This equation illustrates the dependence of the magnetically induced uniaxial anisotropy on the composition of the alloy, i.e. the anisotropy is proportional to c!c~ = C~(l-Cb)2• For a 50% Ni-Fe alloy, the predicted value of Ku is about 2·102. In light of the experimental situation, Robinson and West proposed an additional mechanism to account for the part of uniaxial anisotropy in thin films.
West
They concluded that the stress mechanism could not account for any significant part of the uniaxial anisotropy. The uniaxial anisotropy field ~ determined by the torque magnetometer as a function of the substrate deposition temperature T 1 is shown in Fig.
SUBSTRATE DEPOSITION TEMPERATURE (°C)
Fig. 2-5 Uniaxial anisotropy field ~- for the different Ni compositions as a change of substrate deposition temperature. The anisotropy of the r-phase in fig. 2.7 does not show a peak near 50% composition or much curvature.
FILM COMPOSITION °/oNi
Fig.2-7 Uniaxial K anisotropy as a function of Ni composition in Ni-~e alloy films.u The anisotropy energy constant K is for the Y phase at room temperature. The thickness of the film was about 500 R. The samples were washed off the substrate in water .. and washed in water for about three minutes so that all the NaCl from the substrate was completely dissolved.
Bloch Wall
For reasons described in detail elsewhere~here, the wall width in the present thesis is defined to be. Middlehoek (1961) has also treated the one-dimensional ellipsoidal model for the energy calculation for the wall. The wall energy per area unit y. 0 for the limiting case of the linear wall model, Eq. 4.8), differs from that expressed by Eq.
It is necessary to multiply the wall width of Dietz and Thomas by the factor :n:/2 to obtain the wall width expressed by Eq.
CNeel watn __
THEORETICAL NEEL WALL
COORDINATE IN FILM (A)
A typical Lorentz microscope photograph of crosswalls associated with Bloch lines for a 76% Ni-Fe. Thu.n trun. is briefly given in this section.
The name Neel line is due to the nature of the transition region in which the magnetization lies in the plane of the film.
FILM THICKNESS (A)
Patton and Htwphrey (1966) were able to estimate wall width indirectly from their domain wall mobility measurements. Furthermore, mobility data for thicker films (presumably with Bloch walls) show that the wall widths are even larger. They indirectly measured the wall energy in permalloy films as a function of film thickness and obtained energy values smaller than those calculated with simple wall models.
In the figure, the theoretical predictions by Middlehoek, Collette, Brown and LaBonte and Aharoni are shown for comparison.
FILM THICKNESS (A) 0
Rays from the two domains converge or diverge a·: boundary, depending on the sense of direction of magnetization in the two domains. To calculate the image intensity distribution of the wall, the magnetization distribution across the wall must be known. As a first-order approximation, a simple one-dimensional magnetization distribution can be assumed to calculate e.
For this case it becomes. focal length and ~ is the Lorentz deflection angle far from the wall.
CONVERGENT WALL
Therefore, it is concluded that the Fuller and Hale result is only applicable for the convergent weight case if the ratio between the beam convergence angle (3 and the Lorentz deflection angle w is of. To verify the influence of the final beam divergence on the intensity) maximum and minimum for respectively converging and diverging wall cases, a preliminary experiment was performed.Using the methods described in section 4.4.4, the intensity at the wall center of the converging and diverging wall images was measured,i as a .
First, the basic validity of the classical calculation can be expected to fail for out-of-focus distances greater than approx. 3 mm (see section 4.4.7).
Convergent Wall
Out -of- focus Distance (mm}
Divergent Wall
Out -of- focus Distance ( mm)
Based on the preceding discussion, the wall width determinations were made using only the divergent wall images and using 5 in Eq. The magnification of the microscope in the Lorentz mode was 1600, and was measured using a carbon grid replica (E. A typical example of the profile matching method to determine the wall width experimentally is shown in Fig.
In light of this, only the intensity profile of the divergent wall image was considered.
RESENT WALL SHAPE
NORMAUZED DISTANCE u (XI2580A)
According to this result, only the wall widths obtained by profile matching were presented in the previous sections. In previous discussions, it was assumed that the incoherent electron beam is deflected by the Lorentz force due to the internal flow of the film. In addition, in the approximation that the domain wall represents an opaque region in the sample, Fresnel diffraction fringes may appear at the edges of the domain wall.
