Thermal and thermoelectric properties of granular Co-Ag solids

~ ELSEVIER

Journal of Magnetism and Magnetic Materials 136 (1994) 221-228

Journalof materials

Thermal and thermoelectric properties of granular Co-Ag solids L. P i r a u x a,., M . C a s s a r t a, E . G r i v e i a, M . K i n a n y - A l a o u i a, V. B a y o t J. S a m u e l J i a n g b, J o h n Q . X i a o h, C . L . C h i e n b

a,

a Unit# de Physico-Chimie et de Physique des Mat#riaux, Universit# Catholique de Louvain, Place Croix du Sud 1, B-1348 Louvain-la-Neuve, Belgium b Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21218, USA Received 22 October 1993; in revised form 27 January 1994

Abstract

We report measurements on the temperature and magnetic field dependences of the thermal conductivity, thermoelectric power, and specific heat of granular Co20Ags0 solids annealed at various temperatures. Giant magnetothermal conductivity and giant magnetothermopower are found to be correlated with the giant magnetoresistance. Thermal conductivity is dominated by its electronic contribution, and the Wiedemann-Franz law is found to be satisfied between 2 and 300 K, indicating that large-angle electron scattering processes dominate. The thermoelectric power is negative and its magnitude is considerably reduced by the annealing process. The contrasting relationship between electrical resistivity and thermoelectric power on annealing and in applied field is curved and discussed. No marked variation of specific heat with magnetic field in relation to the giant magnetoresistance has been observed. At very low temperatures, i.e. below T ~ 1 K, a nuclear contribution to the specific heat appears, whose temperature and magnetic field dependences have been explored.

1. Introduction

The discovery of giant magnetoresistance in granular solids [1,2] with values exceeding 80% [3] has created considerable excitement, and prorides a new prospect towards the understanding of this spectacular effect first observed in magnetic multilayers [4,5]. Recently, the correlation between the thermal and thermoelectric transport properties and giant magnetoresistance has been investigated in multilayers [6-9] and in granular magnetic systems [10]. Giant magne-

tothermal conductivity and giant magnetothermopower have been identified for both magnetic systems. In this paper, we expand on our previous reports on the thermal and thermoelectric transport properties of granular C o - A g solids. We report and discuss experimental data on the temperature and magnetic field dependences of the thermal conductivity, thermoelectric power, and specific heat of granular Co20Ags0 solids for various annealing temperatures.

2. Experimental

* Corresponding author.

For our thermal transport measurements, we have used high-rate magnetron sputter deposition

0304-8853/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0 3 0 4 - 8 8 5 3 ( 9 4 ) 0 0 2 6 4 - R

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L. Piraux et aL /Journal of Magnetism and Magnetic Materiab 136 (1994) 221-228

to fabricate very thick ( ~ 100 I~m) and substratefree films. The samples of Co20Ag80 (20 vol%) have been sputtered at room temperature, and subsequently annealed at various temperatures (TA) of 200, 330, 480, and 605°C for 10 minutes in a high vacuum furnace to create a medium of granular Co, a few nm in size, embedded in Ag. The granular nature of the samples has been confirmed by both X-ray diffraction and transmission electron microscopy. The detailed sample characterizations have been described elsewhere [3]. Thermal conductivity and thermoelectric power under a magnetic field (up to 30 kG) between 2 and 120 K have been measured using a traditional static h e a t / s i n k four-probe method. Measurements up to room t e m p e r a t u r e in zero magnetic field have been done in a different setup using a special low-loss sample holder specially designed for thin films and fibers. The details of these sample holders and measurements have been described previously [8,11]. The specific heat measurements were performed by means of a system based on the relaxation-time method [12] in the t e m p e r a t u r e range 0.3-300 K and under magnetic fields up to 15 tesla.

