CRITICAL BEHAVIOUR OF AMORPHOUS FERROMAGNET

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CRITICAL BEHAVIOUR OF AMORPHOUS FERROMAGNET

T. Mizoguchi, K. Yamauchi

To cite this version:

T. Mizoguchi, K. Yamauchi. CRITICAL BEHAVIOUR OF AMORPHOUS FERROMAGNET. Jour-

nal de Physique Colloques, 1974, 35 (C4), pp.C4-287-C4-290. �10.1051/jphyscol:1974453�. �jpa-

00215644�

JOURNAL DE PHYSIQUE Colloque C4, suppliment au no 5, Tome 35, Mai 1974, page C4-287

CRITICAL BEHAVIOUR OF AMORPHOUS FERROMAGNET

T.

MIZOGUCHI and

K.

YAMAUCHI Department of Physics, Gakushuin University

1-5-1 Mejiro, Toshimaku, Tokyo, Japan

Rbumk. - Le comportement critique A proximite de la temptirature de Curie d'un khantillon C o 0 , 7 B u , 2 P ~ . ~ ferromagnetique amorphe a ete etudiC en detail. 11 a CtC montre que la transition de phase est, du second ordre defini par les indices critiques :

B

:= 0,402

+

^{0,007, y = 1,342 f 0,025}

et 6 = 4,39 i 0,05. L'Bquation gknerale d'Ctat s'applique bien dans ce cas. L'alliage amorphe apparait cornme un corps ferrornagnbtique isotrope ideal dans la region critique, oh les fluctuations de I'aimantation sont a longue port&.

Abstract. -- The critical behaviour near the Curie temperature of an amorphous ferromagnet C O O . ~ B O . ~ P O . ~ was investigated in detail. It is proved to show the definite second order phase transition with the critical indices /I = 0.402

c

0.007, y = 1.342 f 0.025 and 6 = 4.39

+

0.05.

The general equation of state holds. The amorphous alloy can be the ideal isotropic ferromagnet in the critical region where the fluctuation of the magnetization becomes long ranged.

2. Experimental procedure and results.

- An amorphous ferromagnetic Co alloy, Coo,,Bo~,Po,,, was prepeared by splat quenching from the melt in a plasma jet furnace. Details of the sample pre- paration were given elsewhere [3]. With this alloy, accurate magnetization measurement are able to be made for the metastable amorphous phase, because 0 its Curie temperature is much lower than the crys-

1. Introduction.

^- For recent years remarkable external fields. The output of the magnetometer and progress has been made in the study of critical pheno- the electro-motive foice of a copper-constantan mena near phase transition. The Curie point of a

ferromagnet is a typical example of the critical point of the second order phase transition, and so far detailed

experimental

studies have been given for several

typical ferromagnetic crystals

[I].

Experimental results

.. -..

show that the equations of state derived from the scaling law

[2]

is valid for those ferromagnetic crystals.

In the present paper an interest is taken in the critical behavior of spin glass, amorphous or disor-

dered spin system, where atomic moments are

. .

^.

. . . . . .

. . _{. .}

.

. .

arranged randomly in space. In this case interactions

. . . . . . . . . . . . .

.

. . . . . .

between atomic moments are not definite even for

. . . . . . . . . .

^.

.

tallization temperature. The measurement were carried

RG, - The temperature dcwndence of the magnetization out by means of

a

vibrating magnetometer near Tc of an amorphous Coo.iBo.2Po.1 alloy in the various with slowly varying temperatures near T, in constant external fields.

the nearest neighbour pairs, but have necessarily a distribution. Individual moments may also be varied according to their microscopic environments. Is there a definite critical point in spin glass systems ? It is expected that characteristic features of a random spin system would be revealed by an experimental ₁₀ study of the critical behaviour of amorphous or disordered alloys.

.

. . . . . . _.

_.

. . . . . . . _. . . . . . . . . . _. . . .

.

.

. . ^{* e x}

I

.

.

. . . . .

_.

. . . . . .

^{7 < 5 j}

-

. _{. .} . . . . . . . . . 1

. . . .

.

. .

.

I

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974453

C4-288 T. MIZOGUCHI AND K. YAMAUCHI

thermo-couple which indicates the temperature of the specimen were alternately measured with a digital volt-meter and recorded automatically.

The experimental results of the temperature depen- dence of the magnetization near T, in various external fields are shown in figure 1. Here magnetization was evaluated at every 0.5 OC by the interpolation from the nearest sets of raw data.

