Spin Gap State Research Articles

Ground-state phase diagram of the one-dimensional t−Js−Jτ model at quarter filling

We study the ground state of the one-dimensional "$t$-$J_s$-$J_{\tau}$ model," which is a variant of the $t$-$J$ model with additional channel degree of freedom. The model is not only a generalization of the $t$-$J$ model but also an effective model of the two-channel Kondo lattice model in the strong-coupling region. The low-energy excitations and correlation functions are systematically calculated by the density matrix renormalization group method, and the ground-state phase diagram at quarter filling consisting of a Tomonaga-Luttinger liquid, spin-gap state, channel-gap state, insulator, and phase separation is determined. We find that weak channel fluctuations stabilize the spin-gap state, while strong channel fluctuations lead to the transition to the insulator.

The Fascinating World of Low-Dimensional Quantum Spin Systems: Ab Initio Modeling.

In recent times, ab initio density functional theory has emerged as a powerful tool for making the connection between models and materials. Insulating transition metal oxides with a small spin forms a fascinating class of strongly correlated systems that exhibit spin-gap states, spin–charge separation, quantum criticality, superconductivity, etc. The coupling between spin, charge, and orbital degrees of freedom makes the chemical insights equally important to the strong correlation effects. In this review, we establish the usefulness of ab initio tools within the framework of the N-th order muffin orbital (NMTO)-downfolding technique in the identification of a spin model of insulating oxides with small spins. The applicability of the method has been demonstrated by drawing on examples from a large number of cases from the cuprate, vanadate, and nickelate families. The method was found to be efficient in terms of the characterization of underlying spin models that account for the measured magnetic data and provide predictions for future experiments.

Spin-singlet Quantum Ground State in Zigzag Spin Ladder Cu(CF3 COO)2.

The copper salt of trifluoroacetic acid, Cu(CF3 COO)2 , offers a new platform to investigate the quantum ground states of low-dimensional magnets. In practice, it realizes the ideal case of a solid hosting essentially isolated magnetic monolayers. These entities are constituted by well-separated two-leg half-integer spin ladders organized in a zigzag fashion. The ladders are comprised of dimeric units of edge-sharing tetragonal pyramids coupled through carbon ions. The spin-gap state in this compound was revealed by static and dynamic magnetic measurements. No indications of long range magnetic ordering down to liquid helium temperature were obtained in specific heat measurements. First principles calculations allow estimation of the main exchange interaction parameters, J⊥ =176 K and J∥ =12 K, consistent with the weakly interacting dimers model.

Ground state properties of the bond alternating spin-1/2 anisotropic Heisenberg chain

Ground state properties, dispersion relations and scaling behaviour of spin gap of a bond alternating spin-$\frac{1}{2}$ anisotropic Heisenberg chain have been studied where the exchange interactions on alternate bonds are ferromagnetic (FM) and antiferromagnetic (AFM) in two separate cases. The resulting models separately represent nearest neighbour (NN) AFM-AFM and AFM-FM bond alternating chains. Ground state energy has been estimated analytically by using both bond operator and Jordan-Wigner representations and numerically by using exact diagonalization. Dispersion relations, spin gap and several ground state orders have been obtained. Dimer order and string orders are found to coexist in the ground state. Spin gap is found to develop as soon as the non-uniformity in alternating bond strength is introduced in the AFM-AFM chain which further remains non-zero for the AFM-FM chain. This spin gap along with the string orders attribute to the Haldane phase. The Haldane phase is found to exist in most of the anisotropic region similar to the isotropic point.

Odd-Parity Superconductivity near an Inversion Breaking Quantum Critical Point in One Dimension.

