Magnetic contribution to low temperature thermal conductivity of amorphous ferromagnets FexNi80−xB20

Journal of Magnetism and Magnetic Materials 72 (1988) 194-198 North-Holland, Amsterdam

194

MAGNETIC CONTRIBUTION TO LOW TEMPERATURE OF AMORPHOUS FERROMAGNETS Fe,Ni,_ ,I&-,

THERMAL

CONDUCTIVITY

P. SVOBODA and P. VASEK Institute of Physics, Czechoslovak Academy of Sciences, Na Slovance 2, 180 40 Prague 8, Czechoslovakia

Received 12 October 1987

A positive magnetic contribution K,(T) to the thermal conductivity of amorphous Fe,Ni,,_,B,c (x = 40,60) has been observed at temperatures T= 2-30 K. The results are qualitatively similar to those found earlier for crystalline Fe-based ferromagnets. They cannot be satisfactorily accounted for by the theory of thermal conductivity of amorphous ferromagnets published recently by Continentino and Pacheco.

1. Introduction

Recently, we have studied the low temperature (T = 2-30 K) thermal conductivity K(T) of amorphous FeXNi,,_,&O alloys in their ferromagnetic regime, i.e. for x 3 40 [l]. We have observed that external magnetic fields B led to a suppression of K(T) at T = 2 K, which is quite an opposite tendency to that found by Mtiller and Pompe in glassy Fe,,&, [2]. The magnitude of the change AK(B)/K(O) was found to reach about 8% in B > 3 T in all our samples, virtually independent on their composition. To elucidate the origin of this magnetic-field-dependent contribution to K(T), we have investigated its temperature dependence in the range T = 2-30 K and in longitudinal magnetic fields B up to 4 T. For the investigation the samples of Fe,Ni,&,-, and F%,Ni 20h0 were used.

2. Theoretical background It is well known both from magnetization measurements and neutron diffraction studies, that in ferromagnetic metallic glasses at sufficiently low temperatures spin wave excitations do exist [3]. Moreover, they can be more easily excited (due to smaller values of the spin wave stiffness D) than

those in analogous crystalline materials and they extend to unusually large temperatures up to about T,/2 [3]. One can thus reasonably expect, that these excitations can contribute to low temperature thermal conductivity. Such a contribution can be twofold. First, these excitations (i.e. magnons) can carry heat, which leads to a contribution K,(T). The total thermal conductivity is given as

where K,,(T) and K+(T) are the electron and phonon part, respectively. Suppression of K,(T) in a high magnetic field then causes a decrease of K(T). This behaviour was reported for crystalline Fe-based alloys [4,5], but as far as we know, it has not been detected in a metallic glass. Magnons can simultaneously act as additional scattering centres for other heat carriers, e.g. phonons. Phonon part of thermal conductivity can be written as K,,(T)

=

C@;,(T))-* 1

i

-‘,

(2)

I

where K&,(T) is a contribution of the i th scattering mechanism. Elimination of the magnon contribution KS(T) would thus enhance the value of K,,(T), i.e. one would observe an increase of the

0304-8853/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

P. Svoboa& P. Vaiek / Magnetic contribution to thetmal conductivi@

thermal conductivity in high magnetic fields. The same effect would have another magnetic-field-dependent scattering mechanism, e.g. the magnetic low energy excitations (MLEE) introduced by Herlach et al. [6] to account for their results obtained on paramagnetic PdSiCuM (M = Fe, Co) glasses. One of these two types of phonon scattering should be responsible for the marked increase of K,,(T) observed by Mtiller and Pompe in amorphous Fe,,&,, at T < 8 K for external magnetic fields up to 6 T [2]. Theoretical calculations of the magnon contribution K,(T) in amorphous ferromagnets have been recently published by Continentino and Pacheco [7]. They introduce three basic mechanisms limiting the magnon mean free path in an amorphous ferromagnet. First of them, the resonant scattering of magnons on structural two-level systems TLS, should be important at very low temperatures (T-c 1 K) only and it is thus irrelevant to our results. The other two mechanisms are the relaxation attenuation of spin waves on TLS and the “magnetic Rayleigh scattering” due to fluctuations in the exchange interaction arising from the static structural disorder. It is expected, that such magnon contribution K,(T) should be most easily observable in systems with small spinwave stiffness D and small spin-wave gap [7]. The theory predicts various types of temperature dependence of K,(T) in different special cases, but resulting formulae contain unknown parameters, which makes any quantitative estimate rather meaningless. It can be seen from fig. 2 in ref. [7], however, that external magnetic field suppresses the K,(T) and that the change AK,(T, B) = K(T, B = 0) - K(T, B) is predicted to decrease in magnitude with increasing temperature in the rangeT>lK. We have mentioned above, that a positive change AK&T, B) has been observed in crystalline Fe-Ni [4] and Fe-Co [5] alloys. The authors interpreted their results on the basis of the standard kinetic theory of thermal conductivity assuming that a meaningful relaxation time 7, can be defined for magnons. They were able to account for their results provided that magnon scattering is dominated by magnon-electron scattering mediated by the s-d exchange interaction in the

