Inverse indirect magnetic exchange

Magnetic moments strongly coupled to the spins of conduction electrons in a nanostructure can confine the conduction-electron motion due to scattering at almost localized Kondo singlets. We study the resulting local-moment formation in the conduction-electron system and the magnetic exchange coupling mediated by the Kondo singlets. Its distance dependence is oscillatory and induces robust ferro- or antiferromagnetic order in multi-impurity systems.

Figure 1

IIME mechanism. Lowest many-body eigenenergies $E_n-E_0$ for $n=0,...,7$ in the entire range $0<J<\infty$ (note the nonlinear scale) for the model (1) with $L=8$ host sites and $R=2$ impurity spins 1/2 at the sites $i_1=3$ and $i_2=5$. Multiplicities are indicated (see numbers). The system smoothly crosses over from conventional indirect RKKY exchange ($J\to 0$) to a state for $J\to \infty$ where two local Kondo singlets lead to the formation of two spins $1/2$ in the host which are coupled to a triplet via a magnetically inert Kondo singlet. Pictograms: dominant spin correlations obtained numerically. Energy scale set by the NN hopping $t=1$.

Figure 2

Crossover from the RKKY regime at weak coupling to the IIME regime at strong coupling. Calculated ordered magnetic moments on different sites of a tight-binding chain with spin-1/2 Kondo impurities as functions of $J$ (solid lines, filled symbols) and with Anderson impurities as functions of $8V^2/U$ at Hubbard $U=8$ (dashed, open)—see pictogram for system geometry. Symbols: Density-matrix renormalization group (DMRG) for a system with $L=49$ uncorrelated sites (A and B), $R=25$ impurities (large symbols at $J=5$: $L=89$, $R=45$), open boundary conditions. Lines: Dynamical mean-field theory (DMFT) for $L=100$, $R=50$, periodic boundary conditions. Energy scale: $t=1$.

Figure 3

Magnetic structure of an IIME-coupled system in an artificial $D=2$ geometry. $R=57$ Kondo impurities (filled and open dots) are placed on an $L=22\times 18$ array of uncorrelated sites and coupled locally ($J=5$). Real-space DMFT results for the ordered magnetic moments (color code) at sites in the uncorrelated layer. Periodic boundary conditions are used. Labels: see text.