Ferromagnetic polarons in the one-dimensional ferromagnetic Kondo model with quantum mechanical $S=3∕2$ core spins

We present an extensive numerical study of the ferromagnetic Kondo lattice model with quantum mechanical $S=3∕2$ core spins. We treat one orbital per site in one dimension using the density-matrix renormalization group and include on-site Coulomb repulsion between the electrons. We examine parameters relevant to manganites, treating the range of low to intermediate doping, $0\lesssim x<0.5$. In particular, we investigate whether quantum fluctuations favor phase separation over the ferromagnetic polarons observed in a model with classical core spins. We obtain very good agreement of the quantum model with previous results for the classical model, finding separated polarons, which are repulsive at short distance for finite $t_{2g}$ superexchange $J^{\prime }$. Taking on-site Coulomb repulsion into account, we observe phase separation for small but finite superexchange $J^{\prime }$, whereas for larger $J^{\prime }$, polarons are favored in accordance with simple energy considerations previously applied to classical spins. We discuss the interpretation of compressibilities and present a phase diagram with respect to doping and the $t_{2g}$ superexchange parameter $J^{\prime }$ with and without Coulomb repulsion.

Figure 1

Local density $⟨n_i⟩$ and core spin-core spin correlations $⟨S_i{S}_{i+1}⟩$ of the DMRG ground state for a chain of length $L=24$ with $J^{\prime }=0.01$ and $U=0$. Three well-separated polarons can be clearly seen.

Figure 2

Ground-state energy $E_0$ as a function of the distance $d$ of two polarons on an $L=24$ site chain with $J^{\prime }=0.01$, $U=0$. The holes are centered at the position of electrostatic impurity potentials $E_{\mathrm{pot}}=-0.1$ and exhibit a symmetric density distribution. The energies for $d⩾5$ are degenerate within the estimated numerical accuracy as designated by the error bars.

Figure 3

(Color online) Dressed core spin correlation function, Eq. (3), for classical core spins with effective spinless fermions for $J^{\prime }=0$, $U=0$, inverse temperature $\beta =1∕T=100$, and an $L=24$ site chain. The ferromagnetic area grows with doping, indicating phase separation.

Figure 4

(Color online) Dressed core spin correlation, Eq. (3), for quantum-mechanical core spins for $U=0$ and (a) $J^{\prime }=0.01$ and (b) $J^{\prime }=0$ on an $L=24$ site chain. In the polaronic regime (a), there is no dependence of the size of the ferromagnetic area on doping, in contrast to the phase separated case (b).

Figure 5

(Color online) Dressed core spin correlation, Eq. (3), for quantum-mechanical core spins for $U=10$ and (a) $J^{\prime }=0.01$ and (b) $J^{\prime }=0$ on an $L=24$ site chain. The pronounced dependence on doping indicates phase separation.

Figure 6

On-site density $⟨n_i⟩$ and core spin-core spin correlations $⟨S_i{S}_{i+1}⟩$ of the DMRG ground state for $J^{\prime }=0.01$, $U=0$ and (a) 6 holes $(x=1∕4)$ and (b) 7 holes.

Figure 7

On-site density $⟨n_i⟩$ and core spin-core spin correlations $⟨S_i{S}_{i+1}⟩$ of the DMRG ground state for $J^{\prime }=0.02$, $U=0$ and (a) 8 holes $(x=1∕3)$ and (b) 9 holes.

Figure 8

(Color online) Phase diagram in the $n-J^{\prime }$ plane for $U=0$. The symbols designate the following characteristics: P, polarons, ILP, island phase (periodic arrangement of polarons); PS, phase separation; FM, ferromagnetic; and FR, central ferromagnetic region with antiferromagnetically oriented sites at the ends of the chain. The symbols (letters) are determined for an $L=24$ site chain.

Figure 9

(Color online) Phase diagram as in Fig. 8, but with $U=10$.

Figure 10

Grand canonical expectation value for the electron density $⟨n⟩$ vs chemical potential $\mu$ for $J^{\prime }=0.01$, $L=24$ and (a) $U=0$, (b) $U=10$. The dashed lines indicate the limits of the (a) polaronic or (b) phase-separated and the FM regimes, respectively.