arXiv subjects

S. Bhattacharjee

Publications and source records attributed to S. Bhattacharjee.

36 records · Page 2Linked to original sources

arXiv2022

An effective bound on Generalized Diophantine m-tuples

For non-zero integers $n$ and $k\geq2$, a generalized Diophantine $m$-tuple with property $D_k(n)$ is a set of $m$ positive integers $S = \{a_1,a_2,\ldots, a_m\}$ such that $a_ia_j + n$ is a $k$-th power for $1\leq i< j\leq m$. Define $M_k(n):= \sup\{|S| : S$ has property $D_k(n)\}$. In a recent work, the second author, S. Kim and M. R. Murty proved that $M_k(n)$ is $O(\log n)$, for a fixed $k$, as we vary $n$. In this paper, we obtain effective upper bounds on $M_k(n)$. In particular, we show that for $k\geq 2$, $M_k(n) \leq 3\,ϕ(k)\, \log n$, if $n$ is sufficiently larger than $k$.

math.NT↗

arXiv2022

Role of chemical disorder in tuning the Weyl points in vanadium doped Co$_2$TiSn

The lack of time-reversal symmetry and Weyl fermions give exotic transport properties to Co-based Heusler alloys. In the present study, we have investigated the role of chemical disorder on the variation of Weyl points in Co\textsubscript{2}Ti\textsubscript{1-x}V\textsubscript{x}Sn magnetic Weyl semimetal candidate. We employ the first principle approach to track the evolution of the nodal lines responsible for the appearance of Weyl node in Co$_2$TiSn as a function of V substitution in place of Ti. By increasing the V concentration in place of Ti, the nodal line moves toward Fermi level and remains at Fermi level around the middle composition. Further increase of the V content, leads shifting of nodal line away from Fermi level. Density of state calculation shows half-metallic behavior for the entire range of composition. The magnetic moment on each Co atom as a function of V concentration increases linearly up to x=0.4, and after that, it starts decreasing. We also investigated the evolution of the Weyl nodes and Fermi arcs with chemical doping. The first-principles calculations reveal that via replacing almost half of the Ti with V, the intrinsic anomalous Hall conductivity increased twice as compared to the undoped composition. Our results indicate that the composition close to the 50\% V doped Co$_2$TiSn, will be an ideal composition for the experimental investigation of Weyl physics.

cond-mat.mtrl-sci↗

arXiv2020

Bouncing scenario in $f(R,T)$ gravity

The present manuscript presents modeling of matter bounce in the framework of $f(R,T)$ gravity where $f(R,T) = R + 2 λT$. We start by defining a parametrization of scale factor which is non-vanishing. The geometrical parameters such as the Hubble parameter and deceleration parameter are derived, from which expressions of pressure, density and Equation of State (EoS) parameter and a qualitative understanding of the initial conditions of the universe at the bounce are ascertained. We found that the initial conditions of the universe are finite owing to the non-vanishing nature of the scale factor thus eliminates the initial singularity problem. Furthermore, we show the violation of energy conditions near the bouncing region and analyzed the stability of our model with respect to linear homogeneous perturbations in Friedmann-Lematre-Robertson-Walker (FLRW) spacetime. We found that our model and hence matter bounce scenarios in general are highly unstable at the bounce in the framework of $f(R,T)$ gravity but the perturbations decay out rapidly away from the bounce safeguarding its stability at late times.

gr-qc↗

arXiv2020

Temporally Varying Universal Gravitational "Constant" and Speed of Light in Energy Momentum Squared Gravity

