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An angular time-dependent probability density function describing Brownian or anomalous rotational dynamics of fixed-length atom-to-atom vectors is presented. The probability density function, which fully incorporates angular boundary conditions, is applied to aqueous ion complexes. The rotational dynamics of ion-$^1$H vectors are shown by molecular dynamics (MD) simulation to be Brownian. A Brownian shell model is presented which yields a closed form expression for the frequency-dependent nuclear-magnetic-resonance spin-lattice relaxation rate $T_1^{-1}(\omega)$ based on a distance parameter and time constant. Appropriate combinations of shell and/or continuum models are shown to provide excellent fully-quantitative fits to experimental $T_1^{-1}(\omega)$ dispersion curves from aqueous manganese(II), iron(III) and copper(II) chloride solutions. The distance parameters and time constants obtained from the fits are in good agreement with independent experimental and MD data in the literature. The Brownian shell model is a significant enhancement to existing particle-particle models that describe the rotational correlation function as a single exponential and are unable to provide the correct distance dependence for a shell of $^1$H spin density preventing a match to experiment without an arbitrary scaling factor., Comment: 39 pages, 7 figures, includes an appendix

Adopting the manifest of low-frequency and low mass for the scalar perturbation, we perform a semi-classical analysis of the superradiance phenomenon for a rotating hairy Horndeski black hole (BH). For the spacetime under study enriched by the hairy Horndeski parameter $h$, in addition to the mass $M$ and spin $a$, we compute the amplification factor of scalar wave scattering indicating the energy extraction from the BH. We find that due to the addition of the hairy parameter $h$ in the geometry, the superradiance scattering and its frequency range enhance compared to the Kerr BH. This implies that Horndeski's gravity belongs to those alternative theories of gravity that make the amplification factor larger than the Kerr BH so that the energy extraction in its framework is more efficient than general relativity. Calculating the outgoing energy flux measured by an observer at infinity verifies the role of the hairy parameter $h$ in the increase of energy extraction efficiency from the rotating BH. By implementing the BH bomb mechanism, we present an analysis of the superradiant instability of the underlying BH spacetime against massive scalar fields. Our analysis indicates that the hairy Horndeski parameter leaves no imprint on the standard superradiant instability regime., 26 pages, 3 figures, 2 tables. v3:discussion improved, Refs added, 1 table added, to be published in PRD

A spark-plasma sintered ${\mathrm{GdCrO}}_{3}$ (SPS-GCO) is found to stabilize in its ferroelectric phase beyond room temperature. The intrinsic nature of this room-temperature ferroelectricity is established using ferroelectric positive-up--negative-down measurements and supported through piezoresponce force microscopy measurements. The SPS-GCO undergoes antiferromagnetic ordering at much lower temperatures, only below $\ensuremath{\approx}170\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. Thus, any role of magnetism to the observed room temperature ferroelectricity in SPS-GCO can be ruled out. This is contrast to the concomitant antiferromagnetic and ferroelectric ordering observed below $\ensuremath{\approx}170\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ in ${\mathrm{GdCrO}}_{3}$ (GCO) (prepared using standard solid-state synthesis technique). Using detailed Rietveld refinements of room-temperature x-ray diffraction patterns, SPS-GCO is found to stabilize in the noncentrosymmetric orthorhombic $Pna{2}_{1}$ space group (the reported low-temperature ferroelectric phase in GCO), while GCO stabilizes in the centrosymmetric $Pbnm$ space group at room temperature. Using first-principles calculations, we investigated the relative energies among various possible structures of ${\mathrm{GdCrO}}_{3}$ and found that the orthorhombic $Pna{2}_{1}$ and $Pbnm$ space groups are the most stable structures. The ferroelectric $Pna{2}_{1}$ phase of SPS-GCO (stabilized at room temperature using the high-pressure and high-temperature spark-plasma sintering process) undergoes transition to the paraelectric centrosymmetric phase upon heating beyond $\ensuremath{\approx}450\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ (as confirmed using dielectric and calorimetric measurements), which on subsequent cooling to room temperature does not undergo a transition back to the ferroelectric phase and remains in the centrosymmetric $Pbnm$ phase.