We study how an inversion-breaking quantum critical point affects the ground state of a one-dimensional electronic liquid with repulsive interaction and spin-orbit coupling. We find that regardless of the interaction strength, the critical fluctuations always lead to a gap in the electronic spin sector. The origin of the gap is a two-particle backscattering process, which becomes relevant due to renormalization of the Luttinger parameter near the critical point. The resulting spin-gapped state is topological and can be considered as a one-dimensional version of a spin-triplet superconductor. Interestingly, in the case of a ferromagnetic critical point, the Luttinger parameter is renormalized in the opposite manner, such that the system remains nonsuperconducting.

Absence of Magnetic Long Range Order in Ba3ZnRu2O9: A Spin-Liquid Candidate in the S = 3/2 Dimer Lattice

We have discovered a novel candidate for a spin liquid state in a ruthenium oxide composed of dimers of $S = $ 3/2 spins of Ru$^{5+}$,Ba$_3$ZnRu$_2$O$_9$. This compound lacks a long range order down to 37 mK, which is a temperature 5000-times lower than the magnetic interaction scale of around 200 K. Partial substitution for Zn can continuously vary the magnetic ground state from an antiferromagnetic order to a spin-gapped state through the liquid state. This indicates that the spin-liquid state emerges from a delicate balance of inter- and intra-dimer interactions, and the spin state of the dimer plays a vital role. This unique feature should realize a new type of quantum magnetism.

Magnetic modeling and effect of biaxial strain on the Haldane chain compoundSrNi2V2O8

Using combination of first-principles density-functional theory and quantum Monte Carlo technique we study the magnetic behavior of $S=1$ spin chain compound ${\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$. The magnetic model, derived in a first-principles Wannier function basis, shows the presence of finite next-neighbor intrachain coupling, in addition to interchain couplings, thereby deviating from the ideal Haldane chain description. The computed single-ion anisotropy turns out to be of easy axis type and of appreciable magnitude. Solution of the first-principles derived spin model confirms the spin-gapped ground state of the compound. The spin gap is found to close at a critical value of magnetic field, which is estimated to be much reduced compared to that of an ideal Haldane chain. Our study highlights the effectiveness of the next-nearest-neighbor intrachain coupling in reducing the spin gap from the ideal Haldane chain limit. Further study on the effect of biaxial strain on the magnetic behavior predicts that the application of tensile strain should enable the closing of the spin gap in the ground state.

Protection against a spin gap in two-dimensional insulating antiferromagnets with a Chern-Simons term

We propose a mechanism for the protection against spin gapped states in doped antiferromagnets. It requires the presence of a Chern-Simons term that can be generated by a coupling between spin and an insulator. We first demonstrate that in the presence of this term the vortex loop excitations of the spin sector behave as anyons with fractional statistics. To generate such a term, the fermions should have a massive Dirac spectrum coupled to the emergent spin field of the spin sector. The Dirac spectrum can be realized by a planar spin configuration arising as the lowest-energy configuration of a square lattice antiferromagnet Hamiltonian involving a Dzyaloshinskii-Moriya interaction. The mass is provided by a combination of dimerization and staggered chemical potential. We finally show that for realistic parameters, anyonic vortex loop condensation will likely never occur and thus the spin gapped state is prevented. We also propose real magnetic materials for an experimental verification of our theory.

Charge Order Induced by Cation Order in δ-Ag2/3V2O5

Several compounds of vanadium bronze have drawn much interest as a stage of various quantum phenomena. The δ-phase of vanadium bronze has been investigated, focusing on the phase transition in δ-Ag2/3V2O5 which shows characteristic supercooling effects. In this study, we reveal that the phase transition accompanied by jumps of magnetic susceptibility and resistivity is caused by the Ag ions ordering. Furthermore, we also reveal that the Ag ion ordering triggers the V4+/V5+ charge ordering. The phase transition in δ-Ag2/3V2O5 is a novel charge ordering phenomenon induced by the cation ordering. A model of the Ag ion ordering is proposed from X-ray diffraction and electron diffraction analyses. A V4+/V5+ charge ordering model is also proposed and the spin-gapped ground state is discussed on the basis of the charge ordering model.

