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arXiv:cond-mat/0507538 · Physical Review B

Structural instability of two- and three-dimensional pyrochlore spin lattices in high magnetic fields

Oleg Derzhko, Johannes Richter

Published Sep 30, 2005• 16 citations
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Abstract

We consider the quantum spin-$s$ $XXZ$ Heisenberg antiferromagnet on the two- and three-dimensional pyrochlore lattices and examine a spin-Peierls mechanism of lowering the total energy by a lattice distortion in a high magnetic field. For the exact eigenstates consisting of several independent localized magnons in a ferromagnetic environment we show the existence of a spin-Peierls instability by rigorous analytical calculations. In addition we report on exact diagonalization data for finite two-dimensional pyrochlore lattices up to $N=64$ sites. We discuss a scenario of the field-tuned changes in the ground-state properties of the frustrated spin lattices due to the coupling between spin and lattice degrees of freedom.

DOI
10.1103/physrevb.72.094437

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We present the results of an exact diagonalization study of the spin-1/21/21/2 Heisenberg antiferromagnet on a two-dimensional version of the pyrochlore lattice, also known as the square lattice with crossings or the checkerboard lattice. Examining the low-energy spectra for systems of up to 24 spins, we find that all clusters studied have nondegenerate ground states with total spin zero, and big energy gaps to states with higher total spin. We also find a large number of nonmagnetic excitations at energies within this spin gap. Spin-spin and spin-Peierls correlation functions appear to be short ranged, and we suggest that the ground state is magnetically disordered.
We study the S=12S=\frac{1}{2}S=21​ pyrochlore Heisenberg antiferromagnet in a magnetic field. Using large-scale density-matrix renormalization group calculations for clusters with up to 128 spins, we find indications of a finite triplet gap, causing a threshold field to nonzero magnetization in the magnetization curve. We obtain a robust saturation field consistent with a magnon crystal, although the corresponding 5/65/65/6 magnetization plateau is very slim and possibly unstable. Most remarkably, there is a pronounced and apparently robust 1/21/21/2 magnetization plateau where the ground state breaks the rotational symmetry of the lattice, exhibiting oppositely polarized spins on alternating kagome and triangular planes. Reminiscent of the kagome ice plateau of the pyrochlore Ising antiferromagnet known as spin ice, it arises via a much more subtle ``quantum order by disorder'' mechanism.
We use a combination of three computational methods to investigate the notoriously difficult frustrated three-dimensional pyrochlore S=12S=\frac{1}{2}S=21​ quantum antiferromagnet, at finite temperature TTT: canonical typicality for a finite cluster of $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ unit cells (i.e., 32 sites), a finite-TTT matrix product state method on a larger cluster with 48 sites, and the numerical linked cluster expansion (NLCE) using clusters up to 25 lattice sites, including nontrivial hexagonal and octagonal loops. We calculate thermodynamic properties (energy, specific heat capacity, entropy, susceptibility, magnetization) and the static structure factor. We find a pronounced maximum in the specific heat at T=0.57JT=0.57JT=0.57J, which is stable across finite size clusters and converged in the series expansion. At $T\ensuremath{\approx}0.25J$ (the limit of convergence of our method), the residual entropy per spin is 0.47kBln20.47{k}_{B}ln20.47kB​ln2, which is relatively large compared to other frustrated models at this temperature. We also observe a nonmonotonic dependence on TTT of the magnetization at low magnetic fields, reflecting the dominantly nonmagnetic character of the low-energy states. A detailed comparison of our results to measurements for the S=1S=1S=1 material NaCaNi2F7{\mathrm{NaCaNi}}_{2}{\mathrm{F}}_{7}NaCaNi2​F7​ yields a rough agreement of the functional form of the specific heat maximum, which in turn differs from the sharper maximum of the heat capacity of the spin ice material Dy2Ti2O7{\mathrm{Dy}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}Dy2​Ti2​O7​.
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We consider the spin-1/2 antiferromagnetic Heisenberg model on the two-dimensional square-kagome lattice with almost dispersionless lowest magnon band. For a general exchange coupling geometry we elaborate low-energy effective Hamiltonians which emerge at high magnetic fields. The effective model to describe the low-energy degrees of freedom of the initial frustrated quantum spin model is the (unfrustrated) square-lattice spin-1/2 XXZ model in a z-aligned magnetic field. For the effective model we perform quantum Monte Carlo simulations to discuss the low-temperature properties of the square-kagome quantum Heisenberg antiferromagnet at high magnetic fields. We pay special attention to a magnetic-field driven Berezinskii–Kosterlitz– Thouless phase transition which occurs at low temperatures.
We present exact diagonalization calculations for the spin-1/2 nearest-neighbor antiferromagnet on the pyrochlore lattice. We study a section of the lattice in the [111] direction and analyze the Hamiltonian of the breathing pyrochlore system with two coupling constants J1{J}_{1}J1​ and J2{J}_{2}J2​ for tetrahedra of different orientations and investigate the evolution of the system from the limit of disconnected tetrahedra (J2=0{J}_{2}=0J2​=0) to a correlated state at J1=J2{J}_{1}={J}_{2}J1​=J2​. We evaluate the low-energy spectrum, two and four spin correlations, and spin chirality correlations for a system size of up to 36 sites. The model shows a fast decay of spin correlations and we confirm the presence of several singlet excitations below the lowest magnetic excitation. We find chirality correlations near J1=J2{J}_{1}={J}_{2}J1​=J2​ to be small at the length scales available at this system size. Evaluation of dimer-dimer correlations and analysis of the nature of the entanglement of the tetrahedral unit shows that the triplet sector of the tetrahedron contributes significantly to the ground-state entanglement at J1=J2{J}_{1}={J}_{2}J1​=J2​.