Spin Nematic States Research Articles

Classical Spin Nematic Transition in LiGa_{0.95}In_{0.05}Cr_{4}O_{8}.

We present the results of a combined ^{7}Li-NMR and diffraction study on LiGa_{0.95}In_{0.05}Cr_{4}O_{8}, a member of the LiGa_{1-x}In_{x}Cr_{4}O_{8} "breathing" pyrochlore family. Via specific heat and NMR measurements, we find that the complex sequence of first-order transitions observed for LiGaCr_{4}O_{8} is replaced by a single second-order transition at T_{f}=11 K. Neutron and x-ray diffraction rule out both structural symmetry lowering and magnetic long-range order as the origin of this transition. Instead, reverse MonteCarlo fitting of the magnetic diffuse scattering indicates that the low-temperature phase may be described as a collinear spin nematic state, characterized by a quadrupolar order parameter. This state also shows signs of short-range order between collinear spin arrangements on tetrahedra, revealed by mapping the reverse MonteCarlo spin configurations onto a three-state color model.

Nuclear Magnetic Resonance Signature of the Spin-Nematic Phase in LiCuVO_{4} at High Magnetic Fields.

We report a ^{51}V nuclear magnetic resonance investigation of the frustrated spin-1/2 chain compound LiCuVO_{4}, performed in pulsed magnetic fields and focused on high-field phases up to 56T. For the crystal orientations H∥c and H∥b, we find a narrow field region just below the magnetic saturation where the local magnetization remains uniform and homogeneous, while its value is field dependent. This behavior is the first microscopic signature of the spin-nematic state, breaking spin-rotation symmetry without generating any transverse dipolar order, and is consistent with theoretical predictions for the LiCuVO_{4} compound.

Crystal Growth of a frustrated J1–J2 chain magnet NaCuMoO4(OH)

In a frustrated J1–J2 chain magnet with ferromagnetic nearest neighbor interactions J1 and antiferromagnetic next-nearest neighbor interactions J2, novel quantum states such as a spin nematic state are theoretically expected to be present. To detect the novel states experimentally, it is required to find a suitable model compound and to obtain its sizeable and high-quality single crystals. Here we report synthesis of a single-crystalline NaCuMoO4(OH), a model compound of frustrated J1–J2 chain magnet, by a hydrothermal method and discuss its magnetic properties. The temperature dependencies of magnetization are almost consistent with those of powder samples at high temperatures, while the peak in heat capacity divided by temperature associated with a magnetic transition becomes sharper and larger in the single crystal. This indicates the improved quality of the single-crystalline sample compared with the powder sample. Single-crystalline NaCuMoO4(OH) should give a new experimental approach to the novel spin-nematic states expected near 26 T.

Theory of NMR1/T1relaxation in a quantum spin nematic in an applied magnetic field

There is now strong theoretical evidence that a wide range of frustrated magnets should support quantum spin-nematic order in applied magnetic field. Nonetheless, the fact that spin-nematic order does not break time-reversal symmetry makes it very difficult to detect in experiment. In this article, we continue the theme begun in [Phys. Rev. B 88, 184430 (2013)], of exploring how spin-nematic order reveals itself in the spectrum of spin excitations. Building on an earlier analysis of inelastic neutron scattering [Phys. Rev. B 91, 174402 (2015)], we show how the NMR 1/T_1 relaxation rate could be used to identify a spin-nematic state. We emphasise the characteristic, universal features of 1/T_1, using a symmetry-based description of the spin-nematic order parameter and its fluctuations.Turning to the specific case of spin-1/2 frustrated ferromagnets, we show that the signal from competing spin-wave excitations can be suppressed through a judicious choice of nuclear site and field direction. As a worked example, we show how P NMR in the square-lattice frustrated ferromagnet BaCdVO(PO_4)_2 is sensitive to spin-nematic order.

Magnetic Excitations of Spin Nematic State in Frustrated Ferromagnetic Chain

By exploiting density-matrix renormalization group techniques, we investigate the dynamical spin structure factor of a spin-1/2 Heisenberg chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange interactions in an applied magnetic field. In a field-induced spin nematic regime, we find gapless longitudinal and gapped transverse spin excitation spectra, in accordance with quasi-long-ranged longitudinal and short-ranged transverse spin correlations, respectively. The gapless point coincides with the dominant longitudinal spin correlation, whereas the gap position exhibits a characteristic field dependence contradicting the dominant transverse spin correlation.

