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arXiv:1709.05642 · Physical review. B./Physical review. B

Frustrated quantum magnetism in the Kondo lattice on the zigzag ladder

Matthias Peschke, Roman Rausch, Michael Potthoff

Published Mar 12, 2018• 7 citations
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Abstract

The interplay between the Kondo effect, indirect magnetic interaction, and geometrical frustration is studied in the Kondo lattice on the one-dimensional zigzag ladder. Using the density-matrix renormalization group, the ground-state and various short- and long-range spin- and density-correlation functions are calculated for the model at half filling as a function of the antiferromagnetic Kondo interaction down to $J=0.3t$, where $t$ is the nearest-neighbor hopping on the zigzag ladder. Geometrical frustration is shown to lead to at least two critical points: Starting from the strong-$J$ limit, where almost local Kondo screening dominates and where the system is a nonmagnetic Kondo insulator, antiferromagnetic correlations between nearest-neighbor and next-nearest-neighbor local spins become stronger and stronger, until at ${J}_{\mathrm{c}}^{\mathrm{dim}}\ensuremath{\approx}0.89t$ frustration is alleviated by a spontaneous breaking of translational symmetry and a corresponding transition to a dimerized state. This is characterized by antiferromagnetic correlations along the legs and by alternating antiferro- and ferromagnetic correlations on the rungs of the ladder. A mechanism of partial Kondo screening that has been suggested for the Kondo lattice on the two-dimensional triangular lattice is not realized in the one-dimensional case. Furthermore, within the symmetry-broken dimerized state, there is a magnetic transition to a ${90}^{\ensuremath{\circ}}$ quantum spin spiral with quasi-long-range order at ${J}_{\mathrm{c}}^{\mathrm{mag}}\ensuremath{\approx}0.84t$. The quantum-critical point is characterized by a closure of the spin gap (with decreasing $J$) and a divergence of the spin-correlation length and of the spin-structure factor $S(q)$ at wave vector $q=\ensuremath{\pi}/2$. This is opposed to the model on the one-dimensional bipartite chain, which is known to have a finite spin gap for all $J>0$ at half filling.

DOI
10.1103/physrevb.97.115124

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The interplay between the Kondo effect, indirect magnetic interaction, and geometrical frustration is studied in the Kondo lattice on the one-dimensional zigzag ladder. Using the density-matrix renormalization group, the ground-state and various short- and long-range spin- and density-correlation functions are calculated for the model at half filling as a function of the antiferromagnetic Kondo interaction down to J=0.3tJ=0.3tJ=0.3t, where ttt is the nearest-neighbor hopping on the zigzag ladder. Geometrical frustration is shown to lead to at least two critical points: Starting from the strong-JJJ limit, where almost local Kondo screening dominates and where the system is a nonmagnetic Kondo insulator, antiferromagnetic correlations between nearest-neighbor and next-nearest-neighbor local spins become stronger and stronger, until at Jcdim\ensuremath≈0.89t{J}_{\mathrm{c}}^{\mathrm{dim}}\ensuremath{\approx}0.89tJcdim​\ensuremath≈0.89t frustration is alleviated by a spontaneous breaking of translational symmetry and a corresponding transition to a dimerized state. This is characterized by antiferromagnetic correlations along the legs and by alternating antiferro- and ferromagnetic correlations on the rungs of the ladder. A mechanism of partial Kondo screening that has been suggested for the Kondo lattice on the two-dimensional triangular lattice is not realized in the one-dimensional case. Furthermore, within the symmetry-broken dimerized state, there is a magnetic transition to a 90\ensuremath∘{90}^{\ensuremath{\circ}}90\ensuremath∘ quantum spin spiral with quasi-long-range order at Jcmag\ensuremath≈0.84t{J}_{\mathrm{c}}^{\mathrm{mag}}\ensuremath{\approx}0.84tJcmag​\ensuremath≈0.84t. The quantum-critical point is characterized by a closure of the spin gap (with decreasing JJJ) and a divergence of the spin-correlation length and of the spin-structure factor S(q)S(q)S(q) at wave vector q=\ensuremathπ/2q=\ensuremath{\pi}/2q=\ensuremathπ/2. This is opposed to the model on the one-dimensional bipartite chain, which is known to have a finite spin gap for all J>0J>0J>0 at half filling.
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.
The interplay between Kondo screening, indirect magnetic interaction, and geometrical frustration is studied in the two-dimensional Kondo-necklace model on the triangular lattice. Using infinite projected entangled pair states (iPEPS), we compute the ground state as a function of the antiferromagnetic local Kondo interaction JK{J}_{K}JK​ and the Ising-type direct spin-spin interaction Iz{I}_{z}Iz​. As opposed to previous studies, we do not find partial Kondo screening (PKS) in the isotropic limit Iz=0{I}_{z}=0Iz​=0 but the same behavior as in the unfrustrated case, i.e., a direct phase transition between the paradigmatic phases of the Doniach competition: (i) a disordered phase consisting of local spin singlets at strong JK{J}_{K}JK​ and (ii) a magnetically ordered phase at weak JK{J}_{K}JK​. For Iz>0{I}_{z}>0Iz​>0, we find a PKS ground state but again oppositely to previous studies, we find that the PKS ground state is in strong competition with a second ground state candidate not found before. This state is characterized by a strongly polarized central spin in each hexagon and its antiparallel, weakly polarized (i.e., partially screened) neighbors. We name it the central spin phase.
We study an isotropic Heisenberg spin-12\frac{1}{2}21​ model on a trellis ladder which is composed of two ${J}_{1}\ensuremath{-}{J}_{2}$ zigzag ladders interacting through antiferromagnetic rung coupling J3{J}_{3}J3​. J1{J}_{1}J1​ and J2{J}_{2}J2​ are ferromagnetic zigzag spin interaction between two legs and antiferromagnetic interaction along each leg of a zigzag ladder. A quantum phase diagram of this model is constructed using the density matrix renormalization group method and linearized spin-wave analysis. In the small J2{J}_{2}J2​ limit, a short-range striped collinear phase is found in the presence of J3{J}_{3}J3​, whereas, in the large J2/J3{J}_{2}/{J}_{3}J2​/J3​ limit, a noncollinear quasi-long-range phase is found. The system shows a short-range noncollinear state in the large J3{J}_{3}J3​ limit. The short-range-order phase is the dominant feature of this phase diagram. We also show that the results obtained by DMRG and linearized spin-wave analysis show a similar phase boundary between the collinear striped and noncollinear short-range phases, and the collinear phase region shrinks with increasing J3{J}_{3}J3​. We apply this model to understand the magnetic properties of CaV2O5{\mathrm{CaV}}_{2}{\mathrm{O}}_{5}CaV2​O5​ and also fit the experimental data of susceptibility and magnetization. We note that J3{J}_{3}J3​ is a dominant interaction in this material, whereas J1{J}_{1}J1​ and J2{J}_{2}J2​ are approximately half of J3{J}_{3}J3​. The variation of magnetic specific heat capacity as a function of temperature for various external magnetic fields is also predicted.
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