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We used17 O NMR to probe the uniform (wavevector q = 0) electron spin excitations up to 800 K in Sr2CuO3 and separate the q = 0 from the q = ± π a staggered components. Our results support the logarithmic decrease of the uniform spin susceptibility below T ∼ 0.015J, where J = 2200 K. From measurement of the dynamical spin susceptibility for q = 0 by the spin-lattice relaxation rate 1/T1, we demonstrate that the q = 0 mode of spin transport is ballistic at the T = 0 limit, but has a diffusion-like contribution at finite temperatures even for T ≪ J. 75.40.Gb, 76.60.EsThe one-dimensional Heisenberg spin chain has one of the simplest Hamiltonians, H = J i S i · S i+1 , yet our understanding of its fascinating quantum mechanical properties is still developing with recent theoretical [1][2][3][4][5][6][7][8] and experimental [9][10][11][12] studies. A recent breakthrough in experimental studies of spin chains is the identification of a nearly ideal 1D S = 1 2 Heisenberg antiferromagnet, Sr 2 CuO 3 , by Motoyama et al. [9] In this system, S = 1 2 spins reside at Cu sites, and the superexchange interaction J is mediated by hybridization with the 2p σ orbital of the in-chain O(1) site, see Fig.1(a). Based on the fit of the uniform spin susceptibility χSr 2 CuO 3 has proven to be an ideal material for the experimental studies of S = Heisenberg spin chain can be probed at unprecedently low scales of temperature and energy. The second major advantage of Sr 2 CuO 3 is that 63 Cu NMR is observable at the magnetic cation site, because the large J suppresses the nuclear relaxation rates. In a series of publications, Takigawa et al. reported detailed 63 Cu NMR investigations of the low energy spin excitations [10][11][12]. They successfully tested the theoretical predictions for the q = ± π a staggered mode in the scaling limit [2], including the low temperature logarithmic corrections to the staggered dynamical susceptibility [4]. The third major advantage of Sr 2 CuO 3 , although it has never been exploited in the earlier NMR works, is the high local symmetry of the crystal structure. The Cu-O-Cu chain is strictly straight and the in-chain O(1) site is located in the middle of adjacent Cu sites as shown in Fig.1(a). Therefore the staggered components of the magnetic hyperfine fields from Cu electron spins are canceled out at the in-chain O(1) sites. Accordingly, one can probe the low energy spin excitations for the q = 0 long wavelength mode (see Fig.1(c) 17 O NMR studies have been reported despite the rich information expected for the unexplored q = 0 mode.In this Letter, we report the first successful 17 O NMR investigation of Sr 2 CuO 3 single crystals. We accurately measured the temperature dependence of the uniform spin susceptibility χ ′ (q = 0) by NMR Knight shift at the in-chain O(1) site without suffering from the contribution by free-spins that limits the accuracy of bulk susceptibility measurements and 63 Cu NMR at low temperatures. We found that χ ′ (q = 0) decreases steeply below T ∼ 0.015J without the signature ...

The discovery of massless Dirac electrons in graphene and topological Dirac-Weyl materials has prompted a broad search for bosonic analogues of such Dirac particles. Recent experiments have found evidence for Dirac magnons above an Ising-like ferromagnetic ground state in a twodimensional (2D) kagome lattice magnet and in the van der Waals layered honeycomb crystal CrI3, and in a 3D Heisenberg magnet Cu3TeO6. Here we report on our inelastic neutron scattering investigation on large single crystals of a stacked honeycomb lattice magnet CoTiO3, which is part of a broad family of ilmenite materials. The magnetically ordered ground state of CoTiO3 features ferromagnetic layers of Co 2+ , stacked antiferromagnetically along the c-axis. We discover that the magnon dispersion relation exhibits strong easy-plane exchange anisotropy and hosts a clear gapless Dirac cone along the edge of the 3D Brillouin zone. Our results establish CoTiO3 as a model pseudospin-1/2 material to study interacting Dirac bosons in a 3D quantum XY magnet.The discoveries of graphene and topological insulators have led to significant advances in our understanding of the properties of electron in solids described by a Dirac equation. In particular, the fruitful analogy between fundamental massless Weyl-Dirac fermions in Nature and electrons in graphene or topological semimetals has allowed physicists to simulate theories of particle physics using tabletop experiments [1][2][3][4][5][6]. Remarkably, the concept of Dirac particles is not limited to electrons or other fermionic quasiparticles, prompting a search for analogues in photonic crystals [7,8], acoustic metamaterials [9], and quantum magnets [10][11][12][13]. In particular, Dirac magnons, or more broadly defined topological magnons [14][15][16][17][18][19], have attracted much attention as platforms to investigate the effect of inter-particle interaction or external perturbations on Dirac bosons, and are proposed to be of potential interest in spintronic applications.In contrast to light and sound, the symmetry broken states and emergent bosonic excitations of quantum magnets depend crucially on dimensionality and spin symmetry, which provides a fertile playground for examining the physics of topological bosons. To date, gapped topological magnons in Ising-like ferromagnets have been reported in a kagome lattice material Cu(1,3bdc) [16] and in a layered honeycomb magnet CrI 3 [17]. On the other hand, magnons exhibiting symmetry protected band crossings have been found only in a single material, a three-dimensional (3D) Heisenberg antiferromagnet Cu 3 TeO 6 [18,20]. It is thus desirable to explore new test-beds with distinct spin symmetries to expand our understanding of the physics of Dirac magnons.In this paper, we present a new model 3D quantum XY magnet realizing gapless Dirac magnons, CoTiO 3 , which has a simple ilmenite crystal structure. The magnetic lattice of Co 2+ ions in CoTiO 3 is a stacked honeycomb lattice, exactly the same as in ABC stacked graphene. Below T N ≈ 38 K, this mate...

We probed the local electronic properties of the mixed-valent Co+4-x triangular lattice in NaxCoO2.yH(2)O by 59Co NMR. We observed two distinct types of Co sites for x > or =1/2, but the valence seems averaged out for x approximately 1/3. Local spin fluctuations exhibit qualitatively the same trend down to approximately 100 K regardless of the carrier concentration x, and hence the nature of the electronic ground state. A canonical Fermi-liquid behavior emerges below approximately 100 K only for x approximately 1/3.

We have measured the magnetic susceptibility of single crystal samples of nonhydrated Na x CoO 2 ͑x Ӎ 0.75, 0.67, 0.5, 0.3͒ and hydrated Na 0.3 CoO 2 · yH 2 O ͑y Ӎ 0 , 0.6, 1.3͒. Our measurements reveal considerable anisotropy between the susceptibilities with H ʈ c and H ʈ ab. The derived anisotropic g-factor ratio ͑g ab / g c ͒ decreases significantly as the composition is changed from the Curie-Weiss metal with x = 0.75 to the paramagnetic metal with x = 0.3. Fully hydrated Na 0.3 CoO 2 · 1.3H 2 O samples have a larger susceptibility than nonhydrated Na 0.3 CoO 2 samples, as well as a higher degree of anisotropy. In addition, the fully hydrated compound contains a small additional fraction of anisotropic localized spins.