0). The detec- tor is situated in the far field where, apart from an irre- levant quadratic phase factor, the complex disturbance is related to that just below the specimen by a Fourier transform; hence the scanning system is arranged so thal in the absence of a specimen the disturbance in the detector plane is stationary as the probe is scanned

206 JN. Chapman et al. /Direct determination of magnetic domain wall profiles

Objoclw aperture , r

.-I-

Objective lens

Coherent probe:. wavefunction sb(x-x0)

Specimen ImnAltonce ‘0 f(x)-o(x)~P[i#x)]

x

/

cOptlc oxis

Wovefunct~on

fIkxd-A(lucJexp~k~o)]

I k

Dolector A Oeloctor B

Fig. 2. Illustration of the complex disturbances in a STEM equipped with a split-detector. (The variable in’ the detector plane is always prpportional to k but only strictly given by k if the product of electron wavelength and camera length is unity).

across the specimen. Denoting the Fourier transform of J/(x, x0) by \Ir(k, xc), the intensity across the detec- tor plane is j\k(k, x0)1* and the required difference signal is

(2)

where sgn(k) = tl for k > 0 and -1 for k < 0. Appli- cation of the convolution theorem enables eq. (2) to be,written in the form

Go) = ((ihx)l@ 44~ x0) QD #‘C-x, XO)L=O , (3)

where @denotes the convolution integral and the suf- fix x = 0 requires the integral to be evaluated at x = 0. Writing eq. (3) out explicitly yields the general expres- sion for the difference signal from a split-detector system to be

S(xo) = -i/nlJl Ix’&“) Q(X’ f x”) exp [i(#(x’ + x”)

- #(x”>)]Jl;(X” - x&)(x’ + x” - X&lx’dx” . (4)

To proceed further the following simplifying assump- tions are made:

(i) a(x) = 1, which is certainty true for purely mag- netic objects;

(ii) the phase function may be adequately described over the distance for which IJlo(x)] is appreciable by the first three terms of a Taylor series, because exchange energy generally precludes rapid changes in the magni-

zation distribution in a domain wall; and (iii) over this distance the maximum value of the third term L 10-l rad. Denoting the first and second derivatives of the phase function by #r(x) and Q*(x), respectively, con- ditions (ii) and

(iii) imply

exp[i$(x)l = exp [Mx0> + 41(X0)(x - x0)1

X (1 + iG2 (x0)(x - xd2/2> ,

provided that

c$2(xg)x;/2 5 10-l )

(5)

(6) where xP is the distance over which the amplitude of the coherent probe is appreciable.

Under these conditions the term

a(x”)a(x’ + x”) exp [i($(x’ t x”) - Cg(x”))]

in eq. (4) simplifies to yield

exp[i~l(xOFl(l +@2(X0>((x” - ~0) +x’/2)x’) ,

and solution of the complete equation involves the determination of two integrals. After some manipu- lation involving both the convolution theorem and the shift theorem for Fourier transforms, the following expressions are obtained:

-i/n ss l/x’ exp [i&(x0)x’] 9:(x”- x0)

x l/lo(x) + x” - xo)dx’dx”

= .I- sgn(k + ~1(xo)/2~)l~o(k)12d~, (7)

and

-i/a ss l/x’ exp[i@r(xo) x’](L#r2(xo)((x” - x0)

+ x’/2)x’)9;(x” - xo)Jlo(x’ -I- xn - Xo)dx’dx”

= (bb2(xo)/4n2)‘i(\kod\k~/dk - ~~d%ddk)-~l(xo)~2n (8)

where the suffix -$r (xo)/2n indicates that the expres- sion in brackets has to be evaluated at the spatial fre- quency k = -41~ (xo)/2n. If \ko(k) = A,(k) exp [in(k)], the signal from the split-detector is given by the sum of eqs. (7) and (8) which may be written as

s(xo) =~sgn(~t~l(x0>/2lr)~,(k)~dk

- (~2(Xo)/2r2>(~1A~)-~r(xg),2n I (9)

