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In solid materials, the parameters relevant to quantum effects, such as the spin quantum number, are basically determined and fixed at the chemical synthesis, which makes it challenging to control the amount of quantum correlations. We propose and demonstrate a method for active control of the classical-quantum crossover in magnetic insulators by applying external pressure. As a concrete example, we perform high-field, high-pressure measurements on CsCuCl$_3$, which has the structure of weakly-coupled spin chains. The magnetization process experiences a continuous evolution from the semi-classical realm to the highly-quantum regime with increasing pressure. Based on the idea of "squashing" the spin chains onto a plane, we characterize the change in the quantum correlations by the change in the value of the local spin quantum number of an effective two-dimensional model. This opens a way to access the tunable classical-quantum crossover of two-dimensional spin systems by using alternative systems of coupled-chain compounds., Comment: 11 + 3 pages, 10 + 2 figures

High-pressure and high-field electron spin resonance (ESR) measurements have been performed on a single crystal of the orthogonal-dimer spin system SrCu$_{2}$(BO$_{3}$)$_{2}$. With frequencies below 1 THz, ESR signals associated with transitions from the singlet ground state to the one-triplet excited states and the two-triplet bound state were observed at pressures up to 2.1 GPa. We obtained directly the pressure dependence of the gap energies, finding a clear first-order phase transition at $P_{c}=1.85\pm0.05$ GPa. By comparing this pressure dependence with the calculated excitation energies obtained from an exact diagonalization, we determined the precise pressure dependence for inter- ($J'$) and intra-dimer ($J$) exchange interactions considering the Dzyaloshinski-Moriya interaction. Thus this system undergoes a first-order quantum phase transition from the dimer singlet phase to a plaquette singlet phase above the ratio $(J'/J)_{c}=0.660\pm0.003$.

A single crystal S=3/2 perfect kagome lattice antiferromagnet $\mathrm{KCr_3(OH)_6(SO_4)_2}$ (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 are determined to be $g_c=1.9704 \pm 0.0002$ and $g_\xi=1.9720 \pm 0.0003$, respectively, by high-frequency ESR observed at 265 K. Antiferromagnetic resonances (AFMR) with the antiferromagnetic gap of 120 GHz are observed at 1.9 K, which is below $T_N$=4.5 K. The analysis of AFMR modes by the conventional molecular field theory shows $d_p=0.27$ K and $d_z=0.07$ K, where $d_p$ and $d_z$ are in-plane and out-of-plane components of DM d vector, respectively. From these results and the estimated exchange interaction J=6.15 K by Okuta et al., the ground state of Cr-jarosite is discussed in connection with the Monte Carlo simulations result with classical Heisenberg spins on the kagome lattice by Elhajal et al. Finally, the angular dependence of linewidth and the lineshape observed at 296 K by X-band ESR show typical behavior of a two-dimensional Heisenberg antiferromagnet, suggesting a good two-dimensionality of Cr-jarosite.

This paper is to study for local triality relations and ist global relations That is, this is a generalization of automorhisms and derivations., Comment: 38pages

We have made a survey of ceramics for the inner parts of the transmission-type pressure cell to achieve the high pressure and the high transmission in THz range. By using the optimal combination of ZrO$_{2}$-based ceramic and Al$_{2}$O$_{3}$ ceramic, we have succeeded in obtaining the pressure up to 1.5 GPa and the frequency region up to 700 GHz simultaneously. We show the high-pressure ESR results of Shastry-Sutherland compound SrCu$_{2}$(BO$_{3}$)$_{2}$ as an application. We observed the direct ESR transition modes between the singlet ground state and the triplet excited states up to the pressure of 1.51 GPa successfully, and obtained the precise pressure dependence of the gap energy. The gap energy is directly proved to be suppressed by the pressure. Moreover, we found that the system approaches the quantum critical point with pressure by comparing the obtained data with the theory. This result also shows the usefulness of high-pressure ESR measurement in THz region to study quantum spin systems.

We give a review of recent works for non-associative algebras, especially Lie algebras satisfying the triality relation. They are also intimately related to S_4 (symmetric group of 4-objects) symmetry of the Lie algebras., Comment: 62 pages

The microscopic magnetic properties of high-quality GdN thin films have been investigated by electron spin resonance (ESR) and ferromagnetic resonance (FMR) measurements. Detailed temperature dependence ESR measurements have shown the existence of two ferromagnetic components at lower temperatures which was not clear from the previous magnetization measurements. The temperature, where the resonance shift occurs for the major ferromagnetic component, seems to be consistent with the Curie temperature obtained from the previous magnetization measurement. On the other hand, the divergence of line width is observed around 57 K for the minor ferromagnetic component. The magnetic anisotropies of GdN thin films have been obtained by the analysis of FMR angular dependence observed at 4.2 K. Combining the X-ray diffraction results, the correlation between the magnetic anisotropies and the lattice constants is discussed.

