MATERIALS SCIENCE &

ENGINEERING g

E L S E V I E R Materials Science and Engineer ing B31 (1995) 213-218

Giant magnetoresistance of artificial Ni-Fe/Cu, Ni-Co/Cu and Co-Fe/Cu superlattices and their temperature dependence

T. Miyazak i , H. K u b o t a , M. Sa to

Department of Applied Physics, Faculty of Engineering, Tohoku University, Sendal 980-77, Japan

Abstract

The dependence of the magnetoresistance (MR) ratio on the composition of the magnetic layers and the temperature (between 4.2 and 300 K) was studied systematically for Fe-Ni/Cu, Ni-Co-Cu and Co-Fe/Cu multilayers. The MR ratio exhibits a maximum near Co, which is in qualitative agreement with the theoretical calculation made by Inoue and coworkers (J. Magn. Magn. Mater., 104-107 (1992) 1883; 136 (1994) L33). The dependence of the MR ratio on the temperature is well explained by the theoretical calculation proposed by Hasegawa (Phys. Rev. B, 47 (1993) 15 073, 15 080).

Keywords: Thin films; Magnetic field effect; Metals; Electrical measurement

1. Introduction

Much effort has been made to understand the mechanism of the giant magnetoresistance (GMR) in artificial superlattices from both experimental and theoretical points of view. In general, the temperature dependence of transport properties is complicated. However , a bet ter understanding of this subject is expected to aid the clarification of the mechanism of G M R and /o r to provide fruitful information on the enhancement of GMR. In contrast with the numerous reports on magnetoresistance (MR) data measured at room temperature , little information is available on the tempera ture dependence of MR in artificial multi- layer films.

Petroff et al. [1] measured the temperature depen- dence of the resistivity of Fe /Cr superlattices for two kinds of sample: one with rough interfaces and large MR and the other with sharp interfaces and small MR. It was shown that the temperature dependence was much more marked for the sample with large MR. They concluded that the enhanced temperature depen- dence of the resistivity could be accounted for by spin mixing scattering. Zhang and Levy [2] discussed the data reported by Petroff et al. [1] and gave a theoret- ical explanation based on the existence of local spin excitations at the roughened Fe /Cr interfaces.

Chaiken et al. [3] studied the temperature depen- dence of two antiferromagnetically coupled F e / C r / F e

Elsevier Science S.A. SSDI 0 9 2 1 - 5 1 0 7 ( 9 4 ) 0 8 0 0 1 - 1

sandwiches. The samples were sandwiches (grown by molecular beam epitaxy (MBE)) deposited epitaxially on a ZnSe(100) surface and evaporated on a glass substrate. The MR of the sandwiches was constant at low temperatures and decreased linearly with increas- ing temperature above about 70 K.

Mattson et al. [4] have measured the temperature dependence of the resistivity for three F e /Cr superlat- tices: two antiferromagnetically and one ferromagneti- cally coupled multilayers. They discussed ApM(T ) = PM(T = 0 ) - pM(T), i.e. the magnetoresistivity, where PM = p ( H = O) - p ( H > Hs), as a function of tempera- ture. They showed that the magnetoresistivity of the antiferromagnetically coupled films decays from its maximum value at low temperature with a T 2 be- haviour below about 100 K, whereas in the ferromag- netically coupled film this behaviour was approxi- mated by T 3/2. Their explanation for the different temperature dependence of ApM is as follows. At finite temperature, the thermal excitations of magnons, which cause local spin disordering in the magnetic layers, reduce the magnetoresistivity ApM. The mag- non occupation number ( n ) r at low temperature is ( n ) T.f . . . . ~ T3/2 for the ferromagnet and (rt)T,antif . . . . . oc T 2 for the antiferromagnet. They also pointed out that the resistivity due to the s -d inter- band scattering Psd differs between antiferromagnet- ically and ferromagnetically coupled films. We applied the discussion described above to the temperature

214 T. Miyazaki et al. / Materials Science and Engineering B31 (1995) 213-218

dependence of the resistivity of many N i - C o / C u , C o - F e / C u and F e - N i / C o multilayers, but did not obtain a satisfactory explanation.

