- Email: [email protected]
Cu multilayers on layer thickness
Journal of Magnetism and Magnetic Materials 114 (1992) 252-254 North-Holland
Dependence of the giant magnetoresistance on layer thicknesses
in Co/Cu
multilayers
D.M. Edwards a, J. Mathon b, R.B. Muniz av1and S.S.P. Par-kin ’ a Dept. of Mathematics, Imperial College, London SW7 282, UK ’ Dept. of Mathematics, City University, London ECIV OHB, UK ’ IBM Almaden Research Center, San Jose, CA 951204099, USA
Observed oscillations in the saturation magnetoresistance of Co/Cu multilayers, as a function of the thickness of the Cu layer, are associate< with corresponding oscillations in the coupling between Co layers. RKKY theory relates the period of oscillations ( = 10 A) to necks in the Cu Fermi surface. New data on the dependence of the magnetoresistance AR/R on the thickness of the Co and Cu layers is interpreted using an extension of our recent theory.
Recently, it was observed [1,2] that in Co/Cu multilayers the saturation magnetoresistance, with current in the plane of the layers, oscillates bepeen low and high values with a period of = 10 A as a function of the Cu spacer thickness. This effect is associated with an exchange coupling between neighbouring magnetic layers which oscillates between ferromagnetic (F) and antiferromagnetic (AF); the high magnetoresistance occurs in AF thicknesses ranges. The role of the coupling is merely to produce such AF configurations in which a saturating field can induce a F configuration of lower resistance. Similar effects were observed earlier with transition metal spacers [3]. The magnetoresistance ratio AR/R is defined as the relative decrease in resistance due to a saturating field. Thus for AF coupling it is given by
AR/R=@,, -R,,)/R,,> where Rtl, Correspondence
R,,
(1)
are the resistivities in the AF
to: Prof. D.M. Edwards, Department of Mathematics, Huxley Building, Imperial College of Science Technology and Medicine, 180 Queens Gate, London SW7 2BZ, UK. ’ Permanent address: Depto. de Fisica, Universidade Federal Fluminense, RJ 24020, Brazil.
and F configurations. We first discu!s exchange coupling and the origin of the 10 A period in Co/Cu, and then compare theoretical calculations of A R/R in Co/Cu with the data of ref. [ 11 and with further data reported here. For a noble metal spacer one expects RKKY coupling whereas for transition metal spacers we developed a different theory [4,5] in which oscillations in the exchange coupling are associated with size quantization of states in the spacer d bands. For a one-band tight-binding model with nearest plane hopping, and layer orientation corresponding to a plane of reflection symmetry in the spacer, the oscillation periods in our theory are determined by caliper measurements of the bulk spacer Fermi surface normal to the layer plane, exactly as in RKKY theory [6]. In this case we showed how long-period oscillations arise when the Fermi surface is close to the zone boundary. The relevant caliper measurement emerges when one consider the surface as repeating periodically in the reciprocal lattice and several authors [7-lo] have elaborated this point in the context of RKKY theory. Bruno and Chappert [9] suggest that RKKY theory and ours differ in the criteria for deducing oscillation periods from the bulk spacer Fermi surface. In fact under conditions where our theory can be related to the
0304~8853/92/$05.00 0 1992 - El sevier Science Publishers B.V. Ah rights reserved
253
D.M. Edwards et al. / Giant magneroresistance in Co / Cu mulhbyers
bulk Fermi surface the criteria are the same. More generally, they point out that in RKKY theory periods 2r/q can be associated with vectors q, normal to the layer plane, which link points on the Fermi surface where the tangent planes are parallel to each other but not necessarily to the layer plane. They consider in detail a Cu spacer, where RKKY theory should apply, and for (111) layers predict a unique period of. 9.36 A. The relevant q spans a neck of the Cu Fermi surface obliquely, making an angle of 70.5” with the neck axis. Thus RKKY theory explains the period = 10 A observed in Co/Cu multilayers which are predominantly (111) textured [l]. The success of RKKY theory in explaining the oscillation period is consistent with a model of Co/Cu multilayers in which an sp conduction band common to Co and Cu runs throughout the structure. This is the basis of our theory of magnetoresistance [ll] in which spin-flip scattering is neglected and conduction electrons of spin u are scattered at a rate largely determined by the local density of final states at the Fermi level N,(E,). The minority spin density of states in Co is dominated by the partially-filled d band so that minority spin electrons in the Co layer are scattered much more strongly than majority ones. This is essential for the giant magnetoresistance. The Boltzmann equation formulation is the same as that of BarnaS et al. [12] but, unlike these and other authors [13,14], we emphasise bulk spin-dependent scattering rather than interfacial scattering. The local inverse mean free paths for each spin in different layers of the magnetic superlattice cell are shown schematically in fig. 1. The Boltzmann equation is solved for the four-component system with continuity and periodic boundary conditions imposed on the distribution function, The resistances for F and AF configurations, and hence AR/R given by eq. cl), are calculated. AR/R depends on the layer thicknesses t,, t,, and on the parameters Imin, (Y= Is/lmin, p = 1,/l,,, where lmin and I,, are the mean free paths for minority and majority spins in Co and 1, is the mean free path for both spins in Cu. For t co < lmin the form of AR/R as a function of t,, does not depend much on Imin. Even the limit lmin+ w, when a simple formula
FERRWAGNTIC
ANTFE~RWAGKTIC
CoNlGlRATlffl
coNlW_RATloN
MNMNIMNMN
B&L T
Fig. 1. Schematic representation of the distribution of local mean free paths I-’ in the magnetic unit cell for the ferromagnetic and antiferromagnetic configurations of the magnetic layers. Both the resistivities in the spin up ( T, and down (I) channels are shown. M and N denote, respectively, the magnetic and nonmagnetic layers.
