Gapless Spin Liquid Ground State Research Articles

Yb delafossites: Unique exchange frustration of 4f spin- 12 moments on a perfect triangular lattice

While the Heisenberg model for magnetic Mott insulators on planar lattice structures is comparatively well understood in the case of transition metal ions, the intrinsic spin-orbit entanglement of $4f$ magnetic ions on such lattices shows fascinating new physics largely due to corresponding strong anisotropies both in their single-ion and their exchange properties. We show here that the Yb delafossites, containing perfect magnetic ${\mathrm{Yb}}^{3+}$ triangular lattice planes with pseudospin $s=\frac{1}{2}$ at low temperatures, are an ideal platform to study these phenomena. Competing frustrated interactions may lead to an absence of magnetic order associated to a gapless spin liquid ground state with a huge linear specific heat exceeding that of many heavy fermions, whereas the application of a magnetic field induces anisotropic magnetic order with successive transitions into different long-range ordered structures. In this comparative study, we discuss our experimental findings in terms of a unified crystal-field and exchange model. We combine electron paramagnetic resonance (EPR) experiments and results from neutron scattering with measurements of the magnetic susceptibility, isothermal magnetization up to full polarization, and specific heat to determine the relevant model parameters. The impact of the crystal field is discussed as well as the symmetry-compatible form of the exchange tensor, and we give explicit expressions for the anisotropic $g$ factor, the temperature dependence of the susceptibility, the exchange-narrowed EPR linewidth, and the saturation field.

Chiral superconductivity in the alternate stacking compound 4Hb-TaS2.

Van der Waals materials offer unprecedented control of electronic properties via stacking of different types of two-dimensional materials. A fascinating frontier, largely unexplored, is the stacking of strongly correlated phases of matter. We study 4Hb-TaS2, which naturally realizes an alternating stacking of 1T-TaS2 and 1H-TaS2 structures. The former is a well-known Mott insulator, which has recently been proposed to host a gapless spin-liquid ground state. The latter is a superconductor known to also host a competing charge density wave state. This raises the question of how these two components affect each other when stacked together. We find a superconductor with a T c of 2.7 Kelvin and anomalous properties, of which the most notable one is a signature of time-reversal symmetry breaking, abruptly appearing at the superconducting transition. This observation is consistent with a chiral superconducting state.

Thermodynamics of the quantum spin liquid state of the single-component dimer Mott system κ−H3(Cat−EDT−TTF)2

Thermodynamic properties of the proton-mediated single component dimer-Mott insulator of $\ensuremath{\kappa}\text{\ensuremath{-}}{\mathrm{H}}_{3}{(\mathrm{Cat}\text{\ensuremath{-}}\mathrm{EDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}$, which has a two-dimensional triangle lattice structure of $S=1/2$ spins, are reported. The extraordinary large electronic heat capacity coefficient $\ensuremath{\gamma}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}58.8\phantom{\rule{0.28em}{0ex}}\mathrm{mJ}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}\phantom{\rule{0.16em}{0ex}}\mathrm{mo}{\mathrm{l}}^{\ensuremath{-}1}$ observed by the low-temperature heat capacity measurements up to 6 T suggests the formation of the gapless spin liquid ground state. Although the magnetic interaction $J/{k}_{\mathrm{B}}$ is quite different from those of other dimer-Mott spin liquids, the thermodynamic feature scales well with the Wilson ratio of 1.4\char21{}1.6. The heat capacity measurements also detected that the deuteration of the proton-linkage changes the ground state to the nonmagnetic one with almost vanishing \ensuremath{\gamma}. Using the data of the deuterated compound, the accurate temperature dependence of the magnetic heat capacity reflecting on the low-energy excitations from the gapless spin liquids ground state is discussed.

The spin-1/2 square-lattice J1-J2 model: the spin-gap issue

We use the coupled cluster method to high orders of approximation in order to calculate the ground-state energy, the ground-state magnetic order parameter, and the spin gap of the spin-1/2 J_1-J_2 model on the square lattice. We obtain values for the transition points to the magnetically disordered quantum paramagnetic phase of J_2^{c1}=0.454J_1 and J_2^{c2}= 0.588 J_1. The spin gap is zero in the entire parameter region accessible by our approach, i.e. for J_2 \le 0.49J_1 and J_2 > 0.58J_1. This finding is in favor of a gapless spin-liquid ground state in this parameter regime.

Gapless spin liquid ground state in the S = 1/2 vanadium oxyfluoride kagome antiferromagnet [NH4]2[C7H14N][V7O6F18

The vanadium oxyfluoride [NH(4)](2)[C(7)H(14)N][V(7)O(6)F(18)] (DQVOF) is a geometrically frustrated magnetic bilayer material. The structure consists of S = 1/2 kagome planes of V(4+) d(1) ions with S = 1 V(3+) d(2) ions located between the kagome layers. Muon spin relaxation measurements demonstrate the absence of spin freezing down to 40 mK despite an energy scale of 60 K for antiferromagnetic exchange interactions. From magnetization and heat capacity measurements we conclude that the S = 1 spins of the interplane V(3+) ions are weakly coupled to the kagome layers, such that DQVOF can be viewed as an experimental model for S = 1/2 kagome physics, and that it displays a gapless spin liquid ground state.

