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arXiv:2210.05966 · Physical review. B./Physical review. B

Spatial spin-spin correlations of the single-impurity Anderson model with a ferromagnetic bath

Peng Fan, Ning-Hua Tong, Zhen‐Gang Zhu

Published Oct 17, 2022• 3 citations

Abstract

We investigate the interplay between the Kondo effect and the ferromagnetism by a one dimensional Anderson impurity model with a spin partially polarized bath, using the projective truncation approximation under a Lacroix basis. The equal-time spatial spin-spin correlation function (SSCF) is calculated. For the case of spin-unpolarized conduction electrons, it agrees qualitatively with the results from the density matrix renormalization group. For a system with partially spin-polarized conduction electrons, an oscillation in the envelope of SSCF emerges due to the beating of two Friedel oscillations associated to two spin-split Fermi surfaces of conduction electrons. The period is proportional to the inverse of magnetic field $h$. A fitting formula is proposed to perfectly fit the numerical results of SSCF in both the short- and long-range regions. For large enough bath spin polarization, a bump appears in the curve of the integrated SSCF. It marks the boundary between the suppressed Kondo cloud and the polarized bath sites.

DOI: 10.1103/physrevb.106.155130

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We investigate the interplay between the Kondo effect and the ferromagnetism by a one dimensional Anderson impurity model with a spin partially polarized bath, using the projective truncation approximation under a Lacroix basis. The equal-time spatial spin-spin correlation function (SSCF) is calculated. For the case of spin-unpolarized conduction electrons, it agrees qualitatively with the results from the density matrix renormalization group. For a system with partially spin-polarized conduction electrons, an oscillation in the envelope of SSCF emerges due to the beating of two Friedel oscillations associated to two spin-split Fermi surfaces of conduction electrons. The period is proportional to the inverse of magnetic field

h

. A fitting formula is proposed to perfectly fit the numerical results of SSCF in both the short- and long-range regions. For large enough bath spin polarization, a bump appears in the curve of the integrated SSCF. It marks the boundary between the suppressed Kondo cloud and the polarized bath sites.

A magnetic moment in a metal or in a quantum dot is, at low temperatures, screened by the conduction electrons through the mechanism of the Kondo effect. This gives rise to spin-spin correlations between the magnetic moment and the conduction electrons, which can have a substantial spatial extension. We study this phenomenon, the so-called Kondo cloud, by means of the density matrix renormalization group method for the case of the single-impurity Anderson model. We focus on the question whether the Kondo screening length, typically assumed to be proportional to the inverse Kondo temperature, can be extracted from the spin-spin correlations. For several mechanisms---the gate potential and a magnetic field---which destroy the Kondo effect, we investigate the behavior of the screening cloud induced by these perturbations.

A magnetic moment in a metal or in a quantum dot is, at low temperatures, screened by the conduction electrons through the mechanism of the Kondo effect. This gives rise to spin-spin correlations between the magnetic moment and the conduction electrons, which can have a substantial spatial extension. We study this phenomenon, the so-called Kondo cloud, by means of the density matrix renormalization group method for the case of the single-impurity Anderson model. We focus on the question whether the Kondo screening length, typically assumed to be proportional to the inverse Kondo temperature, can be extracted from the spin-spin correlations. For several mechanisms -- the gate potential and a magnetic field -- that destroy the Kondo effect, we investigate the behavior of the screening cloud induced by these perturbations.

The paramagnetic metallic phase of the one-dimensional Kondo lattice model is studied by the density matrix renormalization group method. We observe charge and spin Friedel oscillations. They reflect the long- range charge-charge and spin-spin correlation functions. The observed oscillations are consistent with a Tomonaga-Luttinger liquid. From the period of the oscillations it is concluded that the Fermi surface is large, including both the conduction electrons and the localized spins,

{\mathit{k}}_{\mathit{F}}

=\ensuremath{\pi}(1+

{\mathit{n}}_{\mathit{c}}

)/2, where

{\mathit{n}}_{\mathit{c}}

is the density of conduction electrons. \textcopyright{} 1996 The American Physical Society.

We analyze the Kondo effect of a magnetic impurity attached to an ultrasmall metallic wire using the density matrix renormalization group. The spatial spin correlation function and the impurity spectral density are computed for system sizes of up to L=511 sites, covering the crossover from L<l{K} to L>l{K}, with l{K} the spin screening length. We establish a proportionality between the weight of the Kondo resonance and l{K} as a function of L. This suggests a spectroscopic way of detecting the Kondo cloud.

We performed numerical diagonalization studies of the periodic Anderson Model on finite chains up to 6 sites, in the integral valence limit for T=0. We find that in the weak coupling (Kondo) region the hybridization between f and conduction electrons induces pronounced correlations between the f spins. These correlations are ferromagnetic for low filling and become antiferromagnetic close to half-filling, with a smooth transition between the limiting cases. In no limit can the physics be completely described by a Ruderman–Kittel–Kasuya–Yosida effective spin Hamiltonian, as f and conduction band electrons are always correlated. To study the onset of long range order we considered also a simpler model for the half-filled case, called ‘‘Kondo necklace.’’ We studied the model at T=0 by numerical diagonalization and finite-size scaling, on chains up to 12 sites. We find that below a finite critical value of the Kondo coupling there exists a gapless phase with quasi long range antiferromagnetic correlations.