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We have performed a powder neutron diffraction study on CsO$_2$, where the unpaired electron with $s=1/2$ in the $\pi^*$ orbital of the O$_2^-$ ion is responsible for the magnetism. The magnetic reflections 0 $\frac{1}{2}$ 0 and 0 $\frac{1}{2}$ 1 were observed below the N\'{e}el temperature of about 10 K. An antiferromagnetic structure with a propagation vector of (0 ,$\frac{1}{2}$, 0) and magnetic moments parallel to the $a$-axis is the most plausible. The magnitude of the ordered moment is about 0.2 $\mu_B$, which is considered to be strongly suppressed due to the one-dimensionality of the system. We propose a possible $\pi^*$ orbital order that can explain the obtained magnetic structure, and discuss its relation to the one-dimensionality.

We have investigated the low-temperature magnetism of sodium superoxide (NaO$_{2}$), in which spin, orbital, and lattice degrees of freedom are closely entangled. The magnetic susceptibility shows anomalies at $T_{1}=220$ K and $T_{2}=190$ K, which correspond well to the structural phase transition temperatures, and a sudden decrease below $T_{3}=34$ K. At 4.2 K, the magnetization shows a clear stepwise anomaly around 30 T with a large hysteresis. In addition, the muon spin relaxation experiments indicate no magnetic phase transition down to $T=0.3$ K. The inelastic neutron scattering spectrum exhibits magnetic excitation with a finite energy gap. These results confirm that the ground state of NaO$_{2}$ is a spin-singlet state. To understand this ground state in NaO$_{2}$, we performed Raman scattering experiments. All the Raman-active libration modes expected for the marcasite phase below $T_{2}$ are observed. Furthermore, we find that several new peaks appear below $T_{3}$. This directly evidences the low crystal symmetry, namely, the presence of the phase transition at $T_{3}$. We conclude the singlet-ground state of NaO$_{2}$ due to the spin-Peierls instability., Comment: 6 pages, 3 figures

In zeolite low-silica X (LSX), beta-cages with the inside diameter of approx 7 AA{} are arrayed in a diamond structure. Among them, supercages with the inside diameter of approx 13 AA{} are formed and arrayed in a diamond structure by the sharing of windows with the inside diameter of approx 8 AA{}. The chemical formula of zeolite LSX used in the present study is given by Na$_{x}$K$_{12-x}$Al$_{12}$Si$_{12}$O$_{48}$ per supercage (or beta-cage), where Na$_{x}$K$_{12-x}$ and Al$_{12}$Si$_{12}$O$_{48}$ are the exchangeable cations of zeolite LSX and the aluminosilicate framework, respectively. Na-K alloy clusters are incorporated in these cages by the loading of guest K metal at $n$K atoms per supercage (or beta-cage). A N'eel's N-type ferrimagnetism has been observed at $n = 7.8$ for $x = 4$. In the present paper, optical, magnetic and electrical properties are studied in detail mainly for $x = 4$. Ferrimagnetic properties are observed at $6.5 < n < 8.5$. At the same time, the Curie constant suddenly increases. An optical reflection band of beta-cage clusters at 2.8 eV is observed at $n > 6.5$ in accordance with the sudden increase in the Curie constant. An electrical resistivity indicates metallic values at $n$ gtrapprox 6, because a metallic state is realized in the energy band of supercage clusters. The ferrimagnetism is explained by the antiferromagnetic interaction between the magnetic sublattice of itinerant electron ferromagnetism at supercage clusters and that of localized moments at beta-cage clusters. The electrical resistivity in ferrimagnetic samples at $n = 8.2$ for $x = 4$ increases extraordinarily at very low temperatures, such as approx $10^6$ times larger than the value at higher temperatures. Observed anomalies in the electrical resistivity resembles the Kondo insulator, but itinerant electrons of narrow energy band of supercage clusters are ferromagnetic., Comment: 16 pages, 20 figures

K clusters arrayed in zeolite A are investigated in detail. K clusters are generated in regular alpha-cages of zeolite A by the loading of guest K metal at a loading density of K atoms per alpha-cage, $n$. The value of $n$ was changed from 0 to 7.2. It is known that this system shows ferromagnetic properties for $n > 2$, where the Curie temperature increases with $n$, has a peak of approx,8 K at $n approx 3.6$, and decreases to 0 K at $n = 7.2$. The negative Weiss temperature is estimated from the Curie-Weiss law for $n > 2$. A spherical quantum-well (SQW) model for the K cluster with 1$s$, 1$p$, and 1$d$ quantum states has previously been proposed, and the ferromagnetic properties were explained as being due to $s$-electrons in 1$p$ states. A spin-cant model of Mott-insulator antiferromagnetism in a K cluster array has been proposed for the origin of the ferromagnetic properties. However, the SQW model cannot explain either the $n$-dependence of the Curie temperature or that of the Curie constant. In the present study, detailed measurements were made of the optical reflection, magnetic properties, electron spin resonance, and electrical resistivities. An optical reflection band at 0.7 eV is clearly observed for $2 < n < 6$ at low temperatures, and is assigned to the excitation of the sigma-bonding state between 1$p$-states in adjoining alpha-cages. The electrical resistivity indicates an insulating state continuously for $n$. We propose an advanced SQW model with consideration for sigma-bonding, the orbital orthogonality of 1$p$-hole states, and also the superlattice structure. We explain the observed electronic properties using this model based on a correlated polaron system. We propose an enhancement effect of the Dzyaloshinsky-Moriya (DM) interaction between adjoining $1p$ orbitals by the extension of the Rashba mechanism of spin-orbit interaction., Comment: 18 pages, 25 figures

