坂井 徹

The magnetization processes of the S = 3/2 and S = 2 antiferromagnetic chains with the biquadratic interaction are investigated using the numerical diagonalization of the finite-size cluster. It is found that the system does not exhibit the spin nematic phase, which was predicted to occur for the S = 1 antiferromagnetic chain. Instead, the present analysis reveals that the quantum spin triatic and quatic liquid phases appear below the saturation magnetization for sufficiently large negative biquadratic interaction, for S = 3/2 and S = 2 chains, respectively. In addition it is also found that the magnetization jump up to the saturation magnetization appears for the small negative biquadratic interaction. The phase diagrams with respect to the negative biquadratic interaction and the magnetization are presented for the S = 3/2 and S = 2 antiferromagnetic chains.

The magnetization process of the S=1/2 delta chain with the anisotropic ferromagnetic interaction is investigated using the numerical diagonalization of finite-size clusters. It is found that the spin nematic liquid phase appears in higher magnetization region, as well as the SDW liquid one in lower region.

The magnetization process of the S = 1/2 distorted diamond spin chain with anisotropic ferromagnetic interaction is investigated using numerical diagonalization of finite-size clusters. It is found that the spin nematic and SDW Tomonaga-Luttinger liquids can appear for sufficiently large easy axis anisotropy.

Abstract The magnetization process of the S = 1 antiferromagnetic chain with the single-ion anisotropy D and the biquadratic interaction is investigated using the numerical diagonalization. Both interactions stabilize the 2-magnon Tomonaga-Luttinger liquid (TLL) phase in the magnetization process. Based on several excitation gaps calculated by the numerical diagonalization, some phase diagrams of the magnetization process are presented. These phase diagrams reveal that the spin nematic dominant TLL phase appears at higher magnetizations for sufficiently large negative D.

The S = 1/2 distorted diamond spin chain with the anisotropic ferromagnetic interaction is investigated using the numerical diagonalization and the level spectroscopy analysis. It is known that the system exhibits a plateau of the magnetization curve at the 1/3 of the saturation. The present study indicates that as the anisotropy is varied the quantum phase transition occurs between two different mechanisms of the 1/3 magnetization plateau. The phase diagram with respect to the anisotropy and the ferromagnetic coupling is also presented.

<title>Abstract</title> We study the <italic>S</italic> = 1/2 Heisenberg antiferromagnet on the floret pentagonal lattice by numerical diagonalization method. This system shows various behaviours that are different from that of the Cairo-pentagonal-lattice antiferromagnet. The ground-state energy without magnetic field and the magnetization process of this system are reported. Magnetization plateaux appear at one-ninth height of the saturation magnetization, at one-third height, and at seven-ninth height. The magnetization plateaux at one-third and seven-ninth heights come from interactions linking the sixfold-coordinated spin sites. A magnetization jump appears from the plateau at one-ninth height to the plateau at one-third height. Another magnetization jump is observed between the heights corresponding to the one-third and seven-ninth plateaux; however the jump is away from the two plateaux, namely, the jump is not accompanied with any magnetization plateaux. The jump is a peculiar phenomenon that has not been reported.

The magnetization process of the S = 1 antiferromagnetic chain with the biquadratic interaction is investigated using the numerical diagonalization. As a result, it is found that the quantum spin nematic liquid phase appears below the saturation magnetization for sufficiently large negative biquadratic interaction. The ground state phase diagram is also presented. This result is consistent with the previous density matrix renormalization group study. In addition the present study confirms that the two magnon excitation is gapless, while the single magnon one is gapped in the spin nematic liquid phase.

The direct electron paramagnetic resonance (EPR) absorption between the singlet ground state and the triplet excited states of spin gap systems is investigated. Such an absorption, which is forbidden by the conservation of the total spin quantum number in isotropic Hamiltonians, is allowed by some anisotropies; the staggered g-tensor and the Dzyaloshinskii-Moriya interaction. Selection rules in the presence of these interactions were presented in our previous works. We review the selection rules of the EPR transition of the spin gap with some numerical demonstrations and discuss some applications.

We use the Ginzburg-Landau theory for a chiral p-wave superconductor to describe the filamentary superconducting phase nucleating at temperatures higher than the bulk transition temperature near the interfaces between Ru metal and Sr2RuO4 in eutectic Sr2RuO4-Ru. The peculiar phase diagram of magnetic field versus temperature shows very distinct properties for different directions of the magnetic field. A clear feature of the magnetic fields in the basal plane of Sr2RuO4, perpendicular to the chiral axis (c axis), is the occurrence of a second superconducting transition with a new order parameter visible as a zero-bias anomaly in tunneling spectroscopy. For the field along the c axis of Sr2RuO4, two transitions merge, indicating that the field drives the second-order parameter through the paramagnetic coupling to a chiral supercurrent. The resulting phenomenology shows that the assumption of a chiral superconducting order parameter in Sr2RuO4 yields an image reproducing the qualitative properties observed in the experiment. This discussion is qualitatively analogous to the corresponding chiral even- and odd-parity channels.