There is increasing interest in novel magnetoelectric (ME) materials that exhibit robust ME coupling at room temperature (RT) for advanced memory, energy, spintronics, and other multifunctional device applications, by making use of the ability to control polarization with a magnetic field and/or magnetization via an electric field. Obtaining ME materials with strong ME coupling, understanding the origin, and manipulating its processing along with composition to realize large ME coefficients at RT constitute an important step in multiferroic research. To address this, we have investigated the multiferroic and ME properties of Ni-doped $\mathrm{Pb}({\mathrm{Zr}}_{0.20}{\mathrm{Ti}}_{0.80}){\mathrm{O}}_{3}$ (PZT). We find that the ferroelectric $({T}_{\mathrm{C}}\ensuremath{\sim}700\phantom{\rule{0.16em}{0ex}}\mathrm{K})$ and weak ferromagnetic (\ensuremath{\sim}602 K) phase transitions of Ni-doped PZT are well above room temperature (RT), leading to a strong ME coupling coefficient (${\ensuremath{\alpha}}_{E,31}$) of $11.7\phantom{\rule{0.16em}{0ex}}\mathrm{mV}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{--1}\phantom{\rule{0.16em}{0ex}}{\mathrm{Oe}}^{--1}$ (${H}_{\mathrm{ac}}=1\phantom{\rule{0.16em}{0ex}}\mathrm{Oe}$ and $f=1\phantom{\rule{0.16em}{0ex}}\mathrm{kHz}$). While x-ray diffraction suggests a single-phase material, high-resolution transmission electron microscopy reveals regions with and without Ni present; thus magnetoelectric coupling between two phases is possible. First-principles calculations suggest the $(\mathrm{N}{\mathrm{i}}_{\mathrm{Pb}}{)}^{\ifmmode\times\else\texttimes\fi{}}$ defect is likely to be responsible for the experimental observed magnetism and ME coupling in Ni-doped PZT. We further demonstrate that Ni-doped PZT exhibits low loss tangent, low leakage current, large saturation polarization, and weak ferromagnetism. Ultimately, our work demonstrates that Ni-doped PZT is a cost-effective RT multiferroic with strong ME coupling.

Upconversion (UC) in a molecular system is a process in which excitons produced by a multiple absorption of low-energy photons at long wavelengths undergo fusion to produce high energy excitons that consequently recombine to emit anti-Stokes shifted photons. Molecular systems for UC typically require a sensitizer. However, recent experiments show that UC in rubrene occurs even without the presence of the sensitizer. In this system, intermediate states are assumed to absorb photons at near-infrared wavelengths, which either absorb additional photons to populate the emissive singlet state or undergo fusion to generate triplets. The triplets can again undergo fusion to populate the excited singlet state. The final emission is around 600 nm. These models have been tested against the intensity dependence of the UC emission. Here, we have measured the kinetics of UC in rubrene by using intensity modulated photoexcitation at 800 nm to better understand the underlying mechanism. The models of UC that have been proposed so far do not agree with our measurements. Our results show that the yield of UC lags behind excitation significantly, indicating that triplet states are directly excited from the ground state, and their fusion, which depends on the population, becomes prominent after a certain build up time. While the intermediate states could form dynamically after the UC has been initiated and enhance the process, further sensitive absorption measurements are necessary to understand the role of the intermediate states in the process. Our results are important in finding new routes to enhance UC in pristine organic semiconductors for applications in photovoltaics, lasers, bioimaging, optical devices, and lighting.

Materials in which a Mott insulator to metal transition (Mott breakdown) can be induced using a moderate dc current (with an electric field that is much smaller than the corresponding Zener breakdown voltage) is extremely promising for electronic device applications and offer a unique platform for investigation of the underlying emergent mechanism. Here we report a Mott breakdown phenomenon in a spinel compound, namely, ${\mathrm{MgTi}}_{1.2}{\mathrm{V}}_{0.8}{\mathrm{O}}_{4}$, which undergoes a sharp switching of resistivity by several orders of magnitude by application of a dc current. The observed Mott breakdown effect, which is associated with a negative differential resistance as seen in the corresponding electric-voltage ($\mathit{V}$) vs electric-current ($\mathit{I}$) curve (opposite to Ohm's law dependence), occurs beyond a temperature-dependent threshold electric current (${\mathit{I}}_{\mathrm{th}}$), which corresponds to an extremely small threshold electric-field (${\mathit{E}}_{\mathrm{th}}$) (for example, ${\mathit{E}}_{\mathrm{th}}$ is found to be $\ensuremath{\sim}40\phantom{\rule{0.28em}{0ex}}\mathrm{V}/\mathrm{cm}$ at 50 K and further decreases with an increase in temperature). The system remains in the metastable metallic state only in the presence of high-current flow upto the lowest measured temperature and switches back to the highly insulating state when the current flow is switched off. Associated experimental observations suggest against a Joule-heating driven change in state and hint towards an electronic mechanism. Using first-principles calculation and several experimental probes, we further investigate the origin of the driving mechanism. The presence of two Jahn-Teller active ions, i.e., ${\mathrm{Ti}}^{3+}$ ($3{d}^{1}$---one electron among three ${t}_{2\mathrm{g}}$ levels) and ${\mathrm{V}}^{3+}$ ($3{d}^{2}$---two electrons among three ${t}_{2\mathrm{g}}$ levels) in ${\mathrm{MgTi}}_{1.2}{\mathrm{V}}_{0.8}{\mathrm{O}}_{4}$ along with the obtained density of states offers a unique opportunity which seems critical for the Mott breakdown phenomenon as it supports high-current induced excitation of electrons through an activated avalanche process from ${\mathrm{Ti}}^{3+}\phantom{\rule{0.28em}{0ex}}{t}_{2g}$ levels (located at the edge of the valence band) into ${\mathrm{V}}^{3+}\phantom{\rule{4pt}{0ex}}{t}_{2g}$ levels (located at the bottom of the conduction band) thereby removing the orbital degrees of freedom of the V and Ti electrons and leading to melting of the Jahn-Teller driven structural transition into the insulating tetragonal phase.

