THIN FILM PARAMETERS DETERMINED BY TORQUE MAGNETOMETRY

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THIN FILM PARAMETERS DETERMINED BY TORQUE MAGNETOMETRY

A. Collins, A. Green

To cite this version:

A. Collins, A. Green. THIN FILM PARAMETERS DETERMINED BY TORQUE MAGNETOME- TRY. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-137-C1-139. �10.1051/jphyscol:1971144�.

�jpa-00214471�

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JOURNAL DE PHYSIQUE CoIloque C I, suppI&rnent au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1

-

¹³⁷

THIN FILM PARAMETERS DETERMINED BY TORQUE MAGNETOMETRY

A. J. COLLINS and A. GREEN

Wolfson Centre for the Technology of Soft Magnetic Materials, U. W. I. S. T., Cardiff, U. K.

Rbum6. - La mesure du moment magnetique de couches minces au moyen d'une balance de torsion est sujette, en plus des erreurs experimentales, a une erreur systematique like B I'hypothese que l'on fait sur le mode de renversement de l'aimantation. En utilisant des methodes inhabituelles de mesure du moment magnetique, qui minimisent les erreurs expkimentales, on met en kvidence cette erreur systematique. 11 est suggerk que des expkriences de ce type pourraient aussi

&re utilisks pour ktudier les effets d'ondulation de la direction de l'aimantation (ripple et skew), a condition de disposer d'une thkorie du renversement de l'aimantation permettant de relier les mesures de couple a ces phenom6nes.

Abstract. - Torque magnetometer measurements of the magnetic moment of thin films are subject to systematic error as a result of the assumed reversal process, in addition to the experimental errors. By the use of unconventional methods of measuring the magnetic moment, which minimize the experimental errors, the effect of the systematic error is demonstrated. The suggestion is made that experiments of this type could also be used to investigate ripple and skew subject to a satisfactory reversal theory relating torque measurements to these effects.

1. Introduction.

-

Various methods have been for the film suspended with its plane perpendicular described in the literature for measuring the saturation to the suspension.

magnetization M, of ferromagnetic thin films, using Careful assessment of the errors has been made a torque magnetometer. These methods depend on for both the parallel to the plane torque method torque measurements made with the specimen plane (P-mode) and for the normal to the plane method parallel to the sus~ension and a field a~vlied with a (N-mode).

component normaf to the film surface.

n he

commonly

only 2, The&,. - The single domain energy expression

used method is that due to Neugebauer [I], in which for a uniaxially anisotropic film is the applied field is at 4 4 radians to the specimen

plane. Derivation of the M, value from the results E = - M, H c o s 0

+

Ksin2(@

-

8) (1) depends upon the extrapolation of an assumed linear

portion of a hyperbolic type of curve. This is subject to the criticism that for some types of film the linear region is not clearly defined and errors can result from such extraoolation. A referable method is one which does i o t rely upon iuch an extrapolation, and in which the experimental errors can be more readily estimated. Chikazumi [2] described the possi- bilities of torque measurements for fields applied at small angles to the film plane, although he reported no M, determinations. A dynamic version of this method, using a pendulum magnetometer has been described by Meierling and Gartner [3].

Apart from experimental errors in this form of magnetometry, a further source of error arises from the fact that the derivation of M, values from the results involves assumptions about the nature of the reversal process for the field-specimen configuration used. Unless the reversal mechanism has been esta- blished, there exists the possibility of a systematic error in Ms.

For these reasons the authors of the present paper have attempted to examine the effect of such assumptions on torque magnetometer measurements of Ms.

Because of the criticism of the Neugebauer method already mentioned, this was not used. Instead, the determination of M. for the film lane oarallel to

where E = energy per unit volume ; M , = saturation magnetization ; H = applied field ; 0 = angle between M, and H ; @ = angle between H and the easy axis ; K = anisotropy energy.

For the N-mode, K is the perpendicular anisotropy (K,), whereas for the P-mode K is the uniaxial anisotropy (K,).

From the equilibrium condition aE/a8 = 0 and assuming sin 8

-,

8, one obtains

O % ( K s i n 2 C P ) / ( M s H + 2 K c o s 2 @ ) (2) Now, the torque L = M,HV8 for a volume V, giving L = (KV sin 2 @)/(I

+

(2 K cos 2 @)/M, H) (3) Differentiating with respect to @, one obtains

d@/dL =

= (1

+

(2 K cos 2 @)/M, H)'/2 KV(cos 2 @+ 2 KIM, H) For the cases @ = 0, Q, = n/2, (4)

d@/dL = l/Ms H V

+

^{112 KV} ( 5 ) where the

+

^{ve and}^-ve sign refer to @ = 0 and

@ = 4 2 respectively.

Thus, a linear relationship is predicted between dQ,jdL and 1/H, the slope and intercept giving I/MsV and 112 K V respectively.

the suspension was Lade by usingLappliid fields at 3. Experimental Results. - The instrument used small angles to the film plane. Since the reversal beha- was an automatic torque magnetometer of the type viour of thin films for applied fields parallel to the described by Croft et al. [4] capable of detecting a film plane have been studied more extensively than minimum torque of dyne.cm. Torque curves that for fields applied at an angle to the film plane, were plotted for a range of applied fields. The slopes the low-angle torque method was extended to the of the torque curves were determined at CP = 0 for measurement of Ms from torque curves obtained the N-mode and a t CP = 0 and Q, = n/2 for the P-mode.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971144

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A. J. COLLINS AND A. GREEN

Specimen Composition 78-22 Ni-Fe Thickness : 1 960 +_ 30

A

; Diameter : 1.5 cm Method

-

N-mode (@ = 0) P-mode (@ = 0) P-mode (di = n/2) P-mode (@ = 4 4 ) Bulk Value [8]

Corrected value (@ = 0)

M, K, x 1 0 - ~ K x Correlation

(erg1I2. ~ r n - ~ l ' ) (erg. cm- 3, (erg. ~ m - ~ ) Coeff.

