The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the symmetry operations of the site and from site to site is described in detail. The law of spherical tensor coupling is given and illustrated with the example of the electric dipole and quadrupole transitions in x-ray absorption spectroscopy. The main application of the formalism is the reduction of computation time in the calculation of the properties of crystals by band structure methods. The general approach is illustrated by the examples of substitutional chromium in spinel and substitutional vanadium in garnet.
We report results of 27Al-NMR measurements on a single crystal of PrTi2Al20, in which the ground state of Pr3+ ions in the crystalline electric field is the nonmagnetic Gamma3 doublet. From the analysis of NMR spectra with the magnetic field applied precisely along the <111> and <100> directions, we determined the electric field gradient tensors for all three inequivalent Al sites (Al(1) ~ Al(3) sites) and the anisotropic Knight shifts for the Al(3) sites. The hyperfine coupling tensor at the Al(3) sites is strongly anisotropic and much larger than the classical dipolar coupling, indication im…
A single-crystal sample of a DO3-ordered Fe3Si compound was studied by means of the 57Fe Mössbauer spectroscopy. Spectra have been recorded in a transmission geometry in the temperature range between 5 and 850 K. They have been analyzed either in terms of five sextets or five hyperfine field distribution curves. Concerning the former three sub spectra have been attributed to Fe atoms occupying the B sites and having 8Fe, 7Fe1Si and 6Fe2Si atoms in the first coordination shell (1NN), respectively, and two have been attributed to Fe atoms residing on the A and C sites and having 4Fe4Si and 3Fe5S…
The pyrochlore magnet $\rm Yb_2Ti_2O_7$ has been proposed as a quantum spin ice candidate, a spin liquid state expected to display emergent quantum electrodynamics with gauge photons among its elementary excitations. However, $\rm Yb_2Ti_2O_7$'s ground state is known to be very sensitive to its precise stoichiometry. Powder samples, produced by solid state synthesis at relatively low temperatures, tend to be stoichiometric, while single crystals grown from the melt tend to display weak "stuffing" wherein $\mathrm{\sim 2\%}$ of the $\mathrm{Yb^{3+}}$, normally at the $A$ site of the $A_2B_2O_7$…
We have applied the bond valence method to cerium oxides to determine the oxidation states of the Ce ion at the various site symmetries of the crystals. The crystals studied include cerium dioxide and the two sesquioxides along with some selected intermediate phases which are crystallographically well characterized. Our results indicate that cerium dioxide has a mixed-valence ground state with an f-electron population on the Ce site of 0.27 while both the A- and C-sesquioxides have a nearly pure f^1 configuration. The Ce sites in most of the intermediate oxides have non-integral valences. Furt…
We have performed dielectric measurements and neutron diffraction experiments on the double perovskite In2NiMnO6. A ferroelectric polarization, P ~ 30 μC/m2, is observed in a polycrystalline sample below TN = 26 K where a magnetic phase ransition occurs. The neutron diffraction experiment demonstrates that a complex noncollinear magnetic structure with "cycloidal" and "proper screw" components appears below TN, which has the incommensurate propagation vector k = (ka,0,ks; ka ~ 0.274, ks ~ -0.0893). The established magnetic point group 21' implies that the macroscopic ferroelectric polarization…
The singlet dynamics which plays a major role in the physics of the spin-1/2 Quantum Heisenberg Antiferromagnet (QHAF) on the Kagome lattice can be approximately described by projecting onto the nearest-neighbor valence bond (NNVB) singlet subspace. We re-visit here the effective Quantum Dimer Model which originates from the latter NNVB-projected Heisenberg model via a non-perturbative Rokhsar-Kivelson-like scheme. By using Lanczos exact diagonalisation on a 108-site cluster supplemented by a careful symmetry analysis, it is shown that a previously-found 36-site Valence Bond Crystal (VBC) in f…
Inelastic neutron scattering experiments have been carried out to determine the crystal field states of the Kondo lattice heavy fermions CeRuSn3 and CeRhSn3. Both the compounds crystallize in LaRuSn3-type cubic structure (space group Pm-3n) in which the Ce atoms occupy two distinct crystallographic sites with cubic (m-3) and tetragonal (-4m.2) point symmetries. The INS data of CeRuSn3 reveal the presence of a broad excitation centered around 6-8 meV which is accounted by a model based on crystal electric field (CEF) excitations. On the other hand, the INS data of isostructural CeRhSn3 reveal t…
A proposed ground state for the Kagome Lattice Heisenberg Model (KLHM) consists of a Valence Bond Crystal (VBC) with a 36-site unit cell. We calculate the low-lying triplet and singlet excitations in the VBC phase for the infinite-lattice model and for the 36-site cluster. For the infinite lattice, the lowest triplet excitation is found to have a spin gap of approximately $0.08 \pm 0.02 J$ and a bandwidth of only about $0.01 J$. For the 36-site cluster, consisting of a single unit cell with periodic boundary conditions, there are substantial finite-size effects: the spin gap there is estimated…
In order to clarify why the experimental magnetization curve of the spherical kagome cluster in {W72V30} at 0.5 K shows no sign of staircase behavior up to 50 T, we study the effects of Dzyaloshinsky-Moriya (DM) interactions and tilts of the g tensors, both of which lead to the breaking of the total-S z conservation, by using the exact diagonalization method. It is found that the D vector component parallel to the radiation direction of the polyhedron cancels out the staircase in a low magnetic field region efficiently. The tilts of the g tensors are inherent to systems defined on the poly- he…
