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Register a new userInterplay of anisotropy and frustration: triple transitions in a triangular-lattice antiferromagnet
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Pierre-\\'Eric Melchy
Publication date
2009
fields
Physics
and research's language is
English
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The classical Heisenberg antiferromagnet on a triangular lattice with the single-ion anisotropy of the easy-axis type is theoretically investigated. The mean-field phase diagram in an external magnetic field is constructed. Three finite-temperature Berezinskii-Kosterlitz-Thouless transitions are found by the Monte Carlo simulations in zero field. The two upper transitions are related to the breaking of the discrete ${mathbb Z}_{6}$ symmetry group, while the lowest transition is associated with a quasi-long-range ordering of transverse components. The intermediate collinear phase between first and second transitions is the sliding phase predicted by J. V. Jose {it et al}. [Phys. Rev. B {bf 16}, 1217 (1977)].
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The anomalous thermodynamic properties of the paradigmatic frustrated spin-1/2 triangular lattice Heisenberg antiferromagnet (TLH) has remained an open topic of research over decades, both experimentally and theoretically. Here we further the theoretical understanding based on the recently developed, powerful exponential tensor renormalization group (XTRG) method on cylinders and stripes in a quasi one-dimensional (1D) setup, as well as a tensor product operator approach directly in 2D. The observed thermal properties of the TLH are in excellent agreement with two recent experimental measurements on the virtually ideal TLH material Ba$_8$CoNb$_6$O$_{24}$. Remarkably, our numerical simulations reveal two crossover temperature scales, at $T_l/J sim 0.20$ and $T_h/Jsim 0.55$, with $J$ the Heisenberg exchange coupling, which are also confirmed by a more careful inspection of the experimental data. We propose that in the intermediate regime between the low-temperature scale $T_l$ and the higher one $T_h$, the gapped roton-like excitations are activated with a strong chiral component and a large contribution to thermal entropies, which suppress the incipient 120$^circ$ order that emerges for temperatures below $T_l$.
We report a spin S = 3/2 triangular antiferromagnet with nearest-neighbor coupling J = 0.29 meV in La2Ca2MnO7. A genuinely two-dimensional, three-sublattice order develops below 2.80 K << the Weiss constant (25 K). The spin excitations deviate substantially from linear spin-wave theory, suggesting that magnon breakdown occurs in the material. Such a breakdown has been anticipated in recent theoretical studies, although the excitation spectrum remains to be accounted for.
Spin liquids occuring in 2D frustrated spin systems were initially assumed to appear at strongest frustration, but evidence grows that they more likely intervene at transitions between two different types of order. To identify if this is more general, we here analyze a generalization of the spatially anisotropic triangular lattice (SATL) with antiferromagnetic Heisenberg interactions, the spatially emph{completely} anisotropic triangular lattice (SCATL). Using Takahashis modified spin-wave theory, complemented by exact diagonalizations, we find indications that indeed different kinds of order are always separated by disordered phases. Our results further suggest that two gapped non-magnetic phases, identified as distinct in the SATL, are actually continuously connected via the additional anisotropy of the SCATL. Finally, measurements on several materials found magnetic long-range order where calculations on the SATL predict disordered behavior. Our results suggest a simple explanation through the additional anisotropy of the SCATL, which locates the corresponding parameter values in ordered phases. The studied model might therefore not only yield fundamental insight into quantum disordered phases, but should also be relevant for experiments on the quest for spin liquids.
This work examines the critical anisotropy required for the local stability of the collinear ground states of a geometrically-frustrated triangular-lattice antiferromagnet (TLA). Using a Holstein-Primakoff expansion, we calculate the spin-wave frequencies for the 1, 2, 3, 4, and 8-sublattice (SL) ground states of a TLA with up to third neighbor interactions. Local stability requires that all spin-wave frequencies are real and positive. The 2, 4, and 8-SL phases break up into several regions where the critical anisotropy is a different function of the exchange parameters. We find that the critical anisotropy is a continuous function everywhere except across the 2-SL/3-SL and 3-SL/4-SL phase boundaries, where the 3-SL phase has the higher critical anisotropy.
We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo simulations for a hard-hexagon model and adopt known results for an Ising model to discuss the finite-temperature order-disorder phase transition that is driven by a magnetic field at low temperatures. We also discuss an effective-model description around the ideal frustration case and find indications for a spin-flop like transition in the considered isotropic spin model.
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