MAGNETIZATION REVERSAL OF ELECTRODEPOSITED FeNi FILMS

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MAGNETIZATION REVERSAL OF ELECTRODEPOSITED FeNi FILMS

W. Lems, Th. Holtwijk

To cite this version:

W. Lems, Th. Holtwijk. MAGNETIZATION REVERSAL OF ELECTRODEPOSITED FeNi FILMS.

Journal de Physique Colloques, 1968, 29 (C2), pp.C2-140-C2-143. �10.1051/jphyscol:1968220�. �jpa-

00213535�

MAGNETPZATION REVERSAL OF ELECTRODEPOSITED FeNi FILMS

W. LEMS and Th.

HOLTWIJK

Philips Research Laboratories, Eindhoven, Holland

Résumé. -

Le changement de l'aimantation

a

cause d'un champ magnétique a été étudié dans le cas des couches ferromagnétiques du nickel-fer (environ

3

% Ni), qui possèdent des courbes d'hystérésis isotropes et rectangulaires. Les résultats obtenus pour les couches d'une épaisseur

d,

qui est plus large que

2

pm, conforment

à

ce qu'on attend d'une paroi qui pénètre parallèlement

à

la surface dans la couche. La mobilité de cette paroi est principalement limitée par les courants de Foucault. Pour les couches avec une épaisseur

d

<

2

pm le changement de l'aimantation peut être décrit par une relation analogue

à

celle pour une transition de phase isothermique. La dimension de la croissance des domaines inversés diminue avec une diminution de l'épaisseur des couches, si l'épaisseur est au-dessous de

1

pm. Il en résulte qu'en ce cas les parois se déplacent

à

une distance d'environ

1

pm et que le coefficient d'amortissement est de

a N 0,2.

Abstract. -

The magnetization reversa1 due to an applied pulse field of FeNi films (ca.

3 %

Ni), which possess an isotropic square hysteresis loop, is studied. The results obtained on thick films

(d

>

²

pm) are in accordance with the concept of a wall parallel to the surface moving inwards.

The motion of the wall is damped mainly by eddy currents. For thin films

(d

<

2

pm) magnetization reversa1 can be described by a relation anaIogous to an existing one which describes an isothermal phase transition. It follows that the number of directions in which the reversed domains can grow decreases with decreasing film thickness for a thickness below

1

pm. From this fact it is derived that the walls travel a distance of about

1 pin

in this case, and a value for the damping coefficient

a N 0.2

is obtained.

1. Introduction. -

This paper deals with magnet- ization reversal, due to an applied pulse field, of ferromagnetic FeNi films (ca.

3

% Ni). These films are prepared by electrodeposition on drawn copper wire substrates and possess an isotropic square hysteresis loop. The speed of magnetization reversa1 is charac- terized by the switching parameter

S, =

z(H - Ho), where z is the time needed for magnetization reversal, H the applied field, and Ho the threshold field below which no major wall displacement occurs. The damp- ing of wall motion arises from spin relaxation and eddy currents, resulting in a relaxation and eddy current contribution to

Sw.

It depends on the film thickness which of these two dominates. Based on this fact the results can roughly be divided into two groups, those films with thicknesses above 2 pm where

S,

is determined by eddy currents and below 2 pm where

Sw

presumably arises from spin relaxation. Together with the results a short discussion is presented in

terms of the wall damping and wall geometry during reversal. Information concerning the electrochemical conditions that lead to films possessing a square hysteresis loop can be found in reference [la].

Details concerning the experimental set up, and theoretical considerations concerning the damping of wall motion and the kinetics of magnetization reversal in terms of wall geometry will be published elsewhere [lb], here only the main results are given.

2.

Results. -

The films are deposited on drawn copper wire substrates, which have a diameter of 0.5 mm, and have a length of about 3 cm. To measure the magnetization reversal, the film is put in a solen- oid, through which current pulses of alternating polarity are sent, thus driving the magnetization each way in the axial direction of the wire. The induced voltage, picked up by a sense coil, is displayed on a sampling oscilloscope and written by an xy recorder.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1968220

MAGNETIZATION REVERSAL O F ELECTRODEPOSITED FeNI FILMS C 2

-

141

To integrate the output voltage a planimeter was used.

