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Jitender Kumar

Publications and source records attributed to Jitender Kumar.

At least 55 records · Page 3Linked to original sources
arXiv2021

On The Enhanced Power Graph of a Semigroup

The enhanced power graph $\mathcal P_e(S)$ of a semigroup $S$ is a simple graph whose vertex set is $S$ and two vertices $x,y \in S$ are adjacent if and only if $x, y \in \langle z \rangle$ for some $z \in S$, where $\langle z \rangle$ is the subsemigroup generated by $z$. In this paper, first we described the structure of $\mathcal P_e(S)$ for an arbitrary semigroup $S$. Consequently, we discussed the connectedness of $\mathcal P_e(S)$. Further, we characterized the semigroup $S$ such that $\mathcal P_e(S)$ is complete, bipartite, regular, tree and null graph, respectively. Also, we have investigated the planarity together with the minimum degree and independence number of $\mathcal P_e(S)$. The chromatic number of a spanning subgraph, viz. the cyclic graph, of $\mathcal P_e(S)$ is proved to be countable. At the final part of this paper, we construct an example of a semigroup $S$ such that the chromatic number of $\mathcal P_e(S)$ need not be countable.

math.GR↗
arXiv2020

On the commuting graphs of Brandt semigroups

The commuting graph of a finite non-commutative semigroup S, denoted by Δ(S), is the simple graph whose vertices are the non-central elements of S and two distinct vertices x; y are adjacent if xy = yx. In the present paper, we study various graph-theoretic properties of the commuting graph Δ(B_n) of Brandt semigroup B_n including its diameter, clique number, chromatic number, independence number, strong metric dimension and dominance number. Moreover, we obtain the automorphism group Aut(Δ(Bn)) and the endomorphism monoid End(Δ(Bn)) of Δ(Bn). We show that Aut(Δ(Bn)) = S_n \times Z_2, where S_n is the symmetric group of degree n and Z_2 is the additive group of integers modulo 2. Further, for n \geq 4, we prove that End(Δ(Bn)) =Aut(Δ(Bn)). In order to provide an answer to the question posed in [2], we ascertained a class of inverse semigroups whose commuting graph is Hamiltonian.

math.GR↗
arXiv2020

On The Commuting Graph of Semidihedral Group

The commuting graph $Δ(G)$ of a finite non-abelian group $G$ is a simple graph with vertex set $G$ and two distinct vertices $x, y$ are adjacent if $xy = yx$. In this paper, among some properties of $Δ(G)$, we investigate $Δ(SD_{8n})$ the commuting graph of the semidihedral group $SD_{8n}$. In this connection, we discuss various graph invariants of $Δ(SD_{8n})$ including minimum degree, vertex connectivity, independence number, matching number and detour properties. We also obtain the Laplacian spectrum, metric dimension and resolving polynomial of $Δ(SD_{8n})$.

math.GR↗
arXiv2020

Equality of various graphs on finite semigroups

In this paper, we consider various graphs, namely: power graph, cyclic graph, enhanced power graph and commuting graph, on a finite semigroup $S$. For an arbitrary pair of these four graphs, we classify finite semigroups such that the graphs in this pair are equal. In this connection, for each of the graph we also give a necessary and sufficient condition on $S$ such that it is complete. The work of this paper generalize the corresponding results obtained for groups.

math.GR↗
arXiv2020

On the enhanced power graph of a group

The enhanced power graph $\mathcal{P}_e(G)$ of a group $G$ is a graph with vertex set $G$ and two vertices are adjacent if they belong to the same cyclic subgroup. In this paper, we consider the minimum degree, independence number and matching number of enhanced power graphs of finite groups. We first study these graph invariants for $\mathcal{P}_e(G)$ when $G$ is any finite group, and then determine them when $G$ is a finite abelian $p$-group, $U_{6n} = \langle a, b : a^{2n} = b^3 = e, ba =ab^{-1} \rangle$, the dihedral group $D_{2n}$, or the semidihedral group $SD_{8n}$. If $G$ is any of these groups, we prove that $\mathcal{P}_e(G)$ is perfect and then obtain its strong metric dimension. Additionally, we give an expression for the independence number of $\mathcal{P}_e(G)$ for any finite abelian group $G$. These results along with certain known equalities yield the edge connectivity, vertex covering number and edge covering number of enhanced power graphs of the respective groups as well.

