Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions

Abstract

We investigate the quantum Heisenberg model on the pyrochlore lattice for a generic spin S in the presence of nearest-neighbor J1 and second-nearest-neighbor J2 exchange interactions. By employing the pseudofermion functional renormalization group method, we find, for S = 1/2 and S = 1, an extended quantum-spin-liquid phase centered around J2 = 0, which is shown to be robust against the introduction of breathing anisotropy. The effects of temperature, quantum fluctuations, breathing anisotropies, and a J2 coupling on the nature of the scattering profile, and the pinch points, in particular, are studied. For the magnetic phases of the J1-J2 model, quantum fluctuations are shown to renormalize phase boundaries compared to the classical model and to modify the ordering wave vectors of spiral magnetic states, while no new magnetic orders are stabilized. arXiv:1802.09546v3 [cond-mat.str-el] 9 Jan 2019 J 2 / J 1 = 0.22 J 2 / J 1 = 0.13 J 2 / J 1 = 0.06 J 2 / J 1 = 0 J 2 / J 1 = − 0.06 J 2 / J 1 = − 0.13 J 2 / J 1 = − 0.22

Breathing chromium spinels: a showcase for a variety of pyrochlore Heisenberg Hamiltonians

“…However, from our PF-FRG calculations we find that for both oxides, and at all temperatures down till the RG flow breakdown, the maxima of the susceptibility are always located at the high-symmetry W point in the extended Brillouin zone, i.e., at a q = 2π a (2, 1, 0)-type ordering vector (see SI section S2), as found in Ref. 27 for the nearest-neighbor isotropic S = 3/2 Heisenberg antiferromagnet. A direct space schematic illustration for the spin configuration corresponding to this order is shown in Figure 4A.…”

“…According to Ref. 27, we expect that the spectral weight moves away from the pinch point and forms two symmetrical maxima, resulting in a hexagonal cluster pattern of intensities in the [hhl] plane. Indeed, using the exchange couplings obtained for the room temperature structure (see Table 1), we employ PFFRG to calculate the magnetic susceptibility profiles which are shown in Figures 3A-F.…”

“…Indeed, using the exchange couplings obtained for the room temperature structure (see Table 1), we employ PFFRG to calculate the magnetic susceptibility profiles which are shown in Figures 3A-F. They are found to closely resemble the susceptibility of the isotropic J 1 -J 2 pyrochlore magnet for antiferromagnetic J 1 and ferromagnetic J 2 (27). It is worth noting that, due to the relatively weaker effective second nearest-neighbor coupling in LiGaCr 4 O 8 , the pinch points and bow-ties are better preserved at low temperature for LiGaCr 4 O 8 (see Figure 3D) in comparison to LiInCr 4 O 8 ( Figure 3A).…”

“…To make contact with experimental results, it is useful to assess the temperature dependence of the structure factor as calculated within PFFRG. The relation T = (2π/3)S(S + 1)Λ can be used to relate the infrared cut-off Λ employed in the PFFRG framework to temperature T (27,30). The relation is obtained by comparing the classical limit (S → ∞) of PFFRG, where only the RPA diagrams contribute, i.e.…”

Classical spiral spin liquids as a possible route to quantum spin liquids

“…Our second objective is to demonstrate that these spiral spin liquids are good candidate systems for realizing a quantum spin liquid in the S = 1/2 case. Therefore, we employ the pseudofermion functional renormalization group (PFFRG) method 39,40 which is capable of treating strongly frustrated spin systems even in the case of complex two-dimensional 21,30,35,[39][40][41][42] or threedimensional 15,16,[43][44][45] lattice geometries and in the presence of long-range couplings. 15,16,21,30,35,42,44,45 Our numerical results indicate that for both models the coupling regimes of classical spiral degeneracies indeed host extended non-magnetic phases in the S = 1/2 case.…”