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 $\pi$.

18 pages, 17 figures

References in corpus (14)

• Many-body Green's function theory of Heisenberg films
• Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
• Flux expulsion and greedy bosons: frustrated magnets at large N
• Chiral spin states in the pyrochlore Heisenberg magnet: Fermionic mean-field theory and variational Monte Carlo calculations
• Thermodynamics of low dimensional spin-1/2 Heisenberg ferromagnets in an external magnetic field within Green function formalism
• Finite-temperature crossover phenomenon in the $S=1/2$ antiferromagnetic Heisenberg model on the kagome lattice
• Spin Hamiltonian, {Order Out of a Coulomb Phase} and Pseudo-Criticality in the Highly Frustrated Pyrochlore Heisenberg Antiferromagnet FeF${}_3$}
• Thermodynamics of the Antiferromagnetic Heisenberg Model on the Checkerboard Lattice
• Theory of antiferromagnetic Heisenberg spins on breathing pyrochlore lattice
• High-temperature expansion for frustrated magnets: Application to the J1-J2 model on the BCC lattice
• Thermodynamics of the frustrated $J_1$-$J_2$ Heisenberg ferromagnet on the body-centered cubic lattice with arbitrary spin
• Structure Factors of the Kagome-Lattice Heisenberg antiferromagnets at finite temperatures
• Thermodynamics of the pyrochlore Heisenberg ferromagnet with arbitrary spin $S$
• Spin excitations and thermodynamics of the antiferromagnetic Heisenberg model on the layered honeycomb lattice