In a frustrated J_1-J_2 chain with the nearest-neighbor ferromagnetic interaction J_1 and the next-nearest-neighbor antiferromagnetic interaction J_2, 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 NaCuMoO_4(OH), which comprises edge-sharing CuO_2 chains, is a good candidate J_1-J_2 chain antiferromagnet. The exchange interactions are estimated as J_1 = - 51 K and J_2 = 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., Comment: 6 pages, 4 figures

We introduce a notion of Pre-structurable Algebras based upon triality relations and study its relation to structurable algebra of Allison, as well as to Lie algebras satisfying triality., Comment: 19 pages, to be submitted to Linear Algebra and Applications

The gem-stone dioptase Cu6Si6O18.6H2O has a chiral crystal structure of equilateral triangular helices consisting of Cu-3d spins. It shows an antiferromagnetic order with an easy axis along c at TN = 15.5 K under zero field, and a magnetization jump at HC = 13.5 T when the field is applied along c-axis. By 29Si-NMR measurements, we have revealed that the high-field state is essentially the two sub-lattice structure, and that the component within ab-plane is collinear. The result indicates no apparent match with the geometrical pattern of helical spin chain., Comment: SCES2013, Hongo, Tokyo

Symmetry group of Lie algebras and superalgebras constructed from (\epsilon,\delta) Freudenthal- Kantor triple systems has been studied. Especially, for a special (\epsilon,\epsilon) Freudenthal- Kantor triple, it is SL(2) group. Also, relationship between two constructions of Lie algebras from structurable algebra has been investigated.

Left unital Kantor triple systems will be shown to correspond to structurable algebras endowed with an involutive automorphism. A related result is proved for (-1,-1) Freudenthal-Kantor triple systems. Some consequences for the associated 5-graded Lie algebras and superalgebras are deduced too. In particular, left unital (-1,-1) Freudenthal-Kantor triple systems are shown to be intimately related to Lie superalgebras graded over the root system of type B(0,1)., Comment: 17 pages

We clarify that the antiferromagnetic order in the distorted tetrahedral quasi-one dimensional spin system induces electric polarizations. In this system, the effects of the low dimensionality and the magnetic frustration are expected to appear simultaneously. We obtain the magnetic-field-temperature phase diagram in Cu3Mo2O9 by studying the dielectric constant and the spontaneous electric polarization. Around the tricritical point at 10 T and 8 K, the change of the direction in the electric polarization causes a colossal magnetocapacitance. We calculate the charge redistribution in the small spin cluster consisting of two magnetic tetrahedra to demonstrate the electric polarization induced by the antiferromagnetism., Comment: 10 pages 6 figures, in press in J. Phys. Soc. Jpn

High-frequency ESR results on the S=1/2 Heisenberg hexagonal antiferromagnet InCu2/3V1/3O3 are reported. This compound appears to be a rare model substance for the honeycomb lattice antiferromagnet with very weak interlayer couplings. The high-temperature magnetic susceptibility can be interpreted by the S=1/2 honeycomb lattice antiferromagnet, and it shows a magnetic-order-like anomaly at TN=38 K. Although, the resonance field of our high-frequency ESR shows the typical behavior of the antiferromagnetic resonance, the linewidth of our high-frequency ESR continues to increase below TN, while it tends to decrease as the temperature in a conventional three-dimensional antiferromagnet decreases. In general, a honeycomb lattice antiferromagnet is expected to show a simple antiferromagnetic order similar to that of a square lattice antiferromagnet theoretically because both antiferromagnets are bipartite lattices. However, we suggest that the observed anomalous spin dynamics below TN is the peculiar feature of the honeycomb lattice antiferromagnet that is not observed in the square lattice antiferromagnet., Comment: 5 pages, 5 figures

Lie algebras endowed with an action by automorphisms of the dicyclic group of degree 3 are considered. The close connections of these algebras with Lie algebras graded over the nonreduced root system BC1, with J-ternary algebras and with Freudenthal-Kantor triple systems are explored., Comment: 34 pages

High-field electron spin resonance (ESR) measurements have been performed on vesignieite BaCu$_3$V$_2$O$_8$(OH)$_2$, which is considered as a nearly ideal model substance of $S$=1/2 kagome antiferromagnet, in the temperature region from 1.9 to 265 K. The frequency region is from 60 to 360 GHz and the applied pulsed magnetic field is up to 16 T. Observed g-value and linewidth show the increase below 20 K, which suggest the development of the short range order. Moreover, a gapless spin liquid ground state is suggested from the frequency-field relation at 1.9 K., Comment: 5 pages, 6 figures, jpsj2 class file, to be published in J. Phys. Soc. Jpn