the value of 2.45 × 10 -8 V 2 / K 2 for a free electron system. For ordinary metals, where thermal conductivity is purely electronic (K ~ KE), the W - F law (2) applies only at low t e m p e r a t u r e (elastic defect scattering) and above the Debye temperature (large-angle e l e c t r o n - p h o n o n scattering). For intermediate temperatures, the W - F law breaks down because the effectiveness of small-angle e l e c t r o n - p h o n o n scattering in degrading electrical transport is less than for thermal transport and the left-hand side of Eq. (2) is much less than L o [13]. For ordinary alloys, the impact of impurity scattering is twofold. First, the W - F law is obeyed over a more extended temperature range. Second, it reduced KE to a value comparable to the lattice thermal conductivity /(L SO that the measured total thermal conductivity is composed additively of both components (Eq. (1)). For the samples of Co20Ag80 annealed at TA = 330, 480, and 605°C, x ~ KE and the W - F law is found to be satisfied between 2 and 300 K. Such a behavior is illustrated in Fig. 1 showing the data in zero magnetic field for the sample

100 3. Results and discussion 3.1. Thermal conductivity

10

In general, thermal conduction in solids proceeds via two processes: lattice vibrations and free-carrier transport. The total thermal conductivity can be written as K = KE + KL

(1)

where r E and r L are the electronic and lattice contributions respectively. For electrical conductors, the results of the electrical and thermal transport are related by the W i e d e m a n n - F r a n z ( W - F ) law KEP T

=L°

(2)

where p is the electrical resistivity, T is the t e m p e r a t u r e and L o is the Lorenz n u m b e r with

0.1

~

T2

I 10

I 100

T (K) Fig. 1. T e m p e r a t u r e d e p e n d e n c e of the t o t a l t h e r m a l conductivity r for granular Co20Ags0 samples (12: as-deposited

sample; o: sample annealed at TA = 605°C) in the M = 0 state. The solid line is the electronic thermal conductivity r E computed using the Wiedemann-Franz law [Eq. (2)] and the zero-field resistivity data. The lattice component r L for the as-deposited sample is also shown (<>).

L. Piraux et al. /Journal of Magnetism and Magnetic Materials 136 (1994) 221-228 with TA = 605°C. The validity of the W - F law over so wide a t e m p e r a t u r e range gives support for dominant large-angle scattering processes, which mainly arise from elastic scattering at the interfaces and within the two metallic media. There are also contributions to the resistivity due to scattering from phonons and other thermal excitations, although these are relatively small as attested by the small increase of resistivity with increasing t e m p e r a t u r e (Pa00K//P4.2K ~ 1.5). A strict validity of the W - F law in granular C o - A g above T ~ 100 K might, therefore, suggest that the inelastic scattering processes are incoherent, i.e. without conservation of q, giving rise to large-angle scattering. In contrast, one should expect deviations of the W - F law if the temperature-dependent part of the resistivity is dominated by small-angle electron scattering in some t e m p e r a t u r e range. The maximum deviation of the W - F law caused by small-angle electron scattering has been roughly estimated using the p ( T ) data for the Co20Ag80 sample with TA = 605°C. In this calculation, it is assumed that the temperature-dependent term of p ( T ) undergoes the theoretically predicted deviation of the W - F law for a defectfree metal [13], as shown in Fig. 2. In this figure L / L o (with L = K p / T ) is plotted against T / O D

1

0.8

~

/f /

° 0.6

/ / /

0.4 0.2

I I

00

//~x, I defect-free t metal I

I

I

I

i

0.2

0.4

0.6

0.8

1

1.2

T/o D Fig. 2. Temperature variation of L / L o ( . ) with L = ~¢p/T for the Co20Ags0 sample annealed at TA= 605°C. The solid line shows the maximum deviation of the W-F law caused by small-angle electron scattering. The dashed curve shows how L/Lo varies with T/OD for a defect-free metal.

