Magnon-Mediated Interactions between Fermions Depend Strongly on the Lattice Structure

We propose two new methods to calculate exactly the spectrum of two spin-$\frac{1}{2}$ charge carriers moving in a ferromagnetic background, at zero temperature. We find that if the spins are located on a different sublattice than that on which the fermions move, magnon-mediated effective interactions are very strong and can bind the fermions into low-energy bipolarons with triplet character. This never happens in models where spins and charge carriers share the same lattice, whether they are in the same band or in different bands. This proves that effective one-lattice models do not describe correctly the low-energy part of the two-carrier spectrum of a two-sublattice model, even though they may describe the low-energy single-carrier spectrum appropriately.

Figure 1

Models I and II have two bands: one occupied by spins (arrows), and one (empty circles) hosting carriers introduced by doping (filled circles, with arrow showing the spin). In the “parent” model I, these are on different sublattices. In model II, they are on the same lattice. Model III has one band which hosts both spins (arrows) and ZRS-like polaron cores (filled circle).

Figure 2

(a) Model I, and (b) model II density of states ${\rho }_{\downarrow }(k,\omega )=-\frac{1}{\pi }\mathrm{Im}{G}_{\downarrow }(k,\omega )$. Contour plots show exact results. Full lines are Eqs. (1, 2), while dashed lines mark the expected onset of the continuum, at $\underset{q}{min}(E_{k-q,\uparrow }+{\Omega }_q)$. Here $J/t=0.05$, $J_0/t=5$, $\eta /t=0.02$.

Figure 3

Spectral weight $A(k=0,n=n^{\prime }=1,\omega )$ for model I (a) and II (b). Expected continua locations are marked, as are triplet (T) and singlet (S) bipolarons (arrows). Here $J_0/t=20$, $J/t=0.05$, $\eta /t=0.1$ and $U/t=0,1,5$.

Figure 4

The three highest weight configurations contributing to the low-energy bipolaron of model I.