English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study the Kondo effect in a quantum dot coupled to two noncollinearferromagnetic leads. First, we study the spin splitting$\delta\epsilon=\epsilon_{\downarrow}-\epsilon_{\uparrow}$ of an energy levelin the quantum dot by tunnel couplings to the ferromagnetic leads, using thePoor man's scaling method. The spin splitting takes place in an intermediatedirection between magnetic moments in the two leads. $\delta\epsilon \proptop\sqrt{\cos^2(\theta/2)+v^2\sin^2(\theta/2)}$, where $p$ is the spinpolarization in the leads, $\theta$ is the angle between the magnetic moments,and $v$ is an asymmetric factor of tunnel barriers ($-1<v<1$). Hence the spinsplitting is always maximal in the parallel alignment of two ferromagnets($\theta=0$) and minimal in the antiparallel alignment ($\theta=\pi$). Second,we calculate the Kondo temperature $T_{\mathrm{K}}$. The scaling calculationyields an analytical expression of $T_{\mathrm{K}}$ as a function of $\theta$and $p$, $T_{\mathrm{K}}(\theta, p)$, when $\delta\epsilon \ll T_{\mathrm{K}}$.$T_{\mathrm{K}}(\theta, p)$ is a decreasing function with respect to$p\sqrt{\cos^2(\theta/2)+v^2\sin^2(\theta/2)}$. When $\delta\epsilon$ isrelevant, we evaluate $T_{\mathrm{K}}(\delta\epsilon, \theta, p)$ using theslave-boson mean-field theory. The Kondo resonance is split into two by finite$\delta\epsilon$, which results in the spin accumulation in the quantum dot andsuppression of the Kondo effect.Comment: 11 pages, 8 figures, revised versio

Spin splitting and Kondo effect in quantum dots coupled to noncollinear ferromagnetic leads