THERMAL EXPANSION AND MAGNETOSTRICTION OF WEAK ITINERANT FERROMAGNETS Sc3In AND ZrZn2

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THERMAL EXPANSION AND

MAGNETOSTRICTION OF WEAK ITINERANT FERROMAGNETS Sc3In AND ZrZn2

E. Fawcett, P. Meincke

To cite this version:

E. Fawcett, P. Meincke. THERMAL EXPANSION AND MAGNETOSTRICTION OF WEAK ITIN-

ERANT FERROMAGNETS Sc3In AND ZrZn2. Journal de Physique Colloques, 1971, 32 (C1),

pp.C1-629-C1-631. �10.1051/jphyscol:19711214�. �jpa-00214040�

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FERROMA GNETISME FAIBL E

ET ANTIFERROMAGNETISME ITINERANT

THERMAL EXPANSION AND MAGNETO STRICTION OF WEAK ITINERANT FERROMAGNETS Sc,In AND ZrZn,

E. FAWCETT

Bell Telephone Laboratories, Murray Hill, New Jersey, U. S. A. (*) and P. P. M. MEINCKE

Physics Department, University of Toronto, Canada

Resume.

-

Le coefficient de couplage magnetoClastique de ZrZnz et ScJn est determine par des mesures de dila- tation thermique et de magnktostriction. I1 est relit par ]'equation de Belov a la variation mesuree de la temp6rature de transition Ic en fonction de la tempkrature. Pour ZrZn2 I'accord est raisonnable, mais la comparaison est plus difficile pour ScsIn, a cause d'effets non lineaires dans des champs faibles, attribuks a l'anisotropie magnetique et de la variation de Cen fonction de la temperature. On trouve que la quantite a In Tc/2w (w est la determination) est 120 pour ZrZnz et

-

45 pour Sc3In.

Abstract. - The magnetoelastic coupling coefficient C is determined by thermal expansion and magnetostriction measurements in ZrZn2 and Scsln, and related through the Belov equation to the directly-measured pressure-dependence of the transition temperature Te. For ZrZn2 there is reasonably good agreement, but comparison is difficult for Sc3In because of non-linear effects at low fields attributed to magnetic anisotropy and also the temperature dependence of C, We find that the strain dependence

8

In Tc/2w is 120 for ZrZnz and

-

45 for Sc31n.

The magnetic and magnetoelastic properties of a weak itinerant ferromagnet can be described by the Belov equation for the thermodynamic potential [I],

which we have generalized by ascribing temperature dependence to the susceptibility x(T) and the magneto- elastic coefficient C(T). In ZrZn, the magnetic iso- therms [2] and measurements of the magnetostriction and thermal expansion published by Ogawa et al. [3,4]

and ourselves [5] show that x and C are essentially temperature independent. The volume strain o is quadratic in the magnetization M(H, T), as expected from Eq. (1) which for aF/;/do = 0 gives

The value of C obtained from the large positive magnetostriction is greater by about 50 % than the value obtained from the zero-field thermal expansion, which is negative and quadratic in temperature since from Eq. (I) for dF/dM

⁼

0 we have

This discrepancy was attributed [4, 51 t o a

⁽⁽

non- magnetic electronic

D

contribution to the thermal expansion. From our magnetostriction data the value of the pressure dependence of the transition tempera- ture Tc is [I],

where f2 is the molecular volumc. This is in reasonably good agreement with the value aTC/dp = - 2.4 OK/kbar

(*)

Present address

:

Physics Department, University of Toronto, Canada.

obtained [I] from the data of Ogawa et al. [2] and with the directly-measured value [6],

With Tc = 25.80K for our sample and a rough estimate of the compressibility,

K

-- 10-12, we obtain a huge value for the logarithmic volume-dependence of Sc31n is a weak itinerant ferromagnet [7], which Tc, 8 In Tc/ao - ^120.

however shows both field dependence and temperature dependence of X. When the magnetic isotherms for our sample of composition Sc3.,,In are plotted as in figure I , the large deviation from linearity at low

+

ⁱ^no1^{I emu}

FIG. 1. -

Magnetic isotherms of Sc3In.

fields indicates significant effects not included in Eq. (1) and presumably due to magnetocrystalline anisotropy. This restricts the analysis of our thermal expansion and magnetostriction data to the high-field region where x is still temperature dependent but only weakly field-dependent. In this region the magne- tostriction approaches a quadratic field-dependence, but as shown in figure 2 the thermal expansion at the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711214

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C

1

- 630

E. FAWCETT

AND P. P. M. MEINCKE

FIG. 2.