We report the signatures of dynamic spin fluctuations in the layered honeycomb ${\mathrm{Li}}_{3}{\mathrm{Cu}}_{2}\mathrm{Sb}{\mathrm{O}}_{6}$ compound, with a $3d S=1/2 {d}^{9}\phantom{\rule{4pt}{0ex}}{\mathrm{Cu}}^{2+}$ configuration, through muon spin rotation and relaxation ($\ensuremath{\mu}\mathrm{SR}$) and neutron scattering studies. Our zero-field (ZF) and longitudinal-field (LF) $\ensuremath{\mu}\mathrm{SR}$ results demonstrate the slowing down of the ${\mathrm{Cu}}^{2+}$ spin fluctuations below 4.0 K. The saturation of the ZF relaxation rate at low temperature, together with its weak dependence on the longitudinal field between 0 and 3.2 kG, indicates the presence of dynamic spin fluctuations persisting even at 80 mK without static order. Neutron scattering study reveals the gapped magnetic excitations with three modes at 7.7, 13.5, and 33 meV. Our density functional theory calculations reveal that the next-nearest-neighbor (NNN) antiferromagnetic (AFM) exchange (${J}_{\text{AFM}}=31$ meV) is stronger than the NN ferromagnetic (FM) exchange (${J}_{\text{FM}}=\ensuremath{-}21$ meV), indicating the importance of the orbital degrees of freedom. Our results suggest that the physics of ${\mathrm{Li}}_{3}{\mathrm{Cu}}_{2}\mathrm{Sb}{\mathrm{O}}_{6}$ can be explained by an alternating AFM chain rather than the honeycomb lattice.

Considerable attention has been paid recently to $\mathrm{Fe}{\mathrm{Te}}_{2}{\mathrm{O}}_{5}\mathrm{Cl}$ due to reduced dimensionality and frustration in the magnetic subsystem, succession of phase transitions, and multiferroicity. The efforts to grow its selenite sibling resulted in the mixed halide compound $\mathrm{Fe}({\mathrm{Te}}_{1.5}{\mathrm{Se}}_{0.5}){\mathrm{O}}_{5}\mathrm{Cl}$, which was found crystallizing in a different structural type and possessing properties drastically different from those of a parent system. Its magnetic subsystem features weakly coupled ${\mathrm{Fe}}^{3+}\ensuremath{-}{\mathrm{Fe}}^{3+}$ dimers showing the regime of short-range correlations at ${T}_{\mathrm{M}}\ensuremath{\sim}70\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and long-range order at ${T}_{\mathrm{N}}=22\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. In a magnetically ordered state, sizable spin-orbital interactions lead to a small canting of ${\mathrm{Fe}}^{3+}$ moments. Magnetic dipole-dipole interactions contribute significantly to the experimentally observed orientation of magnetization easy axis in the $ac$ plane. The first principles calculations of leading exchange interactions were found in agreement with measurements of thermodynamic properties and Raman spectroscopy.