Energy Momentum Squared Gravity (EMSG) is a cosmological model where the scale factor is non vanishing at all times and hence does not favor big bang cosmology. However, the profile of density in the radiation dominated universe shows that EMSG supports inflationary cosmology. Inflationary cosmological models are successful in providing convincing answers to major cosmological issues like horizon problem, flatness problem and small value of cosmological constant but hitherto no model of inflation has been observationally confirmed. Owing to this, Varying Speed of Light (VSL) were introduced which are a class of cosmological models which disfavor inflation and propose an alternative route to solve these cosmological issues by just allowing the speed of light (and Newtonian Gravitational constant) to vary. VSL theories were motivated to address the shortcomings of inflation but do not address the shortcomings related to the initial big bang singularity. In this spirit, we present here a novel cosmological model which is free from both the "initial big bang singularity" and "inflation" by incorporating a mutually varying speed of light $c(t)$ and Newtonian gravitational constant $G(t)$ in the framework of EMSG. We report that in EMSG, for a dust universe ($ω=0$), cosmological models for a time varying $c(t)$ and $G(t)$ and constant $c$ and $G$ are indistinguishable, whereas for a radiation dominated universe ($ω= 1/3$), a mutually varying $c(t)$ and $G(t)$ provides an exiting alternative to inflationary cosmology which is also free from initial big bang singularity. We further report that for an ansatz of scale factor representing a bouncing cosmological model, the VSL theory can be applied to a quadratic $T$ gravity model to get rid of "inflation" and "big bang singularity" and concurrently solve the above mentioned cosmological enigmas.

gr-qc↗

arXiv2019

Revisiting The Coincidence Problem in $f(R)$ Gravitation

The energy densities of dark matter (DM) and dark energy (DE) are of the same order at the present epoch despite the fact that both these quantities have contrasting characteristics and are presumed to have evolved distinctively with cosmic evolution. This is a major issue in standard $Λ$CDM cosmology and is termed "The Coincidence Problem" which hitherto cannot be explained by any fundamental theory. In this spirit, Bisabr \cite{bisabr} reported a cosmological scenario in $f(R)$ gravity where DM and DE interact and exchange energy with each other and therefore evolve dependently. We investigate the efficiency and model independancy of the technique reported in Bisabr \cite{bisabr} in addressing the Coincidence problem with the help of two $f(R)$ gravity models with model parameters constrained from various observations. Our result confirm the idea that not all scalar-tensor gravity theories and models can circumvent the Coincidence Problem and any cosmological scenario with interacting fluids is highly model dependent and hence alternate model independent theories and ideas should be nominated to solve this mystery.

gr-qc↗

arXiv2019

Cu-substituted Fe2P: An emerging candidates for magnetic RAM application

We propose that Cu-substituted Fe$_2$P, (Fe$_{1-x}$Cu$_x$)$_2$P ($x\sim 0.16$), to be an outstanding contender for the STT-MRAM application. Using first principles based calculations in the framework of density functional theory and through Monte Carlo simulations, we demonstrate that this material can be used as ferromagnetic electrode in the magnetic tunnel junction (MTJ) of STT-MRAM due to its moderate perpendicular magnetic anisotropy (PMA), large tunnel magneto-resistance (TMR), good thermal stability and high ferromagnetic transition temperature. We point out that the simplicity in the synthesis, huge abundance, and non-toxicity make this material a very good candidate to replace the current MTJ materials for STT-MRAM such as FePt,~FeCo or FeCoB.

cond-mat.mtrl-sci↗

arXiv2015

Atomistic Coupling between Magnetization and Lattice Dynamics from First Principles

We formulate a new scheme to study the combined magnetization and lattice dynamics in magnets, so-called magnetoelastics. The coupling between magnetization and lattice are considered through an expansion of electron-phonon coupling, while the magnetization is coupled to electrons through sd-like interaction. We show the that the time-scale of the magnetization dynamics due to coupling between magnetic degrees of freedom and electronic degrees of freedom can be transferred to lattice degrees of freedom and therefore can give rise to lattice dynamics on the same time-scale. This opens a new route to understand and treat ultrafast lattice dynamics induced by magnetization dynamics. We also show that all the parameters necessary to simulate this coupled lattice and magnetization dynamics can be obtained from first-principles.