Figure 1 shows the variation of

Sw

with the film thickness, d. Above a thickness of 2 ym,

Sw

approaches a d2 dependence which is represented by the dashed

r

os

^{I I ,}

0.1 1 1 O

--+ d p m l

FIG. 1. - The switching parameter, S,, as a function of the film thickness, d. The dashed line represents a d2 dependence.

line. Below this thickness

Sw

is much less dependent on d, reaching a minimum at about

d =

0.4 ym. The total flux density switched remained constant as a function of the thickness and the applied field. In al1 cases a value of about 0.75 times the saturation density was observed. We will now examine successive-

O O. 2 O. 4 0.6 0.8 1.0

-, t

FIG. 2. - The output pulses for various film thicknesses for an applied field of 41 CE. The numbers in the figure refer to the film thickness in pm with the appropriate output pulse.

f is measured in microseconds.

ly the results of (a) films with d > 2 ym, and (b) films with d < 2 ym.

a)

Figure 2 shows the induced voltage as a function of time for different values of

d; and for H =

41 CE.

Characteristic is the asymetrical shape which appears for d 2 4 Pm, and also the fact that the output pulses are identical except for their duration. The time dependence of the output voltage from about the peak of the output till near its end is t-0.55, as can easily be verified by plotting the output voltage on a double logarithmic scale.

The results indicate that a wall parallel to the sur- face moves inwards, which explains the fact that the output pulses are identical a t the beginning, as the wall does not

⁽⁽

know » the distance that lies ahead.

There is also the fact that a wall moving in this fashion, and which is damped by eddy currents, gives rise to a t-0.5 dependence of the induced voltage as a function of time which is very close indeed to the observed dependence. Moreover, the

d Z

dependence of

Sw

already suggests that damping of the domain wall motion mainly arises from eddy currents.

This wall, parallel to the surface, may be formed out of growing reversed domains near the film surface followed by their subsequent coalescense, as suggested by Bean and Rodbell [2].

b) The magnetization reversal can be expressed by

:

M

=

Mr[l

-

2 exp ( - N. V(t) }] , ₍₁₎

where M is the magnetization per unit volume, M, the remanence (strictly speaking calling this the reman- ence is of course only permitted if the reversible magnetization is negligible), N is the number of nucleation centres per unit volume, and V ( t ) represents the volume of growing reversed domains.

Generally N can be a function of time, i.e. new nucleation centres are formed during reversal. As, however in nearly al1 square loop materials

z-'

is directly proportional to (H - Ho), N should be a constant in Our case, i.e. only growth of pre-existing domains occurs. If we further assume a distinct type of growth and a wall velocity which does not depend on the position of the wall, relation (1) reduces to

:

where n is a constant which is equal to the number of directions in which reversed domains can grow, which briefly will be called the dimension of growth, and Kn a constant which is proportional to un, where

v

is the domain wall velocity.

This relation is similar to one derived by Hilberg [3],

but also to the much older relations Avrami [4]

derived for an isothermal phase transition. For if the wall velocity does not depend on the position of the wall, i.e. the time during reversal, magnetization reversa1 is completely analogous to the kinetics of an isothermal phase transition which does not involve a change in mean composition. This fact was already pointed out by Pavlov and Sirota

[5],

however, as they were probably unfamiliar with Avrami's work they limited themselves to the case of a constant nucleation rate during reversal, which is not realistic in Our case.

