Thermodynamics of the pyrochlore-lattice quantum Heisenberg antiferromagnet

Abstract

We use the rotation-invariant Green's function method (RGM) and the high-temperature expansion (HTE) to study the thermodynamic properties of the Heisenberg antiferromagnet on the pyrochlore lattice. We discuss the excitation spectra as well as various thermodynamic quantities, such as spin correlations, uniform susceptibility, specific heat and static and dynamical structure factors. For the ground state we present RGM data for arbitrary spin quantum numbers $S$. At finite temperatures we focus on the extreme quantum cases $S=1/2$ and $S=1$. We do not find indications for magnetic long-range order for any value of $S$. We discuss the width of the pinch point in the static structure factor in dependence on temperature and spin quantum number. We compare our data with experimental results for the pyrochlore compound NaCaNi${}_2$F${}_7$ ($S=1$). Thus, our results for the dynamical structure factor agree well with the experimentally observed features at 3 \ldots 8~meV for NaCaNi${}_2$F${}_7$. We analyze the static structure factor $S_{\mathbf{q}}$ to find regions of maximal $S_{\mathbf{q}}$. The high-temperature series of the $S_{\mathbf{q}}$ provide a fingerprint of weak {\it order by disorder} selection of a collinear spin structure, where (classically) the total spin vanishes on each tetrahedron and neighboring tetrahedra are dephased by $\pi$.

arXiv comment18 pages, 17 figures

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• Quantum effects on unconventional pinch point singularities
• Adapting Planck's route to investigate the thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet
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• Spin-half Heisenberg antiferromagnet on a symmetric sawtooth chain: Rotation-invariant Green's functions and high-temperature series
• Thermodynamics of the $S=1/2$ hyperkagome-lattice Heisenberg antiferromagnet
• Structural and spin-glass properties of single crystal $J_{eff}$ = 1/2 pyrochlore antiferromagnet NaCdCo${}_2$F${}_7$ : correlating $T_f$ with magnetic-bond-disorder
• Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice
• Quantum Heisenberg model on a sawtooth-chain lattice: Rotation-invariant Green's function method
• Phase diagram of the antiferromagnetic $J_1$-$J_2$ spin-$1$ pyrochlore Heisenberg model
• Quantitative functional renormalization for three-dimensional quantum Heisenberg models