According to Heidenreich, if the nth maximum in the edges is just visible, the coherence condition requires it.
There is also a marked change observed at this thickness for both measured wall widths (Fig. As discussed in section (4.2), the energy of the ordinary Bloch wall in the crystal was calculated by neglecting the presence of transverse bond walls associated with or Neel lines It was found that the measured width of the domain wall of Ni-Fe alloy films with a thickness of 200 Å to 1800 Å.
However, for films of finite actual thickness, the measured wall width is again much wider than that based on simple one-dimensional models, and for thick films it even exceeds the value calculated for infinite film thickness.
Therefore, it is necessary to discuss possible sources for this discrepancy, such as in the cnse of Ni-Fe alloy films. First of all, it should be noted !.lwt as in the case of Ni-Fe, the quantum mechanical constraints do not apply to this case either, due to the choice of the image of the different wall, the small out-of-focus distance. , and the relatively large divergent angle of the beam. Second, the change in anisotropy in the removal of films from substrates as in the case of Ni-Fe films cannot be an important factor.
Regardless of the discrepancy with theoretical predictions, there is an interesting and significant difference between the experimental results for Ni-Fe alloys and Co films.
Feinberg (1963) that the phase difference S between two points A and F along an electron beam is given by (Fig. 4. It is clear that the interference of the two parts at F will 1, while the other path passes through point x. xl Thus if the road Ax. 1F is taken as the reference path, then Eq. 4.17) gives the phase shift for any arbitrary path Ax2 F. In an effort to provide the coherent source of the electron beam, a special filament was created using one mil. Such a finite source size produces a finite illumination aperture. In a commercial microscope this angle cannot be reduced much below 10 -6 rad. In fact, one of the ways to study the origin is to vary the film parameters to measure a macroscopic parameter related to the ripple through theory. Similarly, for a transverse ripple structure, the change in direction of the magnetization M is only a function of the coordinate normal to the mean magnetization direction. As discussed in the previous section, the source of the ripple structure must arise from an inhomogeneous local anisotropy of some kind. The short wavelength ripple was found to have amplitude of the order of 8, where d is the film thickness. In 1964, Harte made a detailed and more general calculation of the ripple structure in thin films. Fuchs (1961) and Baltz (1964) studied the dependence of waviness on alloy composition in Ni-Fe alloy films. 52Ni-48Fe FILM 25°C IOfL A third method has been devised independently in the course of this research and by Hoffmann. To determine the mean wavelengths by the three different methods described above, photodensitometer traces were taken of the photographs and also the well-defined ripple lines were l'Olmteti visually on the photographs. In light of the above results, one can now conclude that the well-defined ripple periodicity indicates something physically meaningful, e.g. It is important to study the field dependence of ripple if one wants to establish the validity of one of the theories. Easy axis field In any case, the dependence of wavelength on field gives strong evidence supporting the basic hypotheses of the two theories. The present section is concerned with the study of the wrinkling dependence of substrate deposition temperature for 76% Ni-Fe alloy films. On the other hand, the slight dependence of the theoretical wavelength on substrate deposition temperature was not observed. In the previous section, we discussed the dependence of the ripple on the substrate deposition temperature. SUBSTRATE All films were deposited at room temperature and measurements were also taken at room temperature. Also shown are Hoffmann's theoretical prediction and the long wavelength ripple component of Rot'1.er, using the values of K reported by Wilts (1966). The measured wavelength remains essentially constant over the entire composition range. about 1.8 ~), while the theoretical predictions show an increase with Ni composition. Although the agreement between the data and the theoretical predictions is not unreasonable for the composition up to about 76% Ni, the discrepancy between the trends is evident beyond this composition. ROTHER'S PREDICTION Since the ripple angle is predicted to depend strongly on material composition and substrate temperature, this provides an experimental method to simultaneously test the ripple theories and test this measurement method. Measurements have been made for both the variation of the substrate deposition temperature and the variation of the composition discussed earlier in connection with wavelength measurements.Plane
Background
DEPOSIT ION TEMPERATURE
