Searcharxiv⌕ Search

arXiv subjects

N. Narayanan

Publications and source records attributed to N. Narayanan.

10 recordsLinked to original sources
arXiv2023

Magnetic order in the two-dimensional metal-organic framework manganese pyrazinecarboxylate with Mn-Mn dimers

The magnetic properties of [Mn(pyrazinecarboxylate)2]n (Mn-pyrazine), empirical formula C10H6MnN4O4, are investigated through susceptibility, heat capacity and neutron scattering measurements. The structure of Mn-pyrazine consists of Mn-Mn dimers linked on a distorted 2D hexagonal structure. The weak out of plane interactions create a quasi-2D magnetic material within the larger three dimensional metal organic framework (MOF) structure. We show that this material undergoes a two stage magnetic transition, related to the low dimensionality of the Mn lattice. First at 5 K, which is assigned to the initial development of short range order in the 2D layers. This is followed by long range order at 3.3 K. Applied field measurements reveal the potential to induce magnetic transitions in moderately small fields of 2 T. Neutron powder diffraction enabled the determination of a unique magnetic space group P21'/c (#14.77) at 1.5 K. This magnetic structure consists of antiferromagnetically coupled Mn-Mn dimers with spins principally along the out of plane a-axis.

cond-mat.str-el↗
arXiv2022

On distinguishing digraphs by its quasisymmetric B-polynomial

The $B$-polynomial defined by J. Awan and O. Bernardi is a generalization of Tutte Polynomial to digraphs. In this paper, we solve an open question raised by J. Awan and O. Bernardi regarding the expansion of $B$-polynomial in elementary symmetric polynomials. We show that the quasisymmetric generalization of the $B$-polynomial distinguishes a class of oriented proper caterpillars and the class of oriented paths. We present a recurrence relation for the quasisymmetric $B$-polynomial involving the deletion of a source or a sink. As a consequence, we prove that a class of digraph $\mathcal{D}$ is distinguishable if and only if the class $\mathcal{D}^{\vee}$ obtained by taking directed join of $K_1$ with each digraph in $\mathcal{D}$ is distinguishable, which concludes that the digraph analogue of Stanley's Tree conjecture holds for a large class of acyclic digraphs. We further study the symmetric properties of the quasisymmetric $B$-polynomial and its relation with certain digraphs.

math.CO↗
arXiv2021

Extending some results on the second neighborhood conjecture

A vertex in a directed graph is said to have a large second neighborhood if it has at least as many second out-neighbors as out-neighbors. The Second Neighborhood Conjecture, first stated by Seymour, asserts that there is a vertex having a large second neighborhood in every oriented graph (a directed graph without loops or digons). We prove that oriented graphs whose missing edges can be partitioned into a (possibly empty) matching and a (possibly empty) star satisfy this conjecture. This generalizes a result of Fidler and Yuster. An implication of our result is that every oriented graph without a sink and whose missing edges form a (possibly empty) matching has at least two vertices with large second neighborhoods. This is a strengthening of a theorem of Havet and Thomasse, who showed that the same holds for tournaments without a sink. Moreover, we also show that the conjecture is true for oriented graphs whose vertex set can be partitioned into an independent set and a 2-degenerate graph.

cs.DM↗
arXiv2021

Reduced crystal symmetry as origin of the ferroelectric polarization within the incommensurate magnetic phase of TbMn2O5

The precise crystal symmetry and hence the emergence of the electric polarization still remains an open question in the multiferroic materials $R$Mn$_2$O$_5$ ($R$ = rare-earth, Bi, Y). While previous diffraction studies have indicated that $R$Mn$_2$O$_5$ possesses the centro-symmetric space group P$bam$, an atomic displacement allowing for the electric polarization would require a non-centrosymmetric crystal symmetry. Our single crystal neutron diffraction experiments on TbMn$_2$O$_5$ provide direct evidence of a reduced crystallographic symmetry already above the magnetic and ferroelectric phase transitions and a change in magnetic order upon entering the ferroelectric phase. This is indicated through the presence of additional nuclear Bragg reflections that are otherwise forbidden for the space group P$bam$ but are in good agreement with the polar space group P$12_11$. It implies that the exchange-striction, which arises from a symmetric $S_i \cdot S_j$ spin coupling, is the dominating mechanism for the generation of the electric polarization in the commensurate magnetic phase of TbMn$_2$O$_5$. Furthermore, the commensurate magnetic reflections are in accordance with a quartile step spin-spiral along the $c$-axis. Therefore, the antisymmetric $S_i \times S_j$ exchange via the inverse Dzyaloshinskii-Moriya interaction contributes as well and becomes the leading term in the low temperature incommensurate spin-spiral magnetic phase. These new findings provide important information for the understanding of the complex interplay between the magnetic and the structural order throughout the $R$Mn$_2$O$_5$ series of type-II multiferroics.