Lie algebras endowed with an action by automorphisms of any of the symmetric groups S3 or S4 are considered, and their decomposition into a direct sum of irreducible modules for the given action is studied. In case of S3-symmetry, the Lie algebras are coordinatized by some nonassociative systems, which are termed generalized Malcev algebras, as they extend the classical Malcev algebras. These systems are endowed with a binary and a ternary products, and include both the Malcev algebras and the Jordan triple systems., Comment: 35 pages

The classical Tits construction provides models of the exceptional simple Lie algebras in terms of a unital composition algebra and a degree three simple Jordan algebra. A couple of actions of the symmetric group of degree 4 on this construction are given. By means of these actions, the models provided by the Tits construction are related to models of the exceptional Lie algebras obtained from two different types of structurable algebras. Some models of exceptional Lie superalgebras are discussed too., Comment: 26 pages

The normal symmetric triality algebras (STA's) and the normal Lie related triple algebras (LRTA's) have been recently introduced by the second author, in connection with the principle of triality. It turns out that the unital normal LRTA's are precisely the structurable algebras extensively studied by Allison. It will be shown that the normal STA's (respectively LRTA's) are the algebras that coordinatize those Lie algebras whose automorphism group contains a copy of the alternating (resp. symmetric) group of degree 4., Comment: 24 pages

A noncommutative Jordan algebra of a specific type is attached to any (-1,-1)-balanced Freudenthal Kantor triple system, in such a way that the triple product in this system is determined by the binary product in the algebra. Over fields of characteristic zero, the simple noncommutative Jordan algebras of this type are classified., Comment: 19 pages, LaTeX

Any simple Lie superalgebras over the complex field can be constructed from some triple systems. Examples of Lie superalgebras $D(2,1;\alpha)$, G(3) and F(4) are given by utilizing a general construction method based upon $(-1,-1)$ balanced Freudenthal-Kantor triple system., Comment: 8 pages, no figures

Some symmetries of time-dependent Schr\"odinger equations for inverse quadratic, linear, and quadratic potentials have been systematically examined by using a method suitable to the problem. Especially, the symmetry group for the case of the linear potential turns out to be a semi-direct product $SL(2,R) x T_2(R)$ of the $SL(2,R)$ with a two-dimensional real translation group $T_2(R)$. Here, the time variable $t$ transforms as $t \to t^\prime = (ct+d)/(at+b)$ for real constants $a, b, c$, and $d$ satisfying $bc - ad =1$ with an accompanying transformation for the space coordinate $x$., Comment: 33 pages, no figures

We previously showed that the real eigenvalues of 3x3 octonionic Hermitian matrices form two separate families, each containing 3 eigenvalues, and each leading to an orthonormal decomposition of the identity matrix, which would normally correspond to an orthonormal basis. We show here that it nevertheless takes both families in order to decompose an arbitrary vector into components, each of which is an eigenvector of the original matrix; each vector therefore has 6 components, rather than 3., Comment: LaTeX2e, 14 pages

We will derive both quaternion and octonion algebras as the Clebsch-Gordan algebras based upon the su(2) Lie algebra by considering angular momentum spaces of spin one and three. If we consider both spin 1 and 1/2 states, then the same method will lead to the Lie-super algebra osp(1,2). Also, the quantum generalization of the method is discussed on the basis of the quantum group $su_q(2)$., Comment: 17 pages, TEX

We have given some arguments that a two-dimensional Lorentz-invariant Hamiltonian may be relevant to the Riemann hypothesis concerning zero points of the Riemann zeta function. Some eigenfunction of the Hamiltonian corresponding to infinite-dimensional representation of the Lorentz group have many interesting properties. Especially, a relationship exists between the zero zeta function condition and the absence of trivial representations in the wave function., Comment: 13 pages, TEX

Notions of quasi-classical Lie-super algebra as well as Lie-super triple systems have been given and studied with some examples. Its application to Yang-Baxter equation has also been given., Comment: 26 pages, TEX, no figures

A real representation theory of real Clifford algebra has been studied in further detail, especially in connection with Fierz identities. As its application, we have constructed real octonion algebras as well as related octonionic triple system in terms of 8-component spinors associated with the Clifford algebras $C(0,7)$ and $C(4,3)$., Comment: 30 pages, UR1377

We have new solutions to the Yang-Baxter equation, from which we have constructed new link invariants containing more than two arbitrary parameters. This may be regarded as a generalization of the Jones' polynomial. We have also found another simpler invariant which discriminates only the linking structure of knots with each other, but not details of individual knot., Comment: 22 pages

We have found some new solutions of both rational and trigonometric types by rewriting Yang-Baxter equation as a triple product equation in a vector space of matrices., Comment: 8 pages