Disappearance of Gapped Mott Insulating Phase Neighboring Bose Glass Phase in Tl1−xKxCuCl3 Detected by Longitudinal-Field Muon Spin Relaxation

Longitudinal-field muon spin-relaxation (LF-μSR) measurements have been performed in a bond-randomness introduced quantum spin system, Tl1−xKxCuCl3 with x = 0.40, in which the appearance of a Bose glass (BG) phase adjacent to the Bose–Einstein condensation (BEC) phase of excited triplets is observed. In the zero-field limit below 500 G, LF-μSR time spectra shows an exponential-like decay, and the muon spin-relaxation rate does not have a significant temperature dependence down to 25 mK. This indicates that spins fluctuate in time and in space, and that the spin system is not into a spin gapped state. It is suggested that the theoretically predicted gapped Mott insulating phase adjacent to the BG phase disappears in this case. This result obtained by microprobe LF-μSR measurements is consistent with an indication deduced from the results of macroscopic magnetization measurements.

Magnetism and Pressure-Induced Superconductivity of Checkerboard-Type Charge-Ordered Molecular Conductor β-(meso-DMBEDT-TTF)2X (X = PF6 and AsF6)

The metallic state of the molecular conductor β-(meso-DMBEDT-TTF)2X (DMBEDT-TTF = 2-(5,6-dihydro-1,3-dithiolo[4,5-b][1,4]dithiin-2-ylidene)-5,6-dihydro-5,6-dimethyl-1,3-dithiolo[4,5-b][1,4]dithiin, X = PF6, AsF6) is transformed into the checkerboard-type charge-ordered state at around 75–80 K with accompanying metal-insulator (MI) transition on the anisotropic triangular lattice. With lowering temperatures, the magnetic susceptibility decreases gradually and reveals a sudden drop at the MI transition. By applying pressure, the charge-ordered state is suppressed and superconductivity appears in β-(meso-DMBEDT-TTF)2AsF6 as well as in the reported β-(meso-DMBEDT-TTF)2PF6. The charge-ordered spin-gapped state and the pressure-induced superconducting state are discussed through the paired-electron crystal (PEC) model, where the spin-bonded electron pairs stay and become mobile in the crystal, namely the valence-bond solid (VBS) and the resonant valence bonded (RVB) state in the quarter-filled band structure.

Variational Monte Carlo Study of Spin-Gapped Normal State and BCS–BEC Crossover in Two-Dimensional Attractive Hubbard Model

We study properties of normal, superconducting (SC) and CDW states for an attractive Hubbard model on the square lattice, using a variational Monte Carlo method. In trial wave functions, we introduce an interspinon binding factor, indispensable to induce a spin-gap transition in the normal state, in addition to the onsite attractive and intersite repulsive factors. It is found that, in the normal state, as the interaction strength $|U|/t$ increases, a first-order spin-gap transition arises at $|U_{\rm c}|\sim W$ ($W$: band width) from a Fermi liquid to a spin-gapped state, which is conductive through hopping of doublons. In the SC state, we confirm by analysis of various quantities that the mechanism of superconductivity undergoes a smooth crossover at around $|U_{\ma{co}}|\sim |U_{\rm c}|$ from a BCS type to a Bose-Einstein condensation (BEC) type, as $|U|/t$ increases. For $|U|<|U_{\ma{co}}|$, quantities such as the condensation energy, a SC correlation function and the condensate fraction of onsite pairs exhibit behavior of $\sim \exp(-t/|U|)$, as expected from the BCS theory. For $|U|>|U_{\ma{co}}|$, quantities such as the energy gain in the SC transition and superfluid stiffness, which is related to the cost of phase coherence, behave as $\sim t^2/|U|\propto T_{\rm c}$, as expected in a bosonic scheme. In this regime, the SC transition is induced by a gain in kinetic energy, in contrast with the BCS theory. We refer to the relevance to the pseudogap in cuprate superconductors.

