magnetic annealing of ni–fe films that possess a stable structure. ii. the relation between...

S. J. HOROWITZ and M. L. RUDEE: Magnetic Annealing of Ni-Fe Films (11) 671

phys. stat. sol. (a) 6, 671 (1971)

Subject classification: 18.2.1; 21.1.1

Materials Science Group, Rice University, Houston, Texas

Magnetic Annealing of Ni-Fe Films that Possess a Stable Structure

11. The Relation between Anisotropy and Dispersion

BY S. J. HOROWITZ~) and M. L. RUDEE

The uniaxial anisotropy and magnetization dispersion have been measured during isothermal magnetic annealing of a large number of Ni-Fe thin films. The temperatures used varied from 350 to 414 "C, and the compositions studied ranged from 50 to 86% Ni. In order to produce a stable metallurgical structure, the films were recrystallized prior to the magnetic annealing. It was observed that both the anisotropy and dispersion were reversible. The dispersion proved to be proportional to the inverse square of the anisotropy field.

Die einachsige Anisotropie und die Magnetisierungsstreunng wurden wahrend isother- iner Temperungen im Magnetfeld an einer groIjen Anzahl yon Ni-Pe-Aufdampfschichten gemessen. Die Temperaturen lagen zwischen 350 und 414 "C, und die Zusammensetzungen der untersuchten Proben erstreckten sich von 50 bis 86% Ni. Vor den magnetischen Temperungen,, wurden die Proben gegluht, so daS sich eine Gleichgewichtsstruktur bilden konnte. Die Anderungen der Anisotropie und Streuung stellten sich als umkehrbare Vor- gLnge heraus. Es wurde festgestellt, daO die Streuung umgekehrt proportional zum Quadrat des Anisotropiefeldes ist.

1. Introduction

I n a previous paper, we preported the kinetics of changes in the uniaxial anisotropy during magnetic annealing of Ni-Fe films that possessed a stable structure [l]. In this paper, the experimcntal study of Ni-Fe films is extended to consider the interrelationship of the anisotropy field and the magnetization dispersion.

The macroscopically measured magnetization dispersion and anisotropy field are two properties of vapor deposited Ni-Fe thin films that both may be easily measured in the laboratory and indicate the expected behavior of such films during device application. The most prominent model which has been pro- posed to relate these macroscopic properties to each other, and to metallurgical structure, is that of Hoffmann [ 2 ] , which was derived from ripple theory. He predicted that the magnetization dispersion, given by the fall-back angle, ~y~~

or ago, could be related to the anisotropy field, H,, and the structure constant, S, in the following manner :

3 S2 8 n A H K ' ' 5 0 = ~~

l) Present address: Technion, Haifa.

672 S. J. HOROWITZ and M. L. RIJUEE

where A is the exchange constant, and

S = Ks D(2 . Here, Ks is the local anisotropy constant, D is a generalized grain size, and n is the number of crystallites through the film thickness. Both K , and D are general and do not tell anything about the mechanisms which cause the local perturbations in magnetization.

There are numerous and conflicting reports, often based on the examination of very few films, of the dependence of macroscopically measured magnetization dispersion and anisotropy field on metallurgical crystallite diameter [3 to 61. These conflicting reports may, in part, be attributed to the complex structural changes that occur when either an as-deposited film is annealed a t an elevated temperature, or film formation takes place a t varying substrate temperatures. On the other hand, recent results [7 to 101 have shown that only dispersion measurements on small areas (x 0.05 mm2) of a larger film show reasonable agreement with theory. These recent reports, however, have only verified the dependence of the product of anisotropy field and dispersion on the structure constant [lo], not on the grain size or other metallurgical parameters, which change irreversibly during annealing.

In addition, there have been reports that describe the reversible nature of the macroscopically measured magnetization dispersion and anisotropy field following recovery and recrystallization [ l l , 121, processes which clearly result in irreversible changes in metallurgical structure.