195

“dirty limit” l,,q, * 1, where I,, and qm are the electron mean free path and magnon wave vector, respectively. This mechanism (ignored in the analysis performed in ref. [7]) leads to a temperature dependence K,(T) - T312 [5].

3. Experiments The measurement was performed on amorphous ribbons Fe,Ni,%O and FGNi2,1$0, produced by the melt-spinning technique in the Physical Institute of the Slovak Academy of Sciences in Bratislava by P. Duhaj. Samples had a form of packets of 10 pieces cut from the ribbon, about 22 x 5.8 x 0.03 mm3 each, that were pressed together by two miniature copper clamps containing carbon resistor thermometers. Thermal conductivity was measured at temperatures T = 2-30 K by a standard stationary method in a vacuum chamber of the device described earlier [8]. Longitudinal magnetic fields up to about 4 T were generated by a superconducting solenoid. The relative error in the data has been limited mainly by the accuracy of the measured temperature gradient along the sample. It increases from below 1% at T-c 10 to 2% at higher temperatures. Absolute values of K(T, B) should be accurate to about 5% due to uncertainties in sample dimensions. A more thorough description of the experimental arrangement can be found in ref. [l].

4. Results and discussion Thermal magnetoconductivity of our samples at T = 2.2 K is presented in fig. 1. It can be seen that within the accuracy of our measurement the magnitude of AK(B)/K(O) is the same in both samples and it can be approximated by the dashed curve drawn in fig. 1. The curve saturates at B z 3 T and we expect that an external magnetic field B = 4 T is sufficient to remove any magneticfield-dependent contribution to K(T), i.e. we suppose that I&&T, B = 4 T) = 0. To subtract the electron contribution K,,(T), we have a used standard procedure based on the Wiedemann-Franz law. The law is expected to

P. Svoboab, P. VaJek / Magnetic contribution to thermal conductivity

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3

4

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I

I

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0,05

Fig. 1. Thermal magnetoconductivity AK(B)/K(O) = (K(T, B) - K(T, O))/K(T, 0) in longitudinal magnetic fields B at temperature T = 2.2 K: 0 - Fe,Ni,b,, 0 - FkNi,B,,.

I

I

I

I

I

I

2

3

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50

UK1

hold even in magnetic fields, since the elastic electron scattering dominates in a disordered structure [4]. For the residual resistivity p0 we have substituted the measured values of ~(4.2 K) [9]. Very weak temperature dependence p(T) [9] and small longitudinal magnetoresistance +p,, [lo] have been neglected in this procedure, but they would lead to deviations in K,,(T) that are well below resolution of our measurement. Temperature dependence of the quantity K,*(T) = K(T) - K,,(T) in fields B = 0 and B = 4 T is shown in fig. 2 for [Fe,] and in fig. 3 for [Fh] samples. In both cases we have detected a positive magnetic contribution K,(T) = K,*(T, 0) - K,*(T, B = 4 T), which increases in magnitude from about 8% of K,,( T, 0) at T = 2 K to nearly 20% at T + 30 K. The temperature dependence of K,(T) for both samples is given in fig. 4. It was obtained by subtracting the smoothed-out dependences drawn by solid lines in figs. 2 and 3, respectively, that were obtained by a simple polynomial fit to experimental data. This fit is less reliabled at higher temperatures T > 15 K, because the scattering in data points increases with temperature due to decreasing sensitivity of our carbon resistance thermometers. The temperature dependence of K,(T) can be reasonably well approximated by the power law K,(T) - T312 at temperatures T G 20 K for [Fe,] and T & 14 K for [Fh] samples. At higher temperatures the resolution of our measurement is clearly too low

Fig. 2. Temperature dependence of the quantity K,*(T, B) = K(T, B)- K,.(T) for the sample Fe,Ni,BzO: 0 - B =O, l - B = 4.02 T.

to allow any definite conclusions to be deduced. It is rather surprising, that our results are remarkably similar to those obtained for crystalline ferromagnets [4,5]. The theory designed specifically for amorphous ferromagnets predicts other

0,5

2

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0,2

G r‘ YE *y” 0,l

0,05

I

I

I

I

I

I

2

3

5

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20

30

50

T[Kl Fig. 3. Temperature dependence of the quantity K&(T, B) = K(T, B)- K,(T) for the sample FkNi,,bO: 0 - B = 0, 0 - B = 4.0 T.