The one-dimensional Heisenberg antiferromagnets of large-integer-S spins are studied; their Haldane gaps are estimated by the numerical diagonalization method for S = 5 and 6. We successfully obtain a monotonically increasing sequence of finite-size energy difference data corresponding to the Haldane gaps from the huge-scale parallel calculations of diagonalization under the twisted boundary condition and create a monotonically decreasing sequence within the range of system sizes treated in this study from the monotonically increasing sequence. Consequently, the gaps for S = 5 and 6 are estimated to be 0.000050 +/- 0.000005 and 0.0000030 +/- 0.0000005, respectively. The asymptotic formula of the Haldane gap for S -> infinity is examined from the new estimates to determine the coefficient in the formula more precisely.

We synthesized a kagome fluoride Cs2LiTi3F12 with S = 1/2 spins, and studied magnetic properties of the compound. The temperature dependence of the magnetic susceptibility indicates that it has dominant antiferromagnetic interactions and that it has no magnetic order down to 2 K. We found two magnetization plateaus in its magnetization process approximately at 1/3 and 0.8 mu(B) per Ti. The monoclinic crystal structure gives four inequivalent nearest-neighbor exchange interactions. Our density functional theory calculations suggest that three of them are antiferromagnetic and one of them is weakly ferromagnetic, resulting in a magnetic system composed of antiferromagnetically coupled linear chains and Delta chains. This explains the observed suppression of magnetic order. Numerical diagonalization gives a magnetization curve in good agreement with the experimental results.

We investigate the S = 2 antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using the numerical exact diagonalization of finite-size clusters and the level spectroscopy analysis. It is found that a magnetization plateau possibly appears at half of the saturation magnetization for some suitable anisotropy parameters. The level spectroscopy analysis indicates that the 1/2 magnetization plateau is formed by two different mechanisms, depending on the anisotropy parameters. The phase diagram of the 1/2 plateau states and some typical magnetization curves are also presented. In addition, the biquadratic interaction is revealed to enhance the plateau induced by the Haldane mechanism.

We investigate the connection between highly frustrated kagome based Hamiltonians and a recently synthesized family of materials containing Ti3+ S = 1/2 ions. Employing a combination of all electron density functional theory and numerical diagonalization techniques, we establish the Heisenberg Hamiltonians for the distorted kagome antiferromagnets Rb2NaTi3F12, Cs-2 NaTi3F12, and Cs-2 KTi3F12. We determine magnetization curves in excellent agreement with experimental observations. Our calculations successfully clarify the relationship between the experimental observations and the magnetization-plateau behavior at 1/3 height of the saturation and predict characteristic behaviors under fields that are higher than the experimentally measured region. We demonstrate that the studied Ti(III) family of materials interpolates between the kagome strip and kagome lattice.

©2019 The Physical Society of Japan To understand the Rashba effect, the spin–orbit interaction (SOI) term in the Hamiltonian that has the dominant effect needs to be identified. Discrete variational-LDA (DV-LDA) calculations, i.e., LCAO-based DFT calculations, were performed to analyze the Rashba effect on a Au(111) surface. A Au(111) model surface was approximated as a 14-layer slab. Considering the parities of the basis, the potential that causes the SOI can be separated into even and odd parities for the mirror operation (inversion of the coordinate perpendicular to the plane) in the plane including surface atoms. Both parities are related to the Rashba effect; therefore, their contributions to the effect need to be clarified. Results show that for the Rashba effect, the even-parity SOI is dominant and justifies the treatment of the SOI as the conventional l · s.

The S = 1/2 Heisenberg antiferromagnet on the two-dimensional pyramid lattice is studied by the numerical-diagonalization method. This lattice is obtained by the combination of the Lieb lattice and the square lattice. It is known that when interaction on the square lattice is increased from the ferrimagnetic limit of strong interaction on the Lieb lattice, this system shows gradual decrease and disappearance of spontaneous magnetization in the ground state. The present study treats the region near the case of the square-lattice antiferromagnet accompanied by isolated spins by numerical-diagonalization calculations of finite-size clusters with the maximum size of 39 sites. Our numerical results suggest the existence of a new phase with small but nonzero spontaneous magnetization between two zero-spontaneous-magnetization phases. (c) 2018 Author(s).