223

curve (O o is the Debye temperature). The data showing the experimental L / L o for the sample annealed at TA----605°C and the so-estimated maximum deviation of the W - F law are also collected in Fig. 2. For Co20Ag80, specific heat measurements gives Ol> ~ 220 K (see below), which is close to the value for pure silver (OD ~ 215 K). As shown in Fig. 2, the so-estimated K p / T (solid line in Fig. 2) falls by about 10% below L 0 in the t e m p e r a t u r e range 80-300 K. Given the experimental uncertainties of our measurements (indicated by the error bars in Fig. 2), no definitive conclusions can be drawn. Furthermore, the lattice contribution to the total thermal conductivity amounts to a few percent in the t e m p e r a t u r e range 80-300 K, so that it cannot be totally neglected. In contrast, for the as-deposited sample, the lattice contribution to the thermal conductivity KL amounts to about 20%, a r o u n d T ~ 100 K, of the total thermal conductivity (Fig. 1). The lattice component has b e e n estimated with reasonable accuracy by subtracting KE from the total measured thermal conductivity for T < 200 K, where heat losses by radiation; are significantly reduced. As shown in Fig. 1, KL reaches a maximum value of ~ 2 W / m K aroundi T ~ 100 K. At low temperatures, KL approaches a T 2 variation, indicating that phonon scattering from conduction electrons dominates [13]. The reduced lattice contribution to the thermal conductivity in the annealed samples can be understood as follows: annealing leads to a strong decrease in p or increhse in KE (a factor of 4 - 8 for TA > 300°C), whilel it has a much smaller impact on the lattice cOmponent, which is mainly determined by p h o n o n - e l e c t r o n scattering at low temperatures and by p h o n o n - p h o n o n U m k l a p p processes at high temperatures. As a result, the lattice component contributes less than 5 - 1 0 % of the total thermal conductivity in the annealed samples and cannot be determined accurately. U p o n the application of a magneti c field, very large increases in thermal conductivity are observed, correlating with giant magnetoresistance. Results showing the changes with magnetic field in electrical and thermal conductivities on the samples with TA = 480°C and TA = 605°C are re-

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L. Piraux et al. /Journal of Magnetism and Magnetic Materials 136 (1994) 221-228

ported in Fig. 3. In this figure 8/< = r ( H ) - r ( H = 0) and Btr -- t r ( H ) - o,(H -- 0) with tr = 1 / p . It may be seen that &r and 8 r have the same magnetic field dependences, while their magnitudes are in accordance with the W - F law, i.e. 8 x ~ L o T & r . At T ~ 6 K, the electrical and thermal magnetoconductivities are & r / t r ~ 65% and 48% and 8K/x ~ 59% and 44% for the samples with TA = 480"C and TA = 605°C respectively. The small differences between the two relative variations can be ascribed to residual heat losses through the support and connecting wires to the film sample. In Fig. 4, we compare the magnetic field dependence of the electrical resistance and thermal gradient (which is proportional to the thermal resistance) at T ~ 1.9 K for the as-deposited sample. It was previously shown that a maximum in resistance occurs at the coercive field where magnetization is zero [2]. For this particular sample of relatively low thermal conductance, the heat losses represent an appreciable quantity of the power dissipated in the sample heater, and the thermal conductance cannot be estimated accurately. However, the results of Fig. 4 provide a nice illustration of the correlation between the electrical and thermal transport phenomena in granular C o - A g solids.

1.3

I

I

I

I

I

-2

-1

0

1

2

I

I

a

1.2 1.1

1 0.9 0"8'--3

3

H (T) I

I

I

b

0.42 0.4 0.38 "¢1

0.36 0.34 0.32.

-2

-1

0

1

2

3

H (T) Fig. 4. The magnetic field dependence of the electrical resistance R (a) and thermal gradient AT (b) at T = 1.9 K for the as-deposited Co20Ags0sample.

3.2. Thermoelectric p o w e r

,...,

G 0.5

0-- /I 0

J

L

0.4

I

0.8

I

I

1.2

1.6

2

n (T) Fig. 3. Comparison between the giant electrical and thermal magnetoconductivities at T = 6 K for Co2oAgsa samples annealed at T^ = 480"C and TA= 605"C. The symbols are 8K while the dashed lines represent LoT&r.