The ground state of alkali metals when the particle size decreases from bulk to nanometric atomic clusters is inevitably accompanied by quantum effects that can suppress their pristine metallic state. We demonstrate that the metallic nature of rubidium clusters confined and arrayed in the framework of insulating low-silica X zeolite is preserved. The $^{87}$Rb NMR spin-lattice relaxation assigned to rubidium clusters in supercages shows a Korringa behavior from 190~K down to 10~K, which is compatible with a macroscopic observation of low electrical resistivity. The density of states at the Fermi level is found to be enhanced compared to the analogous sodium case, consistent with a Holstein-Hubbard model of alkali-loaded zeolites., Comment: Extended version showing new data, 4+epsilon pages, 4 figures

We report on the experimental results of magnetic susceptibility, specific heat, electron spin resonance (ESR), and high-field magnetization measurements on a polycrystalline sample of the spin-$1/2$ distorted honeycomb-lattice antiferromagnet Cu$_2$(pymca)$_3$(ClO$_4$). Magnetic susceptibility shows a broad peak at about 25~K, which is typical of a low dimensional antiferromagnet, and no long range magnetic order is observed down to 0.6~K in the specific heat measurements. Magnetization curve up to 70~T at 1.4~K shows triple stepwise jumps. Assuming three different exchange bonds $J_{\rm A}$, $J_{\rm B}$ and $J_{\rm C}$ from the structure, the calculated magnetization curve reproduces the observed one when $J_{\rm A}/k_{\rm B} = 43.7~{\rm K}$, $J_{\rm B}/J_{\rm A} = 1$ and $J_{\rm C}/J_{\rm A} = 0.2$ except the magnetization near 70~T, where the observed magnetization indicates another step while the calculated magnetization becomes saturated. The relationship between magnetization plateaus and exchange bonds is discussed based on the numerical calculations., Comment: 5 pages, 5 figures

Alkali superoxide CsO2 is one of candidates for the spin-1/2 one-dimensional (1D) antiferromagnet, which may be sequentially caused by an ordering of the pi-orbital of O2- molecule below TS ~ 70 K. Here, we report on the magnetism in powder CsO2 and high-magnetic field magnetization measurements in pulsed-magnetic fields of up to 60 T. We obtained the low temperature phase diagram around the antiferromagnetic ordering temperature TN = 9.6 K under the magnetic field. At 1.3 K, remarkable up-turn curvature in the magnetization around a saturation field of ~ 60 T is found, which corresponds to the spin-1/2. We will compare it with the theoretical calculation., Comment: 11 pages, 3 figures

We report a $^{23}$Na spin-lattice relaxation rate, $T_1^{-1}$, in low-silica X zeolite. $T_1^{-1}$ follows multiple BPP-type behavior as a result of thermal motion of sodium cations in insulating material. The estimated lowest activation energy of 15~meV is much lower than 100~meV observed previously for sodium motion in heavily Na-loaded samples and is most likely attributed to short-distance jumps of sodium cations between sites within the same supercage., Comment: 2 pages, 1 figure, published in JPSJ

We explore orbital dynamics in the spin liquid candidate Ba3CuSb2O9 using multi-frequency electron spin resonance. We prepared two high quality single crystals. The crystal with a slight copper deficiency shows a structural phase transition at around 200 K due to the cooperative Jahn-Teller effect, accompanied with orbital ordering. In contrast, the crystal with almost perfect stoichiometry shows no orbital ordering down to the lowest temperature of 1.5 K. Dramatic change in the g-factor anisotropy as a function of frequency and temperature demonstrates orbital quantum fluctuations at a nearly constant time scale of ~ 100 ps below 20 K, evidencing the emergence of an orbital liquid state in this quantum spin liquid compound., Comment: 15 pages,4 figures, including 9 pages supplemental material

We report a systematic nuclear magnetic resonance investigation of the $^{23}$Na spin-lattice relaxation rate, $1/T_1$, in sodium loaded low-silica X (LSX) zeolite, Na$_n$/Na$_{12}$-LSX, for various loading levels of sodium atoms $n$ across the metal-to-insulator crossover. For high loading levels of $n \geq 14.2$, $1/T_1T$ shows nearly temperature-independent behavior between 10 K and 25 K consistent with the Korringa relaxation mechanism and metallic ground state. As the loading levels decrease below $n \leq 11.6$, the extracted density of states (DOS) at the Fermi level sharply decreases, although a residual DOS at Fermi level is still observed even in samples that lack the metallic Drude-peak in the optical reflectance. The observed crossover is a result of a complex loading-level dependence of electric potential felt by the electrons confined to zeolite cages, where the electronic correlations and disorder both play an important role., Comment: 7 pages, 5 figures

We report a \^{23}Na and \^{27}Al nuclear magnetic resonance (NMR) investigation of low-silica X (LSX) zeolite with chemical formula Na_{12}Al_{12}Si_{12}O_{48} (Na_{12}-LSX) loaded with n additional guest sodium atoms. Na_{n}/Na_{12}-LSX exhibits an insulator-to-metal transition around n=11.6, which is accompanied by a significant enhancement of bulk magnetic susceptibility. Paramagnetic moments are thermally activated in the metallic Na_{12}/Na_{12}-LSX with an activation energy of around 0.1 eV. At the same time, a new shifted component (SC) appears in the \^{23}Na NMR, whose large and positive NMR shift scales with bulk magnetic susceptibility. Its spin-lattice relaxation rate 1/T_{1} is governed by the fluctuations determined by the same activation energy as obtained from the bulk magnetic susceptibility data. The timescale of these fluctuations is typical for atomic motions, which suggest strong electron-phonon coupling, a hallmark of polaron states. The insulator-to-metal transition in Na_{n}/Na_{12}-LSX is thus discussed within a polaron model., Comment: 7 pages, 6 figures