Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9712051 · Journal of the Physical Society of Japan

Orbital Order Effect of Two-Dimensional Spin Gap System forCaV4O9

Nobuyuki Katoh, Masatoshi Imada

Published Feb 15, 1998• 9 citations
arXivHTMLPDF

Abstract

Effects of possible orbital order in magnetic properties of two-dimensional spin gap system for CaV$_4$O$_9$ are investigated theoretically. After analyzing experimental data, we show that single orbital models assumed in the literature are insufficient to reproduce the data. To understand the origin of the discrepancy, we assume that in $d^1$ state of V, $d_{xz}$ and $d_{yz}$ orbitals have substantial contributions in the lowest-energy atomic level which leads to a double-degeneracy. We study possible configurations of the orbital order. By exact diagonalization and perturbation expansion, we calculate the susceptibility, wavenumber dependence of low-lying excitations and equal-time spin-spin correlations which is related to integrated intensity of the neutron inelastic scattering. These quantities sensitively depend on the configuration of the orbital order. The calculated results for some configurations of the orbital order reproduce many experimental results much better than the previous single-orbital models. However some discrepancy still remains to completely reproduce all of the reported experimental results. To understand the origin of these discrepancies, we point out the possible importance of the partially occupied $d_{xy}$ orbital in addition to orbital order of partially filled $d_{xz}$ and $d_{yz}$ orbitals.

DOI
10.1143/jpsj.67.564

Related papers

Study of Spin System witht2gOrbital Degeneracy for Ladder and Chain

Nobuyuki Katoh

Effective spin Hamiltonians with t 2g orbital degeneracy have been investigated theoretically. We assume that a d electron occupies one of doubly degenerate d z x and d y z orbitals which have the lowest energy in atomic level. The orbital degrees of freedom are represented as Ising iso-spin operators because of the symmetry of the orbital characters. We apply the Hamiltonians to a ladder and a chain lattices and investigate the models using the exact diagonalization. For the ladder model, a spin gap opens above a finite value of the spin exchange coupling on rung, which is qualitatively different from the ladder model with single orbital. For the chain model, the spin gap behavior is observed in the uniform spin correlation at low temperature. Origin of the spin gap is a spin-dimer triggered by the occurrence of the ferromagnetic orbital ordering, which suggests a new mechanism of the spin gap formation.

Journal of the Physical Society of Japan•Jan 15, 1999•5 citations

Effective model with strong Kitaev interactions for α−RuCl3

Takafumi Suzuki, Sei-ichiro Suga

We use an exact numerical diagonalization method to calculate the dynamical spin structure factors of three ab initio models and one ab initio guided model for a honeycomb-lattice magnet $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. We also use thermal pure quantum states to calculate the temperature dependence of the heat capacity, the nearest-neighbor spin-spin correlation function, and the static spin structure factor. From the results obtained from these four effective models, we find that, even when the magnetic order is stabilized at low temperature, the intensity at the $\mathrm{\ensuremath{\Gamma}}$ point in the dynamical spin structure factors increases with increasing nearest-neighbor spin correlation. In addition, we find that the four models fail to explain heat-capacity measurements whereas two of the four models succeed in explaining inelastic-neutron-scattering experiments. In the four models, when temperature decreases, the heat capacity shows a prominent peak at a high temperature where the nearest-neighbor spin-spin correlation function increases. However, the peak temperature in heat capacity is too low in comparison with that observed experimentally. To address these discrepancies, we propose an effective model that includes strong ferromagnetic Kitaev coupling, and we show that this model quantitatively reproduces both inelastic-neutron-scattering experiments and heat-capacity measurements. To further examine the adequacy of the proposed model, we calculate the field dependence of the polarized terahertz spectra, which reproduces the experimental results: the spin-gapped excitation survives up to an onset field where the magnetic order disappears and the response in the high-field region is almost linear. Based on these numerical results, we argue that the low-energy magnetic excitation in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ is mainly characterized by interactions such as off-diagonal interactions and weak Heisenberg interactions between nearest-neighbor pairs, rather than by the strong Kitaev interactions.

arXiv:1802.00545•Physical review. B./Physical review. B•Apr 25, 2018•41 citations

Spin Gap in Two-Dimensional Heisenberg Model for CaV4O9

Nobuyuki Katoh, Masatoshi Imada

We investigate the mechanism of spin gap formation in a two-dimensional model relevant to Mott insulators such as CaV$_4$O$_9$. From the perturbation expansion and quantum Monte Carlo calculations, the origin of the spin gap is ascribed to the four-site plaquette singlet in contrast to the dimer gap established in the generalized dimerized Heisenberg model.

arXiv:cond-mat/9510049•Journal of the Physical Society of Japan•Nov 15, 1995•68 citations

Spin-orbital Energy Gap in One-dimensional Spin-orbital Model

Rui Zhu

The spin-orbital energy gap in a one-dimensional spin-orbital model deduced from a degenerate Hubbard model with intrasite Hund rule coupling is studied.By using a mean-field method with SU(4) constraint fermion representation of spins and orbitals the valence bond order parameter,quasi-particle excitation gap and the spin and orbital density-density correlation functions are calculated.It is found that,as the Hund's coupling strength increases the excitation spectra show a gap and the magnetic configuration changes from a frustrating disordered state to a spin ferromagnetic and orbital antiferromagnetic ordered state at J_1/J_2=1/3.

