Spin Order in One-Dimensional Kondo and Hund Lattices

Abstract

We study numerically the one-dimensional Kondo and Hund lattices consisting of localized spins interacting antiferro or ferromagnetically with the itinerant electrons, respectively. Using the Density Matrix Renormalization Group we find, for both models and in the small coupling regime, the existence of new magnetic phases where the local spins order forming ferromagnetic islands coupled antiferromagnetically. Furthermore, by increasing the interaction parameter |J| we find that this order evolves toward the ferromagnetic regime through a spiral-like phase with longer characteristic wave lengths. These results shed new light on the zero temperature magnetic phase diagram for these models. The interplay between charge and spin degrees of freedom in strongly correlated systems has triggered enormous interest in recent years due to the rich variety of phases found in a plethora of compounds. Charge and spin superstructures with a doping dependent wavevector were found for example in La 2−x Sr x NiO 4 using neutron scattering 1 and electron diffraction 2 . Stripe formation together with incommensurate spin fluctuations in High-Tc superconductors can also be regarded as a manifestation of similar phenomena 3 as well as the charge and spin ordering found in many of the doped manganese perovskites. Another large group of compounds, the heavy fermion materials, present various types of ground states including antiferromagnetically ordered states, the normal heavy fermion state as well as superconducting and insulating phases. Heavy-fermion systems and Kondo insulators are typical examples of systems in which the interactions between conduction electrons and quantum localized spins are essential 4,5 . Their physical properties result from an antiferromagnetic coupling J between these two types of particles, the so-called Kondo lattice model (KLM). The corresponding Hamiltonian has the well-known form:The first term represents the conduction electron hopping between nearest-neighbor sites, c † iσ ( c iσ ) being standard creation (annihilation) operators. In the second term the exchange interaction J is antiferromagnetic (J < 0), andIt is interesting to note that, in recent years, the same model Hamiltonian with ferromagnetic coupling (J > 0) has been considered to contain the basic physics of manganites exhibiting the "colossal" magnetoresistance effect 6,7,8,9 . In this case, both localized spins and itinerant electrons originate from manganese d-states. The system is assumed to contain essentially Mn 4+ ions with three localized t 2g orbitals represented as local spins S i and additional itinerant electrons in the e g orbital. Due to the strong Hund coupling the spin of the e g electron is constrained to be parallel to the local spin on that site. Hund's rule together with the hopping term give rise to the "double-exchange" (DE) interaction that favors ferromagnetic ordering of the local spins 10 . In recent literature this model is often referred to as the ferromagnetic Kondo lattice (FKLM), however to avoid confusion ...

Low-energy effective theories of the two-thirds filled Hubbard model on the triangular necklace lattice

“…The U * = 0 version of this model, i.e., the ferromagnetic Kondo lattice model, has been studied in more detail for various dopings [24,25,27,41], but again, the half-filled case has received scant attention. We are only aware of two very brief reports [24,25] that claim that this model is insulating, with antiferromagnetic correlations with a spin gap and has a ground state which belongs to the Haldane phase.…”

“…This results in the simple form of Eq. (25). Indeed, the only higher-order corrections on the dimer involve both down electrons taking part in such a virtual process.…”

“…This provides a simple picture of the insulating state at two-thirds filling in the Hubbard model. It has previously been argued that both the ferromagnetic Kondo lattice model and the ferromagnetic Hubbard-Kondo lattice model have ground states in the Haldane phase [24][25][26][27].…”

Haldane phase in one-dimensional topological Kondo insulators

“…Intuitively, the physics of the problem can be simply understood: the antiferromagnetic Kondo exchange along the diagonal rungs effectively forces the spins to align ferromagnetically across the rungs, even in the absence of a direct coupling [27]. This situation favors the formation of a local triplet in each supersite, and the system mimics the properties of the spin-1 Heisenberg chain [37] or the ferromagnetic Kondo lattice model [15,38], which are examples of systems realizing an insulating Haldane groundstate. A hallmark of this phase is the presence of two topologically protected spin-1/2 magnetic states at the ends of the chain (i.e.,…”

Incommensurate spin-density-wave and metal-insulator transition in the one-dimensional periodic Anderson model

“…Their increase with N s indicates that the correlations are "long ranged," as opposed to having a constant value if correlations are short ranged. 21 However, one should have in mind that, since the model has SU(2) symmetry and our results are restricted to one dimension, no true long-range order is possible.…”