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Register a new userElastic Softening in Quantum Critical Yb-Al-Au Approximant Crystal and Quasicrystal
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Shinji Watanabe
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The elastic property of quantum critical quasicrystal (QC) Yb$_{15}$Al$_{34}$Au$_{51}$ is analyzed theoretically on the basis of the approximant crystal (AC) Yb$_{14}$Al$_{35}$Au$_{51}$. By constructing the realistic effective model in the AC, we evaluate the 4f-5d Coulomb repulsion at Yb as $U_{fd}approx 1.46$ eV realizing the quantum critical point (QCP) of the Yb-valence transition. The RPA analysis of the QCP shows that softening in elastic constants occurs remarkably for bulk modulus and longitudinal mode at low temperatures. Possible relevance of these results to the QC as well as the pressure-tuned AC is discussed.
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Quantum criticality has been considered to be specific to crystalline materials such as heavy fermions. Very recently, however, the Tsai-type quasicrystal Au51Al34Yb15 has been reported to show unusual quantum critical behavior. To obtain a deeper understanding of this new material, we have searched for other Tsai-type cluster materials. Here, we report that the metal alloys Au44Ga41Yb15 and Ag47Ga38Yb15 are members of the 1/1 approximant to the Tsai-type quasicrystal and that both possess no localized magnetic moment. We suggest that the Au-Al-Yb system is located near the border of the divalent and trivalent states of the Yb ion; we also discuss a possible origin of the disappearance of magnetism, associated with the valence change, by the substitution of the constituent elements.
We report on ac magnetic susceptibility measurements under pressure of the Au-Al-Yb alloy, a crystalline approximant to the icosahedral quasicrystal that shows unconventional quantum criticality. In describing the susceptibility as $chi(T)^{-1} - chi(0)^{-1} propto T^{gamma}$, we find that $chi(0)^{-1}$ decreases with increasing pressure and vanishes to zero at the critical pressure $P_{rm c} simeq 2$ GPa, with $gamma~ (simeq 0.5)$ unchanged. We suggest that this quantum criticality emerges owing to critical valence fluctuations. Above $P_{rm c}$, the approximant undergoes a magnetic transition at $T simeq 100$ mK. These results are contrasted with the fact that, in the quasicrystal, the quantum criticality is robust against the application of pressure. The applicability of the so-called $T/H$ scaling to the approximant is also discussed.
The mechanism of not diverging Gr{u}neisen parameter in the quantum critical heavy-fermion quasicrystal (QC) Yb$_{15}$Al$_{34}$Au$_{51}$ is analyzed. We construct the formalism for calculating the specific heat $C_V(T)$, the thermal-expansion coefficient $alpha(T)$, and the Gr{u}neisen parameter $Gamma(T)$ near the quantum critical point of the Yb valence transition. By applying the framework to the QC, we calculate $C_V(T)$, $alpha(T)$, and $Gamma(T)$, which explains the measurements. Not diverging $Gamma(T)$ is attributed to the robustness of the quantum criticality in the QC under pressure. The difference in $Gamma(T)$ at the lowest temperature between the QC and approximant crystal is shown to reflect the difference in the volume derivative of characteristic energy scales of the critical Yb-valence fluctuation and the Kondo temperature. Possible implications of our theory to future experiments are also discussed.
Quasicrystals are metallic alloys that possess long-range, aperiodic structures with diffraction symmetries forbidden to conventional crystals. Since the discovery of quasicrystals by Schechtman et al. at 1984 (ref. 1), there has been considerable progress in resolving their geometric structure. For example, it is well known that the golden ratio of mathematics and art occurs over and over again in their crystal structure. However, the characteristic properties of the electronic states - whether they are extended as in periodic crystals or localized as in amorphous materials - are still unresolved. Here we report the first observation of quantum (T = 0) critical phenomena of the Au-Al-Yb quasicrystal - the magnetic susceptibility and the electronic specific heat coefficient arising from strongly correlated 4f electrons of the Yb atoms diverge as T -> 0. Furthermore, we observe that this quantum critical phenomenon is robust against hydrostatic pressure. By contrast, there is no such divergence in a crystalline approximant, a phase whose composition is close to that of the quasicrystal and whose unit cell has atomic decorations (that is, icosahedral clusters of atoms) that look like the quasicrystal. These results clearly indicate that the quantum criticality is associated with the unique electronic state of the quasicrystal, that is, a spatially confined critical state. Finally we discuss the possibility that there is a general law underlying the conventional crystals and the quasicrystals.
We report the synthesis of a single-phase sample of the superconducting crystalline approximant Au64.0Ge22.0Yb14.0 and present a structure model refined by Rietveld analysis for X-ray diffraction data.
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