Approaching the quantum critical point in a highly-correlated all-in-all-out antiferromagnet

Continuous quantum phase transition involving all-in–all-out (AIAO) antiferromagnetic order in strongly spin-orbit-coupled 5d compounds could give rise to various exotic electronic phases and strongly-coupled quantum critical phenomena. Here we experimentally trace the AIAO spin order in Sm₂Ir₂O₇ using direct resonant x-ray magnetic diffraction techniques under high pressure. The magnetic order is suppressed at a critical pressure P_c=6.30GPa, while the lattice symmetry remains in the cubic Fd−3m space group across the quantum critical point. Comparing pressure tuning and the chemical series R₂Ir₂O₇ reveals that the approach to the AIAO quantum phase transition is characterized by contrasting evolutions of the pyrochlore lattice constant a and the trigonal distortion surrounding individual Ir moments, which affects the 5d bandwidth and the Ising anisotropy, respectively. We posit that the opposite effects of pressure and chemical tuning lead to spin fluctuations with different Ising and Heisenberg character in the quantum critical region. Finally, the observed low pressure scale of the AIAO quantum phase transition in Sm₂Ir₂O₇ identifies a circumscribed region of P-T space for investigating the putative magnetic Weyl semimetal state

Consistency test and weight generation for additive interval fuzzy preference relations

Some simple yet pragmatic methods of consistency test are developed to check whether an interval fuzzy preference relation is consistent. Based on the definition of additive consistent fuzzy preference relations proposed by Tanino (Fuzzy Sets Syst 12:117–131, 1984), a study is carried out to examine the correspondence between the element and weight vector of a fuzzy preference relation. Then, a revised approach is proposed to obtain priority weights from a fuzzy preference relation. A revised definition is put forward for additive consistent interval fuzzy preference relations. Subsequently, linear programming models are established to generate interval priority weights for additive interval fuzzy preference relations. A practical procedure is proposed to solve group decision problems with additive interval fuzzy preference relations. Theoretic analysis and numerical examples demonstrate that the proposed methods are more accurate than those in Xu and Chen (Eur J Oper Res 184:266–280, 2008b)

Distance-based consensus models for fuzzy and multiplicative 3 preference relations

This paper proposes a distance-based consensus model for fuzzy preference relations where the weights of fuzzy preference relations are automatically determined. Two indices, an individual to group consensus index (ICI) and a group consensus index (GCI), are introduced. An iterative consensus reaching algorithm is presented and the process terminates until both the ICI and GCI are controlled within predefined thresholds. The model and algorithm are then extended to handle multiplicative preference relations. Finally, two examples are illustrated and comparative analyses demonstrate the effectiveness of the proposed methods

Strongly-coupled quantum critical point in an all-in-all-out antiferromagnet

Dimensionality and symmetry play deterministic roles in the laws of Nature. They are important tools to characterize and understand quantum phase transitions, especially in the limit of strong correlations between spin, orbit, charge, and structural degrees of freedom. Using newly-developed, high-pressure resonant x-ray magnetic and charge diffraction techniques, we have discovered a quantum critical point in Cd2Os2O7 as the all-in-all-out (AIAO) antiferromagnetic order is continuously suppressed to zero temperature and, concomitantly, the cubic lattice structure continuously changes from space group Fd-3m to F-43m. Surrounded by three phases of different time reversal and spatial inversion symmetries, the quantum critical region anchors two phase lines of opposite curvature, with striking departures from a mean-field form at high pressure. As spin fluctuations, lattice breathing modes, and quasiparticle excitations interact in the quantum critical region, we argue that they present the necessary components for strongly-coupled quantum criticality in this three-dimensional compound

Incomplete interval fuzzy preference relations and their applications

This paper investigates incomplete interval fuzzy preference relations. A characterization, which is proposed by Herrera-Viedma et al. (2004), of the additive consistency property of the fuzzy preference relations is extended to a more general case. This property is further generalized to interval fuzzy preference relations (IFPRs) based on additive transitivity. Subsequently, we examine how to characterize IFPR. Using these new characterizations, we propose a method to construct an additive consistent IFPR from a set of n − 1 preference data and an estimation algorithm for acceptable incomplete IFPRs with more known elements. Numerical examples are provided to illustrate the effectiveness and practicality of the solution process

