M. Klanjsek

Controlling Luttinger liquid physics in spin ladders under a magnetic field.

We present a 14N nuclear magnetic resonance study of a single crystal of CuBr4(C5H12N)2 (BPCB) consisting of weakly coupled spin-1/2 Heisenberg antiferromagnetic ladders. Treating ladders in the gapless phase as Luttinger liquids, we are able to fully account for (i) the magnetic field dependence of the nuclear spin-lattice relaxation rate T1(-1) at 250 mK and for (ii) the phase transition to a 3D ordered phase occurring below 110 mK due to weak interladder exchange coupling. BPCB is thus an excellent model system where the possibility to control Luttinger liquid parameters in a continuous manner is demonstrated and the Luttinger liquid model tested in detail over the whole fermion band.

Phonon-Modulated Magnetic Interactions and Spin Tomonaga-Luttinger Liquid in the p-Orbital Antiferromagnet CsO2

The magnetic response of antiferromagnetic CsO2, coming from the p-orbital S=1/2 spins of anionic O2(-) molecules, is followed by 133Cs nuclear magnetic resonance across the structural phase transition occurring at T(s1)=61  K on cooling. Above T(s1), where spins form a square magnetic lattice, we observe a huge, nonmonotonic temperature dependence of the exchange coupling originating from thermal librations of O2(-) molecules. Below T(s1), where antiferromagnetic spin chains are formed as a result of p-orbital ordering, we observe a spin Tomonaga-Luttinger-liquid behavior of spin dynamics. These two interesting phenomena, which provide rare simple manifestations of the coupling between spin, lattice, and orbital degrees of freedom, establish CsO2 as a model system for molecular solids.

Statics and dynamics of weakly coupled antiferromagnetic spin-1/2 ladders in a magnetic field

We investigate weakly coupled spin-1/2 ladders in a magnetic field. The work is motivated by recent experiments on the compound (CH12N)CuBr4 (BPCB). We use a combination of numerical and analytical methods, in particular, the density-matrix renormalization group (DMRG) technique, to explore the phase diagram and the excitation spectra of such a system. We give detailed results on the temperature dependence of the magnetization and the specific heat, and the magnetic-field dependence of the nuclear-magnetic-resonance relaxation rate of single ladders. For coupled ladders, treating the weak interladder coupling within a mean-field or quantum Monte Carlo approach, we compute the transition temperature of triplet condensation and its corresponding antiferromagnetic order parameter. Existing experimental measurements are discussed and compared to our theoretical results. Furthermore, we compute, using time-dependent DMRG, the dynamical correlations of a single spin ladder. Our results allow to describe directly the inelastic neutron scattering cross section up to high energies. We focus on the evolution of the spectra with the magnetic field and compare their behavior for different couplings. The characteristic features of the spectra are interpreted using different analytical approaches such as the mapping onto a spin chain, a Luttinger liquid or onto a t-J model. For values of parameters for which such measurements exist, we compare our results to inelastic neutron scattering experiments on the compound BPCB and find excellent agreement. We make additional predictions for the high-energy part of the spectrum that are potentially testable in future experiments.

A high-temperature quantum spin liquid with polaron spins

The existence of a quantum spin liquid (QSL) in which quantum fluctuations of spins are sufficiently strong to preclude spin ordering down to zero temperature was originally proposed theoretically more than 40 years ago, but its experimental realization turned out to be very elusive. Here we report on an almost ideal spin liquid state that appears to be realized by atomic-cluster spins on the triangular lattice of a charge-density wave state of 1T-TaS2. In this system, the charge excitations have a well-defined gap of ∼0.3 eV, while nuclear quadrupole resonance and muon-spin-relaxation experiments reveal that the spins show gapless QSL dynamics and no long-range magnetic order at least down to 70 mK. Canonical T2 power-law temperature dependence of the spin relaxation dynamics characteristic of a QSL is observed from 200 K to Tf = 55 K. Below this temperature, we observe a new gapless state with reduced density of spin excitations and high degree of local disorder signifying new quantum spin order emerging from the QSL. In the charge-density wave state of tantalum sulfide, tantalum atoms group into a Star-of-David arrangement. Experiments show that the polaron spins associated with these atomic clusters can form a quantum spin liquid.

Quantum-critical spin dynamics in quasi-one-dimensional antiferromagnets.

By means of nuclear spin-lattice relaxation rate T(1)(-1), we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system NiCl(2)-4SC(NH(2))(2) and the spin-ladder system (C(5)H(12)N)(2)CuBr(4). In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, T(1)(-1) exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for T(1)(-1), compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.

Observation of two types of fractional excitation in the Kitaev honeycomb magnet

Quantum spin liquid is a disordered but highly entangled magnetic state with fractional spin excitations1. The ground state of an exactly solved Kitaev honeycomb model is perhaps its clearest example2. Under a magnetic field, a spin flip in this model fractionalizes into two types of anyon, a quasiparticle with more complex exchange statistics than standard fermions or bosons: a pair of gauge fluxes and a Majorana fermion2,3. Here, we demonstrate this kind of fractionalization in the Kitaev paramagnetic state of the honeycomb magnet α-RuCl3. The spin excitation gap determined by nuclear magnetic resonance consists of the predicted Majorana fermion contribution following the cube of the applied magnetic field2,4,5, and a finite zero-field contribution matching the predicted size of the gauge flux gap2,6. The observed fractionalization into gapped anyons survives in a broad range of temperatures and magnetic fields, which establishes α-RuCl3 as a unique platform for future investigations of anyons.α-RuCl3, a promising candidate to realize the Kitaev model, has attracted great interest recently. Two types of fractional excitation—gauge fluxes and Majorana fermions—are observed, which contribute to the spin excitation gap in different ways.

Spin Configuration in the 1/3 Magnetization Plateau of Azurite Determined by NMR

High magnetic field (63,65)Cu NMR spectra were used to determine the local spin polarization in the 1/3 magnetization plateau of azurite, Cu3(CO3)(2)(OH)(2), which is a model system for the distorted diamond antiferromagnetic spin-1/2 chain. The spin part of the hyperfine field of the Cu2 (dimer) sites is found to be field independent, negative and strongly anisotropic, corresponding to approximately 10% of fully polarized spin in a d orbital. This is close to the expected configuration of the quantum plateau, where a singlet state is stabilized on the dimer. However, the observed nonzero spin polarization points to some triplet admixture, induced by strong asymmetry of the diamond bonds J1 and J3.

Enhanced superconducting transition temperature in hyper-interlayer-expanded FeSe despite the suppressed electronic nematic order and spin fluctuations

The superconducting critical temperature,

Magnetic structure of azurite above the magnetization plateau at13of saturation

T_{\rm c}

Dichotomy between Attractive and Repulsive Tomonaga-Luttinger Liquids in Spin Ladders

, of FeSe can be dramatically enhanced by intercalation of a molecular spacer layer. Here we report on a