This paper will report on the relationship between the macroscopically measured magnetization dispersion and anisotropy field in a large number of vapor deposited nickel-iron thin films. A standard metallurgical state will be induced by a brief treatment a t a temperature higher than any subsequent annealing temperature. Changes in the macroscopic magnetic properties, H K and ( Y ~ ~ ,

will be induced by isothermal magnetic annealing. These results will show that for the case of recrystallized films, where the structure is invariant, the macroscopically measured magnetization dispersion and anisotropy field do not obey the relation developed by Hoffman [ 2 ] . However, an empirically determined relationship will be presented that should be useful for the control of magnetic annealing.

2. Experimental

The thin films studied in this work were prepared by boat evaporation in a vacuum of Torr andin a magnetic field of 70 Oe. The rate of evaporation was greater than 1000 A j s ; this high rate of evaporation was achieved by pas- sing a current of about 1500 A through a 7.7 x 1 . 9 ~ 0 . 0 5 5 em3 W-boat 1111. The substrate temperature was 240 "C. H K was measured by Kobelev's [13] method and Crowther's [14] method I1 was used to determine ( Y ~ ~ . The composition was determined by X-ray fluorescence. All the films were of approximately the same thickness, 1100 A, and 1 cm in diameter. I n production runs the thickness was controlled by weighing the evaporant ; this method had been calibrated by prior thickness measurement using interferometric methods.

Permalloy thin films containing 50, 61, 72, 77, 82, and 86 wt% Ni were subject to isothermal magnetic anneals a t 350, 356, 388, and 414 "C for cumulative times in excess of 100 h. Prior to the beginning of the isothermal annealing procedure, each group of films was maintained a t 500 "C for one hour with

Magnetic Annealing of Ni-Fe Films that Possess a Stable Structure (11) 673

a magnetic field of 50 Oe aligned in the easy direction. This procedure recrystallized the films and created a stable metallurgical structure, one that remained essentially invariant during subsequent thermomagnetic treatment. All the magnetic annealing was done in a vacuum of better than Torr. A holder for nine films allowed the compositions of interest and controls for grain size determination by transmission electron microscopy to be annealed simultane-

The films which were to be used for grain size determination by transmission electron microscopy were prepared with underlayers of copper and silicon mon- oxide t o facilitate easy removal of the film from the glass substrate. The cry+ tallite size and distibution were obtained from electron micrographs with the aid of a Zeiss particle size analyser.

ously.

3. Results

Least-squares regressions were made of Iog ~y~~ to the log of the magnitude of H K derived from the isothermal anneals described above. All the data for a given composition were combined for these calculations, including the several temperatures and both easy- and hard-axis alignments. These calculations show that the relationship between and HI; may be expressed in the following manner :

Xso = c ( H K ) b . (1)

Within 90% confidence limits, b is independent of composition and equal to 2.0 f 0.5, while c is dependent on the composition. Fig. 1 demonstrates results for films containing 72% nickel, while Fig. 2 summarizes the results for all six compositions. The brackets in Fig. 2 indicate 90% confidence limits, and the straight line is the mean of the data points, all of which fall within two standard deviations from this mean.

Vig. 1 . The simultaneous change of the magnetization dispersion and the anisotropy ,field during annealing

Fig. 2. The variation with composition of the exponrmt in the dispersion-anisotropy I'ddtionship

of two 0.72 Ni-0.28 Ye films

674 S. J. HOROWITZ and M. L. RUDEE

1w

I

M

10

-

blM:t $ 0

- I I I I I I I I I I M 60 70 80 YO

rig. 3 . Thr rrversihle nature of both t he diapersion a n d thr anisotropy during magnetic anncaling of il

0.61 Xi -0.39 J3.c film

N g . 4. The variation with composition of the proyor- tionality constant c

The reversible nature of the magnetization dispersion and anisotropy field was verified by hard-axis annealing of recrystallized films. The state of a given film was changed from one of high H , and low to one of low H K and large

reversible along the same straight line on a plot of log a5,, vs. log H E . This result is shown in Fig. 3 for hard-axis annealing a t 383 "C.

