A multiobjective optimization model for optimal supplier selection in multiple sourcing environment

Supplier selection is an important concern of a firm’s competitiveness, more so in the context of the imperative of supply-chain management. In this paper, we use an approach to a multiobjective supplier selection problem in which the emphasis is on building supplier portfolios. The supplier evaluation and order allocation is based upon the criteria of expected unit price, expected score of quality and expected score of delivery. A fuzzy approach is proposed that relies on nonlinear S-shape membership functions to generate different efficient supplier portfolios. Numerical experiments conducted on a data set of a multinational company are provided to demonstrate the applicability and efficiency of the proposed approach to real-world applications of supplier selectio

Raman Signatures of Strong Kitaev Exchange Correlations in (Na1−x_{1-x}Lix_x)2_2IrO3_3 : Experiments and Theory

Inelastic light scattering studies on single crystals of (Na$_{1-x}$Li$_x$)$_2$IrO$_3$ ($x = 0, 0.05$ and $0.15$) show a polarization independent broad band at $\sim$~2750 cm$^{-1}$ with a large band-width $\sim 1800$~cm$^{-1}$. For Na$_2$IrO$_3$ the broad band is seen for temperatures $\leq 200$~K and persists inside the magnetically ordered state. For Li doped samples, the intensity of this mode increases, shifts to lower wave-numbers and persists to higher temperatures. Such a mode has recently been predicted (Knolle et.al.) as a signature of the Kitaev spin liquid. We assign the observation of the broad band to be a signature of strong Kitaev-exchange correlations. The fact that the broad band persists even inside the magnetically ordered state suggests that dynamically fluctuating moments survive even below $T_{N}$. This is further supported by our mean field calculations. The Raman response calculated in mean field theory shows that the broad band predicted for the spin liquid state survives in the magnetically ordered state near the zigzag-spin liquid phase boundary. A comparison with the theoretical model gives an estimate of the Kitaev exchange interaction parameter to be $J_K\approx 57$~meV.Comment: 14pages 4 figure

Magnetic-field tuning of the spin dynamics in the magnetic topological insulators (MnBi₂Te₄)(Bi₂Te₃₎<i>n</i>

We report a high-frequency/high-magnetic field electron spin resonance (HF-ESR) spectroscopy study in the sub-THz frequency domain of the two representatives of the family of magnetic topological insulators (MnBi2Te4)(Bi2Te3)n with n = 0 and 1. The HF-ESR measurements in the magnetically ordered state at a low temperature of T=4K combined with the calculations of the resonance modes showed that the spin dynamics in MnBi4Te7 is typical for an anisotropic easy-axis type ferromagnet whereas MnBi2Te4 demonstrates excitations of an anisotropic easy-axis type antiferromagnet. However, by applying the field stronger than a threshold value ∼6T, we observed in MnBi2Te4 a crossover from the antiferromagnetic (AFM) resonance modes to the ferromagnetic (FM) modes, whose properties are very similar to the FM response of MnBi4Te7. We attribute this remarkably unusual effect unexpected for a canonical easy-axis antiferromagnet, which, additionally, can be accurately reproduced by numerical calculations of the excitation modes, to the closeness of the strength of the AFM exchange and magnetic anisotropy energies which appears to be a very specific feature of this compound. Our experimental data evidences that the spin dynamics of the magnetic building blocks of these compounds, the Mn-based septuple layers (SLs), is inherently ferromagnetic, featuring persisting short-range FM correlations far above the magnetic ordering temperature as soon as the SLs get decoupled either by introducing a nonmagnetic quintuple interlayer, as in MnBi4Te7, or by applying a moderate magnetic field, as in MnBi2Te4, which may have an effect on the surface topological band structure of these compounds.</p

Spin-glass state and reversed magnetic anisotropy induced by Cr doping in the Kitaev magnet α-RuCl3

Magnetic properties of the substitution series Ru1-xCrxCl3 were investigated to determine the evolution from the anisotropic Kitaev magnet α-RuCl3 with Jeff=1/2 magnetic Ru3+ ions to the isotropic Heisenberg magnet CrCl3 with S=3/2 magnetic Cr3+ ions. Magnetization measurements on single crystals revealed a reversal of the magnetic anisotropy under doping, which we argue to arise from the competition between anisotropic Kitaev and off-diagonal interactions on the Ru-Ru links and approximately isotropic Cr-Ru and isotropic Cr-Cr interactions. In addition, combined magnetization, ac susceptibility, and specific-heat measurements clearly show the destabilization of the long-range magnetic order of α-RuCl3 in favor of a spin-glass state of Ru1-xCrxCl3 for a low doping of x≤0.1. The corresponding freezing temperature as a function of Cr content shows a broad maximum around x ≤ 0.45

Strongly anisotropic spin dynamics in magnetic topological insulators

The recent discovery of magnetic topological insulators has opened new avenues to explore exotic states of matter that can emerge from the interplay between topological electronic states and magnetic degrees of freedom, be it ordered or strongly fluctuating. Motivated by the effects that the dynamics of the magnetic moments can have on the topological surface states, we investigate the magnetic fluctuations across the (MnBi$_{\text{2}}$Te$_{\text{4}}$)(Bi$_{\text{2}}$Te$_{\text{3}}$)$_{\text{n}}$ family. Our paramagnetic electron spin resonance experiments reveal contrasting Mn spin dynamics in different compounds, which manifests in a strongly anisotropic Mn spin relaxation in MnBi$_{\text{2}}$Te$_{\text{4}}$ while being almost isotropic in MnBi$_{\text{4}}$Te$_{\text{7}}$. Our density-functional calculations explain these striking observations in terms of the sensitivity of the local electronic structure to the Mn spin-orientation, and indicate that the anisotropy of the magnetic fluctuations can be controlled by the carrier density, which may directly affect the electronic topological surface states

Chemical tuning between triangular and honeycomb structures in a 5d spin-orbit Mott insulator

We report structural studies of the spin-orbit Mott insulator family K x Ir y O 2 , with triangular layers of edge-sharing IrO 6 octahedra bonded by potassium ions. The potassium content acts as a chemical tuning parameter to control the amount of charge in the Ir-O layers. Unlike the isostructural families with Ir replaced by Co or Rh ( y = 1 ), which are metallic over a range of potassium compositions x , we instead find insulating behavior with charge neutrality achieved via iridium vacancies, which order in a honeycomb supercell above a critical composition x c . By performing density functional theory calculations we attribute the observed behavior to a subtle interplay of crystal-field environment, local electronic correlations, and strong spin-orbit interaction at the Ir 4 + sites, making this structural family a candidate to display Kitaev magnetism in the experimentally unexplored regime that interpolates between triangular and honeycomb structures