P. Suoboda, P. Va.?ek / Magnetic contribution to thermal conductivity

types of the temperature dependence of K,(T) than that observed here for all particular mechanisms of magnon scattering discussed in ref. [7]. We can thus conclude, that in our amorphous samples the magnon-electron scattering via the s-d exchange interaction seems to be much more effective in limiting the magnon mean free path than any of the mechanisms originating from structural disorder suggested by Continentino and Pacheco [7]. We can see in fig. 4 that K,(T) is larger in [FG,] than in the [Fe,] alloy. Within the model discussed in ref. [5] it would imply, that the magnon lifetime 7, is larger in the former alloy and it should be related to a lower density of electron states at the Fermi level N(E,). This tendency is consistent with photoemission data for Fe,Ni,,_,B, glasses [ll]. As we have mentioned above, our results contradict those found by Mtiller and Pompe for seemingly very similar amorphous system Fe,,l&, [2]. In their case the K,(T) has been negative, which means, that magnons should be more effective phonon scatterers than heat carriers. The reason for this discrepancy is not known at present. The quantity K,*(T, B = 4 T) should be equal

TIKI 1 5-z sik5

; =3.z E

197

0,05

2

3

5

TLKI

10

20 30

50

Fig. 5. Composition dependence of the pure phonon part of the thermal conductivity K,,(T) = K,+(T, B = 4 T): 0 - Fe,Ni&&,, 0 - FqcNi2,,b0.

to pure phonon contribution, i.e. K,*(T, B = 4 T) = K,,(T). In fig. 5 we present the dependence of this quantity on the composition of the sample. Such a dependence has been dealt with in our previous paper [l], where in fact the quantity K,*(T,0) instead of Kph(T) was discussed. We have argued in ref. [l], that a magnetic contribution does not influence the conclusions on composition dependence of phonon thermal conductivity reached. It is confirmed by the data summarized in fig. 5, that shows, that the composition dependences of KJT) and K,*(T,0) are virtually the same for Fe,Nis,_,B,, glasses.

5. Conclusions

=21 -

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T%[K'~] Fig. 4. Temperature dependence of the magnetic contribution to the thermal conductivity K,(T) = Kp*( T, 0) - K$( T, B t: 4 T). Curves a and b correspond to Fe,Ni,Bzo and Fq,Ni,,B,,, respectively. Straight lines indicate the range, where the approximation K, - T3/’ holds.

For the first time in an amorphous ferromagnet, we have detected a significant magnon contribution K,(T) to the low temperature thermal conductivity. This contribution can be suppressed by a longitudinal magnetic field B = 4 T. The results are analogous to those found earlier in some crystalline ferromagnets [4,5]. They are not, however, in accord with predictions of the theory of thermal conductivity in amorphous ferromagnets [7].

198

P. Svoboda, P. V&k

/ Magnetic contribution to thermal conductivity

Magnetic contribution to K(T) found in our Fe,Ni,,_,&, glasses is opposite in sign to that observed in amorphous Fe,,B,. The origin of this discrepancy is unclear.

Acknowledgement

The authors wish to thank Dr. P. Duhaj for providing the samples investigated in this work.

References [l] P. Svoboda and P. VaSek, submitted to Phys. Stat. Sol.

121H. Miiller and G. Pompe, Solid State Commun. 59 (1986) 35. [31 F.E. Luborsky, J.L. Walter, H.H. Liebermann and E.P. Wohlfarth, J. Magn. Magn. Mat. 15-18 (1980) 1351. 141 W.B. Yelon and L. Berger, Phys. Rev. B 6 (1972) 1974. PI Y. Hsu and L. Berger, Phys. Rev. B 14 (1976) 4059. WI D.M. Her&h, E.F. Wassermam~ and R. Willnecker, Phys. Rev. Lett. 50 (1983) 529. 171 M.A. Continentino and R.P. Pacheco, Phys. Rev. B 32 (1985) 3234. 181P. VaSek, P. Svoboda and P. St&la, Czech. J. Phys. B 32 (1982) 791. 191 P. Svoboda and P. VaSek, J. Magn. Magn. Mat. 62 (1986) 331. WI S.N. Kaul and M. Rosenberg, Phys. Rev. B 27 (1983) 5698. VI K. Hricovini and J. Krempas~, J. Phys. F 15 (1985) 1321.