ITINERANT ELECTRON FERROMAGNETISM IN INVAR ALLOYS

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ITINERANT ELECTRON FERROMAGNETISM IN INVAR ALLOYS

M. Shimizu

To cite this version:

M. Shimizu. ITINERANT ELECTRON FERROMAGNETISM IN INVAR ALLOYS. Journal de

Physique Colloques, 1971, 32 (C1), pp.C1-1115-C1-1116. �10.1051/jphyscol:19711397�. �jpa-00214437�

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PROBLEME DE L'INVAR ET DE QUELQUES ALLIAGES

ITINERANT ELECTRON FERROMAGNETISM IN INVAR ALLOYS

M. SHIMIZU

Department of Applied Physics, Nagoya University, Nagoya, Japan

RbumB. - Le modele du ferromagnktisme itintrant permet de discuter qualitativement et quantitativement la dkpendance en temptrature de I'aimantation et de la susceptibilitt magnktique des alliages de FeNi (Invar). On tient compte du melange mttastable des phases ferro et paramagnktiques dans la condition de Stoner tlargie de ferromagnetisme pour expliquer une chute rapide et continue de I'aimantation ainsi que les autres anomalies de 1'Invar.

Abstract. - The temperature dependence of the magnetization and the magnetic susceptibility for fcc Fe-Ni Invar alloys are discussed qualitatively and quantitatively in the model of itinerant electron ferromagnetism. The metastable mixing of the ferro- and para-magnetic phases in the extended Stoner condition of ferromagnetism is taken into account to explain a rapid and continuous drop of the magnetization and other anomalies for Invar alloys.

The anomalous properties of Invar alloys were explained before by Kondorsky and Sedov [l] and Weiss 121 in the model of semi-localized moment.The extendLd Stoner conditions of itinerant electron ferromagnetism [3] were applied to the Invar problem by Shimizu and Hirooka [4] and Mizoguchi [5]. A first- order transition was predicted at about 30 at

%

Ni in fcc Fe-Ni alloys. On the other hand, Mathon and Wohlfarth [6] suggested that these aIloys are very weak itinerant ferromagnets. However, the values of the density of states V(E) at the Fermi level of fcc Fe-Ni alloys are fairly large, so that it is difficult to expect the very weak itinerant ferromagnetism without a consi- derable change of v(E). In this paper magnetic properties of fcc Fe-Ni alloys are examined in the same model as before [4] and by taking into account the metastable mixing of ferro- and para-magnetic phases.

In the model of itinerant electron ferromagnetism [3] the equilibrium value of the difference between free energies in the ferro- and para-magnetic states AF, can be expandcd as a function of Ni concentration x in fcc Fe-Ni alloys at the critical concentration x,, where M drops suddenly to zero, as

AF, ⁼

-

A(x

-

xc) (1) with A = (2 [,

-

[+ - [-

+ 5,

M:), and x, can be expanded at lower temperatures and at weak field H a s

with I,, = (M,/A)

>

0 and

2 1

IT ⁼( & n Z k2(2vp - v + - V-) -

5,

M, ) A - , where [,, [+, and [- are Fermi levels of the para- magnetic and ferromagnetic

+

spin and

-

spin states at xc ⁼xo = 0.296 when T ⁼OOK and H = 0, v,, v+, and v- the corresponding values of v(E), Mc the value of M at xo, i. e., about 2 pB per atom, and

5,

and

5,

the coefficients in the change of a molecular field coefficient a given by Aa = 2 <,(x

-

xo)

+

2

CT

T'.

By (2) H extends and T narrows the ferromagnetic region. The transition temperature Tc at H ⁼0 is obtained from AF, ⁼0 as T? = (X

-

xO)/AT, as found in experiments where 1, = 4 x lo-' o K - ~ [7].

Now, the ratio between probabilities of alloys with x in the ferro- and para-magnetic p h a ~ e s f ; ~ , ~ / ( l

-

f x T H ) is assumed to be given by exp(- AFm/kTo) as these

two phases are separated by an energy barrier of the height A (cf. curve (3) in Fig. 2 of ref. 3) and from (1) we have

where q = A/(kTo) and To is an effective temperature for the two magnetic phases to co-exist. The mean magnetization is given by

where MxT, is the magnetization of a pure ferromagnetic phase with x and its temperature variation for H = 0 at lower temperatures is given by the sum of T,/' term due to spin waves and a, T2 term due to Stoner excitations, and

x,

is the susceptibility of the paramagnetic phase. From (2)-(4), we have at H = 0.