cond-mat.str-el↗
arXiv2018

Regularity of Binomial Edge Ideals of Certain Block Graphs

We obtain an improved lower bound for the regularity of the binomial edge ideals of trees. We prove an upper bound for the regularity of the binomial edge ideals of certain subclass of block-graphs. As a consequence we obtain sharp upper and lower bounds for the regularity of binomial edge ideals of a class of trees called lobsters. We also obtain precise expressions for the regularities of binomial edge ideals of certain classes of trees and block graphs.

math.AC↗
arXiv2016

Tropical Dominating Sets in Vertex-Coloured Graphs

Given a vertex-coloured graph, a dominating set is said to be tropical if every colour of the graph appears at least once in the set. Here, we study minimum tropical dominating sets from structural and algorithmic points of view. First, we prove that the tropical dominating set problem is NP-complete even when restricted to a simple path. Then, we establish upper bounds related to various parameters of the graph such as minimum degree and number of edges. We also give upper bounds for random graphs. Last, we give approximability and inapproximability results for general and restricted classes of graphs, and establish a FPT algorithm for interval graphs.

cs.DM↗
arXiv2015

Partitioning a graph into highly connected subgraphs

Given $k\ge 1$, a $k$-proper partition of a graph $G$ is a partition ${\mathcal P}$ of $V(G)$ such that each part $P$ of ${\mathcal P}$ induces a $k$-connected subgraph of $G$. We prove that if $G$ is a graph of order $n$ such that $δ(G)\ge \sqrt{n}$, then $G$ has a $2$-proper partition with at most $n/δ(G)$ parts. The bounds on the number of parts and the minimum degree are both best possible. We then prove that If $G$ is a graph of order $n$ with minimum degree $δ(G)\ge\sqrt{c(k-1)n}$, where $c=\frac{2123}{180}$, then $G$ has a $k$-proper partition into at most $\frac{cn}{δ(G)}$ parts. This improves a result of Ferrara, Magnant and Wenger [Conditions for Families of Disjoint $k$-connected Subgraphs in a Graph, Discrete Math. 313 (2013), 760--764] and both the degree condition and the number of parts are best possible up to the constant $c$.

math.CO↗
arXiv2012

Magnetism and spin-orbit coupling in Ir-based double perovskites La$_(2-x$Sr$_x$CoIrO$_6$

We have studied Ir spin and orbital magnetic moments in the double perovskites La$_{2-x}$Sr$_x$CoIrO$_6$ by x-ray magnetic circular dichroism. In La$_2$CoIrO$_6$, Ir$^{4+}$ couples antiferromagnetically to the weak ferromagnetic moment of the canted Co$^{2+}$ sublattice and shows an unusually large negative total magnetic moment (-0.38\,$μ_{\text B}$/f.u.) combined with strong spin-orbit interaction. In contrast, in Sr$_2$CoIrO$_6$, Ir$^{5+}$ has a paramagnetic moment with almost no orbital contribution. A simple kinetic-energy-driven mechanism including spin-orbit coupling explains why Ir is susceptible to the induction of substantial magnetic moments in the double perovskite structure.

cond-mat.str-el↗
arXiv2009

Magnetism in Re-based ferrimagnetic double perovskites

We have investigated spin and orbital magnetic moments of the Re 5d ion in the double perovskites A2FeReO6 (A = Ba, Sr, Ca) by X-ray magnetic circular dichroism (XMCD) at the Re L(2,3) edges. In these ferrimagnetic compounds an unusually large negative spin and positive orbital magnetic moment at the Re atoms was detected. The presence of a finite spin magnetic moment in a 'non-magnetic' double perovskite as observed in the double perovskite Sr2ScReO6 proves that Re has also a small, but finite intrinsic magnetic moment. We further show for the examples of Ba and Ca that the usually neglected alkaline earth ions undoubtedly also contribute to the magnetism in the ferrimagnetic double perovskites.

cond-mat.mtrl-sci↗