Specific heat of EuxSr1−xO near the ferromagnetic phase transition

Ternary plumbides ATPb2 (A = Ca, Sr, Ba, Eu; T = Rh, Pd, Pt) with distorted, lonsdaleite-related substructures of tetrahedrally connected lead atoms

The plumbides CaTPb2 (T = Rh, Pd), EuTPb2 (T = Rh, Pd, Pt), SrTPb2 (T = Rh, Pd, Pt) and BaTPb2 (T = Pd, Pt) were obtained by direct reactions of the elements in sealed tantalum tubes in an induction furnace. The moisture sensitive polycrystalline samples were characterized by X-ray powder diffraction. They crystallize with the orthorhombic MgCuAl2-type structure, space group Cmcm. The structures of CaRhPb2 (a = 433.78(3), b = 1102.06(8), c = 798.43(6) pm, wR = 0.0285, 432 F2 values and 16 variables) and EuPdPb2 (a = 457.24(5), b = 1158.27(13), c = 775.73(8), wR = 0.0464, 464 F2 values and 16 variables) were refined from single crystal X-ray diffractometer data. The characteristic structural motif is the distorted tetrahedral substructure built up by the lead atoms with Pb–Pb distances of 326–327 pm in CaRhPb2 and of 315–345 pm in EuPdPb2. With increasing size of the alkaline earth (Eu) cation, the lead substructure becomes more anisotropic with a shift of the [TPb2] polyanions from three- to two-dimensional, leading to significantly increased moisture sensitivity. Temperature dependent magnetic susceptibility studies reveal Pauli paramagnetism for SrRhPb2, SrPtPb2, BaPdPb2 and BaPtPb2. EuRhPb2 and EuPdPb2 are Curie–Weiss paramagnets with stable divalent europium as is also evident from 151Eu Mössbauer spectra. EuRhPb2 is a ferromagnet with T C = 17.7(2) K, while EuPdPb2 orders antiferromagnetically at T N = 15.9 K. This is in agreement with the full magnetic hyperfine field splitting of the 151Eu Mössbauer spectra at T = 6 K.

Eu1 − xSrxAu4Cd2: a ferromagnetic solid solution with adjustable Curie temperature

Abstract

Samples of the solid solution Eu1–xSrxAu4Cd2 (YbAl4Mo2 type, space group I4/mmm) with x = 0.2, 0.4, 0.6, and 0.8 were synthesized from the elements by annealing in sealed tantalum ampoules. The structures of Eu0.66Sr0.34Au4.12Cd1.88 and Eu0.22Sr0.78Au4.10Cd1.90 were refined from X-ray single crystal diffractometer data. Besides the expected Eu/Sr mixing on the 2a sites the diffraction data revealed also a small degree of Cd/Au mixing on the 4d sites of the cadmium chains. Temperature dependent magnetic susceptibility data show divalent europium and ferromagnetic ground states for all samples and a linear decrease of the Curie temperature from 16.3 K for EuAu4Cd2 to 2.9 K for Eu0.2Sr0.8Au4Cd2. Magnetization isotherms characterize the Eu1 − xSrxAu4Cd2 samples as soft ferromagnets. The divalent nature of europium is underpinned by 151Eu Mössbauer spectra. The decreasing Curie temperature goes along with a decreasing magnetic hyperfine field at 6 K.

Graphic abstract

Antiferromagnetic ordering in the plumbide EuPdPb

The plumbide EuPdPb was synthesized in polycrystalline form by reaction of the elements in a sealed niobium ampoule in a muffle furnace. The structure was refined from single-crystal X-ray diffractometer data: TiNiSi type, Pnma, a=752.4(2), b=476.0(2), c=826.8(2) pm, wR2=0.0485, 704 F 2 values and 20 variables. The europium atoms are coordinated by two tilted and puckered Pd3Pb3 hexagons (280–289 pm Pd–Pb) with pronounced Eu–Pd bonding (312–339 pm). Temperature-dependent magnetic susceptibility measurements show Curie-Weiss behaviour and an experimental magnetic moment of 7.35(1) μB per Eu atom. EuPdPb orders antiferromagnetically at T N=13.8(5) K and shows a metamagnetic transition at a critical field of 15 kOe. 151Eu Mössbauer spectra confirm divalent europium (δ=–10.04(1) mm s−1) and show full magnetic hyperfine field splitting (B hf=21.1(1) T) at 6 K.

Entropic equation of state and scaling functions near the critical point in uncorrelated scale-free networks

We analyze the entropic equation of state for a many-particle interacting system in a scale-free network. The analysis is performed in terms of scaling functions, which are of fundamental interest in the theory of critical phenomena and have previously been theoretically and experimentally explored in the context of various magnetic, fluid, and superconducting systems in two and three dimensions. Here, we obtain general scaling functions for the entropy, the constant-field heat capacity, and the isothermal magnetocaloric coefficient near the critical point in uncorrelated scale-free networks, where the node-degree distribution exponent λ appears to be a global variable and plays a crucial role, similar to the dimensionality d for systems on lattices. This extends the principle of universality to systems on scale-free networks and allows quantification of the impact of fluctuations in the network structure on critical behavior.