for AR/R is available, gives a reasonable fit to data for thin magnetic layers [ll]. However we now report an extension of the measurements of ref. [l], where all experimental details are given, to study the dependence of AR/R on t,, in Co/Cu multilayers. The data are shown in fig. 2 and for the theoretical curve the parameter lmin = 12 w is chosen to fit the maximum in AR/R. a = 22 and p = 2 were estimated from densities of states of Co and Cu, assuming 1;’ a N&5,). The same parameters were used to calculate AR/R as a function of fcU and in fig. 3 the
100 80 G
60
20
100
Co thickness
200 (A)
Fig. 2. Dependence of the magnetoresistance ratio AR/R on Co layfr thickness for sugerlattice str!ctures of the form Fe(40 A)/[Cdt,,)/Cu(9 A)IN/Cu(20 A) at $2 K. The full line is calculated for an infinite Co(t,,)/Cu(9 A) superlattice.
254
D.M. Edwards et al. / Giant magnetoresistance in Co /CM multilayers
Acknowledgement
We are grateful to SERC (UK) for financial support.
References
01 0
I.
1
s
.
’
’
’
’
10
20
30
40
CU thickness
J
50
(A)
Ifig. 3. Dependence
of AR/R on Cu thickness for Co(l0 A)/Cu(t,.) superlattices, with same parameters LY,p, lmin as in fig. 2, compared with the data of ref. [I].
results are compared with the data of ref. [l]. The calculated A R/R, given by eq. cl), relates only to the data for AF-coupled multilayers with squared data points. We conclude that a reasonable account of the giant magnetoresistance in Co/Cu multilayers is obtained using a model based on spin-dependent bulk scattering rather than interface scattering.
[l] S.S.P. Parkin, R. Bhadra and K.P. Roche, Phys. Rev. Lett. 66 (1991) 2152. [2] D.H. Mosca, F. Petroff, A. Fert, P.A. Scroeder, W.P. Pratt Jr. and R. Laloee, J. Magn. Magn. Mater. 94 (1991) Ll. [3] S.S.P. Parkin, N. More and K.P. Roche, Phys. Rev. Lett. 64 (1990) 2304. [4] D.M. Edwards and J. Mathon, J. Magn. Magn. Mater. 93 (1991) 85. [5] D.M. Edwards, J. Mathon, R.B. Muniz and M.S. Phan, J. Phys.: Condens. Matter 3 (1991) 4941. [6] The requirement of reflection symmetry for the validity of eq. (4.2) of ref. [5] was unfortunately not stated in the final published version. [7] R. Coehoorn, Phys. Rev. B44 (1991) 9331. [S] C. Chappert and J.P. Renard, Europhys. Lett. 15 (1991) 553. [9] P. Bruno and C. Chappert, Phys. Rev. Lett. 67 (1991) 1602. [lo] F. Herman, J. Sticht and M. van Schilfgaarde, J. Appl. Phys. 69 (1991) 4783. [ll] D.M. Edwards, J. Mathon and R.B. Muniz, IEEE Trans. Magn. 27 (1991) 3548. [12] J. BarnaS, A. Fuss, R.E. Camley, R. Griinberg and W. Zinn, Phys. Rev. B 42 (1990) 8110. [13] P.M. Levy, S. Zhang and A. Fert, Phys. Rev. Lett. 65 (1990) 1643. [14] J. Inoue, A. Oguri and S. Maekawa, J. Phys. Sot. Jpn. 60 (1991) 376.
