Evidence of Long-Range and Short-Range Magnetic Ordering in the Honeycomb Na3Mn2SbO6 Oxide.

We present a comprehensive study of the synthesis, structure, and magnetic properties of the honeycomb oxide Na3Mn2SbO6 supported by neutron diffraction, heat capacity, and magnetization measurements. The refinements of the neutron diffraction patterns (150, 50, and 45 K) using the Rietveld method confirm the monoclinic (S. G. C2/m) structure. Temperature-dependent magnetic susceptibilities measured at varying fields along with the heat capacity measurements demonstrate the coexistence of long-range ordering (∼42 K) and short-range ordering (∼65 K). The field-dependent isothermal magnetization measurements at 5 K indicate a spin-flop transition around 5 T. Rietveld refinements of the low-temperature (below 45 K) neutron diffraction data further confirm the long-range magnetic ordering. In addition, the temperature variation of the lattice parameters obtained from the neutron powder diffraction analysis exhibited a distinct anomaly near the antiferromagnetic transition temperature. The appearance of the concomitant broadened backgrounds in the neutron powder diffraction data collected at 80, 50, and 45 K supports the short-range ordering. The resultant magnetic structure consists of spins that are aligned antiparallel with the nearest neighbors and also with the spins of the adjacent honeycomb layers. The occurrence of a fully ordered magnetic ground state (Neel antiferromagnetic (AFM)) in Na3Mn2SbO6 consolidates the significance of fabricating new honeycomb oxides.

Magnetocaloric Effect in a Frustrated Gd-Garnet with No Long-Range Magnetic Order.

In this paper, the hyperkagome lattice of Gd spins in a garnet compound, Gd3CrGa4O12, is studied using bulk measurements and density functional computations, and the observation of large magnetocaloric effect corresponding to an entropy change, ΔSm = 45 J kg-1K-1 (≈ 45 J mol-1K-1) at 2 K, 8 T is reported. Though the compound defies long-range magnetic order down to 0.4 K, a broad feature below 10 K is observed in the specific heat with two low temperature anomalies at T* ≈ 0.7 K and TS ≈ 2.45 K. The anomaly at T* is reminiscent of one in Gd3Ga5O12, where it is related to the development of a complex magnetic phase, whereas the TS-peak is accounted for by a multilevel Schottky-like model. The spin-lattice relaxation times studied by nuclear magnetic resonance experiments show that the relaxation is dominated by the magnetic fluctuations in Cr which has a longer relaxation time compared to that of the garnet, Lu3CrGa4O12 containing a nonmagnetic rare earth. Our first-principles density functional theory calculations agree well with the experimental results and support short-range magnetic order in the Gd-sublattice and antiferromagnetism in the Cr-sublattice. The importance of spin fluctuations and short-range order in the rare earth and transition metal lattices in garnets resulting in large magnetocaloric effect is brought out through this work.

Single Crystals of Cubic Rare-Earth Pyrochlore Germanates: RE2Ge2O7 (RE = Yb and Lu) Grown by a High-Temperature Hydrothermal Technique.

Large single crystals of Yb2Ge2O7 in the cubic Fd3̅ m space group, are synthesized and characterized from a high-temperature hydrothermal method (650°C/200 MPa in 1 M KF). The cubic phase displays spin frustration and possibly nonclassical quantum-spin behavior at low temperature. This is the first report of single crystals of this important phase of size and quality suitable for single-crystal neutron diffraction.

Dielectric and Raman investigations of structural phase transitions in (C2H5NH3)2CdCl4.

Temperature-dependent Raman and dielectric measurements have been carried out on (C2H5NH3)2CdCl4 single crystals. Raman studies reveal the presence of two structural phase transitions below room temperature at 216 K and 114 K. The phase transitions are marked by anomalies in temperature dependence of wave-number and full width half maximum (FWHM) of several vibrational modes. The transitions are also accompanied by anomalies in dielectric measurements. Raman and dielectric data indicate that the transition at 216 K is order-disorder in nature and is driven by re-orientation of organic ions, while the transition at 114 K is due to coupling between the CdCl6 octahedron and the organic chain. Further high temperature dielectric measurements reveal the presence of one more structural phase transition around 473 K across which dispersion in dielectric parameters is observed. The activation energies and relaxation time obtained for high temperature dielectric phases are characteristic of combined reorientation motions of alkyl ammonium cations.

