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arXiv:cond-mat/9809281 · Physical review. B, Condensed matter

Influence of nearest-neighbor Coulomb interactions on the phase diagram of the ferromagnetic Kondo model

André Luiz Malvezzi, Seiji Yunoki, Elbio R. Dagotto

Published Mar 1, 1999• 35 citations
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Abstract

The influence of a nearest-neighbor Coulomb repulsion of strength V on the properties of the ferromagnetic Kondo model is analyzed using computational techniques. The Hamiltonian studied here is defined on a chain using localized $S=1/2$ spins, and one orbital per site. Special emphasis is given to the influence of the Coulomb repulsion on the regions of phase separation recently discovered in this family of models, as well as on the double-exchange-induced ferromagnetic ground state. When phase separation dominates at $V=0,$ the Coulomb interaction breaks the large domains of the two competing phases into small ``islands'' of one phase embedded into the other. This is in agreement with several experimental results, as discussed in the text. Vestiges of the original phase separation regime are found in the spin structure factor as incommensurate peaks, even at large values of V. In the ferromagnetic regime close to density $n=0.5,$ the Coulomb interaction induces tendencies to charge ordering without altering the fully polarized character of the state. This regime of ``charge-ordered ferromagnetism'' may be related with experimental observations of a similar phase by Chen and Cheong [Phys. Rev. Lett. 76, 4042 (1996)]. Our results reinforce the recently introduced notion [see, e.g., S. Yunoki et al., Phys. Rev. Lett. 80, 845 (1998)] that in realistic models for manganites analyzed with unbiased many-body techniques, the ground state properties arise from a competition between ferromagnetism and phase-separation--charge-ordering tendencies.