cond-mat.mtrl-sci↗

arXiv2015

Proximate Kitaev Quantum Spin Liquid Behaviour in α-RuCl$_3$

Topological states of matter such as quantum spin liquids (QSLs) are of great interest because of their remarkable predicted properties including protection of quantum information and the emergence of Majorana fermions. Such QSLs, however, have proven difficult to identify experimentally. The most promising approach is to study their exotic nature via the wave-vector and intensity dependence of their dynamical response in neutron scattering. A major search has centered on iridate materials which are proposed to realize the celebrated Kitaev model on a honeycomb lattice - a prototypical topological QSL system in two dimensions (2D). The difficulties of iridium for neutron measurements have, however, impeded progress significantly. Here we provide experimental evidence that a material based on ruthenium, α-RuCl$_3$ realizes the same Kitaev physics but is highly amenable to neutron investigation. Our measurements confirm the requisite strong spin-orbit coupling, and a low temperature magnetic order that matches the predicted phase proximate to the QSL. We also show that stacking faults, inherent to the highly 2D nature of the material, readily explain some puzzling results to date. Measurements of the dynamical response functions, especially at energies and temperatures above that where interlayer effects are manifest, are naturally accounted for in terms of deconfinement physics expected for QSLs. Via a comparison to the recently calculated dynamics from gauge flux excitations and Majorana fermions of the pure Kitaev model we propose α-RuCl$_3$ as the prime candidate for experimental realization of fractionalized Kitaev physics.

cond-mat.mtrl-sci↗

arXiv2014

Displacive-type ferroelectricity from magnetic correlations within spin-chain

Observation of ferroelectricity among non-d0 systems, which was believed for a long time an unrealistic concept, led to various proposals for the mechanisms to explain the same (i.e. magnetically induced ferroelectricity) during last decade. Here, we provide support for ferroelectricity of a displacive-type possibly involving magnetic ions due to short-range magnetic correlations within a spin-chain, through the demonstration of magnetoelectric coupling in a Haldane spin-chain compound Er2BaNiO5 well above its Néel temperature of (TN=) 32K. There is a distinct evidence for electric polarization setting in near 60 K around which there is an evidence for short-range magnetic correlations from other experimental methods. Raman studies also establish a softening of phonon modes in the same temperature (T) range and T-dependent x-ray diffraction (XRD) patterns also reveal lattice parameters anomalies. Density-functional theory based calculations establish a displacive component (similar to d0-ness) as the root-cause of ferroelectricity from (magnetic) NiO6 chain, thereby offering a new route to search for similar materials near room temperature to enable applications.

cond-mat.str-el↗

arXiv2013

Nanopattern on Carbon and by Carbon

We have reported nanopattern formation on carbon thin film and Si(100) surfaces by low energy inert and carbon ion beams. It is interesting to observe the role of carbon as target as well as projectile for nano patterning. Using carbon thin film as target, nano patterns of carbon are formed by inert (Ar+) and self (C+) ion bombardment, whereas carbon ion beam is used to form well ordered Si nano ripple structure in a cost effective way where implanted carbon plays an important role to form Si ripple in relatively lower fluence than the inert projectile.

cond-mat.mtrl-sci↗

arXiv2012

Atomistic spin dynamic method with both damping and moment of inertia effects included from first principles

We consider spin dynamics for implementation in an atomistic framework and we address the feasibility of capturing processes in the femtosecond regime by inclusion of moment of inertia. In the spirit of an {\it s-d} -like interaction between the magnetization and electron spin, we derive a generalized equation of motion for the magnetization dynamics in the semi-classical limit, which is non-local in both space and time. Using this result we retain a generalized Landau-Lifshitz-Gilbert equation, also including the moment of inertia, and demonstrate how the exchange interaction, damping, and moment of inertia, all can be calculated from first principles.

cond-mat.stat-mech↗

arXiv2011

Ripple topography on thin ZnO films by grazing and oblique incidence ion sputtering

We have investigated the formation and growth of nano sized ripple topography on ZnO thin films by 10 keV O1+ bombardment at impact angles of 80{\degree} and 60{\degree}, varying the ion fluence from 5{times}10^16 to 1{\times}10^18 ions/cm2. At 800 the ripples are oriented along the ion beam direction whereas at 600 it is perpendicular to the ion beam direction. The developed ion induced structures are characterized by Atomic Force Microscopy (AFM) and the alignment, variation of rms roughness, wavelength and correlation length of the structures are discussed with the existing model and basic concept of ion surface interaction.

