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تسجيل مستخدم جديدUltrasound Response in Quantum Critical $beta$-YbAlB$_4$ and $alpha$-YbAl$_{0.986}$Fe$_{0.014}$B$_4$
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Shinji Watanabe
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We analyze the key origin of quantum valence criticality in the heavy electron metal $beta$-YbAlB$_4$ evidenced in the sister compound $alpha$-YbAl$_{0.986}$Fe$_{0.014}$B$_4$. By constructing a realistic canonical model for $beta$-YbAlB$_4$, we evaluate Coulomb repulsion between the 4f and 5d electrons at Yb $U_{rm fd}approx 6.2$ eV realizing the quantum critical point (QCP) of the Yb-valence transition. To reveal the Yb 5d contribution to the quantum critical state, we propose ultrasound measurement. We find that softening of elastic constants of not only the bulk modulus but also the shear moduli is caused by electric quadrupole fluctuations enhanced by critical 4f and 5d charge fluctuations for low temperatures at the valence QCP. Possible relevance of these results to $beta$-YbAlB$_4$ and also $alpha$-YbAl$_{1-x}$Fe$_x$B$_4$ is discussed.
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Density functional theory methods are applied to investigate the properties of the new superconductor $beta$-YbAlB$_4$ and its polymorph $alpha$-YbAlB$_4$. We utilize the generalized gradient approximation + Hubbard U (GGA+U) approach with spin-orbit
(SO) coupling to approximate the effects of the strong correlations due to the open $4f$ shell of Yb. We examine closely the differences in crystal bonding and symmetry of $beta$-YbAlB$_4$ and $alpha$-YbAlB$_4$. The in-plane bonding structure amongst the dominant itinerant electrons in the boron sheets is shown to differ significantly. Our calculations indicate that, in both polymorphs, the localized 4$f$ electrons hybridize strongly with the conduction sea when compared to the related materials YbRh$_{2}$Si$_{2}$ and YbB$_{2}$. Comparing $beta$-YbAlB$_4$ to the electronic structure of related crystal structures indicates a key role of the 7-member boron coordination of the Yb ion in $beta$-YbAlB$_4$ in producing its enhanced Kondo scale and superconductivity. The Kondo scale is shown to depend strongly on the angle between the B neighbors and the Yb ion, relative to the $x-y$ plane, which relates some of the physical behavior to structural characteristics.
$beta$-YbAlB$_4$ is the first Yb-based heavy fermion superconductor with $T_{rm c} = 80$ mK. We measured low temperature magnetization of high-purity single crystals down to $T=$ 25 mK. The measurements have revealed a considerable amount of volume f
ractions of the superconductivity and the upper critical field $B_{c2}$ curve under field along the c axis, consistent with the previous results. In the normal state, the previously observed divergent behavior in the temperature dependence of the magnetization has been confirmed using higher quality samples and under a low field of 22 mT. In addition, the measurements have revealed a power law behavior, namely, $dM/dTpropto T^{3/2}$, which has a slightly higher exponent than the previous results.
We report an angle-resolved photoemission (ARPES) study of $beta$-YbAlB$_4$, which is known to harbor unconventional quantum criticality (QC) without any tuning. We directly observe a quasiparticle peak (QP), emerging from hybridization, characterize
d by a binding energy and an onset of coherence both at about 4 meV. This value conforms with a previously observed reduced Kondo scale at about 40 K. Consistency with an earlier study of carriers in $beta$-YbAlB$_4$ via the Hall effect strongly suggests that this QP is responsible for the QC in $beta$-YbAlB$_4$. A comparison with the sister polymorph $alpha$-YbAlB$_4$, which is not quantum critical at ambient pressure, further supports this result. Indeed, within the limitation of our instrumental resolution, our ARPES measurements do not show tangible sign of hybridization in this locally isomorphic system, while the conduction band we observe is essentially the same as in $beta$-YbAlB$_4$. We therefore claim that we identified by ARPES the carriers responsible for the QC in $beta$-YbAlB$_4$. The observed dispersion and the underlying hybridization of this QP are discussed in the context of existing theoretical models.
$alpha$-YbAlB$_4$ is the locally isostructural polymorph of $beta$-YbAlB$_4$, the first example of an Yb-based heavy fermion superconductor which exhibits pronounced non-Fermi-liquid behavior above $T_{rm c}$. Interestingly, both $alpha$-YbAlB$_4$ an
d $beta$-YbAlB$_4$ have strongly intermediate valence. Our single crystal study of the specific heat, magnetization and resistivity has confirmed the Fermi liquid ground state of $alpha$-YbAlB$_4$ ~in contrast with the quantum criticality observed in $beta$-YbAlB$_4$. Both systems exhibit Kondo lattice behavior with the characteristic temperature scale $T^* sim$ 8 K in addition to a valence fluctuation scale $sim 200$ K. Below $T^*$, $alpha$-YbAlB$_4$ a heavy Fermi liquid state with an electronic specific heat coefficient $gammasim$ 130 mJ/mol K$^2$ and a large Wilson ratio more than 7, which indicates ferromagnetic correlation between Yb moments. A large anisotropy in the resistivity suggests that the hybridization between 4$f$ and conduction electrons is much stronger in the $ab$-plane than along the c-axis. The strongly anisotropic hybridization as well as the large Wilson ratio is the key to understand the unusual Kondo lattice behavior and heavy fermion formation in mixed valent compounds.
Measurements of the electric resistivity $rho(T)$ under pressure up to 8 GPa were performed on high-quality single-crystals of the Yb-based heavy fermion system $beta$-YbAlB$_4$ in the temperature range $2<T<$ 300 K. In the resistivity data, we obser
ved pressure-induced magnetic ordering above the critical pressure $P_{rm c} sim$ 2 GPa. Clear difference in the phase diagram under pressure using two types of pressure mediums indicates that the transition temperature may be further enhanced under application of uniaxial pressure. With pressure, this phase transition temperature $T_{rm M}$ is enhanced reaching 32 K at 8 GPa, which is the highest transition temperature so far recorded for the Yb-based heavy fermion compounds. The power-law exponent $alpha$ in $rho=rho_0+ AT^{alpha}$ below $T_{rm M}$ gradually changes from 3/2 to 5/2 with increasing pressure from 2 to 8 GPa. In contrast, the resistivity exhibits a $T$-linear behavior in the temperature range 2 $le T le$ 20 K and is insensitive to pressure below $P_{rm c}$. In this pressure regime, the magnetization is also nearly independent of pressure and shows no anomaly above 2 K. Our results indicate that a quantum critical point for $beta$-YbAlB$_4$ is also located near $P_{rm c}$ in addition to the strange metal region near the ambient pressure.
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