- - -

888 & 19 - ₆

+

⁶ ^0.998

1 190 & 100 1.90

+

^0.07 ^- ^0.895

1170 k 90 2.02 Jr 0.08 - 0.919

- 1.92 +_ 0.04 - -

860 +_ 30 - - -

Least squares fits were made to the data, assuming the linear relationship between d@/dL and 1/H predicted by equation [5]. From these, values of M,, Ku and KL were derived. Measurement of Ku was also made by the generally accepted method of measuring the peak torque for the P-mode. Correlation coefficients were determined. Also, the standard errors of the parameters were calculated from the known experimental errors.

The measurements were made on a Ni-Fe (78-22) Elm prepared by vacuum deposition at a pressure of torr on to a glass substrate held at 300OC.

Specimen thickness was 1 960

A

(determined inter- ferometrically) and the diameter was 1.5 cm. The results obtained are shown in Table I.

The results show that a linear relationship was followed for the N-mode. Also, the M , value was consistent with the bulk value for this material. No reliable estimate of K, could be made, since the standard error was

-

10' ergs. cm; 3.

For the P-mode, anomalously large values of M, were obtained, together with a lower correlation coef- ficient than for the N-mode. The Ku values were consistent with those obtained from the peak of the high field torque curve.

The experiment indicates that for this specimen the assumed reversal mechanism for the N-mode was more physically acceptable than that for the P- mode. Whilst the P-mode experiments for Oi = O and @ = n/2 gave consistent values for IM, and Ku the M, value was -- 30

%

higher than M, obtained for the N-mode.

As Hoffmann [5] has pointed out, the reversal mechanism in the plane of a thin film is governed by ripple and skew effects. However, in the experiment described, the lowest applied field in the P-mode was estimated to be > 10 KIM, where one would expect the effect of ripple to be small. An estimate of the possible effect of skew, in this experiment was made by application of the simple model described below.

Assume that the film consists of three non-interac- ting volumes V,, V,, V, having easy axes at 0,

+

6,

-

6 respectively with respect to the easy axis of V , and that V, = V3, then, from (4)

dL/dd, =

+

^{2 KV/(1}^_+2 KIM, H ) f 4 KV, x x [( f cos 2 6

+

2 KIM, H)/(1 -+_ 2 Kcos 2 6/M, H)' T

T 1I(1+ 2 KIM, HI] (6)

where the upper and lower signs refer to ^dj= 0 and

@ = n/2 respectively.

The value of M, obtained from the N-mode expe- riment was substituted in equation (6). Two experi- mental values of dL/d@ (for @ = 0) were used to set up two simultaneous equations, from which KV and 6 were derived by a graphical method. The values obtained were Ku = 2.16 x lo3 erg.cmy3 ; 6 = 0.288 rad.

4. Discussion. - For the specimen investigated, the results show that the N-mode values of M, were consistent with the bulk value, whereas the P-mode experiment gave an M , value which was

-

³⁰

^%

higher than the bulk value. Further, the correlation with an assumed linear relationship was better for the N-mode than the P-mode experiments, as can be seen from the calculated correlation coefficients.

A simple model has been proposed, which shows that this anomaly can be explained by assuming the presence of two skewed volumes having a K,, value

-

¹⁵

^%

higher than that derived from the assumed law.

Whib recognizing that this theory is probably over-simplified, it illustrates the point that measurements of M, using torque magnetometry can be subject to errors as a result of the assumptions in the original energy expression. Although for this specimen, agreement was obtained between the bulk value of M, and the N-mode value, this may not necessarily be the case for other specimens. For exam- ple, Yamanaka and Ueda 161 observed high-field torque curve distortion for N-mode experiments which they explain in terms of stripe domaia structure. The authors have observed anomalous values of M, for highly skewed films measured in the N-mode. This will be reported elsewhere.

The conclusion reached is that the departure of a film from the single domain reversal theory for a P-mode torque magnetometer experiment can make the method unsuitable for the accurate determination of Ms. However, the method is sensitive to skew and possibly ripple effects. This suggest that this technique could be used to investigate these effects, subject to a satisfactory theory relating P-mode torque magnetometry to skew and ripple. Such experiments could possibly complement the initial susceptibility techni- ques which Kempter and Hoffmann [7] describe.

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THIN FILM PARAMETERS DETERMINED BY TORQUE

References [ I ] NEUQEBAUER (C.), Phys. Rev., 1959, 116, 1441.

[2] CHIKAZUMI (S.), J. Appl. Phys., 1961, 32, 81s.

[3] MEIERLING (D.), G ~ T N E R (H.), 2. angew. Phys., 1964,

4- n1.Y 1 1 , ,&I>.

[4] CROFT (G.), DONAHOE (F.), LOVE (W.), Rev. Sci.

Instrum., 1955, 26, 360.

[5] HOFFMANN (H.), Phys. stat. sol., 1969, 33, 175.

[6] YAMANAKA ( M . ) , UEDA (R.), J. Phys. Soc. Jap., 1967, 23, 241.

[7] KEMPTER (K.), HOFFMANN (H.), Phys. stat. sol., 1969, 34, 237.

[8] BOZORTH (R.); Ferromagnetism (Van Nostrand), 1968, 109.