math.GR↗
arXiv2019

Investigations of the heterometallic Ludwigite Ni${_2}$AlBO${_5}$

We present magnetic, thermodynamic, dielectric and structural investigations on the aluminoborate Ni${_2}$AlBO${_5}$, belonging to the ludwigite family. Room temperature structural refinement suggests that the system crystallizes in the orthorhombic $Pbam$ symmetry, in similarity with most members of this material class. Magnetic and thermodynamic measurements shows that the system undergoes a phase transition to an antiferromagnetic state at 38K, signatures of which are also seen in the lattice parameters and the dielectric constant. Short range magnetic correlations appear to persist to much higher temperatures - a regime in which the ac susceptibility exhibits a power law temperature dependence, in agreement with that expected for random exchange Heisenberg antiferromagnetic spin chains.

cond-mat.str-el↗
arXiv2019

Dielectric and Raman Spectroscopy in Hematite crystallites across the Morin Transition

We report complex dielectric and Raman spectroscopy measurements in four samples of $α$- Fe$_2$O$_3$, consisting of crystallites which are either hexagonal shaped plates or cuboids. All four samples exhibit the spin reorientation transition from a pure antiferromagnetic (AFM) to a weak-ferromagnetic (WFM) state at the Morin Transition temperature (T$_M$) intrinsic to $α$- Fe$_2$O$_3$. These samples, pressed and sintered in identical conditions for the dielectric measurements, reveal moderate but clear enhancement in the real part of the dielectric constant ($ε'$) in the WFM region. However, a relaxation-like behavior in the imaginary part of $ε''$ is observed only in nano plates or big cuboids. Further still, this relaxation patten is observed only in lower frequency region, lasting upto a few kHz and follows Arrhenius law within this limited range. The activation energy deduced from the fitting is suggestive of polaronic conduction. Temperature dependent Raman spectra reveal anomalies in all major phononic modes and also in 2Eu mode in the vicinity of the Morin transition. A peak like behavior in Raman Shifts, in conjuncture with anharmonic fitting reveals that the nature of spin phonon coupling is different in pure AFM and WFM regions and it is tied to the mild variations, as observed in the dielectric constant of$α$- Fe$_2$O$_3$ near the T$_M$.

cond-mat.str-el↗
arXiv2018

Absence of a multiglass state in some transition metal doped quantum paraelectrics

We critically investigate the purported existence of a multiglass state in the quantum paraelectrics SrTiO${_3}$ and KTaO${_3}$ doped with magnetic 3d transition metals. We observe that the transition metals have limited solubility in these hosts, and that traces of impurity magnetic oxides persist even in the most well processed specimens. Our dielectric measurements indicate that the polar nano-regions formed as a consequence of doping appear to lack co-operativity, and the associated relaxation process exhibits a thermally activated Arrhenius form. At lower temperatures, the dielectric susceptibility could be fit using the Barrett's formalism, indicating that the quantum-paraelectric nature of the host lattices are unaltered by the doping of magnetic transition metal oxides. All these doped quantum paraelectrics exhibit a crossover from the high temperature Curie-Weiss regime to one dominated by quantum fluctuations, as evidenced by a $T{^2}$ dependence of the temperature dependent dielectric susceptibility. The temperature dependence of the magnetic susceptibility indicate that magnetic signatures observed in some of the specimens could be solely ascribed to the presence of impurity oxides corresponding to the magnetic dopants used. Hence, the doped quantum paraelectrics appear to remain intrinsically paramagnetic down to the lowest measured temperatures, ruling out the presence of a multiglass state.

