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The intermediate-valent polymorphs $alpha$- and $beta$-YbAlB$_4$ exhibit quantum criticality and other novel properties not usually associated with intermediate valence. Iron doping induces quantum criticality in $alpha$-YbAlB$_4$ and magnetic order in both compounds. We report results of muon spin relaxation ($mu$SR) experiments in the intermediate-valent alloys $alpha$-YbAl$_{1-x}$Fe$_x$B$_4$, $x = 0.014$ and 0.25. For $x = 0.014$ we find no evidence for magnetic order down to 25 mK@. The dynamic muon spin relaxation rate $lambda_d$ exhibits a power-law temperature dependence $lambda_d propto T^{-a}$, $a = 0.40(4)$, in the temperature range 100 mK--2 K, in disagreement with predictions by theories of antiferromagnetic (AFM) or valence quantum critical behavior. For $x = 0.25$, where AFM order develops in the temperature range 7.5--10 K, where we find coexistence of meso- or macroscopically segregated paramagnetic and AFM phases, with considerable disorder in the latter down to 2 K.
Fermi liquid theory, the standard theory of metals, has been challenged by a number of observations of anomalous metallic behavior found in the vicinity of a quantum phase transition. The breakdown of the Fermi liquid is accomplished by fine-tuning t
We measured the transverse magnetoresistivity of the mixed valence compound $alpha$-YbAlB$_4$. Two configurations were used where current was applied along [110] direction for both and magnetic field was applied along [-110] and $c$-axis. We found th
In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely certain defor
LaCrGe$_3$ has attracted attention as a paradigm example of the avoidance of ferromagnetic (FM) quantum criticality in an itinerant magnet. By combining thermodynamic, transport, x-ray and neutron scattering as well as $mu$SR measurements, we refined
Experimental bulk susceptibility X(T) and magnetization M(H,T) of the S=1-Haldane chain system doped with nonmagnetic impurities, Y2BaNi1-xZnxO5 (x=0.04,0.06,0.08), are analyzed. A numerical calculation for the low-energy spectrum of non-interacting