Resilience of the Aurivillius structure upon La and Cr doping in a Bi5Ti3FeO15 multiferroic.

Combining the experimental techniques of high-resolution X-ray diffraction, magnetometry, specific heat measurement, and X-ray photoelectron, Raman and dielectric spectroscopy techniques, we have studied the influence of La and Cr doping on the crystal structure and magnetism of the room temperature Aurivillius multiferroic Bi5Ti3FeO15 by investigating the physical properties of (Bi4La)Ti3FeO15 and Bi5Ti3 (Fe0.5Cr0.5)O15. The parent (Bi5Ti3FeO15) and the doped ((Bi4La)Ti3FeO15 and Bi5Ti3(Fe0.5Cr0.5)O15) compounds crystallize in the A21am space group, which is confirmed through our analysis of high-resolution synchrotron X-ray diffraction data obtained on phase-pure polycrystalline powders. We determined the oxidation states of the metal atoms in the studied compounds as Fe3+, Ti4+, Cr3+, and La3+ through the analysis of X-ray photoelectron spectroscopy data. The magnetic susceptibilities of the three compounds are marked by the absence of a long-range ordered ground state, but dominated by superparamagnetic clusters with dominant antiferromagnetic interactions. This signature of short-range magnetism is also seen in specific heat as a low temperature enhancement which is suppressed upon the application of external magnetic fields up to 8 T. Our dielectric spectroscopy experiments showed that the three studied compounds display similar features in the dielectric constant measured as a function of frequency. However, upon doping La at the Bi site, the width of the ferroelectric hysteresis loop increases for (Bi4La)Ti3FeO15 compared to that of the parent compound Bi5Ti3FeO15, and with Cr doping, Bi5Ti3(Fe0.5Cr0.5)O15 becomes a leaky dielectric. The resilience of the Aurivillius crystal structure towards doping of La at the Bi site and Cr at the Fe site is clearly seen in the bulk properties of magnetic susceptibility, specific heat and the average crystal structure. The relevance of changes in the local structure is evident from our Raman spectroscopy and X-ray pair distribution function studies.

Magnetic structures and excitations in sawtooth olivine chalcogenides Mn2SiX4 (X = S, Se).

The Mn lattice in olivine chalcogenide Mn2SiX4 (X = S, Se) compounds forms a sawtooth, which is of special interest in magnetism owing to the possibility of realizing flat bands in magnon spectra, a key component in magnonics. In this work, we investigate the Mn2SiX4 olivines using magnetic susceptibility, and X-ray and neutron diffraction. We have determined the average and local crystal structures of Mn2SiS4 and Mn2SiSe4 using synchrotron X-ray, neutron diffraction, and X-ray total scattering data followed by Rietveld and pair distribution function analyses. It is found from the pair distribution function analysis that the Mn triangle that constitutes the sawtooth is isosceles in Mn2SiS4 and Mn2SiSe4. The temperature evolution of magnetic susceptibility of Mn2SiS4 and Mn2SiSe4 shows anomalies below 83 K and 70 K, respectively, associated with magnetic ordering. From the neutron powder diffraction measurements the magnetic space groups of Mn2SiS4 and Mn2SiSe4 are found to be Pnma and Pnm'a', respectively. We find that the Mn spins adopt a ferromagnetic alignment on the sawtooth in both Mn2SiS4 and Mn2SiSe4 but along different crystallographic directions for the S and the Se compounds. From the temperature evolution of Mn magnetic moments obtained from refining neutron diffraction data, the transition temperatures are accurately determined as TN(S) = 83(2) K and TN(Se) = 70.0(5) K. Broad diffuse magnetic peaks are observed in both the compounds, and are prominently seen close to TN, suggesting the presence of a short-range magnetic order. The magnetic excitations studied using inelastic neutron scattering reveal a magnon excitation with an energy corresponding to approximately 4.5 meV in both S and Se compounds. Spin correlations are observed to persist up to 125 K much above the ordering temperature and we suggest the possibility of short-range spin correlations responsible for this.

Magnetic structure, excitations and short-range order in honeycomb Na2Ni2TeO6.