Jisuan wuli•Jan 1, 2007•0 citations

Possible effective model with strong Kitaev interaction for $\alpha$-${\rm RuCl_3}$

Takafumi Suzuki, Sei-ichiro Suga

We calculate dynamical spin structure factors (DSFs) of three ab-initio models and one ab-initio-guided model for a honeycomb-lattice magnet $\alpha$-RuCl$_3$ with an exact numerical diagonalization method. We also calculate temperature dependences of the heat capacity, the nearest-neighbor (NN) spin-spin correlation function, and the static spin structure factor by employing thermal pure quantum states. From the obtained results for the four effective models, we find that, even when the magnetic order appears at a low temperature, the intensity at the $\Gamma$ point in the DSFs grows as the NN spin correlation grows. In addition, we find that the four models fail in explaining the features of both the inelastic-neutron-scattering experiments and the heat capacity measurements. In the four models, when temperature decreases, the heat capacity shows a prominent peak at a high temperature where the nearest-neighbor spin-spin correlation function grows. However, the peak temperatures in the heat capacity are too low in comparison with the observed values in the experiments. Thus, we propose an effective model with the strong ferromagnetic Kitaev coupling. We show that the proposed model quantitatively reproduces the above two experimental features. To discuss the further adequacy of the proposed model, we calculate the field dependence of the polarized terahertz spectra. We find that the proposed model successfully reproduces the experimental results: the spin-gapped excitation surviving up to an onset field where the magnetic order disappears and the almost linear response in the high field region. From the obtained numerical results, we argue that the feature of the low-energy magnetic excitation in $\alpha$-RuCl$_3$ is mainly characterized by the other interactions rather than the most dominant Kitaev interactions such as the off-diagonal interactions on the nearest-neighbor pairs.

•Feb 2, 2018•0 citations

Exact and numerical results for the dimerized spin-orbital model

Marcio Jose Martins, Bernard Nienhuis

We establish exact results for the one-dimensional spin-orbital model for special values of the four-spin interaction $V$ and dimerization parameter $δ$. The first exact result is at $δ=1/2$ and $V=-2$. Because we find a very small but finite gap in this dimerized chain, this can serve as a very strong test case for numerical and approximate analytical techniques. The second result is for the homogeneous chain with $V=-4$ and gives evidence that the system has a spontaneously dimerized ground state. Numerical results indicate that the interplay between dimerization and interaction could result in gapless phases in the regime $0\leq V

