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Ballistic giant magnetoresistance
Journal of Magnetism and Magnetic Materials 156 (1996) 385-386
~i
Journalof magnetism ~ i ~ and magnetic materials
N
ELSEVIER
Ballistic giant magnetoresistance Kees M. Schep
a,b,*, Paul J. Kelly a, Gerrit E.W.
Bauer b
a Philips Research Laboratories, Profi Holstlaan 4, 5656 AA Eindhol,en. The Netherlands h FaculO' of Applied Physics and DIMES Delft University qf Technology. Lorentzweg 1. 2628 CJ De!ft. The Netherhmds Abstract
We present a theoretical study of the giant magnetoresistance in the ballistic regime for C o / C u and F e / C r multilayers which emphasizes the importance of band structure effects, both for the perpendicular (CPP) and the parallel (CIP) geometry.
A giant magnetoresistance (GMR) effect in antiferromagnetically coupled magnetic multilayers arises when the anti-parallel magnetizations of adjacent magnetic layers are forced to become parallel by an external magnetic field. In spite of extensive experimental and theoretical investigations [I] the microscopic origin of the GMR remains unclear. One of the outstanding questions concerns the determination of the relative importance of spindependent band structure mismatch between the two materials constituting the multilayer and spin-dependent scattering at defects either in the bulk or at the interfaces. The focus of both theoretical and experimental work has been on the diffusive transport regime in which the sample dimensions are much larger than the electron mean free path. In this regime the contributions of band structure mismatch and defect scattering are strongly intertwined, thus making an experimental distinction between the two difficult. In this contribution we focus on the ballistic transport regime in which defect scattering no longer contributes to the resistance and a rigorous theoretical evaluation of the band structure effects on the MR is feasible. By making detailed predictions we hope to stimulate experiments in this regime in order to assess the importance of band structure effects and, more generally, because such experiments should help to provide a better understanding of the factors influencing the GMR in macroscopic samples. We consider a multilayer structure where the total resistance is dominated by a classical point contact with a diameter much smaller than the mean free path and much larger than the electron wavelength [2,3]. Even though the electrons passing through the constriction are not scattered
* Corresponding author. Fax: schep@ natlab.research.philips.com.
+31-40-2743365;
email:
out of their Bloch states by detects, the conductance of the point contact is finite due to its finite cross section A. This ballistic (Sharvin) conductance G,: for spin ~r is simply the conductance quantum e 2 / h times the number of conduction channels N,~ [4,5]. N,, is proportional to A and to the sum of the projections S,,,~ of the ~,th sheet of the spin o- Fermi surface onto the plane normal to the transport direction h: e2
G,~(~) = ~-N,~(h)
e2
A
1
h 47r-' _'~ ~S,.,~(h).
(1)
t'
We note that in the absence of detect scattering the conductance is simply a Fermi surface property and thus Eq. (1) can be evaluated straightforwardly using first principles band structure calculations. Ballistic metallic point contacts have already been fabricated [6]. For (100) oriented C o / C u multilayers a MR of up to 120% was calculated [7] in the perpendicular (CPP) geometry, which is comparable with experimental results in the diffusive regime [8,9]. This finding for ideal, crystalline structures should be contrasted with the common belief that giant magnetoresistance is mainly due to spin-dependent defect scattering. It indicates that the differences in the number of conduction channels induced by band mismatch make an important contribution to CPP GMR. The results have been analyzed by switching off the hybridization between the d orbitals and the free elecmm like sp states. The result is a collapse of the magnetoresistance from 120 to 3% for a C o s / C u 5 multilayer, from which we conclude that the s p - d hybridization, neglected in most current theoretical treatments, should be taken into account to describe the effect correctly. For the parallel (C1P) geometry the magnetoresistances we calculate are much smaller than experimental values indicating that in this geometry some additional scattering mechanism should be taken into account.