Fig. 5 shows the temperature dependence of the zero-field thermoelectric power S of granular Co20Aga0 solids at various annealing temperatures. For each samples, S ( H - - 0 ) is negative at all temperatures and the magnitude increases linearly with temperature above T ~ 100 K, suggesting a dominant diffusion thermopower in this temperature range. Around T ~ 70 K, a small negative hump is also observed for each sample. Recent thermoelectric power measurements performed on a Co2oAgs0 granular system with TA = 300"C [14] also revealed a linear T dependence for T > 100 K. However, at lower temperatures

L. Piraux et al. /Journal of Magnetism and Magnetic Materials 136 (1994) 221-228

(i.e. below T ~ 25 K), a change in sign in S(H = O) was reported in Ref. [14], contrasting with the results of Fig. 5. Though the general behavior of S(T) is similar for all samples studied, the magnitude of the thermoelectric power depends sensitively on the annealing temperature TA, i.e. I S I decreases progressively with increasing TA. Since the annealing process also strongly reduces the resistivity of the granular Co20Ags0 solids, the large decrease in I SI with increasing TA likely reflects the change in scattering mechanisms associated with the formation of a phase-separated granular structure with distinct Co and Ag entities. The room-temperature variation of thermoelectric power with the inverse resistivity for Coz0Ag80 solids is plotted in Fig. 6. Of particular interest is the contrasting S vs. O behavior of C o - A g solids under a magnetic field. For all samples, going from the high resistivity state ( M = 0) to the low resistivity state ( M = M s) leads to an increase in [SI. This feature is illustrated in Figs. 7a,b where the magnetothermopower, 8S = S ( H ) - S(H = 0), is curved as a function of 8(1/0) = 1/p(H) - 1/p(H = 0). In addition, a linear relationship between the thermoelectric power and the inverse resistivity has been observed on each sample at all temperatures studied. Some typical data showing the lin-

-4

i

,-,

-4

llt

-6

rll

I

I

I

I

I

i 50

100

~50

20o

250

-8 -10 -12 -14 0

300

T (K) Fig. 5. Thermoelectric power S as a function of temperature in zero magnetic field for the as-deposited Co20Aga0 sample (o) and the samples annealed at TA= 200"C (o), TA= 480"C (o) and TA= 605"C (o).

q

i .aAd

t

/ f

-6 f

-8

/

/

J

/ / -10 -12

/

/ I

P

O 0.02

I 0.04

0.06

0.08

lip

106(flcm)

0.1

0.12

0.14

"t

Fig. 6. Room-temperature plot of the zero-field thermoelectric power versus the inverse resistivity for Co20Agso solids.

earity in the plot of 6S vs. 6 ( l / p ) are collected in Figs. 7a,b. Using the usual Mott expression for the diffusion thermoelectric power [15]

•r 2 k 2 T I a l n p l

s = 3]ei t---if-,

(3)

it was shown [14,16] that the relationship between

S(H) and o(H) can be expressed as B

S( H) =A + p( H----~

(4)

A = (PdSd -- PsSs)/(pd -- p,) and B = Ps) with Pd ( S d ) and Ps (Ss) resistivities (thermopowers) in the demagnetization state and fully magnetized state. In a recent work on a Co20Aga0 granular system [14], deviations from this inverse relationship were found below T = 75 K. This is not consistent with our experimental observations. It is pointed out that the same linearity in t h e S vs. 1/O curves has been observed in C o / C u multilayers in the temperature range 50-300 K [17] and in F e / C r multilayers at room temperature [7], as well as in the liquid helium temperature range [8]. However, in F e / C r mulfilayers, a clear departure from linearity has been observed in the intermediate temperature range, where the magnetothermopower is the sum of two components of opposite sign [8].

PdPs(Ss- Sd)/(Pa-

elI

i

/

where

0

225

L. Piraux et al. /Journal o f Magnetism and Magnetic Materials 136 (1994) 221-228

226

Fig. 8 shows the total change in thermopower between the M = 0 state and the saturation state, /iS, as a function of temperature. For all samples, /iS is negative and its magnitude clearly scales with that of the zero-field thermoelectric power, so that the largest values of AS are obtained for the as-deposited sample. In addition, for this particular sample, the temperature dependence of /iS below T ~ 60 K is similar to that of the zero-field thermopower (see Figs. 5 and 8). On the other hand, IASI is much smaller in the samples with TA = 480°C and 605°C, and the temperature dependences can hardly be discerned

I

°'i"

4,'~

'

o '

c)

T A = 605°C

-1

:3.

