Cr multilayers

Journal of Magnetism and Magnetic Materials 110 (1992) L247-L253 North-Holland

Letter to the Editor

Large magnetothermoelectric power in Co/Cu, Fe/Cu and Fe/Cr multilayers L. Piraux a, A. Fert b, P.A. Schroeder c, R. L o l o e e c and P. Etienne d ° Unit~ de Physico-Chimie et de Physique des Mat~riaux, Unit,ersit~ Catholique de Loucain, place Croix du Sud l, B-1348 Louvain-la-Neuve, Belgium b Laboratoire de Physique des Solides, Universit( Paris-Sud, 91405 Orsay, France c Physics Department and Center for Fundamental Materials Research, Michtgan State Unit;ersity, East Lansing, MI 48824, USA d Laboratoire Central de Recherche Thotnson-CSF, 91404 Orsay, France Received 20 February 1992; in revised form 13 March 1992

We report and discuss experimental data on the thermoelectric power of magnetic multilayers. Measurements of the thermoelectric power of Fe/Cr, Co/Cu and F e / C u multilayers have been carried out in the temperature range 4 K < T < 150 K magnetic fields perpendicular to the layers. All specimens were found to exhibit pronounced magnetothermoelectric power (MTEP) effects correlating with their giant negative magnetoresistance. The main difference between the MTEP and the magnetoresistance is in their temperature dependence. Whereas the magnetoresistance is a decreasing function of temperature, the MTEP. at least in Co/Cu and F e / C u multilayers, is very small at low temperature and increases rapidly above 30-40 K. We ascribe this high temperature part of the MTEP to spin-dependent electron-magnon scattering ani] we propose a theoretical model.

1. Introduction In the last few years, measurements of the electrical resistivity in applied fields for multilayers composed of ferromagnetic and non-magnetic metals have led to the observation of "giant magnetoresistance (MR) effects" [1,2]. The electrical resistivity drops by several tens of percent when the magnetic field is sufficiently large to overcome the antiferromagnetic coupling between the neighbor magnetic layers. Models based on spin dependent scattering have been developed to explain this giant MR [3,4]. Recently, other transport properties of the magnetic multilayers such as Hall effect [5,6] and thermoelectric power [7,8] have also attracted interest. Sakurai et al. [7] have measured the thermoelectric power of F e / C r and C u / C o / N i ( F e ) multilayers in a magnetic field. They found very large magnetothermoelectric power (MTEP) effects correlated with the magnetoresistance. Also, Conover et al. [8] have car-

tied out MTEP measurements at room temperature on Fe(32 ,A)/Cr(x) superlattices with x --- 550 ~. They have found that the MTEP presents the oscillatory behavior as a function of the Cr layer thickness previously observed for the MR [9]. In this work, we present a detailed experimental investigation and analysis of the temperature and magnetic field dependences of the thermoelectric power of Co/Cu, F e / C u and F e / C r multilayers.

2. Samples and experimental methods We have studied (Col 1 ,~,,/Cu9 ,A) × 30, (Co19 ,~,/Cu9 ,~) × 30 and (Fel5 A / C u l 5 ,~,) × 60 multilayers prepared by sputtering at Michigan State University. The three samples are deposited on Si(001) with a buffer layer of iron. The preparation and characterisation are described elsewhere

