Abstract
We use a combination of three computational methods to investigate the notoriously difficult frustrated three-dimensional pyrochlore $S=\frac{1}{2}$ quantum antiferromagnet, at finite temperature $T$: 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-$T$ 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 $T=0.57J$, 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 $0.47{k}_{B}ln2$, which is relatively large compared to other frustrated models at this temperature. We also observe a nonmonotonic dependence on $T$ 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 $S=1$ material ${\mathrm{NaCaNi}}_{2}{\mathrm{F}}_{7}$ 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 ${\mathrm{Dy}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$.
Highlights
The pyrochlore lattice, composed of corner-sharing tetrahedra, is a common motif in materials chemistry; in the context of magnetic materials, it has been prominent in a range of rare-earth [1] and spinel compounds [2,3]
We focus on the thermodynamics—susceptibility and in particular specific heat, Fig. 1, and we consider the spin correlations in the form of the momentum resolved static structure factor
To reach physically relevant temperatures, we demonstrate that the timedependent variational principle (TDVP) [65,66] provides an effective way
Summary
The pyrochlore lattice, composed of corner-sharing tetrahedra, is a common motif in materials chemistry; in the context of magnetic materials, it has been prominent in a range of rare-earth [1] and spinel compounds [2,3]. Pyrochlore magnets and models have played a tremendously important role in the history of frustrated magnetism and topological condensed matter physics. One of the foundational publications, in 1956, was Anderson’s identification of the classical pyrochlore Ising magnet [4] as an interesting model system. The classical Heisenberg model on the pyrochlore lattice, following a pioneering study by Villain [9], turned out to be the first classical Heisenberg spin liquid [10]. This undergoes a very delicate order-by-disorder transition for large spins, as the zero-point energy induced by quantum fluctuations favours a subset of collinear states [11,12].
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