ChemInform Abstract: Unusual Ordered Phases of Highly Frustrated Magnets: A Review

AbstractReview: 194 refs.

Fractionalized gapless quantum vortex liquids

The standard theoretical approach to gapless spin liquid phases of two-dimensional frustrated quantum antiferromagnets invokes the concept of fermionic slave particles into which the spin fractionalizes. As an alternate we explore new kinds of gapless spin liquid phases in frustrated quantum magnets with XY anisotropy where the vortex of the spin fractionalizes into gapless itinerant fermions. The resulting gapless fractionalized vortex liquid phases are studied within a slave particle framework that is dual to the usual one. We demonstrate the stability of some such phases and describe their properties. We give an explicit construction in an XY-spin-1 system on triangular lattice, and interpret it as a critical phase in the vicinity of spin-nematic states.

Theory of inelastic neutron scattering in a field-induced spin-nematic state

The spin-nematic state has proved elusive, due to the difficulty of observing the order parameter in experiment. In this article we develop a theory of spin excitations in a field-induced spin-nematic state, and use it to show how a spin-nematic order can be indentified using inelastic neutron scattering. We concentrate on 2-dimensional frustrated ferromagnets, for which a two-sublattice, bond-centered spin-nematic state is predicted to exist over a wide range of parameters. First, to clarify the nature of spin-excitations, we introduce a soluble spin-1 model, and use this to derive a continuum field theory, applicable to any two-sublattice spin-nematic state. We then parameterise this field theory, using diagrammatic calculations for a realistic microscopic model of a spin-1/2 frustrated ferromagnet, and show how it can be used to make predictions for inelastic neutron scattering. As an example, we show quantitative predictions for inelastic scattering of neutrons from BaCdVO(PO_4)_2, a promising candidate to realise a spin-nematic state at an achievable h\sim 4T. We show that in this material it is realistic to expect a ghostly Goldstone mode, signalling spin-nematic order, to be visible in experiment.

Two-dimensional solitons in spin nematic states for magnets with an isotropic exchange interaction

A study of two-dimensional topological vortex-like solitons, for spin nematic states in magnets with spin S = 1 and S = 3/2. Depending on the parameters of the magnet, we get either pure multipole vortices, with a quadrupole parameter for S = 1, or an octupole parameter for S = 3/2, or vortices with a non-singular core. A vortex core corresponds to a macroscopic area with a disrupted nematic order. A transition to core vortices occurs at critical values of the system parameters. In this case, there is either the formation of a ferromagnetic vortex with a saturated magnetic moment in the core, or a vortex with an antiferromagnetic order at the core. The dynamic properties of the vortex with a ferromagnetic core are characterized by the presence of a gyroforce, whereas vortices with an antiferromagnetic core are Lorentz-invariant, which is typical for sigma-model antiferromagnets.

Unusual ordered phases of highly frustrated magnets: a review

We review ground states and excitations of a quantum antiferromagnet on triangular and other frustrated lattices. We pay special attention to the combined effects of magnetic field h, spatial anisotropy R and spin magnitude S. The focus of the review is on the novel collinear spin density wave and spin nematic states, which are characterized by fully gapped transverse spin excitations with Sz = ± 1. We discuss extensively the R − h phase diagram of the antiferromagnet, both in the large-S semiclassical limit and the quantum S = 1/2 limit. When possible, we point out connections with experimental findings.