We report synthesis of Co substitution at Fe site in Fe1-xCoxSe0.5Te0.5 (x=0.0 to 0.10) single crystals via vacuum shield solid state reaction route using flux free method. Single crystal XRD results showed that these crystals grow in (00l) plane i.e., orientation in c-direction. All the crystals possess tetragonal structure having P4/nmm space group. Detailed scanning electron microscopy (SEM) images show that the crystals are grown in slab-like morphology. The EDAX results revealed the final elemental composition to be near stoichiometric. Powder X-Ray diffraction (PXRD) Rietveld analysis re…
We present the low-temperature magnetic structures of SrGd$_2$O$_4$ combining neutron diffraction methods on polycrystalline and single-crystal samples containing the $^{160}$Gd isotope. In contrast to other members of the Sr$Ln_2$O$_4$ family ($Ln$ = lanthanide) this system reveals two long-range ordered magnetic phases, which our diffraction data unambiguously identify. Below $T_{\rm N1}$ = 2.73~K, a $\mathbf{q}_1$ = (0 0 0) magnetic structure is stabilized where ferromagnetic chains along the $c$~axis (space group $Pnam$) are coupled antiferromagnetically with neighboring chains. On cooling…
System-size dependence of the ground-state energy E^N is investigated for N-site one-dimensional (1D) quantum systems with open boundary condition, where the interaction strength decreases towards the both ends of the system. For the spinless Fermions on the 1D lattice we have considered, it is shown that the finite-size correction to the energy per site, which is defined as E^N / N - \lim_{N \to \infty} E^N / N, is of the order of 1 / N^2 when the reduction factor of the interaction is expressed by a sinusoidal function. We discuss the origin of this fast convergence from the view point of th…
The competition between antiferromagnetic and spin-singlet ground states within quantum spin models and the 1/2-filled band Hubbard model has received intense scrutiny. Here we demonstrate a frustration-induced transition from Néel antiferromagnetism to spin-singlet in the interacting 1/4-filled band on an anisotropic triangular lattice. While the antiferromagnetic state has equal charge densities 0.5 on all sites, the spin-singlet state is a paired-electron crystal, with pairs of charge-rich sites separated by pairs of charge-poor sites. The paired-electron crystal provides a natural descript…
As a possible mechanism of the $γ-α$ phase transition in pristine cerium a change of the electronic density from a disordered state with symmetry Fm-3m to an ordered state Pa-3 has been proposed. Here we include on-site and inter- site electron correlations involving one localized 4f-electron and one conduction 5d-electron per atom. The model is used to calculate the crystal field of $γ$-Ce and the temperature evolution of the mean-field of $α$-Ce. The formalism can be applied to crystals where quadrupolar ordering involves several electrons on the same site.
Copper NMR has been used as a local probe of the oxygen ordering in Ortho--II YBa2Cu3O6.5 crystals grown in BaZrO3 crucibles. Line assignments have been made to each of the expected crystallographically inequivalent sites. The presence of distinct and narrow lines for these sites as well as the lack of a line known to be associated with oxygen defects indicates that these crystals are highly stoichiometric. Our estimate of the lower limit on the chain length is consistent with that derived from X-ray diffraction measurements. In addition, we have found no evidence for static magnetic moments, …
The single ion properties of the zig-zag chain compound SrTm$_2$O$_4$ have been investigated using heat capacity, magnetic susceptibility, magnetization, inelastic neutron scattering, and polarized muon spectroscopy. Two crystal field models are employed to estimate the single ion properties; a Density Function Theory based model and an effective charge model based on the Hutchings point charge model. The latter describes our experimental results well. This model estimates an easy-axis anisotropy for one of the Tm$^{3+}$ sites and an easy-plane anisotropy for the second site. It also predicts …
Twisted double bilayer graphene (tDBLG) is a moiré material that has recently generated significant interest because of the observation of correlated phases near the magic angle. We carry out atomistic Hartree theory calculations to study the role of electron-electron interactions in the normal state. In contrast to twisted bilayer graphene (tBLG), we find that such interactions do not result in significant doping-dependent deformations of the electronic band structure. However, interactions play an important role for the electronic structure in the presence of a perpendicular electric field a…
We report site disorder driven ferromagnetic ordering of nearly 8$\%$ Ce atoms in single crystalline Ce${_3}$Os${_4}$Ge$_{13}$ below 0.5~K. Ce${_3}$Os${_4}$Ge$_{13}$ crystallizes in a cubic structure with space group $\it{Pm\bar{3}n}$. The structural analysis shows the presence of site-disorder in the system, where 2(a) Ge site is partially occupied by the Ce atoms. Due to the small Ce $4f$-ligand hybridization, these Ce atoms are in the Ce$^{3+}$ (magnetic) state while rest of the Ce atoms in the unit cell are in Ce$^{4-δ}$ (non-magnetic) state. The heat capacity shows a peak below 0.5~K corr…
A discrete time crystal is a phase unique to nonequilibrium systems, where discrete time translation symmetry is spontaneously broken. Most of conventional time crystals proposed so far rely on spontaneous breaking of on-site symmetries and their corresponding on-site symmetry operations. In this Letter, we propose a new time crystal dubbed "spatial-translation-induced discrete time crystal (STI-DTC)", which is realized by spatial translation and its symmetry breaking. Owing to the properties of spatial translation, in this new time crystal, various time crystal orders can emerge only by chang…