0304-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved

LETTER TO THE EDITOR

1.. Piraux et aL / Magnetothermoelectric power m multilayers

L24~

[10,11]. In C o / C u , the Co and Cu layers are fcc with a pronounced (111) texture [10]. For Fe15 A,/Cul5 ,~, the Fe and Cu layers are bcc with (110) texture !11,12]. We have also studied a (001)bcc Fe26 A / C r 9 ,~ multilayer grown by MBE on a MgO(001) substrate at the LCR Thomson CSF. The thickness of the non-magnetic layers in these samples corresponds with maximum antiferromagnetic coupling between the magnetic layers at H = 0. Thermoelectric power measurements were performed using a static heat and sink four-probe method. Temperature gradients across the sample were generated by passing an electrical current through a 10 kfl metal-film resistance glued to a copper block in good thermal contact with the sample. At its other end, the sample was thermally bonded to the heat sink using G E 7031 varnish. The temperature gradient across the sample was measured using two carbon glass resistors carefully attached to the sample with G E varnish. The temperature of the sample holder was measured by means of a third carbon glass resistor. The thermometers were first carefully calibrated in several separate runs to check the reproducibility upon cycling. The power dissipated in each carbon glass sensor was limited to 10 -9 W in order to avoid self-heating. Electrical contacts to the sample for electrical conductivity and thermoelectric power measurements were made with platinum paste. Chromel, copper and superconducting NbTi wires were used for voltage measurements. The various voltages were measured using a Keithley K181 nanovoitmeter with a resolution of about 10 -8 V. Magnetic fields up to 5 T were provided by a superconducting magnet. The samples were mounted with the layers perpendicular to the applied magnetic field. Moreover, since both the MR and the MTEP were reversible (very weak hysteresis effects for all the samples), we performed the measurements in one field direction only. The magnetoresistance ratio (MR) is defined as

MR(H) = [p(H) -p(Hs)]/p(H~), where

p(Hs) is

(1)

the saturation value of the resis-

120 I I ~ ~

< [--

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t

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I

i

~

i r i i ----O-- Fe(26)~)/Cr(9,~)

---I-- Co(19,~)/Cu(9,~)

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~

20

o .... 0

-'~---~, ~ j ~ , ~ _ ~

1 2 MAGNETIC

~

3 F I E L D (T)

• 4

Fig. 1. M a g n e t o r e s i s t a n c e at 4.2 K for F e / C r , C o / C u and F e / C u m u l t i l a y e r s m e a s u r e d with the m a g n e t i c field p e r p e n d i c u l a r to the layers; the solid lines are g u i d e s for the eyes.

tivity at the magnetic field H s required to align the magnetization of all the layers. We define the M T E P as a S ( H ) = S ( H ) - S ( H = 0). We call AS the total change in thermoelectric power, i.e. A S = S ( H 5) - S ( H = O) = S F - SAF. In the above notations, SAF is the thermoelectric power for an antiferromagnetic arrangement and S v is the thermoelectric power when the magnetizations of adjacent layers are parallel.

3. E x p e r i m e n t a l results 3.1. M a g n e t o r e s i s t a n c e

The magnetoresistance of C o / C u , F e / C u and F e / C r multilayers at 4.2 K and in applied magnetic field perpendicular to the layers is shown in fig. 1. With increasing temperature, the MR decreases, rapidly for F e / C u and F e / C r multilayers, less rapidly for the C o / C u system. A1 these results are in good agreement with previously reported date on these three spin valve systems [3,9,10,11,13]. Note however that, in our measurements in perpendicular fields, the saturation field is always higher than in longitudinal fields. This is because the saturation is reached when the field overcomes both the interlayer exchange and the shape anisotropy. We also point out that the results on F e / C r are the first published for MBE growth on a MgO substrate. This

L E T T E R TO T H E E D I T O R

L. Piraux et al. / Magnetothermoelectric power in multilayers

gives a remarkably high MR, 108% at 4.2 K, i.e. the highest MR ever obtained for the F e / C r system.