JN. Chapman et al. /Direct determination of magnetic domain wall profiles 201

where n1 is the first derivative of n. The first term in eq. (9) corresponds to the signal

which would be obtained by merely shifting the inten- sity distribution in the detector plane so that it is centred about the special frequency -$r(x,)/2n. It is directly proportional to @r(xc) provided that A,-,(k)2 is effectively constant up to the greatest k value of interest, that is when k assumes the maximum value of 9,(xo)/2n. Furthermore, if the second term is always small compared to the first, the signal obtained is directly proportional to one component of the phase gradient, which is the desired result. For a correctly oriented magnetic domain wall, from eq. (l), @r(x) = eB,,(x) rfi and so the phase gradient is proportional to the domain wall profile. Thus, if the conditions above are satisfied along with inequality (6), a split-detector system appears to overcome the disadvantages associ- ated with the more conventional means of domain wall profile determinations and to provide a rapid and direct means for their determination.

Before considering the likelihood of meeting the several conditions imposed in the above analysis we note that a classical argument would in fact give rise to our final simplified result. It would, however, per- mit no discussion of the range of validity of its appli- cation. If a probe of electrons is incident on a domain wall and the size of the probe is sufficiently small that we may regard the magnetization component to be effectively constant over its extent, the electrons would be deflected through the local Lorentz deflec- tion angle, flL = eB,th/h, on passing through the foil. Thus, in the detector plane the intensity distribution would be shifted to be centred about a spatial frequen- cy of &/A, which would give exactly the signal des- cribed by the first term of eq. (9).

To discuss the applicability of the above analysis it is convenient to consider a specific analytic model for a wall profile. A commonly used model suitable for this purpose is By(x) = B,-,tanh(x/a) so that &(x) = efBo sech* (x/u)/ha. Inequality (6) requires that

erBcsech*(x/a) xt/2fia L 10-l ,

a condition which is the most severe at the wall centre where the inequality becomes

xi < ha/5etB0 = ah/10n/3L0 , (10) where flu, is the classical Lorentz angle, eB,tA/h. The coherent probe size is determined by the electron wave-

length and the spherical aberration coefficient, C,, of the objective lens. It is given approximately by 1.3 (~7,h~)“~ [ 141 provided that the objective aperture has its optimal value of 1. 1(?&J1’4. The numerical values in the expressions quoted are actually those which pertain to the familiar and more realistic two- dimensional probe and differ only slightly from those for a one-dimensional system. For the purpose of this argument their exact value is unimportant. Thus, the Taylor series expansion of the phase in which the third term is small, but not necessarily negligible, is valid if

p&z s 1.9 x 10-z(c&-“z . (11)

It should be noted that this condition may be actually over-restrictive, and because of the l/x term in eq. (4) the only significant contributions to the integral come from regions where x’ 31 x”. If this is so, the distance over which the third term must be small is actually smaller than the coherent probe size. Computer synthe- sis would clarify this point further.

We now consider the relative magnitudes of the two terms in eq. (9). The detector plane is ideally conjugate with the objective aperture plane so that we may write

b(k) = 1 , kGa/A,

= 0, k>ol/h,

(12)

where OL is the semi-angle of the objective aperture and Afis the defocus of the probe. In fact, provided the detector lies in the far field, eq. (12) remains a good approximation. For an aberration-free system with no defocus qr (k) = 0 and there is no cont$bution from the second term. In general, however, we may write the ratio of the second term to the first term, x(x,-,), as

x(xo) _ @Z(XO)h -- 2n

-Af). 1 (13)

Taking for simplicity Af = 0, which is clearly not the optimal case, and substituting the maximum value of e2(xe) #1(x0)2 for our model profile into eq. (13) yields, after some manipulation,

x(Xohnax = 2Cdk0 3 IMa . (14)

To demonstrate that it is feasible to use this technique

208 JN. Chapman et al. /Direct determination of magnetic domain wall profiles

and that in general x(x~),.,.,~ is small, we insert values typical of foils of interest in Lorentz microscopy into inequality (11) and eq. (14). With &o = 10d4 rad, a~15nmandh~4pmwefindfrom(11)CsS2m and insertion of the upper limit of C, into (14) gives X(Xo)max = 5 x 10 -‘. For most magnetic work the specimen must be situated in a region df low magnetic field so that the objective lens is only weakly excited. Even so, proyision of a system with the required spheri- cal aberration coefficient is not difficult. Furthermore, it is apparent that under these conditions x(x,,),,,~~ << 1 and the second term in eq. (9) may be completely neglected.