Quantum spin state in the rare-earth compound YbAl3C3

Magnetic properties of YbAl${}_{3}$C${}_{3}$ with the hexagonal ScAl${}_{3}$C${}_{3}$-type structure have been investigated by the magnetization ($M$) and specific-heat ($C$) measurements under magnetic fields ($H$). YbAl${}_{3}$C${}_{3}$ is reported to show a spin-gap state, which is considered to be ascribed to a magnetic dimer formed in the orthorhombic phase below the structural transition temperature (${T}_{\mathrm{s}}=$ 77 K). Present study has revealed history-dependent magnetic properties below ${T}_{\mathrm{s}}$ and field-induced anomalous magnetic states at low temperatures. The former is considered to be attributed to the cross correlation between the structural deformation and the magnetic field similar to those observed in multiferroic materials, although YbAl${}_{3}$C${}_{3}$ below ${T}_{\mathrm{s}}$ is not in the ferromagnetic state but certainly in the dimer state. The latter is partially similar to that observed in the field-induced ordered phase (FIOP) of $d$-electron dimer systems. The $M$ versus $H$ curve at low temperatures exhibits a kink at a certain magnetic field and then it increases in proportion to the field like that of FIOP. However, neither kink nor peak suggesting the emergence of FIOP is observed in the temperature dependence of both $M$($T$) and $C$($T$). Instead, $C/T$ shows an anomalous increase proportional to $\ensuremath{-}$ln$T$ with decreasing temperature in a finite field range, suggesting an anomalous disordered state such as a non-Fermi-liquid state in a strongly correlated $f$-electron system. These anomalous magnetic states may be partially relevant to characteristics of $f$-electron dimer system.

Heat transport of the quasi-one-dimensional alternating spin chain material (CH3)2NH2CuCl3

We report a study of the low-temperature heat transport in the quasi-one-dimensional S = 1/2 alternating antiferromagnetic-ferromagnetic chain compound (CH_{3})_{2}NH_{2}CuCl_{3}. Both the temperature and magnetic-field dependencies of thermal conductivity are very complicated, pointing to the important role of spin excitations. It is found that magnetic excitations act mainly as the phonon scatterers in a broad temperature region from 0.3 to 30 K. In magnetic fields, the thermal conductivity show drastic changes, particularly at the field-induced transitions from the low-field N\'{e}el state to the spin-gapped state, the field-induced magnetic ordered state, and the spin polarized state. In high fields, the phonon conductivity is significantly enhanced because of the weakening of spin fluctuations.

Existence of Fine Structure inside Spin Gap in CeRu2Al10

We investigate the magnetic field effect on the spin gap state in CeRu2Al10 by measuring the magnetization and electrical resistivity. We found that the magnetization curve for the magnetic field H//c shows a metamagnetic-like anomaly at H*~4 T below T_0=27 K, but no anomaly for H//a and H//b. A shoulder of the electrical resistivity at Ts~5 K for I//c is suppressed by applying a longitudinal magnetic field above 5 T. Many anomalies are also found in the magnetoresistance for Hkc below ~5 K. The obtained magnetic phase diagram consists of at least two or three phases below T_0. These results strongly indicate the existence of a fine structure at a low energy side in a spin gap state with the excitation energy of 8 meV recently observed in the inelastic neutron scattering experiments.

Effect of the dipole–dipole interaction on the low-temperature magnetism of linear spin chains

The magnetic dipole–dipole interaction in a linear chain of spins S=1∕2 with uniaxial exchange anisotropy gives raise to evolution of the system of energy levels. As the magnetic dipole interaction increases, the fastest decrease of the energy of the system is observed for a level with the maximum modulus of the spin of the system. For sufficiently large ratio of the dipole–dipole contribution to the exchange a transition occurs between the spin-gap states—antiferromagnetic and ferromagnetic. An extremely sharp change of the mean-square spin of the system at low temperatures (T&amp;lt;10−3J∕k) followed by a “plateau” in the temperature dependence is characteristic for a narrow neighborhood of the point at which the type of ground state changes.