Dependence of the giant magnetoresistance on layer thicknesses
in Co/Cu
multilayers
D.M. Edwards a, J. Mathon b, R.B. Muniz av1and S.S.P. Par-kin ’ a Dept. of Mathematics, Imperial College, London SW7 282, UK ’ Dept. of Mathematics, City University, London ECIV OHB, UK ’ IBM Almaden Research Center, San Jose, CA 951204099, USA
Observed oscillations in the saturation magnetoresistance of Co/Cu multilayers, as a function of the thickness of the Cu layer, are associate< with corresponding oscillations in the coupling between Co layers. RKKY theory relates the period of oscillations ( = 10 A) to necks in the Cu Fermi surface. New data on the dependence of the magnetoresistance AR/R on the thickness of the Co and Cu layers is interpreted using an extension of our recent theory.
Recently, it was observed [1,2] that in Co/Cu multilayers the saturation magnetoresistance, with current in the plane of the layers, oscillates bepeen low and high values with a period of = 10 A as a function of the Cu spacer thickness. This effect is associated with an exchange coupling between neighbouring magnetic layers which oscillates between ferromagnetic (F) and antiferromagnetic (AF); the high magnetoresistance occurs in AF thicknesses ranges. The role of the coupling is merely to produce such AF configurations in which a saturating field can induce a F configuration of lower resistance. Similar effects were observed earlier with transition metal spacers [3]. The magnetoresistance ratio AR/R is defined as the relative decrease in resistance due to a saturating field. Thus for AF coupling it is given by
AR/R=@,, -R,,)/R,,> where Rtl, Correspondence
R,,
(1)
are the resistivities in the AF
to: Prof. D.M. Edwards, Department of Mathematics, Huxley Building, Imperial College of Science Technology and Medicine, 180 Queens Gate, London SW7 2BZ, UK. ’ Permanent address: Depto. de Fisica, Universidade Federal Fluminense, RJ 24020, Brazil.
and F configurations. We first discu!s exchange coupling and the origin of the 10 A period in Co/Cu, and then compare theoretical calculations of A R/R in Co/Cu with the data of ref. [ 11 and with further data reported here. For a noble metal spacer one expects RKKY coupling whereas for transition metal spacers we developed a different theory [4,5] in which oscillations in the exchange coupling are associated with size quantization of states in the spacer d bands. For a one-band tight-binding model with nearest plane hopping, and layer orientation corresponding to a plane of reflection symmetry in the spacer, the oscillation periods in our theory are determined by caliper measurements of the bulk spacer Fermi surface normal to the layer plane, exactly as in RKKY theory [6]. In this case we showed how long-period oscillations arise when the Fermi surface is close to the zone boundary. The relevant caliper measurement emerges when one consider the surface as repeating periodically in the reciprocal lattice and several authors [7-lo] have elaborated this point in the context of RKKY theory. Bruno and Chappert [9] suggest that RKKY theory and ours differ in the criteria for deducing oscillation periods from the bulk spacer Fermi surface. In fact under conditions where our theory can be related to the
0304~8853/92/$05.00 0 1992 - El sevier Science Publishers B.V. Ah rights reserved
253
D.M. Edwards et al. / Giant magneroresistance in Co / Cu mulhbyers
bulk Fermi surface the criteria are the same. More generally, they point out that in RKKY theory periods 2r/q can be associated with vectors q, normal to the layer plane, which link points on the Fermi surface where the tangent planes are parallel to each other but not necessarily to the layer plane. They consider in detail a Cu spacer, where RKKY theory should apply, and for (111) layers predict a unique period of. 9.36 A. The relevant q spans a neck of the Cu Fermi surface obliquely, making an angle of 70.5” with the neck axis. Thus RKKY theory explains the period = 10 A observed in Co/Cu multilayers which are predominantly (111) textured [l]. The success of RKKY theory in explaining the oscillation period is consistent with a model of Co/Cu multilayers in which an sp conduction band common to Co and Cu runs throughout the structure. This is the basis of our theory of magnetoresistance [ll] in which spin-flip scattering is neglected and conduction electrons of spin u are scattered at a rate largely determined by the local density of final states at the Fermi level N,(E,). The minority spin density of states in Co is dominated by the partially-filled d band so that minority spin electrons in the Co layer are scattered much more strongly than majority ones. This is essential for the giant magnetoresistance. The Boltzmann equation formulation is the same as that of BarnaS et al. [12] but, unlike these and other authors [13,14], we emphasise bulk spin-dependent scattering rather than interfacial scattering. The local inverse mean free paths for each spin in different layers of the magnetic superlattice cell are shown schematically in fig. 1. The Boltzmann equation is solved for the four-component system with continuity and periodic boundary conditions imposed on the distribution function, The resistances for F and AF configurations, and hence AR/R given by eq. cl), are calculated. AR/R depends on the layer thicknesses t,, t,, and on the parameters Imin, (Y= Is/lmin, p = 1,/l,,, where lmin and I,, are the mean free paths for minority and majority spins in Co and 1, is the mean free path for both spins in Cu. For t co < lmin the form of AR/R as a function of t,, does not depend much on Imin. Even the limit lmin+ w, when a simple formula
FERRWAGNTIC
ANTFE~RWAGKTIC
CoNlGlRATlffl
coNlW_RATloN
MNMNIMNMN
B&L T
Fig. 1. Schematic representation of the distribution of local mean free paths I-’ in the magnetic unit cell for the ferromagnetic and antiferromagnetic configurations of the magnetic layers. Both the resistivities in the spin up ( T, and down (I) channels are shown. M and N denote, respectively, the magnetic and nonmagnetic layers.