Before ending this section three further points must be considered: An analysis by Waddell [ 151 has shown that, provided PLO <, (Y/S, the fact that a circular, rather than a one-dimensional probe is incident on the specimen does not effectively change any of the above conclusions. This condition corresponds to the requirement that the distribution in the detector plane by shifted by an amount which is small compared with its diameter. Clearly, if the shift is too large the dif- ference signal is no longer simply proportional to cp,(Xcl)~

Secondly, as the source of electrons is finite in size the probe incident on the specimen will be only par- tially coherent. The resolution with which the domain wall profile can be determined is then likely to depend on the incoherent probe size on the specimen. A further complication concerns inelastic scattering, which will

Sphl oetoctor A I netector B

Fig. 3. The shift of the intensity distribution in the detector plane when the probe (subtending a half-angle, a) is incident on a region of specimen of local Lorentz deflection angle, pi.

certainly occur but which has so far been excluded from tile discussion. However, once again it is not expected that this will significantly change the above conclusions because the distribution of inelastic scat- tering, except where diffraction effects become impor- tant, is radially symmetric. Also, as the characteristic inelastic scattering angle for thin foils is small com- pared with (Y, its only effect is likely to be a slight broadening of the intensity distribution in the detector plane.

Thus, the difference signal from a split-detector system would seem well suited as a means of directly determining domain wall profiles provided that the orientation of the wall with respect to the detector can be suitably controlled.

4. Signal-to-noise considerations

In section 3 no consideration was given to the effect of noise on the signal from a split-detector system. However, since the signal of interest, when magnetic specimens are being examined, is the small difference between two large signals, noise is likely to play a significant role, and it is desirable to estimate the time required to produce a suitable low-noise image or wall profile. It is assumed that the efficiency of the detectors is sufficiently high that all electrons incident on them are detected and that the only source of noise is shot-noise inherent in the electron beam.

From section 3 it was apparent that the effect of the magnetic induction in the foil was to deflect the probe through the local Lorentz deflection angle, pL. Thus, as shown in fig. 3, the signals on the two detec- tors are in the ratio (n&‘/2 + 2ML) : (n&*/2 - 201pL), provided pL S a/5, and the ratio of the difference signal to the total signal is 4flL/7r~. If the diameter of the incoherent probe incident on the specimen is D and the brightness of the electron gun B, the total number of electrons about one point on the specimen in a time 7 is

N= Bn2a2D2r/4e. (19

Thus, the difference and noise signals are given, respec- tively, by

Ns = Bm@LD*T/e (16)

JN. Chapman et al. /Direct determination of magnetic domain wall profiles 209

and

N, = (BT/e)112mD/2 . (17)

Combining eqs. (16) and (17) yields for the signal-to- noise ratio u

a = 2(Br/e)‘12flLD . (18)

Eq. (18) would be valid for a specimen whose only interaction with the electron beam was through its magnetic vector potential. In reality electrons are elastically Bragg-scattered by the periodic electrostatic potential of the specimen, and so far no allowance has been made for this. Since inclusion of these electrons, particularly when buckled single crystal foils are under examination, would severely affect the recorded images, an aperture must be inserted in the detector plane to preclude all Bragg-scattered electrons. This has no effect on the analysis given in section 3 because the smallest Bragg angles of specimens of interest are typically two orders of magnitude greater than &a and one order greater than the values of CY required. Their exclusion does, however, modify eq. (18) which becomes

a = 2(BFr/e)‘12flLD , (19)

where F is the fraction of electrons remaining within the detector aperture.