Spin-gap mode in the charge-ordered phase ofNaV2O5studied by Raman scattering under high pressures

By means of Raman-scattering measurement under pressures at low temperatures we study the ``devil's staircase''-type phase of ${\text{NaV}}_{2}{\text{O}}_{5}$. The spin-gap mode shows a drastic softening with increasing pressure up to 0.9 GPa in ${\text{C}}_{1/4}$ phase and disappears between 0.9 and 1 GPa. It appears again between 1 and 2.3 GPa in ${\text{C}}_{0}$ phase, indicating that this phase is also a spin-gap state. Taking the charge ordering into consideration, we discuss the spin-gap states and clarify that the spin-gap mode is created by the exchange-interaction Raman-scattering mechanism and it comes from a gap between the spin-singlet ground state and the ${S}_{x}=0$ spin-triplet excited one. This model explains that the spin gap is almost independent of the applied magnetic field and it vanishes at about $10\ifmmode^\circ\else\textdegree\fi{}$ lower than the critical temperature in ${\text{C}}_{1/4}$ phase.

NMR and NQR study of pressure-induced superconductivity and the origin of critical-temperature enhancement in the spin-ladder cuprateSr2Ca12Cu24O41

Pressure-induced superconductivity was studied for a spin-ladder cuprate ${\text{Sr}}_{2}{\text{Ca}}_{12}{\text{Cu}}_{24}{\text{O}}_{41}$ using nuclear magnetic resonance under pressures up to the optimal pressure 3.8 GPa. Pressure application leads to a transitional change from a spin-gapped state to a Fermi-liquid state at temperatures higher than ${T}_{c}$. The relaxation rate $1/{T}_{1}$ shows activated-type behavior at an onset pressure, whereas Korringa-like behavior becomes predominant at the optimal pressure, suggesting that an increase in the density of states at the Fermi energy leads to enhancement of ${T}_{c}$. Nuclear quadrupole resonance spectra suggest that pressure application causes transfer of holes from the chain to the ladder sites. The transfer of holes increases DOS below the optimal pressure. A dome-shaped ${T}_{c}$ versus pressure curve arises from naive balance between the transfer of holes and broadening of the band width.

Bose-glass state in one-dimensional random antiferromagnets

One-dimensional random antiferromagnets ${({\text{CH}}_{3})}_{2}{\text{CHNH}}_{3}\text{Cu}{({\text{Cl}}_{x}{\text{Br}}_{1\ensuremath{-}x})}_{3}$ [abbreviated as $\text{IPA-Cu}{({\text{Cl}}_{x}{\text{Br}}_{1\ensuremath{-}x})}_{3}$] show three magnetic phases: Cl rich, intermediate, and Br rich. In this study, to confirm the presence of a gapped or gapless state in addition to a Bose-glass (BG) state of spin triplets at two magnetic phase boundaries, magnetic susceptibility, specific heat, and magnetization were measured. Contrary to our proposed model, the results suggest a gapless state and a BG state at the Br-rich phase boundary, and a spin-gap state at the Cl-rich phase boundary. From the viewpoints of the universality class, the BG state may be interpreted as a result of Anderson localization. Therefore, $\text{IPA-Cu}{({\text{Cl}}_{x}{\text{Br}}_{1\ensuremath{-}x})}_{3}$ are intriguing compounds for studying the BG state because of good one dimensionality.

Electron spin resonance in spin-gap compounds with bond randomness

Electron spin resonance (ESR) was performed on the mixtures of two spin-gap compounds IPA-Cu(ClxBr1−x)3 for 0.87 ⩽ x < 1. Although the ESR line for x = 1 split into two lines below 10 K, no splitting ESR lines appeared down to 1.4 K for x = 0.99 and 0.98. This difference is due to bond randomness, i.e., a change from the pure spin-gap state to bond-randomness-induced disordered states.