Magnetic Phase Diagram Slightly below the Saturation Field in the StackedJ1–J2Model in the Square Lattice with theJCInterlayer Coupling

We study the effect of adding interlayer coupling to the square lattice, $J_1$-$J_2$ Heisenberg model in high external magnetic field. In particular, we consider a cubic lattice formed from stacked $J_1$-$J_2$ layers, with interlayer exchange coupling $J_{\text{C}}$. For the 2-dimensional model ($J_{\text{C}}=0$) it has been shown that a spin-nematic phase appears close to the saturation magnetic field for the parameter range $-0.4 \lesssim J_2/J_1$ and $J_2>0$. We determine the phase diagram for 3-dimensional model at high magnetic field by representing spin flips out of the saturated state as bosons, considering the dilute boson limit and using the Bethe-Salpeter equation to determine the first instability of the saturated paramagnet. Close to the highly frustrated point $J_2/J_1\sim0.5$, we find that the spin-nematic state is stable even for $|J_{\text{C}}/J_1|\sim 1$. For larger values of $J_2/J_1$, interlayer coupling favors a broad, phase-separated region. Further increase of $|J_{\text{C}}|$ stabilizes a collinear antiferromagnet, which is selected via the order-by-disorder mechanism.

NaCuMoO4(OH) as a Candidate Frustrated J1–J2 Chain Quantum Magnet

In a frustrated J1–J2 chain with the nearest-neighbor ferromagnetic interaction J1 and the next-nearest-neighbor antiferromagnetic interaction J2, novel magnetic states such as a spin-nematic state are theoretically expected. However, they have been rarely examined in experiments because of the difficulty in obtaining suitable model compounds. We show here that the quasi-one-dimensional antiferromagnet NaCuMoO4(OH), which comprises edge-sharing CuO2 chains, is a good candidate J1–J2 chain antiferromagnet. The exchange interactions are estimated as J1 = −51 K and J2 = 36 K by comparing the magnetic susceptibility, heat capacity, and magnetization data with the data obtained using calculations by the exact diagonalization method. High-field magnetization measurements at 1.3 K show a saturation above 26 T with little evidence of a spin nematic state expected just below the saturation field, which is probably due to smearing effects caused by thermal fluctuations and the polycrystalline nature of the sample.

Unconventional spin freezing in the highly two-dimensional spin-12kagome antiferromagnetCd2Cu3(OH)6(SO4)24H2O: Evidence of partial order and coexisting spin singlet state on a distorted kagome lattice

$S$ = 1/2 quantum-spin systems of the kagome lattice have received intense recent attention because they are expected to be promising candidates for novel quantum states such as spin liquid, spin nematic, and other unknown exotic states. Here we report an unusual transition in a highly two-dimensional and slightly distorted $S$ = 1/2 quantum kagome system ${\mathrm{Cd}}_{2}{\mathrm{Cu}}_{3}{\mathrm{(OH)}}_{6}({\mathrm{SO}}_{4}){}_{2}{\mathrm{4H}}_{2}$O, which is a purified compound of the recently identified mineral edwardsite, Cd${}_{1.89}$Zn${}_{0.11}$${\mathrm{Cu}}_{3}{\mathrm{(OH)}}_{6}({\mathrm{SO}}_{4}){}_{2}{\mathrm{4H}}_{2}$O. The $S$ = 1/2 spins of Cu${}^{2+}$ ions form a highly two-dimensional kagome lattice with an extraordinarily large interlayer spacing >10 \AA{}, thus providing a unique kagome lattice with minimum interlayer perturbation. The magnetization shows a Curie-Weiss temperature of 40.5 K and moment freezing below around ${T}_{F}$ = 5 K and a magnetic transition feature near 3 K. The muon spin relaxation shows static magnetism below 5 K and saturation below 3 K. However, distinct features have been observed distinguishing it from a spin glass or a conventional order: High-field magnetization until 50 T showed a saturated value of only 1/3 of the full expected moment. Analysis of specific heat suggests that only 1/3 of the spins are related to the magnetic order; on the other hand, the order is destroyed in external field and 1/3 of the spins respond to the field with a Schottky-like behavior while the other 2/3 of the spins remain inactive. These experimental results suggest an unconventional coexistence of the partial order and most probably spin singlets.

