Magnetic field effects for the asymmetric Anderson Hamiltonian

Abstract

Perturbation expansion for the asymmetric single-orbital Anderson Hamiltonian is extended to the case with finite magnetic field, and the self-energy part of the $d$-electron Green function is calculated up to the second order in $u=\frac{U }{\pi \Delta }$ for arbitrary asymmetry $\eta =\frac{1}{2}+\frac{{\epsilon }_d}{U}$ and magnetic field $h$. Zero-temperature density of localized states ${\rho }_{d\sigma }\left(\omega \right)$, magnetic moment $m$ and static spin susceptibility $\chi$, and low-temperature specific heat $C_v=\gamma T$ and magnetoresistance $D$ of a dilute alloy are evaluated within the $u^2$ approximation. Plausible arguments are given (which become exact in the symmetric case) that the higher-order terms do not change the qualitative features of our results. For large enough $u$ the many-body (MB) effects give rise to three different types of behavior, depending on the value of asymmetry: (i) spin-fluctuation behavior for $\eta <\frac{1}{2}$, with large fluctuations of the $d$-level magnetization; (ii) mixed-valence behavior for $\eta \simeq \frac{1}{2}$, with large fluctuations of the $d$-level occupation; (iii) essentially mean-field behavior for $\eta >\frac{1}{2}$, where the MB effects are negligible even for $u\gg 1$. Thus both $\chi$ and $\gamma$ at $h=0\mathrm{}$ are enhanced by the increase of $u$ for $\eta <\frac{1}{2}$, reduced for $\eta >\frac{1}{2}$, and practically unaffected at $\eta \simeq \frac{1}{2}$. As functions of $\eta$ for a fixed $u$, $\chi$ and $\gamma$ have a maximum at $\eta =0\mathrm{}$ and decrease monotonously with increasing $\eta$, and do so more steeply the higher the $u$. For $h\ne 0$ and $\eta \le \frac{1}{2}$, $\chi$ and $\gamma$ decrease monotonously with increasing $h$, the decrease being quicker for higher $u$ and slower for higher $\eta$. For $\eta >\frac{1}{2}$, both

Keywords

• GREEN FUNCTION
• MAGNETIC FIELD
• SECOND ORDER
• HIGHER ORDER
• HARTREE FOCK
• MAGNETIC MOMENT
• SPECIFIC HEAT

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