Na2Ni2TeO6has a layered hexagonal structure with a honeycomb lattice constituted by Ni2+and a chiral charge distribution of Na+that resides between the Ni layers. In the present work, the antiferromagnetic (AFM) transition temperature of Na2Ni2TeO6is confirmed atTN≈ 27 K, and further, it is found to be robust up to 8 T magnetic field and 1.2 GPa external pressure; and, without any frequency-dependence. Slight deviations from nominal Na-content (up to 5%) does not seem to influence the magnetic transition temperature,TN. Isothermal magnetization curves remain almost linear up to 13 T. Our analysis of neutron diffraction data shows that the magnetic structure of Na2Ni2TeO6is faithfully described by a model consisting of two phases described by the commensurate wave vectorsk→c,0.500and0.500.5, with an additional short-range order component incorporated in to the latter phase. Consequently, a zig-zag long-range ordered magnetic phase of Ni2+results in the compound, mixed with a short-range ordered phase, which is supported by our specific heat data. Theoretical computations based on density functional theory predict predominantly in-plane magnetic exchange interactions that conform to aJ1-J2-J3model with a strongJ3term. The computationally predicted parameters lead to a reliable estimate forTNand the experimentally observed zig-zag magnetic structure. A spin wave excitation in Na2Ni2TeO6atE≈ 5 meV atT= 5 K is mapped out through inelastic neutron scattering experiments, which is reproduced by linear spin wave theory calculations using theJvalues from our computations. Our specific heat data and inelastic neutron scattering data strongly indicate the presence of short-range spin correlations, atT>TN, stemming from incipient AFM clusters.

Absence of long-range magnetic order in lithium-containing honeycombs in the Li-Cr-Sb(Te)-O phases.

Li3((LiCr)(Te/Sb))O6compounds where Cr atoms along with Li and Te or Sb are part of a honeycomb and are studied using magnetic susceptibility, specific heat, x-ray photoelectron spectroscopy and neutron diffraction. The oxides stoichiometries as determined from the neutron diffraction studies are Li4.47Cr0.53TeO6and Li3.88Cr1.12SbO6with a stable oxidation state of +3 for Cr. Both the compounds crystallize in space groupC2/mwith intermixing of cations at the 4gsites leaving the 2asites preferentially for Te or Sb. Again, the Li+ions alone predominantly occur in the interlayer sites. Both the compounds show a broad anomaly in specific heat at 8 K, which is robust against 8 T. A corresponding anomaly is absent in the magnetic susceptibility but recovers from its derivative, dχ(T)/dT. We ascertain the magnetic anomaly temperatures (Ta) of Li4.47Cr0.53TeO6and Li3.88Cr1.12SbO6as 5.9 K and 6.7 K respectively from specific heat. Although the physical properties indicated a low temperature anomaly, neutron diffraction data did not reveal a magnetic signal or a structural anomaly down to 1.5 K. This rules out a conventional long-range ordered magnetic ground state in either compounds. Combining the results from specific heat, neutron diffraction and electron paramagnetic resonance, we put forth a scenario of depleted honeycomb lattice of Cr3+with predominant short-range magnetic correlations as the magnetic ground states of the title compounds.

Third Molar Angulation Changes in Class II Div I Malocclusion Subjects Treated with Extraction of Four Premolars: A Retrospective Study.

AIM: The aim of this study was to assess the changes in maxillary and mandibular third molar inclinations in individuals with class II div 1 malocclusion, before and after orthodontic treatment with extraction of all four first premolars. MATERIALS AND METHODS: This retrospective study consisted of the pretreatment and posttreatment records of 30 patients that were obtained from the archives of the department of orthodontics and dentofacial orthopedics in A B Shetty Memorial Institute of Dental Sciences. The maxillary third molar's relation to the palatal plane and the mandibular third molar's relation to the mandibular plane were measured. The paired t test was used to calculate pre- and posttreatment changes. A value of P < 0.05 was considered to be statistically significant. RESULTS: The maxillary third molars showed a mean correction of 6.15° (P < 0.001) and the mandibular third molars showed a mean correction of 5.10° (P < 0.001). CONCLUSION: Maxillary third molars showed more uprighting when compared to the mandibular third molars and that both maxillary and mandibular third molars showed an improvement in their angulations to their respective planes after extraction of the first premolars. However, the results of the study cannot be analyzed to state if the third molars do become fully functional.