Incidentally it may be remarked, that relation (2) with n

=

3 gives exactly the same result as Haynes [6]

obtained for growth of ellipsoidal domains, and with n

=

2 agrees with Lindsey's mode1 [7] for cylindrical domains. However, the relation above is not limited to one particular geometry. From relation (2) the shape of the output pulse can easily be found by differentiat- ing M with respect to time. Figure

3

represents the

FIG. 3. -The drawn curve represents the output pulse of 1 pm film due to an applied field of 14.5 ^(E. The dashed curve represents the theoretical curve for n = 3. The dotted curves are obtained by extrapolating the major peak, which makes it possible to separate the initial and the major peak.

observed output pulse of a 1 pm thick film together with the theoretical curve for n

=

3, which is represent- ed by the dashed curve. By extrapolating the experi- mental major output peak, as indicated by the dotted curve, the contribution of the initial peak can be separated from the total output pulse. As wil be noticed, the agreement between the theoretical curve and the major peak obtained is satisfactory. If relation (2) is valid, plotting log [- ^In L ~ ~ ] ^against

log t gives a straight line, the slope of which gives n.

Figure 4 shows the result of this plot for films 0.4

and 1 pm thick. For the 1 pm film plots are given both for the total output pulse and the major peak, by the drawn and dashed line respectively. Notice that at the

Mr-M

RG. 4. ^- Zn

(-iM;)

as a function of time is represented for two values of d ; crosses : 0.4 pm, triangles : 1 pm. The dashed curve represents the plot for the major:peak of the 1 pm ,film.

beginning of the total output n

=

1. This seems to agree with Nitzan's idea of inelastic minor wall displace- ments causing the initial peak [8]. The major peak gives n

=

3. The 0 . 4 pm film gives

n =

1 for the whole output pulse. For the sake of completeness it should be remarked that this 0 . 4 pm film was deposited on an electropolished substrate. Not polishing the substrate results in a somewhat higher value of n.

Figure 5 shows us n as a function of d, obtained for

the major peak. An increase of n is observed with

increasing d, up to d

N

1 pm. For larger thickness a

slight decrease of n is found. The results of films depos-

ited on polished substrates are also plotted. This

decrease of n with decreasing d for a film thickness

below 1 pm can be partly explained by the fact that if

the average dimension of a region of reverse magnetiza-

tion is of the order of the film thickness, the dimension

of growth of this region must necessarily decrease as

growth in a direction perpendicular to the film sur-

face ceases. As this will start to occur if d

N N i 1 I 3 ,

MAGNETIZATION REVERSAL OF ELECTRODEPOSITED FeNI FILMS C 2

-

143

FIG. 5. -The dimension of growth n as a function of the film thickness, d ; the circles represent films on electropolished substrates, the triangles films deposited on substrates which are not polished.

where No is the number of nucleation centres per unit volume, the experimental result means that No ^N 10'' c m w 3 and the average distance between nucleation centres

1

N cm.

Assuming that the minimum value of

Sw

observed arises from relaxation only, and the distance a wall must travel equals

1

% 1OP4 cm, the relation calculated by Kittel

[9] Sw,

N

ally6,

where

a

is the damping constant,

y

the magnetomechanical ratio, and

6

the wall thickness, leads to

a

N 0.2.

References

[l] LEMS (W.), a) Philips Res. Repts., 1967, 22, 388 ; b) Ibid. 1968, 23, 62.

[2] BEAN (C. P.) and RODBELL (D. S.), J. appl. Physics, 1955,26, 124 ; Ibid. 1955,26,1318.

[3] HILBERG (W.), 2. angew. Physik, 1963, 16, 339.

[4] AVRAMI (M.), J. Chem. Physics, 1939, 7, 1103 ; Ibid.

1940, 8, 212 ; Ibid. 1941, 9, 177.

[5] PAVLOV (V. 1.) and SIROTA (N. N.), SOV. Phys. Sol.

State, 1964, 6,990.

[6] HAYNES (M. K.), J. appl. Physics, 1958,29, 472.

[7] LINDSEY (C. H.), P~oc. ZEE, 1959,106 C, 117.

[8] NITZAN (D.), IEEE Trans. on magn., 1966, 2, 751.

[9] KITTEL (C.), Phys. Rev., 1950,80,918.