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-1.0

3.2. MTEP Co / Cu multilayers The field de,pendence of the MTEP, shown for C o i l A / C u 9 A in fig. 2a, is similar to that of the MR (fig. 1), with saturation at about 2 T in both cases. A similar behavior is observed in a second sample, Co19 ~ / C u 9 ~,. The main difference between the MTEP and the MR is in their temperature dependence. Whereas the MR decreases at increasing temperature [10,13], the MTEP is very small at low temperature and starts increasing above 30-40 K. This appears clearly in fig. 3a where the total change in thermoelectric power, AS = S F - SAt , is plotted versus temperature; AS is positive and very small at low temperature, then becomes negative and increases steeply above 30-40 K. In fig. 4 we show separately the temperature dependences of the thermoelectric power coefficient in the AF ( H = 0) and F ( H > H s) states. Fe / Cu multilayer T h e field dependence of the MTEP, shown for Fel5 A / C u l 5 ,~ in fig. 2b, is very similar to that of the MR (fig. 1). As for the C o / C u system, the main difference between the MTEP and the MR is in their temperature dependence, l aS I increasing rapidly with T whereas the MR decreases rapidly [11]; the temperature dependence of the total MTEP at the saturation field, AS, is shown in fig. 3b. Fe / Cr multilayer The experimentally observed behavior for the MTEP is less simple in F e / C r than in C o / C u and F e / C u . The MTEP aS of a Fe26 A / C r 9 A multilayer is plotted vs. H at several temperatures in fig. 2c. The saturation field agrees with that of the MR, but the field dependence seems to be complicated by some competition between negative and positive contributions. The total change AS, shown in fig. 3c, is positive below 50 K then becomes negative between 50 and 120 K

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MAGNETIC FIELD (T) Fig. 2. MTEP as a function of magnetic field (perpendicular to the !ayers) for C o l l A / C u 9 A (a), Fel5 ,~/Cu15 A (b) and Fe26 A / C r 9 A (c) multilayers at selected temperatures, as indicated; the inset of (a) shows the positive MTEP at low temperature.

and changes again its sign at higher temperature. Experimental MTEP data from Sakurai et al. [7] on a Fe27 ~ / C r 8 A multilayer are also reported in fig. 3c. Though in their experiment the magnetic field was parallel to the layers, we see that the results are very similar.

LETTER TO THE EDITOR

L250

L Piraux et al.

/ Magnetothermoelectric p o w e r

in multilayers

4. Theoretical model I0

In Co/Cu, the MTEP is vanishingly small at low temperature and increases steeply above 3 0 40 K. In F e / C u , AS is thirteen times larger at 127 K than at 23 K. These strong temperature dependences of the MTEP argue in favor of contributions from thermally excited scattering

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On the other hand, the scattering of a spin ~ electron into a spin T state involves the creation of a magnon q and a decrease of the electron energy:

0.5 0.0

processes. We propose a mechanism based on e l e c t r o n - m a g n o n scattering. Considering the contribution from electronmagnon scattering to the thermoelectric power [14,15], the major point to notice is that the scattering processes are essentially different for the spin 1' (majority) and spin ~ (minority) electrons. A spin T electron of wave vector k can be scattered into a spin $ state of wave vector k' = k + q by annihilating a magnon q. The energy of the magnon, Eq, is transferred to the electron e;, ~ = % T + Eq.

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Fig. 4. Temperature dependence of the thermoelectric power coefficient in the A F (SAF) and F (S F) states for Cul I ,~/Co9 ,~ multilayer. Below 50 K, as the experimental data for SAF and S F could not be distinguished at the scale of the figure, only SAF has been plotted.

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rln

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100

150

200

TEMPERATURE

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250

300

(K)

Fig. 3. Temperature dependence of the MTEP at the saturation field, AS, for C o i l A / C u 9 ,~ (a), Fel5 , ~ / C u l 5 ,A (b) and Fe26 ,~,/C.r9 ,~, (c)multilayers. The data reported in ref. [7] for a Fe27 A / C r 8 A multilayer at higher temperature are also indicated in (c).

w(kT ~ k ' $ ) ~ f ( % ) [ 1 - f ( % + E q ) ] ,

(3a)

w(k$ ~k'T)~f(%)[1-f(%-E,)],

(38)

where f is the F e r m i - D i r a c distribution function. One immediately sees that the scattering rate will be maximum below and above the Fermi level for

LETTER TO THE EDITOR

L. Piraux et al. / Magnetothermoelectric power in multilayers

the spin 1' and spin 4' electrons respectively. Consequently, the derivative involved in the classical Mott expression of the thermoelectric power S ~ (1/wktw/dE, where w = ~ --I is the relaxation rate, will have negative and positive signs respectively. We have calculated these derivatives in the conventional model of the electron-magnon scattering based on 3D magnons (Eq -- Dq 2) and free electrons with different spin 1' and spin 4' surfaces [16,17]. Starting from the Mott formula [18] (not strictly valid but reasonably approximate for (1/q)dw/dE ~ (kBT)-I), we find [19]