Absence of a long-range ordered magnetic ground state in Pr3Rh4Sn13 studied through specific heat and inelastic neutron scattering.

Signatures of absence of a long-range ordered magnetic ground state down to 0.36 K are observed in magnetic susceptibility, specific heat, thermal/electrical transport and inelastic neutron scattering data of the quasi-skutterudite compound Pr3Rh4Sn13 which crystallizes in the Yb3Rh4Sn13-type structure with a cage-like network of Sn atoms. In this structure, Pr3+ occupies a lattice site with D 2d point symmetry having a ninefold degeneracy corresponding to J = 4. The magnetic susceptibility of Pr3Rh4Sn13 shows only a weak temperature dependence below 10 K; otherwise remaining paramagnetic-like in the range, 10 K-300 K. From the inelastic neutron scattering intensity of Pr3Rh4Sn13 recorded at different temperatures, we identify excitations at 4.5(7) K, 5.42(6) K, 10.77(5) K, 27.27(5) K, 192.28(4) K and 308.33(3) K through a careful peak analysis. However, no signatures of long-range magnetic order are observed in the neutron data down to 1.5 K, which is also confirmed by the specific heat data down to 0.36 K. A broad Schottky-like peak is recovered for the magnetic part of the specific heat, C 4f, which suggests the role of crystal electric fields of Pr3+ . A crystalline electric field model consisting of 7 levels was applied to C 4f which leads to the estimation of energy levels at 4.48(2) K, 6.94(4) K, 11.23(8) K, 27.01(5) K, 193.12(6) K and 367.30(2) K. The CEF energy levels estimated from the heat capacity analysis are in close agreement with the excitation energies seen in the neutron data. The Sommerfeld coefficient estimated from the analysis of magnetic specific heat is [Formula: see text] mJ K-2 mol-Pr which suggests the formation of heavy itinerant quasi-particles in Pr3Rh4Sn13. Combining inelastic neutron scattering results, analysis of the specific heat data down to 0.36 K, magnetic susceptibility and, electrical and thermal transport, we establish the absence of long-range ordered magnetic ground state in Pr3Rh4Sn13.

Magnetic structure and field-dependent magnetic phase diagram of Ni2In-type PrCuSi.

The magnetic structure of the ternary equiatomic intermetallic compound PrCuSi is investigated using neutron powder diffraction experiments in 0 T as well as in external magnetic fields up to 2 T. The PrCuSi compound crystallizes in the hexagonal Ni2In-type structure, in the space group P63/mmc. In this structure, cationic ordering of Cu and Si takes place. The antiferromagnetic phase transition in the Pr sublattice takes place at [Formula: see text] K in 0 T. Under an external magnetic field of 2 T, a field-induced ferromagnetic phase is observed. Magnetoelastic coupling is evidenced by an increase in the unit cell volume. Clear signatures of a mixed antiferromagnetic and ferromagnetic phase in weak, intermediate fields, 0.4-0.8 T, are obtained from the present study. Using the present set of experimental data, we construct the H - T phase diagram of PrCuSi.

Disordered ferromagnetism in Ho2NiMnO6 double perovskite.

Magnetic and dielectric properties of the double perovskite Ho2NiMnO6 are reported. The compound is synthesized by nitrate route and is found to crystallize in monoclinic P21/n space group. Lattice parameters obtained by refining powder x-ray diffraction data are; a = 5.218(2) Å, b = 5.543(2) Å, c = 7.480(3) Å and the monoclinic angle is [Formula: see text](4). A phase transition is observed at [Formula: see text] K in the temperature-dependent magnetization curve, M(T). The inverse magnetic susceptibility, (1/[Formula: see text]) fits reasonably well with modified Curie-Weiss law by incorporating the paramagnetic response of Ho3+. 1/[Formula: see text] manifests as an upward deviation from ideal Curie-Weiss behaviour well above the ferromagnetic transition. Signs of inherent Griffiths phase pertaining to the Ni/Mn subsystem are visible when one subtracts the Ho3+ paramagnetic contribution from total susceptibility and does the power-law analysis. The magnetic hysteresis at 2 K gives the maximum value of magnetization [Formula: see text] [Formula: see text]/f.u. at 50 kOe. Field-derivative of magnetization at 2 K shows discontinuities which indicates the existence of metamagnetic transitions in this compound. This needs to be probed further. Out of the two dielectric relaxations observed, the one at low temperature may be attributed to phononic frequencies and that at higher temperature may be due to Maxwell-Wagner relaxation. A correlation between magnetic and lattice degrees of freedom is plausible since the anomaly in dielectric constant coincides with T C.

