Christian Rüegg

Bose–Einstein condensation in magnetic insulators

A collection of bosonic particles, such as liquid helium or ultracold gases, can condense into a ground state in which the atoms flow as a ‘superfluid’ without scattering. Magnetic materials further illustrate the generality of the effect, as described in this review.

Thermodynamics of the Spin Luttinger Liquid in a Model Ladder Material

The phase diagram in temperature and magnetic field of the metal-organic, two-leg, spin-ladder compound (C5H12N)2CuBr4 is studied by measurements of the specific heat and the magnetocaloric effect. We demonstrate the presence of an extended spin Luttinger-liquid phase between two field-induced quantum critical points and over a broad range of temperature. Based on an ideal spin-ladder Hamiltonian, comprehensive numerical modeling of the ladder specific heat yields excellent quantitative agreement with the experimental data across the entire phase diagram.

Robustness of Basal-Plane Antiferromagnetic Order and the J(eff)=1/2 State in Single-Layer Iridate Spin-Orbit Mott Insulators

The magnetic structure and electronic ground state of the layered perovskite Ba(2)IrO(4) have been investigated using x-ray resonant magnetic scattering. Our results are compared with those for Sr(2)IrO(4), for which we provide supplementary data on its magnetic structure. We find that the dominant, long-range antiferromagnetic order is remarkably similar in the two compounds and that the electronic ground state in Ba(2)IrO(4), deduced from an investigation of the x-ray resonant magnetic scattering L(3)/L(2) intensity ratio, is consistent with a J(eff)=1/2 description. The robustness of these two key electronic properties to the considerable structural differences between the Ba and Sr analogues is discussed in terms of the enhanced role of the spin-orbit interaction in 5d transition metal oxides.

Field{Controlled Magnetic Order in the Quantum Spin{Ladder System (Hpip)2CuBr4

Neutron diffraction is used to investigate the field-induced, antiferromagnetically ordered state in the two-leg spin-ladder material (Hpip)2CuBr4. This “classical” phase, a consequence of weak interladder coupling, is nevertheless highly unconventional: its properties are influenced strongly by the spin Luttinger-liquid state of the ladder subunits. We determine directly the order parameter (transverse magnetization), the ordering temperature, the spin structure, and the critical exponents around the transition. We introduce a minimal microscopic model for the interladder coupling and calculate the quantum fluctuation corrections to the mean-field interaction.

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.

Spiral spin-liquid and the emergence of a vortex-like state in MnSc2S4

Spirals and helices are common motifs of long-range order in magnetic solids, and they may also be organized into more complex emergent structures such as magnetic skyrmions and vortices. A new type of spiral state, the spiral spin-liquid, in which spins fluctuate collectively as spirals, has recently been predicted to exist. Here, using neutron scattering techniques, we experimentally prove the existence of a spiral spin-liquid in MnSc2S4 by directly observing the ‘spiral surface’—a continuous surface of spiral propagation vectors in reciprocal space. We elucidate the multi-step ordering behaviour of the spiral spin-liquid, and discover a vortex-like triple-q phase on application of a magnetic field. Our results prove the effectiveness of the J1–J2 Hamiltonian on the diamond lattice as a model for the spiral spin-liquid state in MnSc2S4, and also demonstrate a new way to realize a magnetic vortex lattice through frustrated interactions. A detailed and systematic neutron scattering study uncovers a spiral spin-liquid state in the quantum magnet MnSc2S4.

Spin ladders and quantum simulators for Tomonaga–Luttinger liquids

Magnetic insulators have proven to be usable as quantum simulators for itinerant interacting quantum systems. In particular the compound (C(5)H(12)N)(2)CuBr(4) (for short: (Hpip)(2)CuBr(4)) was shown to be a remarkable realization of a Tomonaga-Luttinger liquid (TLL) and allowed us to quantitatively test the TLL theory. Substitution weakly disorders this class of compounds and thus allows us to use them to tackle questions pertaining to the effect of disorder in TLL as well, such as that of the formation of the Bose glass. In this paper we present, as a first step in this direction, a study of the properties of the related (Hpip)(2)CuCl(4) compound. We determine the exchange couplings and compute the temperature and magnetic field dependence of the specific heat, using a finite temperature density matrix renormalization group procedure. Comparison with the measured specific heat at zero magnetic field confirms the exchange parameters and Hamiltonian for the (Hpip)(2)CuCl(4) compound, giving the basis needed to begin studying the disorder effects.

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.

CAMEA—A novel multiplexing analyzer for neutron spectroscopy

The analyzer detector system continuous angle multiple energy analysis will be installed on the cold-neutron triple-axis spectrometer RITA-2 at SINQ, PSI. CAMEA is optimized for efficiency in the horizontal scattering plane enabling rapid and detailed mapping of excitations. As a novelty the design employs a series of several sequential upward scattering analyzer arcs. Each arc is set to a different, fixed, final energy and scatters neutrons towards position sensitive detectors. Thus, neutrons with different final energies are recorded simultaneously over a large angular range. In a single data-acquisition many entire constant-energy lines in the horizontal scattering plane are recorded for a quasi-continuous angular coverage of about 60°. With a large combined coverage in energy and momentum, this will result in a very efficient spectrometer, which will be particularly suited for parametric studies under extreme conditions with restrictive sample environments (high field magnets or pressure cells) and for small samples of novel materials. In this paper we outline the concept and the specifications of the instrument currently under construction.

Crystal Growth of the Nonmagnetic Zn2+ and Magnetic Co2+ Doped Quasi-One-Dimensional Spin Chain Compound SrCuO2 Using the Traveling Solvent Floating Zone Method

We report on the crystal growth of the quasi-one-dimensional quantum spin chain compound SrCuO2 and its doped variants containing magnetic cobalt (0.25%, 0.5%, 1%, and 2.5%) and nonmagnetic zinc (0.5% and 1%) impurities. Crystals are grown using the traveling solvent floating zone (TSFZ) method in a four-mirror optical furnace. Some crucial factors, key to the stability of a TSFZ process, including the choice of solvent composition and its associated melting behavior, are discussed in detail. The grown crystals were characterized using X-ray powder diffraction, scanning electron microscopy, optical microscopy, neutron single crystal diffraction and magnetic susceptibility measurements. Co-doping induces magnetic anisotropy and a corresponding change of magnetic behavior characterized by the presence of a sharp peak in the magnetic susceptibility at low-temperatures (T = 5 K), which is not seen for the pristine compound. The peak position is shown to scale linearly with Co-concentration for low doping leve...