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 NaCaNi2F7 (S = 1). Thus, our results for the dynamical structure factor agree well with the experimentally observed features at 3 . . . 8 meV for NaCaNi2F7. We analyze the static structure factor Sq to find regions of maximal Sq. The high-temperature series of the Sq provide a fingerprint of weak order by disorder selection of a collinear spin structure, where (classically) the total spin vanishes on each tetrahedron and neighboring tetrahedra are dephased by π. PACS numbers: 75.10.-b, 75.10.Jm Keywords: quantum Heisenberg antiferromagnet, pyrochlore lattice, rotation-invariant Green's function method, high-temperature expansion, structure factor

Adapting Planck's route to investigate the thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet

“…We may consider these findings for c(T ) and χ(T ) as an indication to favor a gapless ground state. We mention that the Green's function results indicate gapless magnetic excitations [25], and, as mentioned already above, the data for χ(T ) given in [26] down to T = J/6 seem also to be in favor of gapless excitations.…”

“…. − 0.513, which is much narrower than the wide region reported in the literature ranging from e 0 = −0.57 to e 0 = −0.45 [12,13,15,16,[22][23][24][25]65].…”

“…As a low-temperature input for the EM we need the ground-state energy e 0 . There is a large variety of reported values for e 0 of the spin-half PHAF ranging from e 0 = −0.57 to e 0 = −0.45, namely, e 0 = −0.572 [65], −0.56 [15], −0.49 [12,16], −0.482081 [24], −0.466971 [24], −0.459 [22], −0.457804 [13], −0.45093 [25], −0.4473 [23], i.e., accurate values for e 0 are missing. We also need the low-temperature law for c(T ), where we have to distinguish between gapped and gapless behavior (cf.…”

“…Theoretical studies of the quantum PHAF are mostly focused on ground-state properties, see, e.g., [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], whereas much less attention has been paid to its finitetemperature properties. One reason for that is the lack of methods to study thermodynamics of three-dimensional frustrated quantum spin systems.…”

“…However, this paper does not contain data for χ(T ) and c(T ). Finally, we mention the hightemperature expansion study and the rotation-invariant Green's function study of the S = 1/2 PHAF [25,27]. In these recent papers [11,25,26] no evidence for a finitetemperature phase transition was found, i.e., the spinhalf PHAF is most likely a three-dimensional spin system without singularities in the specific heat and the susceptibility.…”