Magnetic glass state and magnetoresistance in SrLaFeCoO6 double perovskite.

Unusual features in magnetization resembling the kinetic arrest of a magnetic glass state are observed in the La-doped double perovskite, SrLaFeCoO6. Neutron powder diffraction experiments confirm the presence of antisite disorder as well as a lack of long-range magnetic order down to 4 K in this double perovskite which displays spin glass-like features in dc and ac susceptibilities. Magnetic relaxation observed through cooling and heating under unequal fields (CHUF) point towards unusual domain dynamics which is supported by a broad memory effect. Among the two anomalies that are observed at [Formula: see text] 75 K and at [Formula: see text] 250 K in the magnetic measurements, the former is associated with a spin-freezing temperature below which the magnetic glass state is experimentally verified. The magnetometric experiments detailed in the paper bring out the non-equilibrium metastable magnetic states in this disordered magnetic system. The magnetic glass state described above manifests in the electrical resistivity [Formula: see text] through the formation of a 'hard gap' because of the spin-exchange energy following the formation of magnetic glass. It is observed that the combination of disorder and magnetic glass state leads to a large, negative magnetoresistance (MR) of ≈47[Formula: see text] at 5 K in 8 T.

Pr-magnetism in the quasi-skutterudite compound PrFe2Al8.

The intermetallic compound PrFe2Al8 that possesses a three-dimensional network structure of Al polyhedra centered at the transition metal element Fe and the rare earth Pr is investigated through neutron powder diffraction and inelastic neutron scattering in order to elucidate the magnetic ground state of Pr and Fe and the crystal field effects of Pr. Our neutron diffraction study confirms long-range magnetic order of Pr below [Formula: see text] K in this compound. Subsequent magnetic structure estimation reveals a magnetic propagation vector [Formula: see text] with a magnetic moment value of [Formula: see text]/Pr along the orthorhombic c-axis and evidence the lack of ordering in the Fe sublattice. The inelastic neutron scattering study reveals one crystalline electric field excitation near 19 meV at 5 K in PrFe2Al8. The energy-integrated intensity of the 19 meV excitation as a function of [Formula: see text] follows the square of the magnetic form factor of [Formula: see text] thereby confirming that the inelastic excitation belongs to the Pr sublattice. The second sum rule applied to the dynamic structure factor indicates only 1.6(2) [Formula: see text] evolving at the 19 meV peak compared to the 3.58 [Formula: see text] for free [Formula: see text], indicating that the crystal field ground state is magnetic and the missing moment is associated with the resolution limited quasi-elastic line. The magnetic order occurring in Pr in PrFe2Al8 is counter-intuitive to the symmetry-allowed crystal field level scheme, hence, is suggestive of exchange-mediated mechanisms of ordering stemming from the magnetic ground state of the crystal field levels.

Spin reorientation and disordered rare earth magnetism in Ho2FeCoO6.

We report the experimental observation of spin reorientation in the double perovskite Ho2FeCoO6. The magnetic phase transitions in this compound are characterized and studied through magnetization and specific heat, and the magnetic structures are elucidated through neutron powder diffraction. Two magnetic phase transitions are observed in this compound-one at [Formula: see text] K, from paramagnetic to antiferromagnetic, and the other at [Formula: see text] K, from a phase with mixed magnetic structures to a single phase through a spin reorientation process. The magnetic structure in the temperature range 200-45 K is a mixed phase of the irreducible representations [Formula: see text] and [Formula: see text], both of which are antiferromagnetic. The phase with mixed magnetic structures that exists in Ho2FeCoO6 gives rise to a large thermal hysteresis in magnetization that extends from 200 K down to the spin reorientation temperature. At T N2, the magnetic structure transforms to [Formula: see text]. Though long-range magnetic order is established in the transition metal lattice, it is seen that only short-range magnetic order prevails in the Ho3+ lattice. Our results should motivate further detailed studies on single crystals in order to explore the spin reorientation process, spin switching and the possibility of anisotropic magnetic interactions giving rise to electric polarization in Ho2FeCoO6.