It is instructive to compare eq. (19) with the expression derived for the signal-to-noise ratio from a STEM operated in the Fresnel contrast mode des- cribed in section 2. If a converging wall image is to be analysed to yield a wall profile, we may usefully des- cribe the signal as the amplitude of the intensity vari- ations in the fringe structure which make up the wall image. These are superimposed on what may be a considerable background when realistic probe sizes and detector apertures are used to form the image. A measure of the noise in the image will then be the square root of this background. A detailed analysis [ 15,161 shows that the optimum signal-to-noise ratio, based on the model described above, is given by

u 2: 5.6 X 10-2(BFT/e)1’2X/n, (20)

provided that D = 0.22A/&,,-, and fl= 0.1 Sh/PLoAf, where n is the number of fringes in the wall image and /.3 the half angle subtended by the detector aperture.

In practice, for a domain wall profile analysis,

images with at least five fringes will be required. Setting n = 5 and assuming as before PLO = 10d4 rad and D = 0.22h/&, = 9 nm, we see that o(split-detector)/a (single detector) = 40, indicating that once again advan- tage accrues from use of a split-detector system. It should be noted, however, that u for a split-detector depends explicitly on both &c and D, whilst that for a single detector system does not. Furthermore, the

value used for D in the example cited was the optimum value for the single detector system and would not necessarily be correct for the split-detector. The latter, being an in-focus technique, requires that the incoherent probe size be small compared to the domain wall width. For a = 15 nm, D = 9 nm would hardly be adequate for an accurate profile determination, and a reduction in its value would decrease u. However, it would seem that except for very narrow domain walls in materials of low saturation induction the split-detector retains its superiority over a single-detector system when noise characteristics, as well as the considerations of section 3, are compared.

It remains to calculate the dwell time/picture ele- ment (T) required to obtain an image with an accept- ably low noise level. A good profile should be obtained if u = 10 when pL = PLO. Thus, assuming D = 5 nm, and B z= 2 X 109A.me2 sr-l we find r = lob2 s if F = 1. In practice F may be a small fraction, indicating that a prohibitively long time would be required to produce a high quality image of -IO’ picture elements. The value assumed for B was appropriate for a heated tungsten emitter and, whilst it should be possible to operate successfully with such a system, consider- able advantage results if the STEM used is equipped with a field emission gun. Under these circumstances noise should present little problem even at the relati- vely rapid scan rates used in initially locating domain walls of interest and orienting them correctly with respect to the detector. Furthermore, as is described in the next section, the task of achieving an appropri- ately sized probe in effectively field-free space is much easier when the source of electrons is as small as it is in a field emission gun.

5. Experimental details and results

All the experiments described in this section were carried out on the Vacuum Generators HB5 STEM in

210 J3. Chapman et al. /Direct determination of magnetic domain wall profiles

the Cavendish Laboratory, Cambridge. The only instru- mental modification required to obtain images of mag netic domains in the manner described above was the replacement of the electron spectrometer and normal bright field detector by a suitable split-detector. The design of the system chosen is shown in fig. 4 and comprises two calcium fluoride scintilla/tars attached to light-guides leading to two matched EMI 9824A photomultipliers outside the vacuum system. A thin piece of aluminium foil separates the two detectors to minimize cross-talk between them.

The simplest mode of operation to detect the presence of magnetic domains involves use of the condenser lens only. In this mode the specimen is sited in its noimal position and all normal cartridges may be used, thus permitting tilting and other mani- pulations to be performed on it. As the objective lens is off, the requirement that the specimen be in a region of low magnetic field is obviously satisfied. Unfortunately, there is no control of the incoherent probe size which is determined by the effective area of field emission from the tip and the relative dis-

H&sing for

UHV gloss wmdows

Elcclroless ,,nlckel-plated

mlld sleol

Llghl guides

Elecfron beam

Fig. 4. Cross section of the split-detector system attached to the Vaduum Generators HBS.

tances of specimen and source from the condenser lens. In practice the incoherent probe diameter at the specimen -30 nm, and such a value is too high for accurate wall profile determination. However, it is perfectly adequate for revealing the existence of domains, as is shown in fig. 5. The specimen was an evaporated polycrystalline permalloy film, 40 nm thick, and the images shown are those from the two detectors individually, denoted by A and B, the sum signal (A + B), and the difference signal (A - B).