Gijs and Okada [5,6] measured the MR of Fe /Cr superlattices with different Cr thicknesses prepared by sputtering as a function of temperature. They pointed out that the MR ratio of Fe /Cr multilayers decreases at much higher temperatures than that of Co /Cu multilayers. This is speculated to be related to the large magnon scattering for iron, which is a weak ferromagnet , resulting in increased spin mixing at higher temperatures. Nevertheless, despite the efforts described above, the understanding of the tempera- ture dependence of the MR ratio is not sufficient.

2. Exper imenta l details

The sputtering conditions (electric power and argon pressure) were determined on the basis of preparatory experiments. The magnetic and Cu layer films were prepared by r.f. and d.c. magnetron sputtering respec- tively in an argon pressure of 15 mTorr on a glass substrate. The diameter of the magnetic alloy and Cu targets was 75 mm with a thickness of about 2 mm. The purity of Fe-Ni , Ni -Co and Co-Fe was 99.9%, whereas that of Cu was 99.999%. The sputteringorates of the magnetic and Cu layers were 1 and 2.2 A s respectively. The thickness of the layer was controlled by changing the sputtering time. The samples pre- pared were as follows:

(1) Nis,,Fe2,,(50 A)/[Ni,,,0 xFe,(15 A)/Cu(dcu / ~ k ) ] 3 0 ,

x = 0-100, de, , = 2-60 A. (2) [Ni., o xCox(15 A)/Cu(d~, u A.)]30,

x = 0-100, dcu = 5-40 A. (3) [Co,,~0_~Fe~(15 A)/Cu(d£u A)]3,,,

x = 0-100, dcu = 5-43 A.

The MR was measured by a four-probe method in magnetic fields up to 20 kOe. The sample was cooled first to 4.2 K and the temperature dependence of MR was measured with increasing temperature. The struc- tures of the samples were investigated by X-ray diffraction (Cu Kc~) in both low and middle angle regions. All the diffraction patterns measured at middle angles exhibited f.c.c. (111) preferred orienta- tion. The magnetization was measured by a vibrating sample magnetometer in magnetic fields up to 16 kOe at room temperature.

3. Exper imenta l results

3. I. Composition dependence of the MR ratio

Figs. l ( a ) - l ( c ) show the MR ratio at the first, second and third peaks respectively in the MR oscilla-

(21_ ° B_

60 • 4.21< . I o RT . . . . . . .

I . . . . . .'P= Im NFFlffCU(4.2K) 5O I ',i:~2~anan, / i o N ~ - F ~ I R ~

I ...... ~ \ L_ I" reference(4.2K}!

3 0 s.,o

20 (a) K . : ;~ 0

40 . . . . . . . . . . .

100

50

0

100 o_ o B_ <3

3 0 j ~ -

20 50

10

0 0

20 . . . . . . . . . . . 1 O 0 /

i f ( • -" " 5 0 10

[: 0 0

26 27 28 Fe Co N i

N

Fig. 1. MR ratio AP/Po as a function of the electron number of the magnetic layer for various multilayer systems: (a) first peak; (b) second peak; (c) third peak; O, 4.2 K, C), 300 K for Ni-Co/Cu, Co-Fe/Cu; l , 4.2 K, [], 300 K for Fc-Ni/Cu; &, 4.2 K [8,9,14], A, 300 K [8-141.

tion curves measured at 4.2 and 300 K as a function of the electron number N of the magnetic layer for F e - N i / C u , N i - C o / C u and C o - F e / C u multilayer sys- tems. The MR ratio is defined as Ap/po, where P0 is the resistivity at zero field and Ap is the difference between the resistivities at H = 0 and H = 20 kOe. In the figure, the theoretical result calculated by Inoue et al. [7] is shown by the broken line. Also, the ex- perimental data obtained by other workers [8-14] are plotted. As can be seen in the figure, the MR ratio exhibits a maximum at an electron number of about 27 for all peaks. The experimental result is in rough agreement with the calculated result above N = 27. However, much discrepancy is observed with decreas- ing electron number.

