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Register a new userSpin liquids in geometrically perfect triangular antiferromagnets
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The cradle of quantum spin liquids, triangular antiferromagnets show strong proclivity to magnetic order and require deliberate tuning to stabilize a spin-liquid state. In this brief review, we juxtapose recent theoretical developments that trace the parameter regime of the spin-liquid phase, with experimental results for Co-based and Yb-based triangular antiferromagnets. Unconventional spin dynamics arising from both ordered and disordered ground states is discussed, and the notion of a geometrically perfect triangular system is scrutinized to demonstrate non-trivial imperfections that may assist magnetic frustration in stabilizing dynamic spin states with peculiar excitations.
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Motivated by the recent synthesis of the spin-1 A-site spinel NiRh$_{text 2}$O$_{text 4}$, we investigate the classical to quantum crossover of a frustrated $J_1$-$J_2$ 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 $S geq 3/2$ 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 NiRh$_{text 2}$O$_{text 4}$, a modified $J_1$-$J_2^-$-$J_2^perp$ exchange model is found to favor a conventionally ordered Neel 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.
This work examines the critical anisotropy required for the local stability of the collinear ground states of a geometrically-frustrated triangular-lattice antiferromagnet (TLA). Using a Holstein-Primakoff expansion, we calculate the spin-wave frequencies for the 1, 2, 3, 4, and 8-sublattice (SL) ground states of a TLA with up to third neighbor interactions. Local stability requires that all spin-wave frequencies are real and positive. The 2, 4, and 8-SL phases break up into several regions where the critical anisotropy is a different function of the exchange parameters. We find that the critical anisotropy is a continuous function everywhere except across the 2-SL/3-SL and 3-SL/4-SL phase boundaries, where the 3-SL phase has the higher critical anisotropy.
The spin wave excitations of the geometrically frustrated triangular lattice antiferromagnet (TLA) $rm CuFeO_2$ have been measured using high resolution inelastic neutron scattering. Antiferromagnetic interactions up to third nearest neighbors in the ab plane (J_1, J_2, J_3, with $J_2/J_1 approx 0.44$ and $J_3/J_1 approx 0.57$), as well as out-of-plane coupling (J_z, with $J_z/J_1 approx 0.29$) are required to describe the spin wave dispersion relations, indicating a three dimensional character of the magnetic interactions. Two energy dips in the spin wave dispersion occur at the incommensurate wavevectors associated with multiferroic phase, and can be interpreted as dynamic precursors to the magnetoelectric behavior in this system.
Despite the enormous interest in quantum spin liquids, their experimental existence still awaits broad consensus. In particular, quenched disorder may turn a specific system into a spin glass and possibly preclude the formation of a quantum spin liquid. Here, we demonstrate that the glass transition among geometrically frustrated magnets, a materials class in which spin liquids are expected, differs qualitatively from conventional spin glass. Whereas conventional systems have a glass temperature that increases with increasing disorder, geometrically frustrated systems have a glass temperature that increases with decreasing disorder, approaching, in the clean limit, a finite value. This behaviour implies the existence of a hidden energy scale (far smaller than the Weiss constant) which is independent of disorder and drives the glass transition in the presence of disorder. Motivated by these observations, we propose a scenario in which the interplay of interactions and entropy in the disorder-free system yields a temperature-dependent magnetic permeability with a crossover temperature that determines the hidden energy scale. The relevance of this scale for quantum spin liquids is discussed.
Spiral spin liquids are unique classical spin liquids that occur in many frustrated spin systems, but do not comprise a new phase of matter. Owing to extensive classical ground-state degeneracy, the spins in a spiral spin liquid thermally fluctuate cooperatively from a collection of spiral configurations at low temperatures. These spiral propagation wavevectors form a continuous manifold in reciprocal space, textit{i.e.}, a spiral contour or a spiral surface, that strongly governs the low-temperature thermal fluctuations and magnetic physics. In this paper, the relevant spin models conveying the spiral spin liquid physics are systematically explored and the geometric origin of the spiral manifold is clarified in the model construction. The spiral spin liquids based on the dimension and the codimension of the spiral manifold are further clarified. For each class, the physical properties are studied both generally and for specific examples. The results are relevant to a wide range of frustrated magnets. A survey of materials is given and future experiments are suggested.
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