- Magnetostriction and thermal expansion of Sc,In as functions of magnetization.

same field and temperature appears to be a quite different function of M2. This indicates a temperature dependence of C(T) which gives for the coefficient,

KC^ ⁼ ( a ~ / a M ' ) ~ , corresponding to thermal expan- sion in a constant field H, the value,

At the point P in figure 2 the magnetostriction coeffi- cient, KC^ ⁼ ( a ~ / a M ~ ) ~ , has the value

KC^ ⁼

^-

26 x lo-" (e. m. ~ . / r n o l e ) - ~ , whereas the cc thermal expansion >> coefficient is,

KC^ ⁼ - 8.4 x lo-'' (e. m. u./mole)-' .

When we substitute these values in Eq. (2) with M 2

=

0.92 x lo6 (e. m. u./mole)' and

( d ~ ~ / d ~ ~ ) ,

= -

0.0125 x lo6 (e. m. u./mole/deg)' we obtain

(a~C(73/aT')M =

=

- 0.24 x 10-" (e. m. u./mole/deg)-' .

The thermal expansion is very field-dependent except where the three curves cross in figure 3. It is interesting that this occurs close to the transition temperature in zero field, Tc -- 6 OK, which is consistent with Eq. (1).

The corresponding field-independent value of the coefficient, tiC,(TC) = 3 x/(dkf2/dl"), is

- 15 x lo-'' (e. m. u . / m ~ l e ) - ~ . It is of interest to evaluate the pressure dependence of the transition temperature for comparison with the direct measurements [7]. The latter were performed by the c( transformer technique >> in which Tc is iden- tified by the singularity in the initial susceptibility, xo(TC), and so gives the pressure dependence of the zero-field value of T,. Unfortunately the susceptibility at low fields is highly field-dependent and temperature- dependent as shown in figure I, so that the zero-field value from Eq. (3) of the pressure dependence of T,, (dTc/ap)H=,

=

- 2 tiC(T,) xO(Tc) Tc Q, can be

FIG. 3. -

Lincar thermal expansion of ScsIn parallel the applied field H.

determined only very approximately from our data.

The high-field value can be determined more accura- tely since 31 is almost field-independent when

HIM 2 12 (e. m. u./mole)-'

in figure 1. In this region at Tc

2:

7.5 OK (the high-field value) we estimate from figure 1 the value,

z(Tc) = 2.15 x (e. m. u./mole) .

The value of KC(T,) extrapolated from the low- temperature magnetostriction with the above values of

KC^ and ( a ~ c ( T ) / a T ' ) ~ at 1.5 OK is

icC(TC)

= -

40 x lo-'' (e. m. ~ . / r n o l e ) - ~ .

Substitution in Eq. 3 gives dTc/dp = 0.80K/kbar, which is considerably larger than the low-field value determined by Gardner et al. [7],

It is interesting that KC,,(T,) calculated from the thermal expansion at Tc with no correction for the temperature dependence of C(T) gives a value, dTc/ap ⁼ 0.3 OK/kbar, in better agreement with the directly-measured pressure dependence of Tc. The logarithmic volume-dependence of T, corresponding to our value, aT,/dp

=

0.8 OK/kbar, and the compressi- bility

^K⁼

23.4 x 10-l3 c. g. s. is alnTc/ao = - 45.

These very large values of alnTc/ao result from the strongly-enhanced susceptibility rather than an unu- sually large value of the volume dependence of the exchange interaction. Thus writing

x

=

1/2(t - I)-' x(I

=

O),

where I ⁼ IN(&,) is the product of the exchange interaction and the density of states a t the Fermi surface, and x(I = 0) is the paramagnetic susceptibi- lity without exchange enhancement, we obtain,

For ZrZn, with (7

^-

I ) - ' -- ²⁵⁰ ^{[I] and}

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THERMAL EXPANSION AND MAGNETOSTRICTION OF WEAK ITINERANT FERROMAGNETS C

1

- 631 we obtain a ln ?/am z 1 . The striking difference between Acknowledgements. - We are indebted to E. Co- Sc,In and most other ferromagnets is that 8 In I/ao, renzwit for the Sc,In sample and to L.-F. Holmes while still of order unity, is negative. for the magnetization measurements.

References

[I] WOHLFARTH (E. P.), J. Phys. C . (Solid St. Phys.), 144.1 MEINCKE (P. P. )M. and FAWCETT (E.), Solid State

1969, 2, 68. Comm., 1969, 7 , 1643.

[2] OGAWA (S.) and SAKAMOTO (N.), J. Phys. Soc. Japan, [5] WAYNE (R. C.) and EDWARDS (L. R.), (priv. comm.).

1967, 22, 1214. [6] GARDNER ( W . E.), SMITH (T. F.), HOWLETT (B. W . ) , [3] OGAWA (S.) and WAKI (S.), J. Phys. Soc. Japan, 1967, CHU (C. W.), and SWEEDLER (A.), Phys. Rev.,