31el

w

-(+)

31el R ( T ' '

(4) where R(T) is a coefficient of the order of unity which varies slowly with temperature (except at very low temperature where R vanishes exponentially). The main points can be summarized as follows: (a) S " 1' and S " ,[. have opposite signs, which results from the different signs of the derivative of the relaxation rate at the Fermi-level as expected from eqs. (3a) and (3b). (b) S " 1" and S " J, have the order of magnitude of w2ka/31el which results from the steep variation of w at the Fermi level, i.e. (1/w)dw/d~ = __(kBT) -l from eq. (3) with Eq =kBT. In contrast, the order of magnitude of similar terms arising from electric scattering is rather ~r2k2T/3lelev, thus smaller by a factor kBT/E F [18]. Now, we assume that the current is carried in two dependent channels by the electrons with spin + and spin - respectively. The resulting thermoelectric power is given by:

S = (i+S++i_S_)/(i.+i_),

(5)

where i÷ (i_) and S+ (S_) are the current density and thermoelectric power coefficient in the channel + ( - ) . First suppose that the only contribution to S+ and S_ is from electron-magnon scattering and also that the minority electrons are more strongly scattered, i.e. p 1" <

L251

spin + electrons ( s p i n - electrons) are, for example, spin1' electrons (spin4'electrons)in all the magnetic layers, with consequently, i_ ~ p - ~ T >> i ~ p - 1 4 ' and, from eq. (5), S F---S"1'. At zero field, in the AF state and for thin enough layers, the spin 1' and spin J, characters are symmetrically mixed in each current, which leads to a balance between positive and negative contribution to the thermoelectric power and to SAy = 0. T h e total change will be AS --- Sin1` = -'tr2ka/31el ( + s i g n for the opposite case p 1" >> p 4'). In fact, in addition to the electron-magnon scattering there are other scattering processes, primarily due to elastic scattering by defects or impurities. Consequently, the contribution from the magnons to the thermoelectric power must be reduced in proportion. Finally, the contribution from the magnons to AS can be expressed as follows [19] AS m

~r2kBR(T) (P $ -P1')(P,I, +/91`) -

31el

K

pl'

J,,

(6a) with

K= [pTp4' + p T 4'(pT + p J,)][p 1` + p J, +4p1" 4'],

(6b)

where p 1' J, is the so-called spin-mixing resistivity, proportional to the electron-magnon scattering rate [15]. A S " is negative for p 4' > p T and positive for p ,L < p 1'. As a function of temperature, [ A S " [ is zero at T = 0 K (pT4' =0), increases with p 1' 4', goes through a maximum for p 1' 4' = 0.5 (p 1' p 4' )1/2 and decreases to zero for p 1, 4' >> (p 1` p 4')~/2. By taking into account published data on p 1` 4' in ferromagnetic alloys [15] and the measured resistivity of our samples, a maximum above room temperature is expected. In the temperature range investigated in this work (with p 1" 4' relatively small compared to the residual resistivity), the order of magnitude of AS m should be "rr2ka/3lel ( = 240 × 10 -6 V / K ) reduced by the ratio of p 1' $ to the resistivity of the multilayer.

LETTER TO THE EDITOR

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L. Ptraux et al. / Magnetothermoelectric power in multilayers

In the next section, we discuss how the main features of the experimental M T E P results can bc explained by the e l e c t r o n - m a g n o n contribution. Of course, there should be additional contributions arising from spin-dependent elastic scattering. These additional contributions have certainly to be taken into account at low temperature when the magnon contribution vanishes. Nevertheless, our general feeling is that, in bulk ferromagnets [15] as well as in multilayers, the major contribution to the M T E P at not too low temperature should come from the e l e c t r o n magnon term.

