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Journal of Physics Condensed Matter

Patterns of symmetry breaking in systems of coupled tetrahedra

Valeri N. Kotov, Michael E. Zhitomirsky, Maged Elhajal, Frédéric Mila

Published Mar 4, 2004• 4 citations
Publisher

Abstract

The phases of a system of weakly coupled tetrahedra (S = 1/2), in the presence of both Heisenberg and antisymmetric Dzyaloshinsky?Moriya interactions, are discussed. While non-magnetic dimer order is dominant for the specific interactions considered, we find that Dzyaloshinsky?Moriya induced magnetic long-range order can also emerge. The presence of antisymmetric interactions also leads to non-trivial effects (e.g.?ordering) in an external magnetic field.

DOI
10.1088/0953-8984/16/11/047

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The phases of a system of weakly coupled tetrahedra (S = 1/2), in the presence of both Heisenberg and antisymmetric Dzyaloshinsky?Moriya interactions, are discussed. While non-magnetic dimer order is dominant for the specific interactions considered, we find that Dzyaloshinsky?Moriya induced magnetic long-range order can also emerge. The presence of antisymmetric interactions also leads to non-trivial effects (e.g.?ordering) in an external magnetic field.
We analyze the phases of an S=1∕2S=1∕2S=1∕2 spin model on a lattice of coupled tetrahedra. The presence of both Heisenberg and antisymmetric, Dzyaloshinsky-Moriya interactions can lead to two types of symmetry-broken states: nonmagnetic dimer order and, unexpectedly, exotic four-sublattice weak antiferromagnetic order---a state with a generically small ordered moment and nonzero chirality. The external magnetic field also induces weak antiferromagnetism coexisting with strong dimer correlations in the ground state. These states are formed as a result of broken Ising symmetries and exhibit a number of unusual properties.
Several exactly solvable quantum spin models with incommensurate magnetic structures, which manifest quantum phase transitions between incommensurate and commensurate phases, are proposed. The ground-state and thermodynamic characteristics of these quantum spin antiferromagnetic models with the Dzyaloshinsky-Moriya antisymmetric exchange interaction and spin-frustrating next-nearest-neighbor, three-spin, and four-spin (ring exchange) interactions are exactly studied. We investigated the ground state phases of the considered models, as function of the magnetic anisotropy, Dzyaloshinsky-Moriya interaction, next-nearest-neighbor coupling constants, and external magnetic field. Several quantum phase transitions between magnetically incommensurate phases and between incommensurate and ferromagnetic phases are predicted, and the behavior of thermodynamic characteristics of those models at phase transitions is studied. We have shown that for models with chiral three-spin interactions the Dzyaloshinsky-Moriya coupling yields the onset of the weak ferromagnetism, similar to three-dimensional ordered antiferromagnets, but not present in other quantum spin chains with the antisymmetric exchange. Considered models appeared to be important for several quasi-one-dimensional spin systems, studied in recent experiments.
We show that Dzyaloshinskii-Moriya (DM) interactions can substantially modify the phase diagram of spin-1/2 Heisenberg ladders in a magnetic field provided they compete with exchange. For nonfrustrated ladders, they induce a local magnetization along the DM vector that turns the gapless intermediate phase into an Ising phase with broken translational symmetry, while for frustrated ladders, they extend the Ising order of the half-integer plateau to the surrounding gapless phases of the purely Heisenberg case. Implications for experimental ladder and dimer systems are discussed.
We study the interplay of doping and an external magnetic field H on dimerized antiferromagnetic S = 1/2 systems with a finite spin gap Δ. We show that for sufficiently small three-dimensional coupling J′ the long-range antiferromagnetic order known to result from doping with nonmagnetic impurities is destroyed by a weak magnetic field H>Hc1. The lower critical field Hc1 is proportional to the impurity concentration, above Hc1 the system remains in the disordered (plateau) phase up to the much higher upper critical field Hc2 ≃Δ. We discuss the phase diagram in the (H,J') and (H,T) planes and suggest that the reentrant behavior can be experimentally observed in KCuCl3. It is argued that similar phenomena can arise in other weakly coupled quasi-one-dimensional gapped systems.
The ground-state phase diagram of a spin S=12XXZS=\frac{1}{2}\phantom{\rule{4pt}{0ex}}\text{XXZ}S=21​XXZ Heisenberg chain with spatially modulated Dzyaloshinskii-Moriya interaction $\mathcal{H}={\ensuremath{\sum}}_{n}{J\left({S}_{n}^{x}{S}_{n+1}^{x}+{S}_{n}^{y}{S}_{n+1}^{y}\right)+{J}_{z}{S}_{n}^{z}{S}_{n+1}^{z}+[{D}_{0}+{(\ensuremath{-}1)}^{n}{D}_{1}]({S}_{n}^{x}{S}_{n+1}^{y}\ensuremath{-}{S}_{n}^{y}{S}_{n+1}^{x})}$ is studied using the continuum-limit bosonization approach and extensive density-matrix renormalization group computations. It is shown that the effective continuum-limit bosonized theory of the model is given by the double-frequency sine-Gordon model (DSG) where the frequencies, i.e., the scaling dimensions of the two competing cosine perturbation terms, depend on the effective anisotropy parameter ${\ensuremath{\gamma}}^{*}={J}_{z}/\sqrt{{J}^{2}+{D}_{0}^{2}+{D}_{1}^{2}}$. Exploring the ground-state properties of the DSG model we show that the zero-temperature phase diagram contains the following four phases: (i) the ferromagnetic phase at ${\ensuremath{\gamma}}^{*}\ensuremath{\le}\ensuremath{-}1$; (ii) the gapless Luttinger-liquid (LL) phase at $\ensuremath{-}1<{\ensuremath{\gamma}}^{*}<{\ensuremath{\gamma}}_{\text{C1}}^{*}=\ensuremath{-}1/\sqrt{2}$; (iii) the gapped composite (C1) phase characterized by coexistence of the long-range-ordered (LRO) dimerization pattern $\ensuremath{\epsilon}\ensuremath{\sim}{(\ensuremath{-}1)}^{n}({\mathbf{S}}_{n}{\mathbf{S}}_{n+1})$ with the LRO alternating spin chirality pattern $\ensuremath{\kappa}\ensuremath{\sim}{(\ensuremath{-}1)}^{n}\left({S}_{n}^{x}{S}_{n+1}^{y}\ensuremath{-}{S}_{n}^{y}{S}_{n+1}^{x}\right)$ at ${\ensuremath{\gamma}}_{\text{C1}}^{*}<{\ensuremath{\gamma}}^{*}<{\ensuremath{\gamma}}_{\text{C2}}^{*}$; and (iv) at ${\ensuremath{\gamma}}^{*}>{\ensuremath{\gamma}}_{\text{C2}}^{*}>1$ the gapped composite (C2) phase characterized in addition to the coexisting spin dimerization and alternating chirality patterns, by the presence of LRO antiferromagnetic order. The transition from the LL to the C1 phase at ${\ensuremath{\gamma}}_{\text{C1}}^{*}$ belongs to the Berezinskii-Kosterlitz-Thouless universality class, while the transition at ${\ensuremath{\gamma}}^{*}={\ensuremath{\gamma}}_{\text{C2}}^{*}$ from C1 to C2 phase is of the Ising type.