- -

where M,, = MxT0, Mx = Mxoo is a straight line of the Slater-Pauling curve, and f, ⁼fxo,. The value of a;

is estimated from the V(E) shown before [4] as a;

--

lo-* OK-' at x = 0.3 and is very small. The best agreement. between the calculated and observed [8] values o f M X o = M,

f,

is obtained by ^r]= 35.6 in f,. From (3) and (5) with AT = 4 x lo-' OK-' [7]

and q = 35.6, a2 is calculated as shown by curve a in figure 1, and curve b is obtained by the same assump tion of the distribution of x as before [4]. Small open [8] and solid [9] circles in figure 1 are the experi- mental values obtained from the observed M-T curves and the values of calculated by the data of spin wave spectra.

The mean magnetic susceptibility is given from (2)- (4) as

where x,,, is the so-called high-field susceptibility. A main part of the dependence on T of ji,,, due to spin waves vanishes at 0 OK. At 0 ^OK,(6) can be written as

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711397

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.I- \\.

^a t w o magnetic phases

b concentratcon d8str$Dullon _o CrangleB Hallam (1963)

i

f C o c h r a n e ~ Graham (1970)

FIG. 1 . - Calculated (curves a and b) and observed (small circles) results of the coefficient a2 of T2 term in M-T depen-

dences for fcc Fe-Ni alloys.

where

x''

is the sum of the average of the usual high- field and paramagnetic spin susceptibilities,

xhf,

and

xos,

and orbital susceptibility and here its value is e. m. u.

assumed as a constant, 2.5 x lod4 ---

,

for all x.

mole

From (3) and (7) and the observed value of

zxH

for x = 0.35 a t about 50 kOe and 4.2

OK

[lo], the value of 2 , is determined as

A,,

= 2.3 x Oe-'. By using this value of A, and q = 35.6, the values of

5ix0

are calculated from (3) and (7) as shown by curve a in figure 2, where curve b is obtained in the same way as before [4] by adjusting the value of AH so as to fit the observed value of

Lo

at x = 0.35. The

xPs

below

x = 0.296 and

zhfs

above x = 0.296 are shown by broken curve and the observed values for fcc Fe-Ni alloys [9, 101 are shown in figure 2. The main field

8 6 a s ela 9 0

\ .

^at w o magnet~c phases

I

b c o n c e n t r a t ~ o n d t s t r ~ b u t ~ o n

- 0 \ a

0 Yamada e t a 1 (1970)

L---_---__---

3 0 4 0 50

at.% Ni in Fe-Ni

FIG. 2. - Calculated (curves a and b) and obsewed (small circles) results of susceptibility for fcc Fe-Ni alloys.

dependence of

X,,

is obtained from the shift of x, given by (2), and

, %,

is very large even at very high field. From the values of

v,

A,, and A, and the shape of

V ( E ) [4] used above, the values of To, t,/a, and t,/u are

obtained as 166 OK, 0.3, and 1.2 x lo-' 0KV2, respectively, and this To is comparable to the value of A/k = 243 OK at x = 0.3 [4].

Finally, it is concluded that the combined model of the first-order transition in the band model with the mixing of two magnetic phases can satisfactorily explain the various observed anomalies of Invar alloys.

References

[I] KONDORSKY (E. I.) and SEDOV (V. L.), J. Appl. Phys. [7] BOLLING (G. F.), ARROTT (A.) and RICHMAN (R. H.)

1960, 31, 331 S. Phys. Stat. Sol., 1968, 26, 743.

[2] W~rss (R. J.), Proc. Phys. Soc., 1963,82, 281. [8] CRANGLE (J.) and HALLAM (G. C.), Proc. Roy. Soc., [3] SHIMIZU (M.), Proc. Phys. Soc., 1964, 84, 397 ; 1965, 1963, A 272, 119.

86, 147.

[4] SHIMIZU (M.) and HIROOKA (S.), Phys. Letters, 1968,

Igl

^'OCHRANE ( R v and GRAHAM (G. ^J.

27 A, 530 ; 1969, 30 A, 133. Phys., 1969, 48, 264.

[5] Mrzocucw (T.), J. Phys. Soc. Japan, 1968, 25, 904. [lo] YAMADA ( 0 . 1 9 PAUTHENET (Re) and P l c o c ~ ~ (J. C.), [6] MATHON (J.) and WOHLFARTH (E. P.), Phys. Stat. ^{t h ~ s}Conference.

Sol., 1968, 30, K131.