High-spin states of $^{38}\mathrm{K}$ above the $31.67\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$ (${\ensuremath{\tau}}_{m}$) isomer, populated through the $^{12}\mathrm{C}(^{28}\mathrm{Si},\phantom{\rule{0.16em}{0ex}}np)^{38}\mathrm{K}$ reaction with a 110 MeV $^{28}\mathrm{Si}$ beam, have been studied by using the Indian National Gamma Array (INGA) facility. Two new levels and four new transitions have been added to the existing level scheme. The spins and parities of most of the levels above the isomer have been assigned, modified, and confirmed from ${R}_{\mathrm{DCO}}$, ${R}_{\mathrm{ADO}}$, and linear polarization measurements. The multipole mixing ratios ($\ensuremath{\delta}$) for a few transitions have been measured. Large-basis shell-model calculations have been performed to understand the microscopic origin of these levels. In our calculations, different particle restrictions in $sd$- and $pf$-shell orbitals were used to reproduce the experimental level energies. Two-nucleon transfer spectroscopic factors have also been calculated for the levels above the isomer to support the new spin and parity assignments. Prediction of collective excitation at high excitation energy in $^{38}\mathrm{K}$ is also discussed.

We study the anomalous $W^+W^-V$ ($V=\gamma,Z$) couplings in $e^+e^-\to W^+W^-$ using the complete set of polarization observables of $W$ boson with longitudinally polarized electron ($e^-$) and positron ($e^+$) beams. For the effective $W^+W^-V$ couplings, we use the most general Lorentz invariant form factor parametrization as well as $SU(2)\times U(1)$ invariant dimension-$6$ effective operators. We estimate simultaneous limits on the anomalous couplings using the Markov-Chain--Monte-Carlo (MCMC) method for an $e^+e^-$ collider running at center of mass energy of $\sqrt{s}=500$ GeV and the integrated luminosity of ${\cal L}=100$ fb$^{-1}$, $3.2$ ab$^{-1}$ and $4$ ab$^{-1}$. The best limits on the anomalous couplings are obtained for $e^-$ and $e^+$ polarization being $(\pm 0.8,\mp 0.6)$ for both $100$ fb$^{-1}$ and $3.2$ ab$^{-1}$ of luminosity.

We present a physically plausible solution representing Einstein's cluster mimicking the behaviors of compact star in the context of teleparallel equivalent of general relativity. The Teleparallel gravity (TEGR) is an alternative formulation of gravity which uses tetrads as the dynamical variables. We focus on two particularly interesting scenarios. First, we develop the Einstein clusters in TEGR field equations using effective energy-momentum tensor for diagonal as well as off-diagonal tetrad. We then study the clusters in modified $f(T)-$gravity for anisotropic fluid distribution. Based on these two theories, we further study the solution without net electric charge and then for charged solution. For charge parameter $k \rightarrow 0$, the charged solution reduces to neutral one. Our calculations show that when charge increases, the stiffness of the EoS also increases. This is due to increase in adiabatic index and sound speed approaching speed of light. When the charge increase beyond a certain limit ($0\le k \le 1.3 \times 10^{-5}$ and $0\le k \le 1 \times 10^{-6}$), the compactness parameter crosses the Buchdahl limit i.e. $2M/R>8/9$ and the solution start violating the causality condition. We test the Tolman-Oppenheimer-Volkoff (TOV) limit for such compact objects. We analyze the static stability criterion of the Einstein clusters for both charged and uncharged case, and the stability of such compact objects is enhanced by the presence some net electric charge. Finally, we compare our solution for pure general relativity. As a result, we concluded that the Einstein cluster solution do exist in pure GR, however, physically unfit to mimic compact stars. We have also extend our findings by assuming the diagonal or off-diagonal tetrad and specific case of $f(T)$. In such models, Einstein's cluster solutions do exist however can't mimic the properties of a compact star., 15 pages, 21 figures. Accepted in Phys.Rev.D

Using Wannier function formulation and total energy calculations by first-principles density functional theory (DFT), we derive the underlying spin model of a recently synthesized compound, ${\mathrm{Cs}}_{2}{\mathrm{CuAl}}_{4}{\mathrm{O}}_{8}$, having zeolitelike network structure. The computed magnetic interactions show that the interchain Cu-Cu interactions are negligibly small compared to intrachain Cu-Cu interactions, thus characterizing ${\mathrm{Cs}}_{2}{\mathrm{CuAl}}_{4}{\mathrm{O}}_{8}$ as a prototypical one-dimensional (1D) spin-$\frac{1}{2}$ system. Interestingly, the DFT-derived 1D spin model features a combination of alternating ferromagnetic-antiferromagnetic interactions, together with the presence of both nearest- and next-nearest-neighbor interactions, making it an unprecedented case. The solution of the derived spin model of the compound using the quantum Monte Carlo technique shows reasonably good agreement with the experimental susceptibility data, measured in the presence of the magnetic field. The presence of spin gap is suggested by quantum Monte Carlo simulations in the zero-field condition, which is cross-checked by a more rigorous exact diagonalization study. Motivated by the intricacy of the derived spin model, we further examine the ground-state properties of this model in the parameter space of exchange interactions, which shows the possibility of driving quantum phase transition between gapped and gapless spin excitation. Our study is expected to shed light on the fascinating world of 1D quantum spin systems.