cond-mat.str-el↗
arXiv2018

Maximal subsemigroups of finite transformation and diagram monoids

We describe and count the maximal subsemigroups of many well-known monoids of transformations and monoids of partitions. More precisely, we find the maximal subsemigroups of the full spectrum of monoids of order- or orientation-preserving transformations and partial permutations considered by V. H. Fernandes and co-authors (12 monoids in total); the partition, Brauer, Jones, and Motzkin monoids; and certain further monoids. Although descriptions of the maximal subsemigroups of some of the aforementioned classes of monoids appear in the literature, we present a unified framework for determining these maximal subsemigroups. This approach is based on a specialised version of an algorithm for determining the maximal subsemigroups of any finite semigroup, developed by the third and fourth authors. This allows us to concisely present the descriptions of the maximal subsemigroups, and to more clearly see their common features.

math.GR↗
arXiv2018

Coupled magnetic and ferroelectric states in the distorted honeycomb system Fe$_{4}$Ta$_{2}$O$_{9}$

We report on the magnetic, thermodynamic, dielectric, and pyroelectric measurements on the hitherto unreported Fe${_4}$Ta${_2}$O${_9}$. This system is seen to exhibit a series of magnetic transitions, many of which are coupled to the emergence of ferroelectric order, making Fe${_4}$Ta${_2}$O${_9}$ the only genuine multiferroic in its material class. We suggest that the observed properties arise as a consequence of an effective reduction in the dimensionality of the magnetic lattice, with the magnetically active Fe${^{2+}}$ ions preferentially occupying a quasi 2D buckled honeycomb structure. The low temperature $H$-$T$ phase diagram of Fe${_4}$Ta${_2}$O${_9}$ reveals a rich variety of coupled magnetic and ferroelectric phases, in similarity with that observed in the distorted Kagome systems.

cond-mat.str-el↗
arXiv2017

Magnetic and dielectric investigations of $γ$ - Fe${_2}$WO${_6}$

The magnetic, thermodynamic and dielectric properties of the $γ$ - Fe${_2}$WO${_6}$ system is reported. Crystallizing in the centrosymmetric $Pbcn$ space group, this particular polymorph exhibits a number of different magnetic transitions, all of which are seen to exhibit a finite magneto-dielectric coupling. At the lowest measured temperatures, the magnetic ground state appears to be glass-like, as evidenced by the waiting time dependence of the magnetic relaxation. Also reflected in the frequency dependent dielectric measurements, these signatures possibly arise as a consequence of the oxygen non-stoichiometry, which promotes an inhomogeneous magnetic and electronic ground state.

cond-mat.str-el↗
arXiv2017

Magneto-Dielectric Behavior in $La_{0.53}Ca_{0.47}MnO_{3}$

We prospect magneto-dielectricity in $La_{0.53}Ca_{0.47}MnO_{3}$ across its paramagnetic (PMI) to ferromagnetic (FMM) isostructural transition at $T_{C} \sim 253K$, by magnetic ($(M)$), caloric ($(W)$), dielectric ($(ε')$), magneto-resistive (MR), and magneto-capacitance (MC) investigations. Skew-broadened first-order transition character is confirmed via heating/cooling hystereses in $(M)(T)$ and $(W)(T)$, with superheating temperature $T**$ almost next to $T_C$ and supercooling temperature $T*$ exhibiting kinetics. Above $T_C$, linearly-related MC and MR reflect purely magneto-resistance effect. Near $T_C$, the high-frequency MC(5T) much exceeds the magneto-losses, and is uncorrelated with dc MR(5T) in the FM-ordered state. The intrinsic magneto-dielectricity manifest below $T_C$ and above ~kHz is traced to an intra-granular Maxwell-Wagner-type effect at the interface-region of PMI-FMM phase-coexistence.