3.2. Temperature dependence of the MR ratio

Fig. 2 shows the MR ratio as a function of tempera- ture for N i - C o / C u and C o - F e / C u muitilayer systems. Here, the MR ratio is defined as Ap/ps, where Ps is

T. Miyazaki et al. / Materials Science and Engineering B31 (1995) 213-218 215

100

80

o~ 60

< 40

6 u ° ° ° O o o °

o

I ° 4 l ' ~ O 0 • • • •

# • g i g

/ ° o o # [ ]

o o

• o

o • 13

[]

I I

~k

A

o

• o o

O •

O ~ .

ll & •

2 0 ' ~ & & & • & & • • • &

{ i ~ l ~ r , m m m m

~- .~..ioe + + • + l l • • ~ + i ÷1~

0 100 200 300

T(K)

Fig. 2. Temperature dependence of the MR ratio for Ni-Co/Cu and Co-Fe/Cu multilayers at the first peak: ©, Co-Cu; m, NiT Co~,,/Cu; ~ , Ni/Cu; +. C04,,Fe~./Cu; O, Ni30CoT~,/Cu; ~. NisoCoz./Cu; O. Co~2Fels/Cu; ~, Fe/Cu; ff], Nis.Co5o/Cu; &, Ni. .Co. . /Cu; !1., Co~oFe40/Cu.

the saturated resistivity at 20 kOe. Except for the N i /Cu multilayer, the MR ratio decreases slowly below about 50 K and rapidly between 100 and 300 K. In the case of the Ni /Cu multilayer, the MR ratio is small and nearly constant below 50 K but increases rapidly above 100 K. It exhibits a maximum at about 300 K. This behaviour was also observed for the Ni-based N i - F e / C u and N i - C o / C u multilayers. Con-

5 0

40 ,., I . . o ]Mmm

v 3 0 ~ " 2 []

--. ~,,~. • ~ , , • o Q- 201- ~ , 4~' t~ '~ " • • •

L.o.o.o,oo 0. o o ,° ' " " ' ' " 0

0 100 200 300

o

T (K) Fig. 3. Temperature dependence of the MR ratio for Fe Ni/Cu multilayers at the first peak: ©. Ni/Cu; O. Nig,,Felo/Cu; A Ni~.Fe,./Cu; I Ni~oFe~o/Cu; D, NisoFes.JCu; &, NL,~Fe~(,/Cu.

50

40

o~ 30 Q.

o_ 20

10 ~ ~k l~Jk

o o

~ t ~ t , ; ' . . , ; , o •

t, , •

' Ih 'AIIAI ' t I •AAAL A A X • •

• + ÷ + +

,m p

T(K)

+

0 ' " 0 100 200 300

Fig. 4. Temperature dependence of the MR ratio for Ni-Co/Cu, Co-Fe/Cu and Fe-Ni/Cu multilayers at the second peak: ©, Co/ Cu; m NivoCo3./Cu; D, Ni/Cu; +, C04oF%0/Cu; O, Ni3iiCoTo/Cu; /h Ni~oCo2./Cu; O, Cos2Fe]s/Cu; [~, Fe/Cu; [5], Nis.Coso/Cu; &, Ni,.Com/Cu; O, C06.Fe4./Cu; x, NisoFe20/Cu.

cerning this point, a more detailed explanation will be described elsewhere [14a].

Fig. 3 shows the t empera ture dependence of the MR ratio for the F e - N i / C u multi layer system. The characteristic features of the dependence are almost the, same as those of the N i - C o / C u multi layer system. Fig. 4 shows the tempera ture dependence of the M R ratio for the samples corresponding to the second peak in the MR vs. Cu thickness data. As can be seen in the figure, the MR ratio is nearly constant or exhibits a broad maximum below about 100 K. However , it decreases linearly with increasing t empera tu re be- tween 100 and 300 K.

4. Discussion

4.1. Dependence of the MR ratio on the composition of the magnetic layer

As shown in Fig. 1, the calculated result of the M R ratio, which takes into account the spin-dependent scattering of the conduction electrons in the magnetic atoms at the interface, roughly explains the ex- perimental result above N = 27 but not below N = 27. The reason for the discrepancy below N = 27 can be considered as follows. In the theory, both the struc- ture of the multilayers and the chemical composi t ion at the interfaces are assumed to be constant. Further- more, the s - d mixing potential V~d is t reated as a parameter• Different values of V~d are taken for N X 26.2 in order to fit the magnetic momen t of Fe and Co. On the other hand, in the exper iment , a change in structure can be expected from sample to sample. In practice, the X-ray diffraction pat terns of the C o - F e /

216 T. Miyazaki et al. / Materials" Science and Engineering B31 (199,5) 213 218

Cu multilayer system become broader with increasing Fe content [15]. The result suggests that the structures of the interfaces of the multilayers also change sig- nificantly with increasing Fe content. The resistivity is very sensitive to structural changes. Chemical inhomo- geneities occurring around the Invar composition in the Fe -Ni alloy system and near the phase boundary are well known. These two points can be understood by examining the composition dependence of the resistivity [16].