DOI
10.1103/physrevb.59.7033

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The influence of a nearest-neighbor Coulomb repulsion of strength V on the properties of the ferromagnetic Kondo model is analyzed using computational techniques. The Hamiltonian studied here is defined on a chain using localized S=1/2S=1/2S=1/2 spins, and one orbital per site. Special emphasis is given to the influence of the Coulomb repulsion on the regions of phase separation recently discovered in this family of models, as well as on the double-exchange-induced ferromagnetic ground state. When phase separation dominates at V=0,V=0,V=0, the Coulomb interaction breaks the large domains of the two competing phases into small islands'' of one phase embedded into the other. This is in agreement with several experimental results, as discussed in the text. Vestiges of the original phase separation regime are found in the spin structure factor as incommensurate peaks, even at large values of V. In the ferromagnetic regime close to density $n=0.5,$ the Coulomb interaction induces tendencies to charge ordering without altering the fully polarized character of the state. This regime of charge-ordered ferromagnetism'' may be related with experimental observations of a similar phase by Chen and Cheong [Phys. Rev. Lett. 76, 4042 (1996)]. Our results reinforce the recently introduced notion [see, e.g., S. Yunoki et al., Phys. Rev. Lett. 80, 845 (1998)] that in realistic models for manganites analyzed with unbiased many-body techniques, the ground state properties arise from a competition between ferromagnetism and phase-separation--charge-ordering tendencies.
We present an extensive numerical study of the ferromagnetic Kondo lattice model with quantum mechanical S=3∕2S=3∕2S=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, $0\ensuremath{\lesssim}x<0.5$. 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 t2g{t}_{2g}t2g​ superexchange ${J}^{\ensuremath{'}}$. Taking on-site Coulomb repulsion into account, we observe phase separation for small but finite superexchange ${J}^{\ensuremath{'}}$, whereas for larger ${J}^{\ensuremath{'}}$, 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 t2g{t}_{2g}t2g​ superexchange parameter ${J}^{\ensuremath{'}}$ with and without Coulomb repulsion.
We study the effects of the Coulomb interaction in the one-dimensional Kondo lattice model on the phase diagram, the static magnetic susceptibility, and electron spin relaxation. We show that onsite Coulomb interaction supports ferromagnetic order and nearest-neighbor Coulomb interaction drives, depending on the electron filling, either a paramagnetic or a ferromagnetic order. Furthermore, we calculate electron quasiparticle lifetimes, which can be related to electron spin relaxation and decoherence times, and explain their dependence on the strength of interactions and the electron filling in order to find the sweet spot of parameters where the relaxation time is maximized. We find that effective exchange processes between the electrons dominate the spin relaxation and decoherence rate.
Using a non-Abelian density matrix renormalization group method we determine the phase diagram of the Kondo lattice model in one dimension, by directly measuring the magnetization of the ground state. This allowed us to discover a second ferromagnetic phase missed in previous approaches. The phase transitions are found to be continuous. The spin-spin correlation function is studied in detail, and we determine in which regions the large and small Fermi surfaces dominate. The importance of double-exchange ordering and its competition with Kondo singlet formation is emphasized in understanding the complexity of the model.
Ferromagnetism in the one-dimensional Hubbard model with the next-nearest-neighbor hopping is explored by using the exact-diagonalization method in a small cluster and the equation-of-motion method in the thermodynamic limit with electron density n = 3/2. With these two complementary methods, it is found that an intermediate value of the next-nearest-neighbor hopping amplitude t1 tends to stabilize the fully polarized ferromagnetic state under the condition that the on-site coulomb interaction U is sufficiently large in our model. The ground-state phase diagram of the model is presented in the t1—U plane.
A wide variety of experimental platforms, ranging from semiconductor quantum-dot arrays to moiré materials, have recently emerged as powerful quantum simulators for studying the Hubbard model and its variants. Motivated by these developments, here, we investigate a generalization of the Hubbard model which includes the effects of long-range Coulomb interactions. Working on finite-sized two-dimensional square and triangular lattices, we use exact diagonalization and density-matrix renormalization group calculations to probe the magnetic structure of the ground state in the strong-coupling regime, where UUU (the onsite repulsion) ≫\gg≫ ttt (the nearest-neighbor hopping). For small electron dopings above the half-filled antiferromagnet, we numerically uncover a rich variety of magnetically ordered states, and in conjunction with theoretical arguments, infer the phase diagram of the system as a function of doping and interaction strengths. In particular, we find that the inclusion of long-range Coulomb interactions induces an instability of high-spin states$\unicode{x2014}$such as the saturated Nagaoka ferromagnet$\unicode{x2014}$towards phase separation and stripe ordering. We also present proposals for the observation of some of our key findings in experiments that would shed further light on this paradigmatic strongly correlated system.
The effect of next-nearest-neighbor hopping t2{t}_{2}t2​ on the ground-state phase diagram of the one-dimensional Kondo lattice is studied with density-matrix renormalization-group techniques and by comparing with the phase diagram of the classical-spin variant of the same model. For a finite t2{t}_{2}t2​, i.e., for a zigzag-ladder geometry, indirect antiferromagnetic interactions between the localized spins are geometrically frustrated. We demonstrate that t2{t}_{2}t2​ at the same time triggers several magnetic phases which are absent in the model with nearest-neighbor hopping only. For strong JJJ, we find a transition from antiferromagnetic to incommensurate magnetic short-range order, which can be understood entirely in the classical-spin picture. For weaker JJJ, a spin-dimerized phase emerges, which spontaneously breaks the discrete translation symmetry. The phase is not accessible to perturbative means but is explained, on a qualitative level, by the classical-spin model as well. Spin dimerization alleviates magnetic frustration and is interpreted as a key to understand the emergence of quasi-long-range spiral magnetic order, which is found at weaker couplings. The phase diagram at weak JJJ, with gapless quasi-long-range order on top of the twofold degenerate spin-dimerized ground state, competing with a nondegenerate phase with gapped spin (and charge) excitations, is unconventional and eludes an effective low-energy spin-only theory.