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We present the results of field-and temperature-dependent resistivity and magnetization M measurements which show that colossal magnetoresistance in semimetallic EuB 6 is not associated with its bulk Curie temperature T C ϭ12.6 K, determined by a scaling analysis of M (H,T), but with a second phase transition at T M ϭ15.5 K. We propose that metallization occurs at T M via the overlap of magnetic polarons. The separation of the charge delocalization and bulk magnetic ordering transitions implies electronic and magnetic phase separation.The discovery of colossal magnetoresistance ͑CMR͒ in rare-earth manganites and manganese pyrochlores has renewed interest in the properties of magnetic polarons. 1 As has often been noted, CMR was also observed in a very different class of rare-earth magnets ͓EuO, 2 EuB 6 , 3-5 Gd 1Ϫx Eu x Se ͑Ref. 6͔͒ almost 30 years ago. It is generally believed that magnetic polarons are present in all of these materials, and that the sensitivity of polaronic transport to field is responsible for CMR. Although EuB 6 has historically been grouped with charge-doped rare-earth chalcogenides and oxides, in which the polaronic carriers are extrinsic, it has recently been shown that this intriguing material is a rare example of a low carrier density semimetal which also orders ferromagnetically. 7-9 We present here a detailed study of the field-and temperature-dependent resistivity and magnetization M of EuB 6 which suggests the presence of magnetic polarons in this system, and demonstrates that bulk magnetic order and metallization occur at different temperatures. This is a phenomenon unique to EuB 6 , and we will argue that it implies electronic and magnetic phase separation.EuB 6 crystallizes in the simple cubic CaB 6 structure. The electronic structure is derived primarily from the hybridization of the boron p bands, filled by electrons donated by the Eu ions, which are found to be divalent by both photoemission 10 and Mössbauer 11 measurements. Electronic structure calculations 7 indicate that small dilations of the boron octohedra cause overlap of the conduction and valence bands at the X points, rendering EuB 6 semimetallic. Shubnikov-de Haas and de Haas-van Alphen measurements 8,9 as well as angle-resolved photoemission ͑ARPES͒ measurements 10 confirm that EuB 6 is a semimetal. Quantum oscillation studies found that the sample studied here has an intrinsic carrier density of 1.2ϫ10 20 cm Ϫ3 . 9 Neutron-diffraction measurements on EuB 6 ͑Ref. 12͒ find that the spontaneous moment first appears near ϳ16 K, increases slowly as the temperature is lowered, and then displays quasi-mean-field behavior below ϳ12-13 K. The saturation moment of 6.9Ϯ0.2 B , measured at 1.5 K, is somewhat reduced from the nominal Eu 2ϩ value of 7.94 B , but is in good agreement with the 7.02 B predicted by bandstructure calculations. 7 Signatures of a second phase transition at 15.5 K have been found in the resistivity, the lowfield magnetization, and the zero-field specific heat. 13,14 Currently, there is no explanation fo...

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Nanonetwork-structured materials can be found in nature and synthetic materials. A double gyroid (DG) with a pair of chiral networks but opposite chirality can be formed from the self-assembly of diblock copolymers. For triblock terpolymers, an alternating gyroid (GA) with two chiral networks from distinct end blocks can be formed; however, the network chirality could be positive or negative arbitrarily, giving an achiral phase. Here, by taking advantage of chirality transfer at different length scales, GA with controlled chirality can be achieved through the self-assembly of a chiral triblock terpolymer. With the homochiral evolution from monomer to multichain domain morphology through self-assembly, the triblock terpolymer composed of a chiral end block with a single-handed helical polymer chain gives the chiral network from the chiral end block having a particular handed network. Our real-space analyses reveal the preferred chiral sense of the network in the GA, leading to a chiral phase.

We study the influence of particle size asymmetry on structural evolution of randomly jammed binary sphere mixtures with varying large-sphere/small-sphere composition. Simulations of jammed packings are used to assess the transition from large-sphere dominant to small-sphere dominant mixtures. For weakly asymmetric particle sizes, packing properties evolve smoothly, but not monotonically, with increasing small sphere composition, f . Our simulations reveal that at high values of ratio α of large to small sphere radii, (α ≥ αc ≈ 5.75) evolution of structural properties such as packing density, fraction of jammed spheres and contact statistics with f exhibit features that suggest a sharp transition, either through discontinuities in structural measures or their derivatives. We argue that this behavior is related to the singular, composition dependence of close-packing fraction predicted in infinite aspect ratio mixtures α → ∞ by the Furnas model, but occurring for finite values range of α above a critical value, αc ≈ 5.75. The existence of a sharp transition from small-to large-f values for α ≥ αc can be attributed to the existence of a sub-jamming transition of small spheres in the interstices of jammed large spheres along the line of compositions f sub (α). We argue that the critical value of finite size asymmetry αc 5.75 is consistent with the geometric criterion for the transmission of small sphere contacts between neighboring tetrahedrally close packed interstices of large spheres, facilitating a cooperative sub-jamming transition of small spheres confined within the disjoint volumes.