4 .2 . T e m p e r a t u r e d e p e n d e n c e o f t he M R r a t i o

As described in Section 1, phenomenological discus- sions of the dependence of the MR ratio on tempera- ture have been made for Fe /Cr and Co/Cu multi- layers. On the other hand, the theoretical treatment of the G M R at finite temperature has been carried out recently by Hasegawa [17,18]; he took into account the scattering due to the spin fluctuation, and derived an expression for the conductivity of a multilayer consisting of two magnetic and non-magnetic layers using the coherent potential approximation. Further- more, he made model calculations based on a numeri- cal study for the Fe /Cr multilayer. In his formula, the MR ratio at finite temperature can be expressed as

dip ( a - 1) 2 Ps 4a (1)

with

g ( B + m ) 2 + IX2 _ m 2

a - Ix2 m 2 (2) g ( B - m ) 2 + --

2 ~ + 1 B - - - - ( 3 )

~/<(MA)2> (MA> IX- M0 , m - M(, (4)

where g is the concentration of non-magnetic atoms in the magnetic layers. ~A(B) is given by

gA = ea + U / 2 , g• = % (5)

where CA(B) is the atomic potential of the magnetic (non-magnetic) metal and U is the on-site e lec t ron- electron interaction of the magnetic atom. a 0 is the value of a at T = 0. M 0 and M A a r e the magnetic moments at 0 K and at a finite temperature respective- ly. IX and m are the normalized absolute value of the local magnetic moment and the normalized mean value of the magnetic moment respectively. The latter corresponds to the experimental value of M s ( T ) / M s ( O

K). Eq. (1) is a very simple form because we neglect the additional term in Hasegawa's expression of the MR ratio which originates from the hopping probabili- ty between the magnetic layers.

In contrast with the Fe /Cr multilayer system, e A (A, magnetic atom) is always higher than % (B, Cu atom) in the multilayer systems including a Cu spacer. Therefore the value of a 0 in Eq. (3) is always smaller than unity. In the Fe /Cr multilayer, a 0 is always larger than unity. If we apply Hasegawa's theory to the present experimental data, we must regard e A as the atomic potential of the 3d electrons and % as that of the 4s electrons of Cu, because the 3d states of Cu are filled completely with electrons. Fur thermore , to calculate the dependence of the MR ratio on tempera- ture using the above equations, we need IX and m. We measured the dependence of the magnetization on temperature for several multilayers and confirmed that IX and m can be roughly expressed as [19]

tx = 1, m = ~/1 - ( T / T c ) 2 (6)

in the temperature range T ~< 0.5T c. Our experimental data described in Section 3.2 were fitted using Eqs. (1)-(4). Figs. 5 and 6 show the best fit results (full curves) for the samples corresponding to the N i - C o / Cu, C o - F e / C u and N i - F e / C u multilayer systems. The values of a 0 and g used for the fitting procedure are listed in the figures. As can be seen, the ex- perimental data are well fitted by the calculation, except for the Ni/Cu multilayer. The full curves in Fig. 7 show the best fit results for the samples corresponding to the second peak of the multilayers described in Figs. 5 and 6. It can be seen that the experimental data are well fitted by the theoretical

100 , , , , , , , , ,

( a o , g ) 2 .o co (o.19, o.o4) ~ . NiaoCozo (0.20, 0.05) ~,,"~ <> Coe2Fe m (0.22, 0.03) ~ ° ' c k [] Ni~Coso (0.23, 0.04)

-'---. ~ k~ • Ni,oCO3o (0.29, 0.04) ~ " ~ ,~ NisoCo2o (0.34, 0.04) - ' ~ ~-~ " aigoCo,o (0.41, 0.04)

0.. *' Ni 5 0 - bo=0

0. ,~ -

J

0 0.5 T / T o

Fig. 5. MR ratio as a function of the normalized temperature for Ni Co/Cu and Co Fe/Cu multilayers (first peak). Full lines show the best fit calculations.

T. Miyazaki et al. / Materials Science and Engineering B31 (1995) 213-218 217

0 I I I I I I I I I

t (ao, g) • Ni6oFe4o (0.31, 0.02)

4 0 * NisoFeao (0.32, 0.05) • NisoFe5o (0.36, 0.01)

,~ , ~ [] NigoFelo (0.38, 0.02) o ~ "~',~ ~' Ni4oVe6o (0.43, 0.02) "'~ 30 ~ ~x\ • Ni

<3 20-

A

10

4,e.