Fig. 4 shows the composition dependence of the constant of proportionality, c , calculated from the data for films annealed a t 350, 356, and 414 "C. Films annealed at 388 "C, prepared in different deposition groups than the films annealed at 350, 356, and 414 "C, produced a proportionality constant which dis- played considerably more scatter than that shown in Fig. 4. There was also some variation noted between films annealed a t the various temperatures.

A transmission electron microscope study of the grain structure demonstrated that the average crystallite size in films in the as-deposited state was approximately 100 A , and approximately 1000 A for films pre-annealed for 60 min a t 500 "C. I n addition, i t has been determined that the average grain diameter and observable microstructure remained essentially invariant during the course

annealing time (hl - Pig. 6 . The change of grain siac during isothrrmal arinealing

Magnetic Annealing of Ni-Fe Films that Possess a Stable Structure (11) 675

of subsequent isothermal magnetic annealing, even for the extreme case of 100 h a t a temperature of 414 “C. This is illustrated in Fig. 5. The distribution of grain diameter about the mean was found to be log-normal.

4. Discussion

The present study of the relationship between macroscopically measured magnetization dispersion and anisotropy field has been conducted under condi- tions in which changes in metallurgical structure have been kept to a minimum. This allows a comparison with available theory; one free of ambiguities due to structural changes. In a situation, such as has been established here, where there are no changes in the structure constant, Hoffmann’s model predicts a simple inverse relationship between iy50 and HI:. This theory, however, has been shown by Fujii et al. [lo] to agree with experimental observations only in the case of microscopic measurements of the magnetization dispersion. For macroscopic determinations, as reported here, deviations from microscopic behavior and from Hoffmann’s calculation, are therefore not surprising. Moreover, some of the assumptions included in Hoffmann’s development have recently been ques- tioned by Brown [15].

Previously, Uchiyama et al. [8] and Leaver [16] noted that the differences observed between macroscopic and microscopic measurements could be explained by the occurrence of a long-wavelength or extrinsic component of the magnetization dispersion. This long-wavelength component seemed to have the same origin as skew. This could suggest that the present results are a manifesta- tion of this long-wavelength contribution, thought to have its origin in a stress mechanism. The present work, however, does not offer any evidence to support this suggestion. The composition dependence of the magnetization dispersion, reported by others [7], can be explained by the usual composition dependence of the anisotropy field through equation (1) . An examination of the composition dependence of the constant of proportionality, c, did not indicate any inflection or dip a t either the compositions of zero magnetostriction or zero magnetocrystalline anisotropy. There did seem to be some dependence of the proportionality constant on annealing temperature, and variations between films produced in different deposition groups, but no clear dependence has emerged. If a magnetostriction mechanism contributes to measured macroscopically, the variations observed for different evaporation groups might be explained by variations in substrate cleanliness causing variations in film-substrate adhesion.

One set of experimental data with which the present work can be compared is that reported by Landler [17]. He produced films possessing a wide range of values of anisotropy field and of macroscopic magnetization dispersion by deposition in the presence of anelliptically rotating magnetic field. For deposition a t a given substrate temperature, the values of H K and ( Y ~ ~ were independent of film structure. Landler’s results are reproduced in Fig. 6. The curve drawn is that for a50 =9.5 ( H K ) -1.‘J4, the best fit relationship derived from a least- squares regression of log ( Y ~ ~ to log H,. The exponent, -1.94, is in excellent agreement with the present results.

During the course of the present study we have also observed the kinetics of the isothermal annealing of the magnetization dispersion. These observations [I81 could be best described in a manner similar to that reported for the aniso-

676 S. J. HOROWITZ and M. L. BUDEE

Fig. 6. The rlisperaion as n function of anisotropy, after Landlrr [ I 7 1 I I tropy field [l], with the magnetization dispersion,

entering through equation (1). The relaxation times predicted by this analysis were in good agreement with those derived from fitting the anisotropy field data alone, further supporting the present report of the dependence of ayj0 on H K . as shown above.

