Quantum Spin Liquids in Frustrated Spin-1 Diamond Antiferromagnets

Abstract

Motivated by the recent synthesis of the spin-1 A-site spinel NiRh2O4, we investigate the classical to quantum crossover of a frustrated J1-J2 Heisenberg model on the diamond lattice upon varying the spin length S. Applying a recently developed pseudospin functional renormalization group (pf-FRG) approach for arbitrary spin-S magnets, we find that systems with S ≥ 3/2 reside in the classical regime where the low-temperature physics is dominated by the formation of coplanar spirals and a thermal (order-by-disorder) transition. For smaller local moments S=1 or S=1/2 we find that the system evades a thermal ordering transition and forms a quantum spiral spin liquid where the fluctuations are restricted to characteristic momentum-space surfaces. For the tetragonal phase of NiRh2O4, a modified J1-J − 2 -J ⊥ 2 exchange model is found to favor a conventionally ordered Néel state (for arbitrary spin S) even in the presence of a strong local single-ion spin anisotropy and it requires additional sources of frustration to explain the experimentally observed absence of a thermal ordering transition.In the field of frustrated magnetism, spinel compounds of the form AB 2 X 4 (with X=O, Se, S) have long been appreciated as a source of novel physical phenomena [1]. Bsite spinels with magnetic B ions and non-magnetic A ions, such as ACr 2 O 4 or AV 2 O 4 (with A=Mg, Zn, Cd), realize pyrochlore antiferromagnets where geometric frustration manifests itself in a vastly suppressed ordering temperature relative to the Curie-Weiss temperature. Conceptually, the pyrochlore Heisenberg antiferromagnet is a paradigmatic example of a three-dimensional spin liquid [2,3], in both its classical [4,5] and quantum [6,7] [9,10] that, similar to the B-site spinels, exhibit a dramatic suppression of their ordering temperature. At first sight counterintuitive due to the unfrustrated nature of the diamond lattice, it was conceptualized [11] that a sizable nextnearest neighbor coupling (connecting spins on the fcc sublattices of the diamond lattice) induces strong geometric frustration. Indeed it could be shown that the classical Heisenberg model with both nearest and next-nearest neighbor exchangeexhibits highly-degenerate coplanar spin spiral ground states for antiferromagnetic J 2 > |J 1 |/8. Describing a single coplanar spin spiral by a momentum vector q (indicating its direction and pitch), the degenerate ground-state manifold can be captured by a set of q vectors that span a "spin spiral surface" in momentum space [11] as illustrated in Fig. 1. While these spiral surfaces bear a striking resemblance to Fermi surfaces [12], they are considerably more delicate objects that can be easily destroyed by small perturbations to the Hamiltonian (1) (such as further interactions) or even by fluctuations [11,13] that will induce an order-by-disorder transition into a simple magnetically ordered state (typically captured by a single q vector). Such a description of the magnetism of A-site spinels in terms of classical local moments has proved sufficient to...

Renormalization group analysis of dipolar Heisenberg model on square lattice

“…The preservation of fermion number constraint within pf-FRG has been numerically demonstrated in Ref. 32 (see also Ref. 25 for more details).…”

NiRh2O4 : A spin-orbit entangled diamond-lattice paramagnet

“…An early theoretical study [25] of NiRh 2 O 4 considered a model with antiferromagnetic (AFM) first and secondneighbor Heisenberg exchanges (J 1 and J 2 ), applicable to frustrated spinels, and proposed that the non-magnetic ground state might arise from large single-ion anisotropy DS 2 z , with D>0 favoring local S z =0. A pseudospin functional renormalization group study of the J 1 -J 2 model [26] found that while the S = 1 case favors a quantum spiral spin liquid ground state, the impact of tetragonal distortion or large D/J 1 > ∼ 8 is to respectively favor Néel order or the S z =0 ground state. Both studies effectively ignored orbital degrees of freedom.…”

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

“…Two paradigmatic systems harboring spiral spin liquids are the Heisenberg models on the two-dimensional honeycomb and the three-dimensional diamond lattice with nearest neighbor J 1 and antiferromagnetic second neighbor J 2 > 0 couplings. [13][14][15][16][17] Even though these systems are bipartite and, hence, show unfrustrated ferromagnetic or Néel magnetic order in the J 1 -only case, when J 2 > 0 is tuned beyond a certain critical coupling ratio J 2 /|J 1 |, spiral contours or surfaces begin to form marking the onset of a spiral spin liquid. Various numerical studies indeed indicate that both models retain their non-magnetic ground states when replacing the classical S → ∞ spins by quantum S = 1/2 spins possibly realizing a quantum spin-liquid phase.…”