ISSN 1063-7834, Physics of the Solid State, 2009, Vol. 51, No. 3, pp. 540–546. © Pleiades Publishing, Ltd., 2009. Original Russian Text © N.Kh. Useinov, 2009, published in Fizika Tverdogo Tela, 2009, Vol. 51, No. 3, pp. 508–513. 540 MAGNETISM AND FERROELECTRICITY 1. INTRODUCTION Experiments on the magnetoresistance (MR) of magnetic nanocontacts with atomic sizes between fer- romagnetic metals have revealed a giant increase in the magnetoresistance in weak magnetic fields at room temperature [1–11]. Therefore, magnetic nanocompo- nents have been proposed as the main operating units in the design of new spintronic devices, such as magne- toresistive sensors and nanosize read heads for com- puter hard disks [12]. In order to explain the experimental data on the giant magnetoresistance of magnetic nanocontacts, it has been proposed to take into account the enhance- ment of scattering of a conduction electron from impu- rities in its motion in the inhomogeneous potential pro- duced by the domain wall [13] and the additional scat- tering from the potential of the domain wall due to the limited geometry of the contact [14–16], because the domain wall appears to be constrained in a narrow con- tact with atomic sizes (2–50 Å). The theory of conductance and magnetoresistance of magnetic nanocontacts includes the quasi-classical and quantum regimes [14–20]. The ballistic magnetore- sistance in the quasi-classical approximation can easily reach several hundreds of percent in the case of strong polarization of the conduction bands of ferromagnetic metals. In the regime of conductance quantization, the ballistic magnetoresistance of the magnetic nanocon- tact additionally increases in several first open conduc- tion channels for the parallel alignment of the magneti- zations of single-domain sides of the contact [14, 16]. The regime of conductance quantization through nanocontacts was considered and the conductances for the parallel (P) and antiparallel (AP) alignment of the magnetizations of contacting magnetic domains were calculated in [15–19]. In the case of the parallel align- ment of the magnetizations, one spin conduction chan- nel is open, whereas the conductance of the nanocon- tact for the antiparallel alignment of the magnetizations is equal to zero due to the quantization. In this case, the ballistic magnetoresistance infinitely increases because the conductance for the antiparallel alignment enters into the denominator in the formula defining the mag- netoresistance (1) This effect, which is associated with the control of the magnetoresistance of the magnetic point contact, was termed the quantum spin valve regime [17]. However, it is clear that any spin-flip process accompanying the electron transmission through the nanocontact destroys the blockage of the antiparallel conductance as a result of the quantization. In this case, the magnetoresistance becomes limited. In order to prove this statement, we calculate the quantized conductance for the parallel and antiparallel alignments of the magnetizations of magnetic domains between two identical ferromagnets. In this case, we take into account a partial interaction of a conduction electron with the domain-wall profile, which is respon- sible for the electron spin flip. MR G P G AP – G AP ---------------------. = Spin-Flip Conductance and Magnetoresistance of Magnetic Nanocontacts N. Kh. Useinov Kazan State University, Kremlevskaya ul. 18, Kazan, 420008 Tatarstan, Russia e-mail: nuseinov@mail.ru Received February 4, 2008; in final form, June 17, 2008 Abstract—The quantized conductance of nanocontacts with atomic sizes is calculated with allowance made for the conduction-electron spin flip in terms of the quantum scattering theory. The exact solution of the Schrödinger equation describing the electron motion in a piecewise-smooth potential is used as the zeroth-order approximation of the perturbation theory. The probabilities of electron transmission (reflection) through a mag- netic domain wall, as well as the spin-conserving and spin-flip conductances of the nanocontact, are calculated. It is demonstrated that the spin-flip conductance imposes the natural limitation on the formally infinite increase in the ballistic magnetoresistance of the nanocontact when its cross-sectional area tends to zero. PACS numbers: 72.25.Ba, 75.47.Jn, 81.07.Lk DOI: 10.1134/S1063783409030184