Magnetic, specific heat and electrical transport properties of Frank-Kasper cage compounds RTM2Al20 [R = Eu, Gd and La; TM = V, Ti].

Single crystals of Frank-Kasper compounds RTM2Al20 (R = Eu, Gd and La; TM = V and Ti) were grown by self-flux method and their physical properties were investigated through magnetization (M), magnetic susceptibility (χ), specific heat (C P) and electrical resistivity (ρ) measurements. Powder x-ray diffraction studies and structural analysis showed that these compounds crystallize in the cubic crystal structure with the space group [Formula: see text]. The magnetic susceptibility for the compounds EuTi2Al20 and GdTi2Al20 showed a sudden jump below the Néel temperature T N indicative of plausible double magnetic transition. Specific heat (C P) and electrical resistivity (ρ) measurements also confirm the first-order magnetic transition (FOMT) and possible double magnetic transitions. Temperature variation of heat capacity showed a sharp phase transition and huge C P value for the (Eu/Gd)Ti2Al20 compounds' full width at half-maximum (FWHM) (<0.2 K) which is reminiscent of a first-order phase transition and a unique attribute among RTM2Al20 compounds. In contrast, linear variation of C P is observed in the ordered state for (Eu/Gd)V2Al20 compounds suggesting a λ-type transition. We observed clear anomaly between heating and cooling cycle in temperature-time relaxation curve for the compounds GdTi2Al20 (2.38 K) and EuTi2Al20 (3.2 K) which is indicating a thermal arrest due to the latent heat. The temperature variation of S mag for GdTi2Al20 saturates to a value [Formula: see text] while the other magnetic systems exhibited still lower entropy saturation values in the high temperature limit. [Formula: see text] versus T plot showed a maximum near 27 K for all the compounds indicating the presence of low frequency Einstein modes of vibrations. Resistivity measurements showed that all the samples behave as normal Fermi liquid type compounds and [Formula: see text] due to electron-phonon scattering follows Bloch-Grüneisen-Mott relation in the paramagnetic region.

Polarity-tunable spin transport in all-oxide multiferroic tunnel junctions.

A multiferroic tunnel junction (MFTJ) promisingly offers multinary memory states in response to electric- and magnetic-fields, referring to tunneling electroresistance (TER) and tunneling magnetoresistance (TMR), respectively. In spite of recent progress, a substantial number of questions concerning the understanding of these two intertwined phenomena still remain open, e.g. the role of microstructural/chemical asymmetry at the interfaces of the junction and the effect of an electrode material on the MFTJ properties. In this regard, we look into the multiferroic effect of all-complex-oxide MFTJ (La0.7Sr0.3MnO3/Pb(Zr0.3Ti0.7)O3/La0.7Sr0.3MnO3). The results reveal apparent TER-TMR interplay-captured by the reversible electric-field control of the TMR effect. Finally, microscopy analysis on the MFTJ revealed that the observed TER-TMR interplay is perhaps mediated by microstructural and chemical asymmetry in our nominally symmetric MFTJ.

Magnetic ordering in double perovskites R2CoMnO6 (R = Y, Tb) investigated by high resolution neutron spectroscopy.

We have investigated low energy nuclear spin excitations in double perovskite compounds R(2)CoMnO(6) (R=Y, Tb) by inelastic neutron scattering with a high resolution back-scattering spectrometer. We observed inelastic signals at about 2.1 µeV for Y(2)CoMnO(6) and also for Tb(2)CoMnO(6) at T = 2 K in both energy-loss and energy-gain sides. We interpret these inelastic peaks to be due to the transitions between the hyperfine split nuclear levels of the (59)Co nucleus. The inelastic peaks move towards the central elastic peak and finally merge with it at the magnetic ordering temperature T(C). The energy of the low energy excitations decreases continuously and becomes zero at T(C) ≈ 75 K for Y(2)CoMnO(6) and T(C) ≈ 100 K for Tb(2)CoMnO(6). For Tb(2)CoMnO(6), which contains magnetic rare earth ions, additional quasielastic scattering due presumably to the fluctuations of large Tb magnetic moments was observed. The present study reveals the magnetic ordering of the Co sublattice. The results of this investigation along with that obtained by us for other compounds indicate the presence of unquenched orbital moments in some of the Co compounds.