for AR/R is available, gives a reasonable fit to data for thin magnetic layers [ll]. However we now report an extension of the measurements of ref. [l], where all experimental details are given, to study the dependence of AR/R on t,, in Co/Cu multilayers. The data are shown in fig. 2 and for the theoretical curve the parameter lmin = 12 w is chosen to fit the maximum in AR/R. a = 22 and p = 2 were estimated from densities of states of Co and Cu, assuming 1;’ a N&5,). The same parameters were used to calculate AR/R as a function of fcU and in fig. 3 the
100 80 G
60
20
100
Co thickness
200 (A)
Fig. 2. Dependence of the magnetoresistance ratio AR/R on Co layfr thickness for sugerlattice str!ctures of the form Fe(40 A)/[Cdt,,)/Cu(9 A)IN/Cu(20 A) at $2 K. The full line is calculated for an infinite Co(t,,)/Cu(9 A) superlattice.
254
D.M. Edwards et al. / Giant magnetoresistance in Co /CM multilayers
Acknowledgement
We are grateful to SERC (UK) for financial support.
References
01 0
I.
1
s
.
’
’
’
’
10
20
30
40
CU thickness
J
50
(A)
Ifig. 3. Dependence
of AR/R on Cu thickness for Co(l0 A)/Cu(t,.) superlattices, with same parameters LY,p, lmin as in fig. 2, compared with the data of ref. [I].
results are compared with the data of ref. [l]. The calculated A R/R, given by eq. cl), relates only to the data for AF-coupled multilayers with squared data points. We conclude that a reasonable account of the giant magnetoresistance in Co/Cu multilayers is obtained using a model based on spin-dependent bulk scattering rather than interface scattering.
[l] S.S.P. Parkin, R. Bhadra and K.P. Roche, Phys. Rev. Lett. 66 (1991) 2152. [2] D.H. Mosca, F. Petroff, A. Fert, P.A. Scroeder, W.P. Pratt Jr. and R. Laloee, J. Magn. Magn. Mater. 94 (1991) Ll. [3] S.S.P. Parkin, N. More and K.P. Roche, Phys. Rev. Lett. 64 (1990) 2304. [4] D.M. Edwards and J. Mathon, J. Magn. Magn. Mater. 93 (1991) 85. [5] D.M. Edwards, J. Mathon, R.B. Muniz and M.S. Phan, J. Phys.: Condens. Matter 3 (1991) 4941. [6] The requirement of reflection symmetry for the validity of eq. (4.2) of ref. [5] was unfortunately not stated in the final published version. [7] R. Coehoorn, Phys. Rev. B44 (1991) 9331. [S] C. Chappert and J.P. Renard, Europhys. Lett. 15 (1991) 553. [9] P. Bruno and C. Chappert, Phys. Rev. Lett. 67 (1991) 1602. [lo] F. Herman, J. Sticht and M. van Schilfgaarde, J. Appl. Phys. 69 (1991) 4783. [ll] D.M. Edwards, J. Mathon and R.B. Muniz, IEEE Trans. Magn. 27 (1991) 3548. [12] J. BarnaS, A. Fuss, R.E. Camley, R. Griinberg and W. Zinn, Phys. Rev. B 42 (1990) 8110. [13] P.M. Levy, S. Zhang and A. Fert, Phys. Rev. Lett. 65 (1990) 1643. [14] J. Inoue, A. Oguri and S. Maekawa, J. Phys. Sot. Jpn. 60 (1991) 376.