It should be noted that the present observations include points in which the observed values of magnetization dispersion were quite large, in all likelihood a region in which both the assumptions of ripple theory and the assumptions inherent in

7 2 3 4 5 6 the measurement technique are breaking down. These points, however, low H , and large usor re- peatedly fell on the same straight line as those ob-

servations which were made in regions of greater confidence, high H , and low aBo. Some deviations were noted for the extreme values of

As the metallurgical structure remained essentially invariant during the isothermal annealing procedure, any contribution to the magnetization dispersion through a mechanism based on magnetocrystalline or magnetoelastic anisotropies would also be expected to remain constant. The pretreatment, of course, removed any significant contribution from non-equilibrium crystal defects. On the other hand, the fact that the metallurgical structure enters only as a constant parameter does not preclude a structure sensitive magnetic contribution such as that from magnetocrystalline or magnetostrictive anisotropies. The effect of the random or perturbing anisotropy, which would result from magnetocrystalline or magnetoelastic interactions, is observable as an inverse function of the induced anisotropy.

HKfOe) --

5. Conclusions

The anisotropy field and dispersion has been measured in a large number of Xi-Fe thin films. The films were first recrystallized. The magnetic properties were altered by field-annealing a t temperatures that were less than the recrystallization temperature, thereby eliminating changes in the metallurgical structure during the magnetic annealing.

It was observed that the anisotropy and the dispersion, both measured macroscopically, were reversible and obeyed the relationship given as equation (1). Within goo/, confidence limits, b is 2.0 & 0.5, and is independent of composition. There exists a composition dependence of c , but this dependence does not give evidence of relating to either magnetostriction or magnetocrystalline anisotropy.

The observed value of b deviates significantly from unity, the value predicted by Hoffman [ 2 ] . However, due to the approximations made in his treatment, it is not surprising that it does not apply to our macroscopic measurements. Nevertheless, the relationship reported here should be valuable for controlling the useful properties of Ni-Fe films by magnetic annealing.

Nagnetic Aririealing of Xi-Pe Films that Possess Stable Structure (11) 677

A rlcnoiuledgements

This research was supported by the National Science Foundation and by the NASA Materials Grant to Rice University.

References

[ I ] S. J . HOROWITZ and M. L. RUDEE, phys. stat. sol. (a) 5, 427 (1971). [2] H. HOFFMANN, phys. stat. sol. 5, 187 (1964). [3] F. G. WEST and C. L. SIMMONS, J. appl. Phys. 37, 1283 (1966). [4] H. HOBFMANN, Z. angew. Phys. 18, 499 (1965). [5] A. POCKER, Z. angew. Phys. 25, 346 (1968). [6] T. IWATA and F. B. HAGEDORN, J. appl. Phys. 40, 2258 (1969). 171 T. FUJII, S. UCHIYAMA, E. YAXADA, and Y. SAKAKI, Japan. J. appl. Phys. 6, 1 (1967). [8 ] 8. UCHIYAMA, T. FUJII, M. MaSuDa, and Y. SAKAKI, Japan. J. appl. Pliys. 6, 512

[9] S. UCHIYAMA, T. FUJII, M. MASUDA, and Y. SAKAKT, IEEE Trans. Magnetics 4, 495

[lo] T. FUJII, S. UCHIYAMA, S. TSUKASIIIMA, and Y. S ~ K A K I , IEEE Trans. Magnetics 5,

[ll] K. R. CARSON, Ph. D. Dissertation, Rice University, 1969. 1121 H. H. ZAPPE, IEEE Trans. Magnetics 4, 655 (1968). [13] V. V. KOBELEV, Fiz. Metallov i Mrtallovedenie 13, 467 (1962). [14] T. S. CROWTHER, M.I.T. Lincoln Labor. Group Rep. 51-2 (1959). [15] W. F. BROWN, IEEE Trans. Magnetics 6, 121 (1970). (161 K. D. LEAVER, J. appl. Phys. 39, 1157 (1968). [17] P. F. J. LANDLER, J. appl. Phys. 39, 1563 (1968). [18] S. J. HOROWITZ, P1i.D. Dissertation, Rice University, 1970.

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(Received June 21, 1971)

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magnetic annealing of ni–fe films that possess a stable structure. ii. the relation between...

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