As the probe size is greater than the crystallite size in the foil, no amplitude contrast, which is what the signal (A t B) reveals [3], is expected and none is ob- served. What is noticeable is the very low contrast of the individual signals A and B although, as predicted in section 4, there is no problem from noise in the required difference signal. It should be noted that the micrograph shown to illustrate use of the split-detector system has domains oriented approximately parallel to the split. If the domain structure comprised, for example, 180’ walIs running perpendicular to this direction, their presence would remain undetected. For this reason a rotation holder is a very useful access- ory .

To obtain sufficiently small incoherent probe sizes for higher resolution studies a second mode is necessary in which both condenser and objective lenses are excited. In this mode a special cartridge, one compa- tible with the existing specimen exchange mechanism, is used and permits the specimen to be sited anywhere from 20 mm to 40 mm beyond its normal seating posi- tion. Thus, once again it is in a region of suitably low magnetic field. When the specimen is in the former position the incoherent probe diameter k4.5 nm and the spherical aberration coefficient of the objective lens is estimated to be 0.5 m. This results in an optimal value for OL = 2 X 10d3 rad and a coherent probe diameter =3 nm. It wiIl be seen that these values are all comparable with those calculated in section 3 as adequate for detailed investigation of typical domain walls.

Fig. 6a shows the (A - B) image of a suitably oriented domain wall in the same foil shown in fig. 5 taken in the second mode. One consequence of the superior resolution is that contrast from the crystahites themselves is now very apparent. Examination of fig. 6b of a line trace across the wall shows just how marked this contrast is and at least serves to show that the reso-

JJV. Chapman et al. /Direct determination of magnetic domain wall profiles 211

(a)

:_

Fig. 5. Images of a 40 nm thick evaporated polycrystalline permalloy fiim: (a) detector A; (b) detector B; (c) sum signal (A + B); (d) difference signal (A - B). x denotes the direction of differentiation: incoherent probe diameter -30 nm; accelerating voltage = 80 kV; recording time = 50 s.

lution of the technique is much better than the wall width. The effect of the crystallite contrast is to pre- vent determination of the wall profile from a single line scan, but an estimate of the wall width may still be made directly. Furthermore, provided that the wall is straight and the thickness of the film is unchanging, a wall profile may still be obtained by averaging over a length of wall, either numerically using a computer or by a microdensitometer trace, using a long slit, across the photographic negative. The result of the latter procedure for the wall of fig. 6a is shown in fig. 7.

If domain walls in single-crystal fdms are the subject of investigation the problem of contrast from smail crystallites does not arise, although contrast from such non-magnetic origins as a bend in the foil may well be present. Fig. 8 shows both the (A +B) and (A - B) images from an electropolished single-crystal iron foil. In the former, familiar diffraction contrast features are observed, whilst in the latter the domain structure is readily visible. Of particular note is the fact that even in thick regions of foil, where little detail of any sort can be seen in the (A + B) image, the domain bounda- ries remain clearly distinguished in the corresponding

212 JJV. Chapman et al. /Direct determination of magnetic domain wall profiles

b)

150nm

> X

J

Fig. 6. (a) Difference signal (A - B), from the same fiim shown in fig. 5 but with incoherent probe diameter e4.5 nm. Other parameters remain unchanged and x denotes the direc- tion of differentiation. (b) Line trace approximate perpendicu- lar to the domain wall output directly from the HBS; recording time = SOS. The rapid intensity variations arise from the crys- tabtes.

(A - B) image. As an appreciable amount of inelastic scattering would be expected from such regions, this supports the suggestion made in section 3 that this

Fig. 7. Microdensitometer trace perpendicular to the domain wall shown in fig. 6a. The trace is the average profile over a 500 nm length of wall.

technique is relatively insensitive to the adverse effects of such events.