0304-8853/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0 3 0 4 - 8 8 5 3 ( 9 5 ) 0 0 9 1 0 - 8
386
K.M. Schep et al. / Journal of Magnetism and Magnetic Materials 156 (1996) 385-386
We have also performed calculations of the Sharvin conductance for F e / C r multilayers, both in the (100) and in the (110) orientation and for a large number of different layer thicknesses. The calculated MR in the CPP geometry lies between 100 and 200%, which is again comparable to the experimental values [10]. In contrast to C o / C u where most of the current is carried by the majority spin electrons, the conductance in F e / C r is dominated by the minority spin bands which can be understood in terms of the bulk band structures of Fe and Cr. In the CPP geometry for (100) oriented F e / C r we find a pronounced quantum size effect in the MR, see Fig. l, mainly as a function of the Fe thickness. Size effects were also found in C o / C u , but in F e / C r they can be much larger making an experimental observation more likely in this system. Another difference with C o / C u is that for (100) oriented F e ~ / C r m (i.e. each bilayer consists of n monolayers of Fe and m monolayers of Cr) the calculated CIP MR is somewhere in between 40 and 70% and does not vary much as a function of layer thickness as shown in Fig. 2 for m = n. This result can be interpreted in terms of the atomic structure of the interface. In the (100) orientation of a bcc multilayer the density of atoms in the atomic planes is low while the different atomic planes are close together, which gives rise to an interface that is not very flat, although it is atomically sharp! This modulated interface causes backscattering of the electrons at the Brillouin zone boundaries which depends on the magnetic configuration and the spin direction and can thereby give rise to a considerable decrease in
80--~,,, g 6o
0.4
r, ~
0.6
.....
0.8 1.0 Thickness (rim)
,,,,
'(1~ ~O0)t
1.2
1.4
Fig. 2. The layer thickness dependence of the CIP MR for F e . / C r n multilayers in the (100) ( 0 ) and the (110) (O) orientation. Note that the layer thickness is plotted in nanometers because the thickness per monolayer is different for the two orientations. the CIP conductance when switching from the parallel to the anti-parallel configuration, as in the CPP geometry. The (110) interface is much flatter and indeed we find for (110) oriented F e / C r multilayers a CIP MR of only a few percent (Fig. 2), as in C o / C u [7]. This difference between the (100) and the (110) orientation indicates that the CIP GMR is very sensitive to the interface structure down to the monolayer level.
References ~
~
o~
'
0.4
'
' ~
~
--200
!
Groin
!
100~
r..) ~ 0.0
~ ~J 1 2
3
~
~ 4
~ 5
o ~-~D GAP
~ 6
, _ , 7 8
Iron thickness (monolayers)
_0 i
Fig. 1. The iron thickness dependence for (100) oriented Fe~/Cr 6 multilayers of the MR (Q) and of the conductances G for the majority (©) and the minority ([]) spin in the parallel configuration and for both spins in the anti-parallel configuration (O), all in the CPP geometry. The MR is defined as (Gm~j+Gmi~ -
2Gp)/2Gp.
[1] P.M. Levy, Solid State Phys. 47 (1994) 367 and references therein. [2] Yu.V. Sharvin, Zh. Eksp. Teor. Fiz. 48 (1965) 984; Sov. Phys. JETP 21 (1965) 655. [3] G. Wexler, Proc. Phys. Soc. London 89 (1966) 927. [4] G.E.W. Bauer, A. Brataas, K.M. Schep and P.J. Kelly, J. Appl. Phys. 75 (1994) 6704. [5] K.M. Schep, P.J. Kelly and G.E.W. Bauer, Mater. Res. Soc. Symp. Proc. 384 (1995) 305. [6] P.A.M. Holweg, J.A. Kokkedee, J. Caro, A.H. Verbruggen, S. Radelaar, A.G.M. Jansen and P. Wyder, Phys. Rev. Lett. 67 (1991) 2549. [7] K.M. Schep, P.J. Kelly and G.E.W. Bauer, Phys. Rev. Len. 74 (1995) 586; J. Magn. Magn. Mater. 140-144 (1995) 503. [8] W.P. Pratt, Jr., S.-F. Lee, P. Holody, Q. Yang, R. Loloee, J. Bass and P.A. Schroeder, J. Magn. Magn. Mater. 126 (•993) 406. [9] M.A.M. Gijs, J.B. Giesbers, M.T. Johnson, J.B.F. aan de Stegge, H.H.J.M. Janssen, S.K.J. Lenczowski, R.J.M. van de Veerdonk, W.J.M. de Jonge, J. Appl. Phys. 75 (1994) 6709. [10] M.A.M. Gijs, S.K.J. Lenczowski and J.B. Giesbers, Phys. Rev. Lett. 70 (1993) 3343.
