Spin liquid close to a quantum critical point in Na4Ir3O8

Abstract

Na4Ir3O8 is a candidate material for a 3-dimensional quantum spin-liquid on the hyperkagome lattice. We present thermodynamic measurements of heat capacity C and thermal conductivity κ on high quality polycrystalline samples of Na4Ir3O8 down to T = 500 mK and 75 mK, respectively. Absence of long-range magnetic order down to T = 75 mK strongly supports claims of a spin-liquid ground state. The constant magnetic susceptibility χ below T ≈ 25 K and the presence of a small but finite linear-T term in C(T ) suggest the presence of gapless spin excitations. Additionally, the magnetic Grüneisen ratio shows a divergence as T → 0 K and a scaling behavior which clearly demonstrates that Na4Ir3O8 is situated close to a zero-field QCP.In geometrically frustrated materials long range order is prohibited and a liquid-like ground state of spins, the spinliquid (SL) state, can occur. Since Anderson's proposal of a valence bond state for a triangular lattice [1], search for such quantum spin liquids (QSL) has been pursued intensely. In the past decade several new materials have been proposed as SL candidates (see recent reviews 2-4). A small spin and quasi-low-dimensionality are considered ingredients which can lead to a SL state. Indeed, most of the proposed QSL candidates are materials with S = 1/2 moments sitting on quasi-low-dimensional structures. These include the 2-dimensional (2D) triangular lattice organic compounds κ- on a frustrated hyperkagome lattice has been proposed as a candidate QSL [11]. Using thermodynamic measurements at T ≥ 2 K it was shown that Na 4 Ir 3 O 8 does not order inspite of strong antiferromagnetic interactions (θ = −650 K). The magnetic specific heat showed a bump around 30 K, a temperature much smaller than θ, and displays a low temperature power-law dependence with exponent close to 2 [11] similar to several of the 2D materials listed above [8,10]. Subsequently using classical and semi-classical spin-models of Heisenberg spins on a hyperkagome lattice the ground state was found to be highly degenerate and either a classical spin nematic order with long range dipolar spin correlations is chosen at T ≈ 1 K by an order-by-disorder mechanism [12] or a 120 o coplanar magnetically ordered state [13] were predicted. This coplanar magnetic order was found to give way, through a quntum phase transition, to a gapped topological Z 2 'bosonic' spin liquid phase (characterized by the absence of long-range dipolar order) when quantum fluctuations are turned on [13]. The elementary excitations of this gapped spin liquid state were predicted to be chargeless S = 1/2 spinons [13]. The prediction of a gapped spin liquid is however at odds with experiments which gave a Sommerfeld's coefficient γ ≈ 2 mJ/Ir mol K 2 suggesting gapless spin excitations unless the gap was vanishingly small or had nodes. In a completely different line of approach a Fermionic spin liquid model was developed [14,15]. This led naturally to gapless spin liquids as stable phases. These spin liquids had a Fermi surface of chargeless spinons ...

Nature of the possible magnetic phases in a frustrated hyperkagome iridate

“…Firstly we assume that polycrystalline grain size is as small as 1µm ∼ 0.1µm and we regard that a broad peak in specific heat observed around T ≃ 35K in experiments [17][18][19] corresponds to the onset temperature of the Z 6 SB phase (T c ). The FNS argument above claims that, below but near T c , a system smaller than the crossover system size Λ * = ξ ν6/ν behaves as if it has no Z 6 anisotropy term.…”

“…Early thermodynamic measurements such as magnetic specific heat, heat capacity, and magnetic susceptibility indicate spin liquid feature in Na-438 17,18 , while recent neutron scattering and muon spin relaxation experiments on powder samples suggest possibilities of a short-range ordered quasistatic spin state (dubbed as "configurationally degenerate phases with fluctuating order") or spin-freezing like phase in Na-438 19,20 . One of the major obstacles toward comprehensive understanding of low-T magnetic properties of Na-438 stems from its low crystal symmetry, which results in complexity of electronic band structure and effective exchange model of localized spins.…”

“…[3][4][5] Mott insulating materials with bonddependent spin-anisotropic interactions possibly stabilize gapless quantum spin liquid state with exotic excitations such as Majorana fermions 6 . Honeycomb-lattice Na 2 IrO 3 , 7-10 α, β, γ-Li 2 IrO 3 , 11,13,15 and hyperkagomelattice Na 4 Ir 3 O 8 (Na-438) [17][18][19][20] are being intensively explored along this research interest. Throughout thermodynamic measurements, 7,11,13,15 resonant inelastic Xray 8,14,16 and neutron scattering experiments 9,10 , the nature of low-temperature magnetic phases in all the honeycomb iridate compounds has been mostly clarified.…”

“…From the high-temperature expansion of eq. (4), the CurieWeiss temperature for polycrystalline samples is given by 3J − G. From experimental Curie-Weiss fittings of the magnetic susceptibility of powder samples [17][18][19] , we focus only on 3J > G region.…”

Frozen State and Spin Liquid Physics inNa4Ir3O8: An

“…This has led theorists to promote, for example, the Heisenberg-Kitaev model [19] and the spin-orbit Mott insulator [20]. Na 4 Ir 3 O 8 also appears to be close to an insulator-metal transition [21][22][23][24][25] and weak Mottness has been proposed as a possible scenario for a spin-liquid ground state [26,27], like in the case of organic triangular spin-liquids [12].The macroscopic susceptibility, χ, is typical of J eff = 1 2 moments with antiferromagnetic interactions J ∼ 300 K [14,28]. Heat capacity, C, shows no sign of a bulk transition and has two remarkable features: at 24 K ∼ J/10 a broad maximum and at low temperatures C = γT + βT n where 2 < n < 3 [14,21].…”