cond-mat.mtrl-sci↗
arXiv2017

Quantum Paraelectric Glass State in SrCu3Ti4O12

Magnetic and dielectric studies of SrCu3Ti4O12 carried out over 5-300K confirm antiferromagnetic (AFM) ordering of Cu-spins at TN =23K. Dielectric constant ε' measured across 1Hz-1MHz signifies quantum paraelectric character, Barrett-fittable almost down to TN. Competition of athermal fluctuations and the literature-reported magneto-phonon-softening near TN manifests a maiden quantum paraelectric glass (QPG) state. Emergent AFM-field tunes the otherwise quantum ordering (at absolute-zero) of the dipoles to finite-temperature kinetic glass transition; spectral dispersion of dielectric constant unambiguously manifested and characterized. Vogel-Fulcher glass-kinetics parameterization sets the almost relaxation-free QPG state in SrCu3Ti4O12 apart from an emergent scaling-class, to which typical ferroelectric relaxors belong.

cond-mat.mtrl-sci↗
arXiv2017

Nanosize effect: Enhanced compensation temperature and existence of magneto-dielectric coupling in SmFeO3

In transition metal oxides, quantum confinement arising from a large surface to volume ratio often gives rise to novel physico-chemical properties at nanoscale. Their size dependent properties have potential applications in diverse areas, including therapeutics, imaging, electronic devices, communication systems, sensors, and catalysis. We have analyzed structural, magnetic, dielectric, and thermal properties of weakly ferromagnetic SmFeO3 nanoparticles of sizes about 55 nm and 500 nm. The nano-size particles exhibit several distinct features that are neither observed in their larger-size variants nor reported previously for the single crystals. In particular, for the 55 nm particle, we observe six-fold enhancement of compensation temperature, an unusual rise in susceptibility in the temperature range 550 to 630 K due to spin pinning, and coupled antiferromagnetic-ferroelectric transition, directly observed in the dielectric constant.

cond-mat.mes-hall↗
arXiv2017

Improper multiferroicity and colossal dielectric constants in Bi$_{2}$CuO$_{4}$

The layered cuprate Bi$_{2}$CuO$_{4}$ is investigated using magnetic, dielectric and pyroelectric measurements. This system is observed to be an improper multiferroic, with a robust ferroelectric state being established near the magnetic transition. Magnetic and dielectric measurements indicate the presence of a region above the antiferromagnetic Neel temperature with concomitant polar and magnetic short range order. Bi$_{2}$CuO$_{4}$ is also seen to exhibit colossal dielectric constants at higher temperatures with clearly distinguishable grain and grain boundary contributions, both of which exhibit non-Debye relaxation.

cond-mat.str-el↗
arXiv2016

A reentrant superspin glass state and magnetization steps in the oxyborate Co2AlBO5

An oxyborate Co2AlBO5 belonging to the ludwigite family is investigated using structural, thermodynamic, dielectric and magnetic measurements. Magnetic measurements indicate that this system is seen to exhibit long range magnetic ordering at T{_N} = 42 K, signatures of which are also seen in the specific heat, dielectric susceptibility, and the lattice parameters. The absence of a structural phase transition down to the lowest measured temperatures, distinguishes it from the more extensively investigated Fe-based ludwigites. At low temperatures, the system is seen to stabilize in a reentrant superspin glass phase at T{_G} = 10.6 K from within the magnetically ordered state. This ground state is also characterized by magnetic field induced metamagnetic transitions, which at the lowest measured temperatures exhibit a number of sharp magnetization steps, reminiscent of that observed in the mixed valent manganites.

cond-mat.str-el↗
arXiv2016

Identification of a Griffiths singularity in a geometrically frustrated antiferromagnet

We report the observation of a Griffiths Phase in the geometrically frustrated antiferromagnet DyBaCo${_4}$O${_{7+δ}}$. Its onset is determined using measurements of the thermoremanent magnetization, which is shown to be superior to conventional in-field measurement protocols for the identification of the Griffiths Phase. Within this phase, the temporal relaxation of magnetization exhibits a functional form which is expected for Heisenberg systems, reflecting the nature of spin interactions in this class of materials. Interestingly, the effective Co${^{2+}}$/Co${^{3+}}$ ratio tailored by varying the oxygen non-stoichiometry $δ$ is only seen to influence the antiferromagnetic ordering temperature ($T{_N}$), leaving the Griffiths Temperature ($T{_G}$) invariant.

cond-mat.str-el↗