arXiv:cond-mat/0004238•Apr 14, 2000•0 citations
Effects of possible orbital order in magnetic properties of two-dimensional spin gap system for CaV4_44​O9_99​ are investigated theoretically. After analyzing experimental data, we show that single orbital models assumed in the literature are insufficient to reproduce the data. To understand the origin of the discrepancy, we assume that in d1d^1d1 state of V, dxzd_{xz}dxz​ and dyzd_{yz}dyz​ orbitals have substantial contributions in the lowest-energy atomic level which leads to a double-degeneracy. We study possible configurations of the orbital order. By exact diagonalization and perturbation expansion, we calculate the susceptibility, wavenumber dependence of low-lying excitations and equal-time spin-spin correlations which is related to integrated intensity of the neutron inelastic scattering. These quantities sensitively depend on the configuration of the orbital order. The calculated results for some configurations of the orbital order reproduce many experimental results much better than the previous single-orbital models. However some discrepancy still remains to completely reproduce all of the reported experimental results. To understand the origin of these discrepancies, we point out the possible importance of the partially occupied dxyd_{xy}dxy​ orbital in addition to orbital order of partially filled dxzd_{xz}dxz​ and dyzd_{yz}dyz​ orbitals.
Effective spin Hamiltonians with t 2g orbital degeneracy have been investigated theoretically. We assume that a d electron occupies one of doubly degenerate d z x and d y z orbitals which have the lowest energy in atomic level. The orbital degrees of freedom are represented as Ising iso-spin operators because of the symmetry of the orbital characters. We apply the Hamiltonians to a ladder and a chain lattices and investigate the models using the exact diagonalization. For the ladder model, a spin gap opens above a finite value of the spin exchange coupling on rung, which is qualitatively different from the ladder model with single orbital. For the chain model, the spin gap behavior is observed in the uniform spin correlation at low temperature. Origin of the spin gap is a spin-dimer triggered by the occurrence of the ferromagnetic orbital ordering, which suggests a new mechanism of the spin gap formation.
We use an exact numerical diagonalization method to calculate the dynamical spin structure factors of three ab initio models and one ab initio guided model for a honeycomb-lattice magnet $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. We also use thermal pure quantum states to calculate the temperature dependence of the heat capacity, the nearest-neighbor spin-spin correlation function, and the static spin structure factor. From the results obtained from these four effective models, we find that, even when the magnetic order is stabilized at low temperature, the intensity at the $\mathrm{\ensuremath{\Gamma}}$ point in the dynamical spin structure factors increases with increasing nearest-neighbor spin correlation. In addition, we find that the four models fail to explain heat-capacity measurements whereas two of the four models succeed in explaining inelastic-neutron-scattering experiments. In the four models, when temperature decreases, the heat capacity shows a prominent peak at a high temperature where the nearest-neighbor spin-spin correlation function increases. However, the peak temperature in heat capacity is too low in comparison with that observed experimentally. To address these discrepancies, we propose an effective model that includes strong ferromagnetic Kitaev coupling, and we show that this model quantitatively reproduces both inelastic-neutron-scattering experiments and heat-capacity measurements. To further examine the adequacy of the proposed model, we calculate the field dependence of the polarized terahertz spectra, which reproduces the experimental results: the spin-gapped excitation survives up to an onset field where the magnetic order disappears and the response in the high-field region is almost linear. Based on these numerical results, we argue that the low-energy magnetic excitation in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ is mainly characterized by interactions such as off-diagonal interactions and weak Heisenberg interactions between nearest-neighbor pairs, rather than by the strong Kitaev interactions.
We investigate the mechanism of spin gap formation in a two-dimensional model relevant to Mott insulators such as CaV4_44​O9_99​. From the perturbation expansion and quantum Monte Carlo calculations, the origin of the spin gap is ascribed to the four-site plaquette singlet in contrast to the dimer gap established in the generalized dimerized Heisenberg model.
The spin-orbital energy gap in a one-dimensional spin-orbital model deduced from a degenerate Hubbard model with intrasite Hund rule coupling is studied.By using a mean-field method with SU(4) constraint fermion representation of spins and orbitals the valence bond order parameter,quasi-particle excitation gap and the spin and orbital density-density correlation functions are calculated.It is found that,as the Hund's coupling strength increases the excitation spectra show a gap and the magnetic configuration changes from a frustrating disordered state to a spin ferromagnetic and orbital antiferromagnetic ordered state at J_1/J_2=1/3.
Possible effective model with strong Kitaev interaction for α\alphaα-RuCl3{\rm RuCl_3}RuCl3​
We calculate dynamical spin structure factors (DSFs) of three ab-initio models and one ab-initio-guided model for a honeycomb-lattice magnet α\alphaα-RuCl3_33​ with an exact numerical diagonalization method. We also calculate temperature dependences of the heat capacity, the nearest-neighbor (NN) spin-spin correlation function, and the static spin structure factor by employing thermal pure quantum states. From the obtained results for the four effective models, we find that, even when the magnetic order appears at a low temperature, the intensity at the Γ\GammaΓ point in the DSFs grows as the NN spin correlation grows. In addition, we find that the four models fail in explaining the features of both the inelastic-neutron-scattering experiments and the heat capacity measurements. In the four models, when temperature decreases, the heat capacity shows a prominent peak at a high temperature where the nearest-neighbor spin-spin correlation function grows. However, the peak temperatures in the heat capacity are too low in comparison with the observed values in the experiments. Thus, we propose an effective model with the strong ferromagnetic Kitaev coupling. We show that the proposed model quantitatively reproduces the above two experimental features. To discuss the further adequacy of the proposed model, we calculate the field dependence of the polarized terahertz spectra. We find that the proposed model successfully reproduces the experimental results: the spin-gapped excitation surviving up to an onset field where the magnetic order disappears and the almost linear response in the high field region. From the obtained numerical results, we argue that the feature of the low-energy magnetic excitation in α\alphaα-RuCl3_33​ is mainly characterized by the other interactions rather than the most dominant Kitaev interactions such as the off-diagonal interactions on the nearest-neighbor pairs.
We establish exact results for the one-dimensional spin-orbital model for special values of the four-spin interaction VVV and dimerization parameter δδδ. The first exact result is at δ=1/2δ=1/2δ=1/2 and V=−2V=-2V=−2. Because we find a very small but finite gap in this dimerized chain, this can serve as a very strong test case for numerical and approximate analytical techniques. The second result is for the homogeneous chain with V=−4V=-4V=−4 and gives evidence that the system has a spontaneously dimerized ground state. Numerical results indicate that the interplay between dimerization and interaction could result in gapless phases in the regime $0\leq V