Electron Spin Resonance in Triangular Spin Tubes

We performed electron spin resonance (ESR) on polycrystalline S = 3/2 compounds consisting of equilateral and non-equilateral triangular spin tubes in CsCrF4 and α-KCrK4, respectively. In CsCrK4, a gapless spin-liquid ground state was realized at 1.5 K. Linewidth of the ESR spectra dramatically increased below 100 K and appeared to diverge around 50 K although no magnetic long-range order occurred above 1.5 K. Furthermore, temperature dependence of integrated intensity of the ESR spectra indicates that the intrinsic ESR spectra can not be observed below 40 K. On the other hand, in α-KCrK4, successive antiferromagnetic long-range order occurred at TNI = 2.5(1) K and TN2 = 4.0(1) K. ESR spectra slightly change not only around TN2 but also around TN1. We considered that the spin structure in TN1 < T < TN2 may slightly change from the quasi-120° spin structure below TN1.

Nonmagnetic impurity effect on equilateral triangle spin tubes CsCrF4

A chemical impurity substitution in gapped spin-liquid ground states often leads to antiferromagnetic long-range order. However, few experimental studies have been conducted on the substitution effect in gapless spin-liquid ground states. We performed X-ray diffraction and magnetic susceptibility experiments on equilateral triangle spin tubes composed of CsCr1−xAlxF4 (x = 0∼0.06). Because the gapless spin-liquid ground state is realized in CsCrF4 (CsCr1−xAlxF4 with x = 0), for x > 0, we expected competition between the geometrical spin frustration in each triangular plane and the impurity-induced antiferromagnetic long-range order. We verified that for x = 0∼0.06 no anomaly that indicates an antiferromagnetic long-range order appeared and that the gapless spin-liquid ground state was robust with respect to the effect of nonmagnetic impurity; we suggested that this is because geometrical spin frustration exists in the equilateral triangular plane.

Numerical Diagonalization Study on the S = 1/2 Frustrated Three-Leg Quantum Spin Ladder Systems

The spin ladder systems have attracted a lot of interest in the field of low-dimensional physics. It is well known that the S = 1/2 two-leg spin ladder has a spin gap, while the three-leg one has a gapless spin liquid ground state. Some spin liquid behaviors were observed in the recent experiments of some frustrated systems; the distorted triangular lattice and kagome lattice antiferromagnets etc. Thus we consider the S = 1/2 three-leg spin ladder system with the next-nearest-neighbor interaction to investigate the effect of frustration on the spin liquids. Using the exact numerical diagonalization of finite-cluster systems, we study the ground state of this system. The phase diagram with respect to some exchange interaction constants is presented. It is revealed that sufficiently large next-nearest-neighbor coupling leads to a ferrimagnetic phase, which has a frustration-induced spontaneous magnetization. In addition we find two spin liquid phases, one of which corresponds to a Néel-like spin configuration and the other a collinear spin configuration. As a result of the numerical study, we find a new phase which is different from three phases.

Interplay of thermal and quantum spin fluctuations in the kagome lattice compound herbertsmithite

We present a Raman spectroscopic investigation of the herbertsmithite ${\text{ZnCu}}_{3}{(\text{OH})}_{6}{\text{Cl}}_{2}$, a realization of a Heisenberg $s=1/2$ antiferromagnet on a perfect kagome lattice. Focusing on its magnetic excitation spectrum we find two components, a high-temperature quasielastic signal and a low temperature, broad maximum. The latter has a linear low-energy slope and extends to high energy. We have investigated the temperature dependence and symmetry properties of both signals. Our data agree with previous calculations and point to a gapless spin liquid ground state.

High-Field ESR Measurements of S=1/2 Kagome Lattice Antiferromagnet BaCu3V2O8(OH)2

High-field electron spin resonance (ESR) measurements have been performed on vesignieite BaCu 3 V 2 O 8 (OH) 2 , which is considered as a nearly ideal model substance of S =1/2 kagome antiferromagnet, in the temperature region from 1.9 to 265 K. The frequency region is from 60 to 360 GHz and the applied pulsed magnetic field is up to 16 T. Observed g -value and linewidth show the increase below 20 K, which suggest the development of the short range order. Moreover, a gapless spin liquid ground state is suggested from the frequency–field relation at 1.9 K.

Spin-Liquid State Study of Equilateral Triangle S=3/2 Spin Tubes Formed in CsCrF4

Topological effects on spin frustration in equilateral triangle S =3/2 spin tubes formed in CsCrF 4 were studied by magnetic susceptibility, heat capacity [ C ( T )], and electron spin resonance experiments. The experimental data show that there is no magnetic long-range order down to T =1.3 K, and that no spin gap due to a chiral spin structure appears. Furthermore, since the C ( T ) curve has a T -linear component, a gapless spin-liquid ground state in one-dimensional antiferromagnets, the so-called Tomonaga–Luttinger liquid, is realized. This is characteristic of equilateral triangle spin tubes with S = half-integer.

Quest for the ground state in two-dimensional antiferromagnetic solid 3He

A low-density solid 3He film adsorbed on graphite surface forms an ideal two-dimensional (2D) quantum spin system with nuclear spin S=1/2 on a triangular lattice. In the antiferromagnetic region called the 4/7 phase, the existence of the competing higher order multiple spin exchange (MSE) interactions in addition to a geometrical frustration, makes the system strongly frustrated. The ground state has been investigated both theoretically and experimentally, but it is still an open question. The NMR measurements for the 4/7 phase adsorbed on both one layer of 4He and two layers of HD preplated graphite have been made down to the temperatures of 10 μK which is by a factor of 10 lower than the previous. The observed susceptibility shows a gradual increase with no abrupt change. This fact strongly suggests that the triangular antiferromagnet with the higher order multiple exchanges has a gapless spin liquid ground state.