Fig. 9 shows a profile from a domain wall in the iron foil shown in fig. 8. Although, as stated previously, there is no “crystallite contrast”, contrast of a non- magnetic origin is still present. It arises from lack of uniformity of the foil, probably as a result of slightly incorrect electropolishing conditions. This could cer- tainly be avoided with care, but even with it present a good estimate of wall width may be made, and most importantly, it may be made whilst the experimenter is actually working on thE! microscope.

6. Conclusions

Although many techniques of transmission Lorentz microscopy have been practised, all have suffered from the disadvantage that interpretation of the images to yield accurate domain wall profdes has been difficult and no single interpretation technique has gained universal acceptance. In addition, as most results have been obtained using a CTEM, the extraction of the required intensity data for analysis is always accom- plished long after the user has left the instrument, thus preventing any data deemed inadequate being retaken easily. In this paper we have proposed that a technique involving a STEM equipped with a split-detector will certainly allow the rapid acquisition of electron inten-

JN. Chapman et al. /Direct determination of magnetic domain wall profiles 213

Fig. 8. Images of an electropolished single crystal iron foil: (a) sum signal (A + B); (b) difference signal (A - B). x denotes the direction of differentiation: incoherent probe diameter e4.5 nm; accelerating voltage = 80 kV; recording time = 50 s.

sity data, and the difference signal from the two detec- tors provides a direct determination of domain wall profile. The conditions under which the latter asser- tion is true have been extensively investigated and, when signal-to-noise calculations are also considered, have been shown to be generally realizable using a commercially available STEM equipped with a field emission gun. To demonstrate the use of the tech-

Fig. 9. Line trace approximately perpendicular to a domain wall in the iron foil shown in fig. 8 output directly from the HBS: incoherent probe diameter r~4.5 nm; accelerating vol- tage = 80 kV; recording time = 50 s.

nique, results from both polycrystalline and single- crystal foils have been presented.

Thus, a differential phase contrast method based on the system of Dekkers and de Lang would seer-h very well snited to investigate quantitatively many micromagnetic phenomena. Disadvantages do exist though, the main one being that for highly anisotropic ferromagnets with large magnetic moments the wall width may be as small as S-10 nm. Under these circumstances it would be very difficult to satisfy inequality (6) (the requirement for a small coherent probe) whilst maintaining the specimen in a region of low magnetic field. In fact, for such materials it may be possible to relax this low field requirement, which the result that the specimen may be sited rather nearer the objective lens, which will then be more highly excited and consequently will have a lower spherical aberration coefficient. Under such circum- stances the incoherent probe size will also be reduced, which is clearly desirable for an a&rate determina- tion of narrow profiles, although noise is likely to be more of a problem.

A way round this problem, at least in theory, would be to use an alternative method of differential phase contrast electron microscopy. Rather than using a detector with a response function of the form sgn(k), as used here, one which responds to the first moment

214 JN. Chapman et al. /Direct determination of magnetic domain wall profiks

of the electron intensity distribution is suggested. Waddell et al. 1171 have shown that the signal from such a system is linearly related to the phase gradient of the transmittance of any phase object irrespective of its form. Thus, with such a detector system the accurate wall profiles, even of highly anisotropic ferro- magnets, could be determined. Clearly,‘practical con- siderations would render implementation of a first- moment detector system difficult, but some possible methods have been discussed by Waddell [ 151.

We therefore conclude that differential phase con- trast performed on a STEM offers an exciting and relatively straightforward means of carrying out quan- titative micromagnetic investigations.

Acknowledgements

We would like to thank Dr. A.J. Craven for his advice on using the HB5 electron microscope and Dr. L.M. Brown for making the facility available. In addi- tion we are grateful to SRC for supporting this pro- ject and for the provision of maintenance grants for two of us (PEB and EMW). Finally we would like to thank Dr. N.H. Dekkers and Professor R.E. Burge for critically reading this manuscript.

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