~i
Journalof magnetism ~ i ~ and magnetic materials
N
ELSEVIER
Ballistic giant magnetoresistance Kees M. Schep
a,b,*, Paul J. Kelly a, Gerrit E.W.
Bauer b
a Philips Research Laboratories, Profi Holstlaan 4, 5656 AA Eindhol,en. The Netherlands h FaculO' of Applied Physics and DIMES Delft University qf Technology. Lorentzweg 1. 2628 CJ De!ft. The Netherhmds Abstract
We present a theoretical study of the giant magnetoresistance in the ballistic regime for C o / C u and F e / C r multilayers which emphasizes the importance of band structure effects, both for the perpendicular (CPP) and the parallel (CIP) geometry.
A giant magnetoresistance (GMR) effect in antiferromagnetically coupled magnetic multilayers arises when the anti-parallel magnetizations of adjacent magnetic layers are forced to become parallel by an external magnetic field. In spite of extensive experimental and theoretical investigations [I] the microscopic origin of the GMR remains unclear. One of the outstanding questions concerns the determination of the relative importance of spindependent band structure mismatch between the two materials constituting the multilayer and spin-dependent scattering at defects either in the bulk or at the interfaces. The focus of both theoretical and experimental work has been on the diffusive transport regime in which the sample dimensions are much larger than the electron mean free path. In this regime the contributions of band structure mismatch and defect scattering are strongly intertwined, thus making an experimental distinction between the two difficult. In this contribution we focus on the ballistic transport regime in which defect scattering no longer contributes to the resistance and a rigorous theoretical evaluation of the band structure effects on the MR is feasible. By making detailed predictions we hope to stimulate experiments in this regime in order to assess the importance of band structure effects and, more generally, because such experiments should help to provide a better understanding of the factors influencing the GMR in macroscopic samples. We consider a multilayer structure where the total resistance is dominated by a classical point contact with a diameter much smaller than the mean free path and much larger than the electron wavelength [2,3]. Even though the electrons passing through the constriction are not scattered
* Corresponding author. Fax: schep@ natlab.research.philips.com.
+31-40-2743365;
email:
out of their Bloch states by detects, the conductance of the point contact is finite due to its finite cross section A. This ballistic (Sharvin) conductance G,: for spin ~r is simply the conductance quantum e 2 / h times the number of conduction channels N,~ [4,5]. N,, is proportional to A and to the sum of the projections S,,,~ of the ~,th sheet of the spin o- Fermi surface onto the plane normal to the transport direction h: e2
G,~(~) = ~-N,~(h)
e2
A
1
h 47r-' _'~ ~S,.,~(h).
(1)
t'
We note that in the absence of detect scattering the conductance is simply a Fermi surface property and thus Eq. (1) can be evaluated straightforwardly using first principles band structure calculations. Ballistic metallic point contacts have already been fabricated [6]. For (100) oriented C o / C u multilayers a MR of up to 120% was calculated [7] in the perpendicular (CPP) geometry, which is comparable with experimental results in the diffusive regime [8,9]. This finding for ideal, crystalline structures should be contrasted with the common belief that giant magnetoresistance is mainly due to spin-dependent defect scattering. It indicates that the differences in the number of conduction channels induced by band mismatch make an important contribution to CPP GMR. The results have been analyzed by switching off the hybridization between the d orbitals and the free elecmm like sp states. The result is a collapse of the magnetoresistance from 120 to 3% for a C o s / C u 5 multilayer, from which we conclude that the s p - d hybridization, neglected in most current theoretical treatments, should be taken into account to describe the effect correctly. For the parallel (C1P) geometry the magnetoresistances we calculate are much smaller than experimental values indicating that in this geometry some additional scattering mechanism should be taken into account.