5. Discussion of the results 5.1. MTEP at high temperature

We begin with the simpler case of the C o / C u and F e / C u systems. We propose to ascribe the rapid increase of the M T E P above 30 K to the onset of the contribution from e l e c t r o n - m a g n o n scattering calculated in the preceding section. The initial increase of this contribution is expected to be proportional to the spin-mixing term p 1' ,L. The existing data on p 1` $ (in bulk ferromagnets) indicate an increase approximately proportional to T 2 at low temperature (see for example ref. [15]) which, from eq. (6), would lead to AS roughly proportional to T 2, in reasonable agreement with the experimental data (figs. 2a and b). Taking published data for p T ,L in Fe [15] and estimating p 1`, p ,L from the resistivity of the multilayers leads to the correct order of magnitude for AS (via eq. (6)). Also, we point out that, although the M R is much higher in C o / C u than in F e / C u , their M T E P are not strongly different. This suggest a larger p 1` $ in F e / C u in agreement with a smaller value of the D constant of the magnon dispersion curve in Fe (in agreement also with the more pronounced temperature dependence of the MR in F e / C u ) . In F e / C r , AS becomes positive and starts increasing at about 120 K. In the data of Sakarai et al. [7] on Fe27 ,A/Cr8 ,~, this increase continues up to room temperature. The positive sign is predicted by eq. (6) for p T > p $ which is actually

in agreement with the strong resonant scattering of the spin 1" conduction electrons by Cr atoms in Fe (p + / p 1" --- 0.17 in bulk alloys). This is also in agreement with the theoretical arguments developed for multilayers by Inoue et al. [20]. In contrast, the negative sign of the M T E P for C o / C u and F e / C u corresponds to p 1' < p ,L, as expected from electronic structure arguments [11,21]. 5.2. M T E P at low temperature

At low temperature, the M T E P in C o / C u and F e / C u becomes positive and very small (see inset to fig. 2a for C o / C u ; for F e / C u the magnetic field-induced emf signals fall almost within the experimental uncertainties so that it was not possible to determine accurately the M T E P values). As the contribution from e l e c t r o n - m a g n o n scattering vanishes at low temperatures, the positive residual M T E P is probably due to the contribution from elastic scattering. From eq. (5), and as for the magnon term, the crossover from spinmixed channels at low field to separated spin T and spin J, channels at high field should also change the contribution from elastic scattering to the thermoelectric power. This M T E P term has been calculated by Inoue et al. [21] and is expected to be proportional to T with a positive sign for C o / C u (in agreement with our sign for AS below 20 K) and a negative sign for F e / C u (in contrast to our positive sign for AS observed at the lowest temperatures). According to our results for C o / C u and F e / C u , the crossover from a small and positive "elastic term" to a much larger and negative " m a g n o n term" occurs around 40 K. The behavior of the M T E P for F e / C r is more complex than in C o / C u and F e / C u . Fig. 2c suggests some competition between a negative contribution (generally predominant at low field) and a positive contribution saturating at the saturation field of the magnetoresistancc. This complexity is also reflected by the two changes of sign observed in the low temperature range, as shown in fig. 3c. We believe that this behavior is due to additional spin-dependent scatterings by the spins induced on the Cr atoms near the F e / C r interfaces.

LETTER TO THE EDITOR

L. Piraux et al. / Magnetothermoelectric power in multilayers

L253

6. Conclusions

References

We have measured the thermoelectric power of three spin valve structures, C o / C u , F e / C u and F e / C r muitilayers, as a function of temperature and magnetic field and the p a p e r has been focused on the the very large M T E P found in these systems. We found that MR and M T E P exhibit contrasting temperature dependences since, whereas the MR is a decreasing function of temperature, the MTEP, at least in C o / C u and F e / C u systems, is very small at low temperature and increases rapidly above 30-40 K. We have proposed a theoretical model based on spin-dependent e l e c t r o n - m a g n o n scattering in order to explain this rapid variation of the M T E P with temperature. A corollary to this model is that the sign of the M T E P should depend on whether the ratio of the impurity resistivities in the two spin directions is greater or less than unity. In agreement with this model, we found that the M T E P is negative for F e / C u and C o / C u multilayers where p 1" < p 3, while the M T E P is positive above 120 K for a F e / C r multilayer where P T > p $. We will present the details of the theoretical model and a more extended report on our M T E P data in further publications.