cond-mat.mes-hall↗

arXiv2011

Key factors of ion induced nanopatterning

We have reported the dependence of projectile mass, chemical reactivity and effect of molecular beams on the ion induced nano structure formation, when 8 keV He1+, N1+, O1+, Ar1+ atomic ions and 16 keV N21+ and O21+ molecular ions are bombarded on the Si(100) surface at an incidence angle of 60^{\circ}. Atomic force microscopy (AFM) measurement shows that the initiation and growth of ripple structures are determined not only by the collision cascades but also by the chemical reactivity and molecular state of the projectiles. This experimental investigation explores the necessary requirements for ion induced controlled nanopatterning.

cond-mat.mtrl-sci↗

arXiv2011

Tuning of dielectric properties and magnetism of SrTiO3 by site-specific doping of Mn

Combining experiments with first principles calculations, we show that site-specific doping of Mn into SrTiO3 has a decisive influence on the dielectric properties of these doped systems. We find that phonon contributions to the dielectric constant invariably decrease sharply on doping at any site. However, a sizable, random dipolar contribution only for Mn at the Sr site arises from a strong off-centric displacement of Mn in spite of Mn being in a non-d0 state; this leads to a large dielectric constant at higher temperatures and gives rise to a relaxor ferroelectric behavior at lower temperatures. We also investigate magnetic properties in detail and critically reevaluate the possibility of a true multi-glass state in such systems.

cond-mat.mtrl-sci↗

arXiv2010

Projectile's mass, reactivity and molecular dependence on ion nanostructuring

We have reported the dependence of projectile mass along with the chemical reactivity and nonlinear effects on ion beam induced nano structure formation when 8 keV He1+, N1+, O1+, Ar1+ atomic ions and 16 keV N21+ and O21+ molecular ions are bombarded on the Si (100) surface at an incidence angle of 600. Ex situ atomic force microcopy (AFM) measurements reveals the ripple structure development of various forms and dimensions depending on the projectiles mass, chemical reactivity and molecular state. This experimental study explores the necessary requirements for ion induced nanopatterning and their control.

cond-mat.mes-hall↗

arXiv2009

Coulomb explosion sputtering of selectively oxidized Si

We have studied multiply charged Arq+ ion induced potential sputtering of a unique system comprising of coexisting Silicon and Silicon oxide surfaces. Such surfaces are produced by oblique angle oxygen ion bombardment on Si(100), where ripple structures are formed and one side of each ripple gets more oxidized. It is observed that higher the potential energy of Arq+ ion, higher the sputtering yield of the non conducting (oxide) side of the ripple as compared to the semiconducting side. The results are explained in terms of Coulomb explosion model where potential sputtering depends on the conductivity of the ion impact sites.

cond-mat.mtrl-sci↗

arXiv2009

Confinement-deconfinement transition in a generalized Kitaev model

We present a spin model, namely, the Kitaev model augmented by a loop term and perturbed by an Ising Hamiltonian and show that it exhibits both confinement-deconfinement transitions from spin liquid to antiferromagnetic/spin-chain/ferromagnetic phases and topological quantum phase transitions between gapped and gapless spin liquid phases. We develop a Fermionic mean-field theory to chart out the phase diagram of the model and estimate the stability of its spin liquid phases which might be relevant for attempts to realize the model in optical lattices. We also conjecture that some of the confinement-deconfinement transitions in the model, predicted to be first order within the mean-field theory, may become second order via a defect condensation mechanism.

cond-mat.str-el↗

arXiv2005

Survival of orbiting in $^{20}$Ne (7 - 10 MeV/nucleon) + $^{12}$C reactions

The inclusive energy distributions of fragments with Z $\geq$ 3 emitted from the bombardment of $^{12}$C by $^{20}$Ne beams with incident energies between 145 and 200 MeV have been measured in the angular range $θ_{lab} \sim$ 10$^\circ$ - 50$^\circ$. Damped fragment yields in all cases have been found to be characteristic of emission from fully energy equilibrated composites; for B, C fragments, average Q-values, $ $, were independent of the centre of mass emission angle ($θ_{c.m}$), and the angular distributions followed $\sim$1/sin$θ_{c.m}$ like variation, signifying long life times of the emitting di-nuclear systems. Total yields of these fragments have been found to be much larger compared to the standard statistical model predictions of the same. This may be indicative of the survival of orbiting like process in $^{12}$C + $^{20}$Ne system at these energies.

nucl-ex↗