0304-8853/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0 3 0 4 - 8 8 5 3 ( 9 5 ) 0 0 9 1 0 - 8
386
K.M. Schep et al. / Journal of Magnetism and Magnetic Materials 156 (1996) 385-386
We have also performed calculations of the Sharvin conductance for F e / C r multilayers, both in the (100) and in the (110) orientation and for a large number of different layer thicknesses. The calculated MR in the CPP geometry lies between 100 and 200%, which is again comparable to the experimental values [10]. In contrast to C o / C u where most of the current is carried by the majority spin electrons, the conductance in F e / C r is dominated by the minority spin bands which can be understood in terms of the bulk band structures of Fe and Cr. In the CPP geometry for (100) oriented F e / C r we find a pronounced quantum size effect in the MR, see Fig. l, mainly as a function of the Fe thickness. Size effects were also found in C o / C u , but in F e / C r they can be much larger making an experimental observation more likely in this system. Another difference with C o / C u is that for (100) oriented F e ~ / C r m (i.e. each bilayer consists of n monolayers of Fe and m monolayers of Cr) the calculated CIP MR is somewhere in between 40 and 70% and does not vary much as a function of layer thickness as shown in Fig. 2 for m = n. This result can be interpreted in terms of the atomic structure of the interface. In the (100) orientation of a bcc multilayer the density of atoms in the atomic planes is low while the different atomic planes are close together, which gives rise to an interface that is not very flat, although it is atomically sharp! This modulated interface causes backscattering of the electrons at the Brillouin zone boundaries which depends on the magnetic configuration and the spin direction and can thereby give rise to a considerable decrease in
80--~,,, g 6o
0.4
r, ~
0.6
.....
0.8 1.0 Thickness (rim)
,,,,
'(1~ ~O0)t
1.2
1.4
Fig. 2. The layer thickness dependence of the CIP MR for F e . / C r n multilayers in the (100) ( 0 ) and the (110) (O) orientation. Note that the layer thickness is plotted in nanometers because the thickness per monolayer is different for the two orientations. the CIP conductance when switching from the parallel to the anti-parallel configuration, as in the CPP geometry. The (110) interface is much flatter and indeed we find for (110) oriented F e / C r multilayers a CIP MR of only a few percent (Fig. 2), as in C o / C u [7]. This difference between the (100) and the (110) orientation indicates that the CIP GMR is very sensitive to the interface structure down to the monolayer level.
References ~
~
o~
'
0.4
'
' ~
~
--200
!
Groin
!
100~
r..) ~ 0.0
~ ~J 1 2
3
~
~ 4
~ 5
o ~-~D GAP
~ 6
, _ , 7 8
Iron thickness (monolayers)
_0 i
Fig. 1. The iron thickness dependence for (100) oriented Fe~/Cr 6 multilayers of the MR (Q) and of the conductances G for the majority (©) and the minority ([]) spin in the parallel configuration and for both spins in the anti-parallel configuration (O), all in the CPP geometry. The MR is defined as (Gm~j+Gmi~ -
2Gp)/2Gp.
[1] P.M. Levy, Solid State Phys. 47 (1994) 367 and references therein. [2] Yu.V. Sharvin, Zh. Eksp. Teor. Fiz. 48 (1965) 984; Sov. Phys. JETP 21 (1965) 655. [3] G. Wexler, Proc. Phys. Soc. London 89 (1966) 927. [4] G.E.W. Bauer, A. Brataas, K.M. Schep and P.J. Kelly, J. Appl. Phys. 75 (1994) 6704. [5] K.M. Schep, P.J. Kelly and G.E.W. Bauer, Mater. Res. Soc. Symp. Proc. 384 (1995) 305. [6] P.A.M. Holweg, J.A. Kokkedee, J. Caro, A.H. Verbruggen, S. Radelaar, A.G.M. Jansen and P. Wyder, Phys. Rev. Lett. 67 (1991) 2549. [7] K.M. Schep, P.J. Kelly and G.E.W. Bauer, Phys. Rev. Len. 74 (1995) 586; J. Magn. Magn. Mater. 140-144 (1995) 503. [8] W.P. Pratt, Jr., S.-F. Lee, P. Holody, Q. Yang, R. Loloee, J. Bass and P.A. Schroeder, J. Magn. Magn. Mater. 126 (•993) 406. [9] M.A.M. Gijs, J.B. Giesbers, M.T. Johnson, J.B.F. aan de Stegge, H.H.J.M. Janssen, S.K.J. Lenczowski, R.J.M. van de Veerdonk, W.J.M. de Jonge, J. Appl. Phys. 75 (1994) 6709. [10] M.A.M. Gijs, S.K.J. Lenczowski and J.B. Giesbers, Phys. Rev. Lett. 70 (1993) 3343.