[1] M.N. Baibich, J.M. Broto, A. Fort, F. Nguyen Van Dau, F. Petroff. P. Etienne. G. Creuzet, A. Friederich and J. Chazelas, Phys. Rev. Len. 61 (1988) 2472. [2] G. Binasch, P. Griinberg, F. Saurenbach and W. Zinn, Phys. Rev. B 39 (1989) 4828. [3] R.E. Camley and J. Barnas, Phys. Rev. Left. 63 (1989) 664. [4] P.M. Levy, S. Zhang and A. Fert, Phys. Rev. Lett. 65 (1990) 1643. [5] W. Vavra, C.H. Lee, F.L. Lamelas, Hui He, R. Clarke and C. Uher, Phys. Rev. B 42 (1990) 4889. [6] S.N. Song, C. Sellers and J.B. Ketterson, Appl. Phys. Lett. 59 (1991) 479. [7] J. Sakurai, M. Horie, S. Araki, H. Yamamoto and T. Shinjo, J. Phys. Soc. Jpn. 60 (1991) 2522. 181 M.J. Conover, M.B. Brodsky, J.E. Mattson, C.H. Sowers and S.D. Bader, J. Magn. Magn. Mater. 102 (1991) 15. [9] S.S.P. Parkin, N. More and K.P. Roche, Phys. Rev. Len. 64 (1990) 2304. [10] D.H. Mosca, F. Petroff, A. Fert, P.A. Schroeder, W.P. Pratt and R. Loloee, J. Magn. Magn. Mater. 94 (1991) 1. [11] F. Petroff, A. Barth~l~my, D.H. Mosca, D.K. Lottis, A. Fert, P.A. Schroeder, W.P. Pratt, R. Loloee and S. Lequien, Phys. Rev. B 44 (1991) 5355. For the preparation and properties of Co/Cu see also S.S.P. Parkin, Z.G. Li and D. Smith, Appl. Phys. Lett. 58 (1991) 2710. [12] S. Pizzani, F. Baudelet, D. Chanderris, A. Fontaine, H. Magnan, J.M. Georges, F. Petroff, A. Fert, R. Loloee and P.A. Schroeder, to be published. [13] S.S.P. Parkin, R. Bhadra, K.P. Roche, Phys. Rev. Lett. 6 (1991) 2152. [14] I.Y. Korenblit and Y.P. Lazarenko. Soy. Phys. JETP 33 (1971) 837. [15] I.A. Campbell and A. Fert, Ferromagnetic Materials, vol. 3, ed. E.P. Wohlfarth (North-Holland, Amsterdam, 1982) p. 747. A. Fert and I.A. Campbell, J. Phys. F 6 (1976) 849. [16] D.A. Goodings, Phys. Rev. 132 (1963) 542. [17] D.L. Mills, A. Fert and 1.A. Campbell, Phys. Rev. B 4 (1971) 16. [18] F.J. Blatt, P.A. Schroeder, C.L. Foiles and D. Greig, Thermoelectric Power of Metals (Plenum, New York, 1976). [19] A. Fert and L. Piraux, to be published. [201 J. Inoue, A. Oguri and S. Maekawa, J. Phys. Soc. Jpn. 60 (1991) 376. [21] J. Inoue, H. Itoh and S. Maekawa, preprint.

Acknowledgement This work was partly funded by the United States National Science Foundation under grant no. DMR-88-013287 and by the Michigan State University, Center for Fundamental Materials Research. The work performed in Louvain-laNeuve was in the framework of the programme "Action de Recherche Concert~e" sponsored by the Belgian State (Ministry of Scientific Policy). L.P. is Research Associate of the National Fund for Scientific Research (Belgium).