We explore the ground-state phase diagram of the S = 1/2 two-leg ladder with different leg interactions. The xy- and z-components of the leg interactions between nearest-neighbor spins in the a (b) leg are respectively denoted by J(1,a) and Delta(1)J(1,a )(J(1,b) and Delta(1)J(1,b)). On the other hand, the xy- and z-components of the uniform rung interactions are respectively denoted by Gamma(r)J(r) and J(r). In the above, Delta(1) and Gamma(r) are the XXZ-type anisotropy parameters for the leg and rung interactions, respectively. This system has frustration when J(1,a) J(1,b) < 0 irrespective of the sign of J(r). The phase diagram on the Delta(1)(vertical bar Delta(1)vertical bar <= 1.0) versus J(1,b) ( -2 . 0 <= J(1,b), <= 3.0) plane in the case where J(1,a) = 0.2, J(r) = -1.0, and Gamma(r) = 0.5 is determined numerically. We employ physical considerations and perform level spectroscopy and phenomenological renormalization-group analyses of the numerical data obtained by the exact diagonalization method. The resultant phase diagram contains the ferromagnetic, Haldane, Neel, nematic Tomonaga-Luttinger liquid (TLL), partial ferrimagnetic, and XY1 phases. Interestingly enough, the nematic TLL phase appears in the strong-rung unfrustrated region as well as in the strong-rung frustrated region. We perform first-order perturbational calculations from the strong-rung coupling limit to elucidate the characteristic features of the phase diagram. Furthermore, we carry out density-matrix renormalizationgroup calculations for some physical quantities such as the energy gaps, the local magnetization, and the spin correlation functions to supplement the reliability of the phase diagram. The phase diagram on the Gamma(r) (0.0 <= Gamma(r <=) 1.0) versus J(1,b) (-1.0 <= J(1,b) <= 2.0) plane in the case where J(1,a), = 0.2, J(r) = -1.0, and Delta(1) = 1.0 is also discussed briefly.

The Haldane gap of the S = 2 Heisenberg antiferromagnet in a one-dimensional linear chain is examined by a numerical-diagonalization method. A precise estimate for the magnitude of the gap is successfully obtained by a multistep convergence-acceleration procedure applied to finite-size diagonalization data under the twisted boundary condition.

The magnetization process of the spin-1/2 antiferromagnetic Heisenberg model on two-dimensional square-kagome lattice is studied theoretically. The metamagnetic jumps exist in the magnetization process at the higher edge of the 1/3 and 2/3 plateaus. The parameter-dependencies of the critical field and the magnitude of the magnetization jump at the higher edge of the 1 /3 plateau are obtained by using the approximated state in the unit cell and compared with the numerical results of the exact diagonalization of 42 sites.

The S = 1/2 triangular - and kagome-lattice Heisenberg antiferromagnets are investigated under a magnetic field using the numerical-diagonalization method. A piocedure is proposed to extract data points with very small finite-size deviations using the numerical-diagonalization results tor capturing the magnetization curve. For the tnangulai-lattice antifenomagnet, the plateau edges at one-third the height of the saturation and the saturation field are successfully estimated. This study additionally presents results of magnetization process for a 45-site cluster of the kagome-lattice antiferromagnet; the present analysis suggests that the plateau does not open at one-ninth the height of the saturation.

The S = 1/2 kagome- and triangular-lattice Heisenberg antiferromagnets are investigated using the numerical exact diagonalization and the finite-size scaling analysis. The behaviour of the field derivative at zero magnetization is examined for both systems. The present result indicates that the spin excitation is gapless for each system.

The S = 1 spin ladder with the easy-axis single-ion anisotropy is investigated using the numerical diagonalization and the finite-size scaling analysis. It is found that the field-induced nematic Tomonaga-Luttinger liquid phase appears above the critical field. In addition, there exists another critical field at which the quantum phase transition from the nematic Tomonaga-Luttinger liquid phase to the conventional field-induced Tomonaga-Luttinger liquid phase occurs. Besides some phase diagrams are presented.

The spin-1/2 triangular-lattice Heisenberg antiferromagnet with a root 3 x root 3-type distortion is studied by the numerical-diagonalization method. We examine this model between the two cases, one is the undistorted triangular lattice and the other is the model on the honeycomb lattice with isolated spins. When the distortion is controlled, we find a nontrivial region where the ground states shows spontaneous magnetization; the magnitude increases gradually as the distortion is larger and is smaller than one third of the saturated magnetization.