-2

-3 as-deposited -4

0

I

i

I

J

20

40

60

80

100

T (K) OI

I

I

I

605°C

Fig. 8. T e m p e r a t u r e dependence of the total magnetothermopower, AS, for the as-deposited Co20Ags0 sample (e) and the samples annealed at TA = 200°C (o), TA = 480*C ( ~ ) and TA = 605°C (o).

-0.2

-0.4 =L r,o

-0.6 -0.8 a -1 0

I 0.02

I 0.04

I 0.06

0.08

~i(1/P) lO~(~cm) "1 0( _

T=5K

o6

i"

-1.2

T

8.5~.

with good precision due to experimental uncertainties. It is pointed out that the values of AS for the as-deposited sample are also much larger than those observed in magnetic multilayers. Indeed, previous magnetothermopower measurements performed on C o / C u and F e / C u multilayers [8] showed that AS is very small at low temperature (i.e. typically AS <0.5 I~V/K for T < 50 K). A model based on a dominant contribution from electron-magnon scattering to the thermoelectric power has been proposed to account for the large enhancement of AS above T ~ 50 K [8]. This interpretation of the magnetothermopower seems inconsistent with the very large values of AS observed on the as-deposited sample in the low temperature range.

3.3. Specific heat -1.8

-2.4 0

I 0.005

I 0.01

8(1/p)

10~(flem)"1

b 0.015

Fig. 7. (a) 8S = S ( H ) - S ( H = 0) vs. 8 ( l / p ) = 1 / o ( H ) 1 / p ( H = 0) at T = 72 K for granula r Coz0Ag80 solids annealed at various temperatures, as indicated; (b) same as in (a) for the as-deposited sample at three selected temperatures, as indicated.

The specific heat C of a granular Co20Ags0 sample between 0.3 and 200 K is shown in Fig. 9. The total specific heat is composed additively of an electronic component, a lattice component, and a contribution of nuclear spin orientation. However, the latter contribution to specific heat is only important at very low temperature, i.e. below T ~ 1 K, and gives rise to a huge Schottky peak in the millikelvin temperature range [18]. At

L. Piraux et al. /Journal of Magnetism and Magnetic Materials 136 (1994) 221-228

227

the lowest temperatures, the measured specific heat can be expressed in the form 0.05

(5)

C = y T + f i T 3 + a T -2

where yT is the electronic specific heat, /3T 3 is the lattice specific heat for T << @D and a T -2 is the nuclear specific heat. Fitting the low-temperature data shown in Fig. 9 using Eq. (5) gives Y ~ 2 × 10 -5 j g - l K - 2 , fl ~ 2.5 × 10 - 6 j g - l K - 4 , and a ~ 8.8 × 10 -6 j g - l K . The value of @D ~ 210 K follows from the value of/3. Calculation of t h e effective field Herf from the coefficient a gives Heel= 17.2 T, which is somewhat smaller than the value for pure Co [18] ( H e n ~ 22 T). The experimental C ( T ) curve for granular Co20Ags0 samples shown in Fig. 9 is consistent with the calculated one using the data for pure Co, Ag, and a Co volume fraction of 20%. The specific heat of the as-deposited sample was also measured for T < 2 K, and the results agree with those of the annealed samples within experimental error. In particular, the values of a or Heft for the as-deposited sample (or ~ 8.6 × 10 -6 j g - l K , H~ff = 17 T) remains almost unchanged with respect to those of the annealed sample. Since a modification in H~ff is usually observed in Cobased alloys [18], this result indicates that Co clusters already exist in the as-deposited Co20Ags0 sample. Fig. 10 shows the influence of magnetic field, up to 15 T, on the specific heat of the Co20Ags0

~

.

0.01

0.5

. . . .