The coexistence of ferroelectricity and magnetism---for a long time considered mutually exclusive phenomena---now underpins the flourishing field of magnetoelectric multiferroicity. The authors investigate the multiferroic properties induced by spin ordering in a complex oxide that in many respects differs from any magnetoelectric material studied to date. Besides its general interest, this compound would seem to be of direct relevance for exquisitely sensitive measurements of magnetic fields.

We study strange stars in the framework of $f\left(R,\mathcal{T}\right)$ theory of gravity where the strange quark matter distribution inside the stellar system is governed by the phenomenological MIT Bag model equation of state (EOS). Further, for a specific value of $B$ and observed values of mass of the strange star candidates we obtain the exact solution of the modified Tolman-Oppenheimer-Volkoff (TOV) equation in the framework of $f\left(R,\mathcal{T}\right)$ gravity and have studied in detail the dependence of the different physical parameters due to the chosen different values of $\chi$. To check the physical acceptability and stability of the stellar system based on the obtained solutions we have performed different physical tests, viz., the energy conditions, Herrera cracking concept, adiabatic index etc. In this work, we also have explained the effects, those are arising due to the interaction between the matter and the curvature terms in $f\left(R,\mathcal{T}\right)$ gravity, on the anisotropic compact stellar system. It is interesting to note that as the values of $\chi$ increase the strange stars become more massive and their radius increase gradually so that eventually they gradually turn into less dense compact objects. The present study reveals that the modified $f\left(R,\mathcal{T}\right)$ gravity is a suitable theory to explain massive stellar systems like recent magnetars, massive pulsars and super-Chandrasekhar stars, which can not be explained in the framework of GR. However, for $\chi=0$ the standard results of Einsteinian gravity are retrieved.

The (im)possibility of local distinguishability of orthogonal multipartite quantum states still remains an intriguing question. Beyond $\mathbb{C}^{3}\otimes\mathbb{C}^{3}$, the problem remains unsolved even for maximally entangled states (MES). So far, the only known condition for the local distinguishability of states is the well-known orthogonality preservation (OP). Using an upper bound on the locally accessible information for bipartite states, we derive a very simple necessary condition for any set of pairwise orthogonal MES in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$ to be perfectly locally distinguishable. This condition is seen to be stronger than the OP condition. This is particularly so for any set of $d$ number of pairwise orthogonal MES in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$. When testing this condition for the local distinguishability of all sets of four generalized Bell states in $\mathbb{C}^{4}\otimes \mathbb{C}^{4}$, we find that it is not only necessary but also sufficient to determine their local distinguishability. This demonstrates that the aforementioned upper-bound may play a significant role in the general scenario of local distinguishability of bipartite states., Comment: 11 pages. The content is essentially the same as the previous version, with the language having been simplified a bit. Also, the appendix has been shortened

We propose a unique stellar model under the $f(R,\mathcal{T})$ gravity by using the conjecture of Mazur-Mottola [P. Mazur and E. Mottola, Report No. LA-UR-01-5067, P. Mazur and E. Mottola, Proc. Natl. Acad. Sci. USA 101, 9545 (2004)] which is known as gravastar and a viable alternative to the black hole as available in literature. This gravastar is described by the three different regions, viz., (I) Interior core region, (II) Intermediate thin shell, and (III) Exterior spherical region. The pressure within the interior region is equal to the constant negative matter density which provides a repulsive force over the thin spherical shell. This thin shell is assumed to be formed by a fluid of ultrarelativistic plasma and the pressure, which is directly proportional to the matter-energy density according to Zel'dovich's conjecture of stiff fluid [Y. B. Zel'dovich, Mon. Not. R. Astron. Soc. 160, 1 (1972)], does counterbalance the repulsive force exerted by the interior core region. The exterior spherical region is completely vacuum and assumed to be de Sitter spacetime which can be described by the Schwarzschild solution. Under this specification we find out a set of exact and singularity-free solution of the gravastar which presents several other physically valid features within the framework of alternative gravity.