The S=1/2 kagome-lattice antiferromagnet is investigated using the numerical diagonalization of finite-size clusters. The analysis of the susceptibility at the zero magnetization indicates that the magnetic excitation of the system is gapless. It is consistent with our previous finite-scaling analysis of the spin gap. The application of the method for the triangular-lattice antiferromagnet confirms the validity of the analysis.

We investigate the spin-1/2 twisted three-leg antiferromagnetic quantum spin tube in the presence of the easy-plane anisotropy, using the numerical diagonalization of finite-size clusters. We show cases of the existence and the absence of magnetization plateau at 1/3 height of saturation magnetization when the anisotropy is tuned. The phenomenological-renormalization group analysis indicates a quantum phase transition between the 1/3 magnetization plateau phase and the plateauless one. The phase diagram is also presented. (C) 2017 Elsevier Ltd. All rights reserved.

An S = 1/2 triangular-lattice Heisenberg antiferromagnet with next-nearest-neighbor (NNN) interactions is investigated under a magnetic field by the numerical-diagonalization method. It is known that, in both cases of weak and strong NNN interactions, this system reveals a magnetization plateau at one-third of the saturated magnetization. We examine the stability of this magnetization plateau when the amplitude of NNN interactions is varied. We find that a nonplateau region appears between the plateau phases in the cases of weak and strong NNN interactions.

The S = 1/2 kagome-lattice antiferromagnet is studied using the numerical diagonalization of finite clusters and a finite-size scaling. The susceptibility analysis at the zero magnetization indicates that the system has a gapless spin excitation. It is consistent with our previous finite-size scaling analysis of the spin gap. (C) 2017 Published by Elsevier Ltd.

The ground state of the spin-1/2 Heisenberg antiferromagnet on a distorted triangular lattice is studied using a numerical-diagonalization method. The network of interactions is the root 3 x root 3 type; the interactions are continuously controlled between the undistorted triangular lattice and the dice lattice. We find new states between the nonmagnetic 120-degree-structured state of the undistorted triangular case and the up-up-down state of the dice case. The intermediate states show spontaneous magnetizations that are smaller than one third of the saturated magntization corresponding to the up-up-down state.

We study frustrated quantum spin systems consisting of dimers of spin-1/2 spins. We derive several models that have the exact ground state of the form of the direct product of dimer states. The ground states realized include the product state of dimer singlets, that of dimer triplets with zero magnetization, those of dimer-spin-nematic states, and those of a mixture of the dimer states. Pseudo spin-1/2 operators emerging in each dimer are also introduced.

The S = 1/2 kagome-lattice antiferromagnet is studied using the numerical diagonalization of finite clusters and a finite-size scaling. The susceptibility analysis at the zero magnetization indicates that the system has a gapless spin excitation. It is consistent with our previous finite-size scaling analysis of the spin gap. (C) 2017 Elsevier Ltd. All rights reserved.

A single-crystal S = 3/2 perfect kagome lattice antiferromagnet, KCr3(OH)(6)(SO4)(2) (Cr-jarosite), has been studied by X-band and high-frequency electron spin resonance (ESR). The g-values perpendicular to the kagome plane (c-axis) and in the plane were determined to be g(c) = 1.9704 +/- 0.0002 and g(xi) = 1.9720 +/- 0.0003, respectively, by high-frequency ESR observed at 265 K. Antiferromagnetic resonances (AFMRs) with an antiferromagnetic gap of 120 GHz were observed at 1.9 K, which is below T-N = 4.5 K. The analysis of AFMR modes using the conventional molecular field theory gave d(p) = 0.27K and d(z) = 0.07 K, where d(p) and d(z) are in-plane and out-of-plane components of d vector of the Dzyaloshinsky-Moriya (DM) interaction, respectively. On the basis of these results and the exchange interaction of J = 6.15K estimated by Okuta et al., the ground state of Cr-jarosite was discussed in connection with the Monte Carlo simulation results with classical Heisenberg spins on the kagome lattice by Elhajal et al. Finally, the angular dependence of the linewidth and lineshape observed at 296K by X-band ESR showed the typical behavior of a two-dimensional Heisenberg antiferromagnet, suggesting the good two-dimensionality of Cr-jarosite.

The S=1/2 kagome-lattice antiferromagnet is investigated using the numerical diagonalization up to the 42-spin cluster. The analysis of the field derivative of the magnetization at the zero magnetization indicates that the magnetic excitation ot the system is gapless. It is consistent with our previous finite-scaling analysis of the spin gap.