A chi-square method for priority derivation in group decision making with incomplete reciprocal preference relations

This paper proposes a chi-square method (CSM) to obtain a priority vector for group decision making (GDM) problems where decision-makers’ (DMs’) assessment on alternatives is furnished as incomplete reciprocal preference relations with missing values. Relevant theorems and an iterative algorithm about CSM are proposed. Saaty’s consistency ratio concept is adapted to judge whether an incomplete reciprocal preference relation provided by a DM is of acceptable consistency. If its consistency is unacceptable, an algorithm is proposed to repair it until its consistency ratio reaches a satisfactory threshold. The repairing algorithm aims to rectify an inconsistent incomplete reciprocal preference relation to one with acceptable consistency in addition to preserving the initial preference information as much as possible. Finally, four examples are examined to illustrate the applicability and validity of the proposed method, and comparative analyses are provided to show its advantages over existing approaches

Invited Article: High-pressure techniques for condensed matter physics at low temperature

Condensed matter experiments at high pressure accentuate the need for accurate pressure scales over a broad range of temperatures, as well as placing a premium on a homogeneous pressure environment. However, challenges remain in diamond anvil cell technology, including both the quality of various pressure transmitting media and the accuracy of secondary pressure scales at low temperature. We directly calibrate the ruby fluorescence R1 line shift with pressure at T=4.5 K using high-resolution x-ray powder diffraction measurements of the silver lattice constant and its known equation of state up to P=16 GPa. Our results reveal a ruby pressure scale at low temperatures that differs by 6% from the best available ruby scale at room T. We also use ruby fluorescence to characterize the pressure inhomogeneity and anisotropy in two representative and commonly used pressure media, helium and methanol:ethanol 4:1, under the same preparation conditions for pressures up to 20 GPa at T=5 K. Contrary to the accepted wisdom, both media show equal levels of pressure inhomogeneity measured over the same area, with a consistent Delta P/P per unit area of +/- 1.8 %/(10^(4) µm^(2)) from 0 to 20 GPa. The helium medium shows an essentially constant deviatoric stress of 0.021 +/- 0.011 GPa up to 16 GPa, while the methanol:ethanol mixture shows a similar level of anisotropy up to 10 GPa, above which the anisotropy increases. The quality of both pressure media is further examined under the more stringent requirements of single crystal x-ray diffraction at cryogenic temperature. For such experiments we conclude that the ratio of sample-to-pressure chamber volume is a critical parameter in maintaining sample quality at high pressure, and may affect the choice of pressure medium

Direct probe of Fermi surface evolution across a pressure-induced quantum phase transition

The nature of a material's Fermi surface is crucial to understanding its electronic, magnetic, optical, and thermal characteristics. Traditional measurements such as angle-resolved photoemission spectroscopy and de Haas–van Alphen quantum oscillations can be difficult to perform in the vicinity of a pressure-driven quantum phase transition, although the evolution of the Fermi surface may be tied to the emergence of exotic phenomena. We demonstrate here that magnetic x-ray diffraction in combination with Hall effect measurements in a diamond anvil cell can provide valuable insight into the Fermi surface evolution in spin- and charge-density-wave systems near quantum phase transitions. In particular, we track the gradual evolution of the Fermi surface in elemental chromium and delineate the critical pressure and absence of Fermi surface reconstruction at the spin-flip transition

Pressure tuning of competing magnetic interactions in intermetallic CeFe_2

We use high-pressure magnetic x-ray diffraction and numerical simulation to determine the low-temperature magnetic phase diagram of stoichiometric CeFe_2. Near 1.5 GPa we find a transition from ferromagnetism to antiferromagnetism, accompanied by a rhombohedral distortion of the cubic Laves crystal lattice. By comparing pressure and chemical substitution we find that the phase transition is controlled by a shift of magnetic frustration from the Ce-Ce to the Fe-Fe sublattice. Notably the dominant Ce-Fe magnetic interaction, which sets the temperature scale for the onset of long-range order, remains satisfied throughout the phase diagram but does not determine the magnetic ground state. Our results illustrate the complexity of a system with multiple competing magnetic energy scales and lead to a general model for magnetism in cubic Laves phase intermetallic compounds