3. Analysis and discussion.

-

The following asymp- totic relation have been proposed for the critical behaviour of the magnetization M of a ferromagnet near the Curie temperature T,,

lim M -

^{M ,}

^{u (T,}

^-

^{T ) ~ ,}

H-.O

(T < Tc) (1)

Here H and Tare the magnetic field and temperature respectively. The scaling law gives a relation between above critical indices,

Furthermore it is expected that the following equation of state of the scaled magnetization and the scaled

field,

165 170 175 180 T

Mi

I -

Tc

lo

⁼ (Hi

I -

^Tc

Ips)

(5) ma. 3. - The temperature dependence of the spontaneous

holds for any system that undergo the second order

magnetization, Ms.

phase transition.

First the spontaneous magnetization M, and the

FIG. 2. - M2.5 VS. (H/M)0.75 for various temperatures ^FIG. 4. - The temperature dependence of the inverse initial

near T,. susceptibility

~5'.

CRITICAL BEHAVIOUR OF AMORPHOUS FERROMAGNET C4-289

initial susceptibility X, must be evaluated. Eq. (3) and eq. (4) suggest that the plots of Mila vs. (H/M)'IY should be alined on a straight line at T,. However the value of p and

y

have not yet been known. Arrot and Noakes [4] found that M2.5 _{VS. plots} at constant temperature near T, are alined on a straight line for Ni metal. The same plots for this amorphous alloy are shown in figure 2. The dema-

FIG. 7.

-

The magnetization curve at T,.

RG. 5. - (d In Ms/dT)-1 vs. Tplots.

FIG. 8. - M/ I T - Tc VS. H/ 1 T - Tc

la6

plots for the amor- FIG. 6. - (d In X i l / d ~ ) - l vs. T plots. phous Co0.7Bo.zPo.l alloy.

C4-290 T. MIZOGUCHI A N D K. YAMAUCHI

gnetizing field correction was made for the thin foil

specimens with their surface parallel to the field.

M , and

x i 1 were obtained by the linear extrapolation of those plots and shown in figure 3 and figure 4.

In order to get the precise value of T,, 0 and

^{y ,}

Kouvel and Fisher [5] proposed the (d In M , / d ~ ) - l vs. T o r (d In X i l / d ~ ) - l vs. T plots, as a linear relation should be expected for those plots from the relation (1) or (2). Results are shown in figure 5 and figure 6.

Slight discrepancy from the linear relation is observed about 7 OC or more above Tc in figure 6. The magne- tization curve at

Tc is given in figure 7, from which

we get the critical index 6.

The obtained critical indices and Tc are

=

0.402 + 0.007,

y =

1.342 + ^{0.025 ,}

6

=

4.39 + 0.05 and T,

⁼

179.30

f

0.07 OC .

The relation between critical indices, eq.

(4),

is satisfied.

Figure 8 shows the

M/

I

^{T -} Tc

IP vs. H/ I T

-

T, lP'

plots for various field and temperatures near Tc.

The plots indicate strongly that the general equation of state, eq. (3, holds for the amorphous fer'romagnet.

It should be noted that the amorphous ferromagnetic alloy has a definite Curie temperature as the critical point of the second order phase transition in spite of the randomness of the microscopic circumstances.

In the critical region the fluctuation of the magneti- zation becomes long ranged, therefore the microscopic randomness may be averaged out. In this sense it would be allowed to say that an amorphous alloy can be an isotropic ideal ferromagnet in the critical region.

Finally some experimental investigation of critical behaviour for disordered Cuo.,Nio,, alloy is mentioned very shortly. In this disordered alloy the general asymptotic relations of critical phenomena seem to hold only at temperatures very close to the Curie point (1 T

-

Tc I/Tc 5 0.006). In this narrow tempe- rature range the homogeneous spin fluctuation over the whole spin system is supposed to be realized.

Acknowledgment.

-

The authors are indepted to Dr. Sekizawa and Dr. Okada, Institute of Physical and Chemical Research, for the loan of a vibrating sample magnetometer.

References

[I] KADANOEF, L. P. et al., Rev. Mod. Phys. 39 (1967) 395. [4] ARROTT, A. and NOAKES, J. E., Phys. Rev. Lett. 19 (1967) 786.

[2] WIDOM, B., J . Chern. Phys. 43 (1965) 3898.

[3] MIZOGUCHI, T., YAMAUCHI, K. and MIYAJIMA, H., Proceed- r51 KOUVEL~ J. M, and M. ^E.y P h ~ s . Rev. 136 ings of the International Conference on Magnetism, A 1626.

Moscow, 1973.