Kondo effect in quantum dots coupled to ferromagnetic leads: Effect of noncollinear magnetization

We study the Kondo effect in a quantum dot coupled to two noncollinear ferromagnetic leads. First, we study the spin splitting delta epsilon = epsilon(down arrow) - epsilon(up arrow) in the quantum dot by the tunnel coupling to the ferromagnetic leads, using the Poor man's scaling method. The spin splitting takes place in an intermediate direction between magnetic moments in the two leads. delta epsilon proportional to p cos(theta / 2), where p is the spin polarization in the leads and theta is the angle between the magnetic moments; spin splitting is maximal in the parallel alignment of two ferromagnets (theta = 0) and minimal in the antiparallel alignment (theta = pi). Second, we calculate the Kondo temperature T-K. The scaling calculation yields an analytical expression of TK as a function of theta and p, T-K(theta, p), when delta epsilon << T-K. When delta epsilon is relevant, we evaluate T-K(delta epsilon, theta, p) using the slave-boson mean-field method. The Kondo resonance is split into two by finite delta epsilon, which results in the suppression of Kondo effect.