Thermoelectric power of Gd(Al1-xCux)2

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Thermoelectric power of Gd(Al1-xCux)2

T. Yamamoto, J. Sakurai, Y. Komura

To cite this version:

T. Yamamoto, J. Sakurai, Y. Komura. Thermoelectric power of Gd(Al1-xCux)2. Journal de Physique Colloques, 1979, 40 (C5), pp.C5-120-C5-121. �10.1051/jphyscol:1979542�. �jpa-00218959�

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JOURNAL DE PHYSIQUE Colloque C5, supplément au n° 5, Tome 40, Mai 1979, page C5-120

Thermoelectric power of Gd^Al^xCu^

T. Yamamoto, J. Sakurai and Y. Komura

Faculty of Science, Hiroshima University, Hiroshima, 730, Japan

Résumé. — Le pouvoir thermoélectrique (PTE) de composés intermétalliques GdCAlj - ^ C u ^ est mesuré dans la gamme de température 10 ~ 250 K. La contribution magnétique au PTE due à l'ordre ferromagnétique au-dessous de Tc varie progressivement et change de signe en fonction de la concentration x de Cu. Ce fait semble donner une indication évidente de la conception de l'interaction d'échange partielle Jt dans le modèle RKKY entre les composants de Fonde partielle des électrons de conduction et les (4f) électrons.

Abstract. — The thermoelectric power (TEP) of the intermetallic compounds GdCA^ ^xC\ix)2 was measured in the temperature range 10 ~ 250 K. Magnetic contribution to the TEP from ferromagnetic ordering below rc varies gradually and changes its sign as a function of the Cu content x. This fact seems to give a clear evidence of the concept of the partial exchange interactions J^t in RKKY model between the spartial wave components of conduction electrons and the (4f) electrons.

The electrical resistivity of the GdCAlj ^ C u ^ sys- tem was previously measured by us [1] (we call it as Paper A). The resistivity contribution due to disorder- ed magnetic moments of Gd above the ferromagnetic Curie temperature Tc was found to depend very much on x. This fact was understood to give an experimental evidence that the exchange constant J of RKKY interaction is not a mere constant, but is the sum of exchange interactions Jt between (4f) electrons and the partial wave components of conduction electrons. The thermoelectric power (TEP) is proportional to the energy derivative of electrical conductivity and will reflect the exchange constant of the RKKY interaction more subtly and profoundly than electrical resistivity does. The results of our measurements of TEP of Gd(Al^t _^xCu^x)² are reported in this paper.

Q / 50 X > ^ 1 0 0 1 5 0 \ 260 250

\ X x=ooo

- 3 - T(K)

Fig. 1.—Examples of thermoelectric power (TEP) of Gd(All_ICac)2

are plotted against the temperature. The arrows indicate the ferro- magnetic Curie temperature Tc.

Sample is prepared by arc-melting. Gd(Alx -.xCu^)2 . 0 ^ x ^ 0.30 have the cubic C1S crystal structure and are ferromagnetic. Details are to be referred to Paper A. The method of TEP measurement is standard one.

The TEP of some samples is plotted against the temperature T (K) in figure 1. Above Te, the TEP is that due to electron diffusion (Se) and is proportional to temperature. dSjdT for GdCA^ _xCux)2 changes gradually its value and also its sign as the variation of x as shown in figure 2. Below Te, but not at very low temperature where magnon or phonon drag may be important, TEP consists of Se and a second contri- bution (Sm3g) due to onset of ferromagnetic order.

Smag is thus the difference between observed value of TEP and S^ extrapolated from high temperature region T > Ta. With the assumption of a constant exchange interaction J of the RKKY theory between

la

1 / *

0 ~/ 010 020 O30 -1 • X

Fig. 2. — ASJdT, the slope of line of TEP for T > Tc shown in figure 1, of Gd(Alj _,Cux)2 is plotted against Cu content x.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979542

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THERMOELECTRIC POWER OF Gd(A1,-,CuJ,

a single s character band and (4f) electrons, Kasuya

-

gave an expression for S as follows [2], Y wT

where z is equal to H,/kT, H, being the molecular field effective for (40 electrons, H,, the molecular field effective for conduction electrons, is equal to 2@ - 1) ( j, ) J, E, is the Fermi energy and others are with standard meanings. Using the values of S,,, at T = 0.8 T, together with the Brillouin function with S = 712, the energy ratio J / E , is estimated from eq. (1) and is plotted in figure 3. The value as well as the sign of J for Gd(A1, _,Cu,), is seen to change with the variation of x (E, could be well supposed to be a constant for our compounds) ; this fact is outstanding because it contradicts with the starting assumption for eq. (I), namely J being a constant. From figure 3, the value of J becomes zero for x around 0.08 ; this fact again contradicts with the observation [I] that Gd(A1,-,Cu,), is always ferromagnetic with Tc smoothly varying for 0.0 < x < 0.30. Thus we concluded inapplicability of eq. (1) for TEP of our sample. Instead, we tried to incorporate, into TEP calculation of RKKY theory [2], the partial wave

Fig. 3. - JIE,, the constant of exchange interaction divided by the Fermi energy, estimated from TEP values of Gd(A1,-xCu,), at T = 0.8 T, using eq. (1) is plotted against Cu content x.

approximation of a general band structure, and the resulting partial exchange interactions Ji as discussed by Freeman and Watson as given by [3]

After long calculation with certain approximations, the expressions corresponding to equation (1) are obtained for the case H,/kT 4 1 as follows [4] :

where Di is the normalized state density of i-th partial wave (C ^Di⁼¹⁾^andbi is the energy derivative of Di. S,,, is noted to be proportional to H, which is, here, equal to 2(g - 1)

<

^J,⁾ ^.Ii^{Di. For}

Gd(Al1 -.CuX)2

with different values of ^s,each of J i may be assumed to be constant, but D i is expected to change. Therefore our samples may have either sign of H, and hence of S,,,, while they are always ferromagnetic. (The Curie temperature is related to the sum of J?.) We believe

that the observation of the change of sign of S,,, gives a new and strong experimental evidence of the necessity of concept of the component exchange interaction Ji, reconfirming our conclusion in Paper A.

The sign of S, depends on Di and Di in eq. (3). While in figure 2, dSe/dT for T > T, is seen to change the sign for x near to 0.03. This fact seems to indi- cate that the component state densities Di for Gd(A1,-,Cux), is actually changing with the variation of x.

References

[I] SAKURAI, J., ISHIMASA, T. and KOMURA, Y., J. Phys. Soc.

Japan 43 (1977) 1589.

[2] KASUYA, T., Prog. Theor. Phys. 22 (1959) 227.

[3] WATSON, R. E. and FREEMAN, A. J., Phys. Rev. 152 (1966) 566.

[4] SAKURAI, J., Unpublished.