Quantum transport properties of a two-channel atomic-sized magnetic contact
C. A. Dartora and G. G. Cabrera
Instituto de Física “Gleb Wataghin,” Universidade Estadual de Campinas (UNICAMP), Caixa Postal 6165,
Campinas 13083-970 SP, Brazil
Received 25 October 2004; revised manuscript received 1 June 2005; published 31 August 2005
We propose a simple model to theoretically study the conductance of atomic-sized magnetic contacts. Our
approach considers in detail the case of two-atom contacts with two spin channels, and the conductance is
calculated using Landauer theory in the ballistic regime. For ferromagnetic contacts, we examine the large
magnetoresistance effect obtained, when changing the magnetic configuration of the leads from parallel to
antiparallel. We also discuss nonmagnetic transition metals nanocontacts, where conductance measurements
display a behavior similar to magnetic contacts. Our treatment of the above phenomena reveals the important
role played by quantum fluctuations in the contact region.
DOI: 10.1103/PhysRevB.72.064456 PACS numbers: 75.75.+a, 75.47.Jn, 72.25.-b, 73.23.-b
I. INTRODUCTION
The study of electronic transport properties in mesoscopic
magnetic structures is attracting growing interest due to po-
tential applications in microelectronics and information tech-
nologies in their drive for reducing the size of devices.
1–5
Of
most interest is the change in resistivity due to applied mag-
netic fields, namely, the magnetoresistance MR effect
which occurs in ferromagnetic nanocontacts
6–9
and in mag-
netic tunneling junctions MTJ’s.
10
The effect is order of
magnitude larger in nanocontacts, with values of MR in the
range of 300–3000 %, as been reported in the current
literature.
8,9
In contrast, typical MR values encountered in
MTJ’s are at most of the order of 30%.
10
The dissimilar
behavior of the above systems is due to different scattering
mechanisms that dominate their transport properties. For
MTJ’s, the majority and minority spin densities of states at
both sides of the tunneling junction are interchange with the
applied magnetic field, being the transport governed by tun-
neling and density of states effects.
11–15
In nanocontacts, the
MR effect is attributed to strong electron scattering from
narrow domain walls which are formed in the contact
region.
1–5,8
Due to the constricted geometry and the rapid
variation of the magnetization across the domain wall, the
electron spin cannot follow adiabatically the local
magnetization,
2
as it is the case in bulk ferromagnets.
16
In
this paper, we discuss atomic-sized point contacts, a situation
that has been realized in practice in some experiments.
6,7,17
When the size of the contact region is reduced to atomic
dimensions, the physics involved is ruled by pure quantum
phenomena. If two ferromagnetic electrodes are joined by a
ferromagnetic nanowire, transport of conduction electrons
will be affected by the magnetic profile across the wire.
When the electrode magnetizations are oriented antiparallel,
a quantum wall or “kink” will be generated at the center of
the nanowire. The width of this atomic wall depends on the
relative strength of quantum fluctuations, which in turn will
scatter conduction electrons through the spin magnetic cou-
pling. The above interaction lifts the spin degeneracy of con-
ducting channels, reducing the conductance quantum to
e
2
/2 for each channel. Differently from the phenomena
discussed above, where the MR effect is associated with nar-
row domain walls in the region of the nanocontact, for quan-
tum walls the local magnetic moment varies significantly
over an atomic scale. We are aware that a practical imple-
mentation of the above idealized setup is still a challenge for
experimentalists.
6
Several theoretical approaches to this problem have been
presented.
6,18,19
In this paper we propose a simple model to
describe the conductance of an atomic-sized contact, relating
the above to microscopic parameters of the theory in a very
intuitive way. In particular, concerning the MR effect, we
stress the important role of quantum fluctuations. For a quali-
tative understanding of the physics involved, we solve an
example which can be worked out analytically, i.e., the case
of an atomic contact made up of two atoms, with two spin
channels. The atoms are connected to ferromagnetic elec-
trodes, which for simplicity are assumed to be identical. Also
the atoms are of the same species as the electrodes we dis-
cuss ferromagnetic transition metals. This is a crude, but not
trivial, simplification of the case discussed above. The prob-
lem can be readily extended to N-site atomic wires, but in
general, one has to rely on numerical solutions.
For the atoms at the contact, the d orbitals will be more
localized than in the bulk. Their higher degree of localization
and the reduced dimensionality produce an enhancement of
the local magnetic moment in the contact region.
20
Our ideal
setup of the contact selects only two spin channels coming
from the same orbital function, which for simplicity, is as-
sumed to be of s character. The local moments couple among
themselves and with the magnetic electrodes via the ex-
change interaction. The former will be treated with some
detail in order to consider the strong quantum fluctuations at
the contact and the latter will be handled within an effective
field theory which models the electrodes as spin reservoirs.
Carriers flowing through the contact interact with the mag-
netic moments via the s-d exchange
21
H
sd
=-
i
J
sd
iS
i
·
x - x
i
, 1
which depends on the contact magnetic configuration and
originates the MR effect. In relation 1, S
i
and
are the
PHYSICAL REVIEW B 72, 064456 2005
1098-0121/2005/726/0644569/$23.00 ©2005 The American Physical Society 064456-1