Theory of spin excitations in a quantum spin-nematic state

The idea that a quantum magnet could act like a liquid crystal, breaking spin-rotation symmetry without breaking time-reversal symmetry, holds an abiding fascination. However, the very fact that spin nematic states do not break time-reversal symmetry renders them ``invisible'' to the most common probes of magnetism---they do not exhibit magnetic Bragg peaks, a static splitting of lines in NMR spectra, or oscillations in $\ensuremath{\mu}$SR. Nonetheless, as a consequence of breaking spin-rotation symmetry, spin-nematic states $\mathit{do}$ possess a characteristic spectrum of dispersing excitations which could be observed in experiment. With this in mind, we develop a symmetry-based description of long-wavelength excitations in a spin-nematic state, based on an SU(3) generalization of the quantum nonlinear $\ensuremath{\sigma}$ model. We use this field theory to make explicit predictions for inelastic neutron scattering, and argue that the wavelike excitations it predicts could be used to identify the symmetries broken by the otherwise unseen spin-nematic order.

ChemInform Abstract: Effects of Hole‐Doping and Disorder on the Magnetic States of Delafossite CuCrO2 Having a Spin‐3/2 Antiferromagnetic Triangular Sublattice

AbstractReview: 88 refs.

Classification of spin-nematic squeezing in spin-1 collective atomic systems

In spin-1 collective atomic systems, the spin and nematic-tensor operators constitute the su(3) Lie algebra whose su(2) subalgebras are shown to give two distinct classes of squeezing which are unitarily equivalent to spin squeezing and spin-nematic squeezing. We explicitly construct a unitary operator that generates an arbitrary squeezed spin-nematic state from an arbitrary Fock state. In particular, we demonstrate that squeezed spin states can be generated from a polar state and that squeezed spin-nematic sates can be generated from a fully spin-polarized state.

Magnetic superfluid state in the frustrated spinel oxide CdCr2O4revealed by ultrahigh magnetic fields

We investigated the magnetic-field-induced phases of a typical three-dimensional frustrated magnet, CdCr${}_{2}$O${}_{4}$, in magnetic fields of up to 120 T using both the electromagnetic induction method and magneto-optical spectroscopy of the $d$-$d$ transitions and the exciton-magnon-phonon transitions. Anomalies were observed in the magneto-optical absorption intensity as well as the differential magnetization prior to a fully polarized magnetic phase, revealing a magnetic phase associated with changes in both the crystal and magnetic structures accompanied by the first-order phase transition. A magnetic superfluid state, such as an umbrella-like magnetic structure or a spin-nematic state, is proposed as a candidate for this phase, which is found universally in the series of chromium spinel oxides, $A$Cr${}_{2}$O${}_{4}$ ($A$ $=$ Zn, Cd, Hg).

Engineering Spin Waves in a High-Spin Ultracold Fermi Gas

We report on the detailed study of multicomponent spin waves in an s=3/2 Fermi gas where the high spin leads to novel tensorial degrees of freedom compared to s=1/2 systems. The excitations of a spin-nematic state are investigated from the linear to the nonlinear regime, where the tensorial character is particularly pronounced. By tuning the initial state we engineer the tensorial spin-wave character, such that the magnitude and the sign of the counterflow spin currents are effectively controlled. A comparison of our data with numerical and analytical results shows good agreement.

Stability of Three-Sublattice Order inS=1 Bilinear–Biquadratic Heisenberg Model on Anisotropic Triangular Lattices

The S=1 bilinear-biquadratic Heisenberg model on anisotropic triangular lattices is investigated by several complementary methods. Our focus is on the stability of the three-sublattice spin nematic state against spatial anisotropy. We find that, deviated from the case of isotropic triangular lattice, quantum fluctuations enhance and the three-sublattice spin nematic order is reduced. In the limit of weakly coupling chains, by mapping the systems to an effective one-dimensional model, we show that the three-sublattice spin nematic order develops at infinitesimal interchain coupling. Our results provide a complete picture for smooth crossover from the triangular-lattice case to both the square-lattice and the one-dimensional limits.

Spin nematic states in spin-1 antiferromagnets with easy-axis anisotropy

It is well known that spin nematic phases can appear in either frustrated magnets or in those described by Hamiltonians with large exotic non-Heisenberg terms like biquadratic exchange. We show in the present study that non-frustrated spin-1 1D, 2D and 3D antiferromagnets with single-ion easy-axis anisotropy can show nematic phases in strong magnetic field. For 1D case we support our analytical results by numerical ones.