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arXiv:1612.07609 · Physical review. B./Physical review. B

Crossover from an incommensurate singlet spiral state with a vanishingly small spin gap to a valence-bond solid state in dimerized frustrated ferromagnetic spin chains

Cliò Efthimia Agrapidis, Stefan‐Ludwig Drechsler, Jeroen van den Brink, Satoshi Nishimoto

Published Jun 13, 2017• 16 citations
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Abstract

Motivated by the magnetic properties of the spin-chain compounds ${\mathrm{LiCuSbO}}_{4}\ensuremath{\equiv}{\mathrm{LiSbCuO}}_{4}$ and ${\mathrm{Rb}}_{2}{\mathrm{Cu}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{12}$, we study the ground state of the Heisenberg chain with dimerized nearest-neighbor ferromagnetic (FM) (${J}_{1},{J}_{1}^{\ensuremath{'}}<0$) and next-nearest-neighbor antiferromagnetic (${J}_{2}>0$) couplings. Using the density-matrix renormalization group technique and spin-wave theory, we find a first-order transition between a fully polarized FM and an incommensurate spiral state at $2\ensuremath{\alpha}=\ensuremath{\beta}/(1+\ensuremath{\beta})$, where $\ensuremath{\alpha}$ is the frustration ratio ${J}_{2}/|{J}_{1}|$ and $\ensuremath{\beta}$ the degree of dimerization ${J}_{1}^{\ensuremath{'}}/{J}_{1}$. In the singlet spiral state the spin-gap is vanishingly small in the vicinity of the FM transition, corresponding to a situation of ${\mathrm{LiCuSbO}}_{4}$. For larger $\ensuremath{\alpha}$, corresponding to ${\mathrm{Rb}}_{2}{\mathrm{Cu}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{12}$, and smaller $\ensuremath{\beta}$ there is a crossover from this frustration induced incommensurate state to an Affleck-Lieb-Kennedy-Tasaki-type valence-bond solid state with substantial spin gaps.

DOI
10.1103/physrevb.95.220404

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Coexistence of valence-bond formation and topological order in the Frustrated Ferromagnetic J1J_1J1​-J2J_2J2​ Chain
Frustrated one-dimensional (1D) magnets are known as ideal playgrounds for new exotic quantum phenomena to emerge. We consider an elementary frustrated 1D system: the spin- \frac{1}{2} 1 2 ferromagnetic ( J_1 J 1 ) Heisenberg chain with next-nearest-neighbor antiferromagnetic ( J_2 J 2 ) interactions. On the basis of density-matrix renormalization group calculations we show the existence of a finite spin gap at J_2/|J_1|>1/4 J 2 / | J 1 | > 1 / 4 and we find the ground state in this region to be a valence bond solid (VBS) with spin-singlet dimerization between third-neighbor sites. The VBS is the consequence of spontaneous symmetry breaking through order by disorder. Quite interestingly, this VBS state has a Affleck-Kennedy-Lieb-Tasaki-type topological order. This is the first example of a frustrated spin chain in which quantum fluctuations induce gapped topological order.
Using the density matrix renormalization group and a bosonization approach, we study a spin-1/2 antiferromagnetic Heisenberg chain with near-neighbor coupling J1{\mathit{J}}_{1}J1​ and frustrating second-neighbor coupling J2{\mathit{J}}_{2}J2​, particularly in the limit J2{\mathit{J}}_{2}J2​\ensuremath{\gg}J1{\mathit{J}}_{1}J1​. This system exhibits both dimerization and incommensurate spiral spin correlations. We argue that this system is closely related to a doped, spin-gapped phase of the one-dimensional Kondo lattice. \textcopyright{} 1996 The American Physical Society.
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The spin-1/21/21/2 Heisenberg chain with a ferromagnetic first-neighbor exchange coupling J1{J}_{1}J1​ and an antiferromagnetic second-neighbor J2{J}_{2}J2​ has a Haldane dimer ground state with an extremely small spin gap. Thus the ground state is readily altered by perturbations. Here, we investigate the effects of XXZ exchange magnetic anisotropy of both the easy-axis and easy-plane types and an alternation in J1{J}_{1}J1​ on the ground state, the spin gap, and magnetic properties of the frustrated ferromagnetic spin-1/21/21/2 chain. It is found that there are two distinct dimerized spin-gap phases, in one of which the spin gap and the magnetic susceptibility are extremely small around the SU(2) symmetric case and in the other they are moderately large far away from the SU(2) symmetric case. A small alternation in the amplitude of J1{J}_{1}J1​ rapidly shortens the pitch of spin correlations towards the four-spin periodicity, as in the limit of ${J}_{1}/{J}_{2}\ensuremath{\rightarrow}0$. These effects are not sufficient to quantitatively explain overall experimentally observed magnetic properties in the quasi-one-dimensional spin-gapped magnetoelectric cuprate Rb2Cu2Mo3O12{\mathrm{Rb}}_{2}{\mathrm{Cu}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{12}Rb2​Cu2​Mo3​O12​ that exhibits ferroelectricity stabilized by a magnetic field. Our results are also relevant to Cs2Cu2Mo3O12{\mathrm{Cs}}_{2}{\mathrm{Cu}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{12}Cs2​Cu2​Mo3​O12​, where the ferromagnetic intrachain and antiferromagnetic interchain order has recently been found, in a single chain level. We also reveal the nature of symmetry-protected topological phase transitions in the model by mapping onto effective spin-1 chain models.
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We use the coupled cluster method for infinite chains complemented by exact diagonalization of finite periodic chains to discuss the influence of a third-neighbor exchange J(3) on the ground state of the spin-½ Heisenberg chain with ferromagnetic nearest-neighbor interaction J(1) and frustrating antiferromagnetic next-nearest-neighbor interaction J(2). A third-neighbor exchange J(3) might be relevant to describe the magnetic properties of the quasi-one-dimensional edge-shared cuprates, such as LiVCuO(4) or LiCu(2)O(2). In particular, we calculate the critical point J(2)(c) as a function of J(3), where the ferromagnetic ground state gives way for a ground state with incommensurate spiral correlations. For antiferromagnetic J(3) the ferro-spiral transition is always continuous and the critical values J(2)(c) of the classical and the quantum model coincide. On the other hand, for ferromagnetic J3 is < or approximately equal to -(0.01...0.02)|J1|. the critical value J(2)(c) of the quantum model is smaller than that of the classical model. Moreover, the transition becomes discontinuous, i.e. the model exhibits a quantum tricritical point. We also calculate the height of the jump of the spiral pitch angle at the discontinuous ferro-spiral transition.