Determination of internal stresses distribution for a nearly-zero magnetostriction amorphous alloy

Journal

of Magnetism

and Magnetic

Materials

54-57

261

(1986) 261-262

DETERMINATION OF INTERNAL STRESSES DISTRIBUTION MAGNETOSTRICTION AMORPHOUS ALLOY J.M. GONZALEZ, Lahorutorio

M. VAZQUEZ

de Magnetismo,

FOR A NEARLY-ZERO

and J.L. VICENT

Farultad de Ctencias FIS~IS, Unioersidad Complurense.

28040 Madrid, Spain

Surface and bulk magnetization curves have been measured by means of the magneto-optic Kerr effect and the conventional induction method, respectively, for the Metglas* 2705 M alloy. From the analysis of the experimental measurements and using a simplified model, the angular and intensity distributions of the internal stresses have been evaluated.

2. Results and discussion

1. Introduction and experimental Magnetoelastic originated fabrication

anisotropies

by the internal process.

The

stresses

in

metallic

glasses

are

introduced

during

the

direction

of

these

local

ani-

fixes the domain structure. In the case of alloys with large magnetostriction, the appearance of regions has been reported where the anisotropy axis is perpendicular to the ribbon plane and consequently, the magnetization is oriented along this direction. Nevertheless, for most alloys with nearly-zero magnetostriction, those regions are very restricted because the demagnetizing field is large compared to the local anisotropy field so that these alloys behave as if the anisotropies were distributed only in the ribbon plane. In this work, we present a study about the internal stresses distribution for a particular nearly-zero magnetostriction amorphous alloy. Samples of Metglas* 2705 M (ribbons 24 urn thick and 25 mm wide) from the Allied Chemical Co. have been studied. Ribbons used for susceptibility measurements were chemically etched to a circular shape, (9 mm diameter) and to a ribbon-like shape (2 mm wide and 70 mm long) for remanence measurements. The free surface of as-cast circular samples was good enough to observe the Bitter pattern and to measure the magneto-optic Kerr effect (MOKE). Two pairs of crossed Helmholtz coils and a rotating sample holder have allowed us to apply magnetic fields in any direction in the sample plane. A photodiode or a pick-up coil has been used to evaluate the magnetization when measuring respectively MOKE signals or transverse susceptibility. Bulk transverse susceptibility was measured by applying an alternating field (peak value 10 mOe. frequency 430 Hz) and orthogonally to this one, a dc bias field was superimposed varying up to 320 Oe. Magnetization changes detected along the alternating field direction were measured by means of a phase sensitive lock-in amplifier [I]. Bulk switching magnetization curves for the ribbon shaped samples and their dependence on applied tensile stresses have been carried out with the help of a conventional induction method. Remanences and low field susceptibilities were also obtained. sotropies

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Fig. 1 shows a Bitter pattern of the sample. One can notice the presence of long straight 180” walls equally spaced (0.3 mm mean value) running along a direction making a small angle with respect to the ribbon axis. It is also noticeable that the zones with magnetization perpendicular to the ribbon plane are absent. Fig. 2 shows a polar diagram of the low field susceptibility (MOKE technique) as a function of the angle between the applied field (parallel to the measured magnetization) and the ribbon axis. The maximum value of the susceptibility (easy axis) is obtained for a diretion a few degrees away from the ribbon axis and there is a well defined minimum (hard axis) for its transverse direction. This result qualitatively agrees with the above observed domain structure. The MOKE hysteresis loops corresponding to the results represented in fig. 2 are almost squared when the measuring direction is close to the easy axis, the susceptibility being determined by wall displacements. The hysteresis loops are constricted for directions near the hard axis and then, the susceptibility is roughly ruled by magnetization rotations. Therefore, from fig. 2 the stress angular distribution can be qualitatively deduced. The bulk transverse susceptibility x, shows small differences when applying a dc magnetic field along the ribbon axis direction or along its transverse direction. In fig. 3 extrapolation from the high field linear region of the x,’ vs. Hdc plot, gives a value for a mean anisotropy energy density of 15 Jme3. According to ref. [2], the fact that this extrapolation

Fig. 1. Domain nique.

B.V.

structure

picture

obtained

by the Bitter

tech-

-

t-o.5

Fig. 2. Polar plot of low field susceptibility (arbitrary a function of the in-plane measuring direction.

units) as

FITTING

t

Fig. 4. Dependence

of the reduced

remanence

on applied

stress.

been considered corresponding respectively to tensile or compressive stresses. Here, since the magnetostriction is negative, o must be negative because the easy magnetization direction approaches the ribbon axis. Considering the fractional volume LI,,as:

does not cut symmetrically the bias magnetic field axis is related with the existence of dispersion in the anisotropy. In fig. 4, we show the evolution of the reduced remanence, m r as a function of the applied tensile stress after the demagnetizing field correction was considered. Upon applying the stress, a,, the magnetization tries to lie in the direction perpendicular to the ribbons axis because of the negative value of the magnetostriction. The fractional volume, c’~ with magnetization perpendicular to the ribbon axis increased and consequently the remanence decreases as the stress is applied. Considering the clearly anisotropic distribution of the easy directions shown in figs. 1 and 2, we have simplified this distribution by assuming the existence of two fractional volumes vI and u,, where tensile, Us. or respectively (the compressive, 0,) stresses predominate, stresses axis being oriented parallel to the ribbon axis). Then. m,( Us) = u,,( Us), holds [3]. Let us assume a Gaussian distribution of internal stresses:

we have fitted the experimental dependence of M, on a, (see fig. 4) taking 5 = - 90 MPa and up = 60 MPa. Fig. 4 shows a value of m, lower than 1 for zero applied stress. It can be interpreted as due to the fact that the easy axis does not coincide with the ribbon axis or alternatively because there is a small fractional volume (>I characterized by tensile stresses. That is consistent with the considered stress distribution and the MOKE experimental results. Then. we can infer that the surface and bulk stresses distributions are roughly the same. The magnetostriction, A, has been evaluated from the dependence of the initial inverse susceptibility. x, ‘, on applied tensile stresses according to [3]:

p(u)=

A = - (/wK?3)(dx,‘/d~,).

(2”ur)~1’2

exp{ -(u-@)2/2uz}.

(1)

where a and ur, are the mean and dispersion values of the distribution. Positive and negative values of u have

X1 (orb

unlts)

/:

-6 .Hdcuribbon -4

+HdcL

-2 L)/#/--T*

A ’

I’

~1x1s .// ‘8

*&

*R 100

Fig. 3. Inverse transverse

200

susceptibility

ti,jc

vs. dc applied

(Od

field.

I

=/mXp(+o, g.,

(2)

(3)

Taking pLoM, = 0.8 T, the value obtained for h is -6 x 10 -‘. Considering the mean value of the stresses a, this gives an anisotropy energy density. K, along the easy axis, K = 10 Jrn-‘. This value is also consistent with the one obtained from the transverse susceptibility results. [I] J.M. GonzBlez and J.L. Vicent, J. Appl. Phya. 57 (1985) 5400. [2] E. Feldkeller. Phys. Lett. 7 (1963) 9. [3] M. VBzquez, W. Fernengel and H. Kronmtiller. Phya. Stat. Sol. (a) 80 (1983) 195.