O0 0.5

T / T c Fig. 6. MR ratio as a function of the normalized temperature for F e - N i / C u multilayers (first peak). Full lines show the best fit calculations.

5 0 / , , , , , , , , ,

t ( a o , g ) o Co,Fern(0.30, 0.02) • Nia0CoTo (0.32, 0.02)

40 ~ o Co (0.33, 0.01) ~ - - ' 6 " o Nis0COso (0.33, 0.03) ~ % " NiToC03o (0.37, 0.02)

°~ ~l~-k, ~ aisoCoao (0.41, 0.02) "-" 30 " ~Lak"k,.. : NisoFeao (0.43, 0.02)

~ '~ '~ '~ NigoCO,o (0.43, 0.02) ~ 'ko~g"X 6 * Ni (0.60, 0.02)

<3 20

10

I I I I I I 00 0.5 1

T / T c Fig. 7. MR ratio as a function of the normalized temperature for the samples corresponding to the second peak of Ni-Co/Cu, Co- Fe /Cu and F e - N i / C u multilayers. Full lines show the best fit calculations.

expression. Fur thermore , the tempera ture dependence of the M R ratio reported by others [1,5,8] is also described well by the theory.

It is of interest to discuss the dependence of the values of a 0 and g on the composit ion of the magnetic

1 . 0

0 . 8

0.6

0 . 4

0.2

0.0 0.10

0 . 0 5

0.00

i = =

• 1st peak(Ni-Co/Cu, Co-Fe/Cu) o 1st peak(Ni-Fe/Cu) • 2nd peak • Bulk bulk Ni/Cu Z~ references

NiaoFe~Cu

bulk Fe/Cu bulk Co/Cu ~ ) ~ (Parkin) ' ~ ' , ~ . . . . ~ . .

Co/Cu(Parkin) ( a )

I

=

(b)

Fe/Cr(Fert)

~A F e/Cr(Gijs)

2 6

Fe

i = i

NiaoFezo/Cu Co/Cu (Parkin) (Pa.rkin) ) ~

Q i A a o.. = i ~ . . m

I I I

27 2 8

Co Ni N

Fig. 8. Fitting parameters a 0 (a) and g (b) as a function of the electron number of the magnetic layer alloys. The open and filled triangles represent the values obtained by theoretical fitting using MR vs. T data and bulk data reported in Refs. [20] and [21] respectively.

atoms. Figs. 8(a) and 8(b) summarize all the values of a 0 and g obtained in the present study as a function of the number of electrons of the 3d atoms. As can be seen in Fig. 8(b), the value of g is independent of the electron number . This result implies that the degree of interface mixing of atoms is roughly constant. On the other hand, the value of a 0 depends on the electron number (Fig. 8(a)). In Fig. 8(a), the bulk values for Fe, Co, Ni and Cu, calculated using EA(B) [20] and U [21], are also shown. It should be noted that the calculated values of a 0 agree well with those obtained from the fitting procedure for the samples corre- sponding to the second peak. On the other hand, a 0 obtained f rom the first peak is slightly smaller than that from the second peak. This may be due to the fact that the thickness of the magnetic and Cu layers was disregarded in the model.

5. Conclusions

The dependence of the M R ratio on the composi- tion of the magnetic layers and the t empera ture was studied systematically for F e - N i / C u , N i - C o / C u and C o - F e / C u multilayers. The MR ratio at the first, second and third peaks for N i - C o / C u and C o - F e / C u

218 T, Miyazaki et ai. / Materials Science and Engineering B31 (1995) 213-218

multilayers exhibited a maximum near N = 27, which was in qualitative agreement with the theoretical calculation made by lnoue et al. [7]. The MR ratio at the first peak for N i - F e / C u multilayers exhibited a maximum near N = 27.5.

Except for N i - C u multilayers, the MR ratio de- creased with increasing temperature and the depen- dence was well explained by the theoretical calculation proposed by Hasegawa [17,18]. On the other hand, the MR ratio for the sample corresponding to the first peak of the Ni /Cu multilayer exhibited a maximum at about 300 K and the abnormal temperature depen- dence was unresolved.

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