•

14~

1

T (K) Fig. 10. Low-temperature specific heat for a Co20Agso sample with TA ffi 605°C in various magnetic fields. The symbols are the experimental data and the dashed and solid curves represent the fit using Eq. (5).

sample with TA = 605°C in the lowest temperature range. A drastic decrease in C is observed, due to the reduction of the a T -2 coefficient. Such behavior is ascribed to the fact that the internal effective field is negative in 3d transition ferromagnets [18], i.e. antiparallel to the direction of the magnetization. So, the maximum in the nuclear specific heat is expected to occur at smaller temperature in a large external magnetic field. In contrast, no marked variation of specific heat with magnetic field has been observed at T ~ 2.4 K where the contribution from the nuclear spins is negligible and where the lattice and electronic contributions are almost the same. In particular, no detectable changes in specific heat with magnetic field in relation to giant magnetoresistance have been found.

100 D

d~

/

10 1

4. C o n c l u s i o n s

/

0.1

/

q~nD ~

/

I

I

I

1

10

100

T (K) Fig. 9. Specific heat vs. temperature in zero magnetic field for a granular Co20Ags0 sample.

The temperature and magnetic field dependences of thermal conductivity, thermoelectric power and specific heat of granular Co-Ag solids have been investigated. The fact that the Wiedemann-Franz law holds is strong evidence that large-angle electron scattering dominates in these systems. For the annealed samples, since thermal conductivity is purely electronic, a giant magnetothermal conductivity effect of same magnitude than giant magnetoresistance is observed. The

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L. Piraux et aL /Journal of Magnetism and Magnetic Materials 136 (1994) 221-228

thermoelectric power is negative at all temperatures and its magnitude increases under a magnetic field while it is strongly reduced by annealing, giving rise to a contrasting S vs. p dependence. Finally, no detectable variation of specific heat with magnetic field in relation to giant magnetoresistance has been observed.

Acknowledgement The work performed in Louvain-la-Neuve was carried out under the financial support of the programme 'Action de Recherche Concert6e' sponsored by the 'DGESR de la Communaut6 Fran~aise de Belgique'. L.P. is a Research Associate of the National Fund for Scientific Research (Belgium). V.B. is a Senior Research Assistant of the National Fund for Scientific Research (Belgium).

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[3] J.Q. Xiao, J.S. Jiang and C.L. Chien, Phys. Rev. B 46 (1992) 9266. [4] M.N. Baibich, J.M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich and J. Chazelas, Phys. Rev. Lett. 61 (1988) 2472. [5] G. Binasch, P. Griinberg, F. Saurenbach and W. Zinn, Phys. Rev. B39 (1989) 4828. [6] J. Sakurai, M. Horie, S. Axaki, H. Yamamoto and T. Shinjo, J. Phys. Soc. Jpn. 60 (1991) 2522. [7] M.J. Conover, M.B. Brodsky, J.E. Mattson, C.H. Sowers and S.D. Bader, J. Magn. Magn. Mater. 102 (1991) 15. [8l L. Piraux, A. Fert, P.A. Schroeder, R. Loloee and P. Etienne, J. Magn. Magn. Mater. 110 (1992) [,247. [9] H. Sato, Y. Aoki, Y. Kobayashi, H. Yamarnoto and T. Shinjo, J. Phys. Soc. Jpn. 62 (1993) 431. [10] L. Piraux, M. Cassart, J. Samuel Jiang, John Q. Xiao and C.L. Chien, Phys. Rev. B48 (1993) 638. [11] L Piraux, J.P. Issi and P. Coopmans, Measurement 5 (1987) 2. [12] R.L. Fagaly and R.G. Bohn, Rev. Sci. Instrum. 48 (1977) 1502. [13] R. Berman, Thermal Conduction in Solids (Clarendon, Oxford, 1976). [14] J. Shi, E. Kita, L. Xing and M.B. Salamon, Phys. Rev. B 48 (1993) 16119. [15] F.J. Blatt, P.A. Schroeder, C.L. Foiles and D. Greig, Thermoelectric Power of Metals (Plenum, New York, 1976). [16] J. Shi, S.S.P. Parkin, L Xing and M.B. Salamon, J. Magn. Magn. Mater. 125 (1993) L251. [17] J. Shi, R.C. Yu, S.S.P. Parkin and M.B. Salamon, J. Appl. Phys. 73 (1993) 5524. [18] A.J. Freeman and R.E. Watson, in: Magnetism, vol. II A, ed. by G.T. Rado and H. Suhl (Academic Press, New York-London, 1965), p. 186.