T/B Scaling in β-YbAlB₄

Abstract

The scaling behavior over four decades of the ratio of temperature T to magnetic field B observed in the magnetization in β-YbAlB 4 is theoretically examined. By developing a theoretical framework that exhibits the quantum critical phenomena of Yb-valence fluctuations under a magnetic field, we show that the T/B-scaling behavior can appear near the quan- Quantum critical phenomena in itinerant electron systems that do not follow the conventional spin-fluctuation theory [1][2][3][4] have attracted attention in condensed matter physics. 5) The heavy-electron metal β-YbAlB 4 has recently attracted great interest since the unconventional quantum criticality, such as the magnetic susceptibility χ ∼ T −0.5 , the electronic specific-heat coefficient C e /T ∼ − log T , and approximately T -linear resistivity, has been observed at low temperatures at least below 3 K down to a few hundred mK. 6,7) Interestingly, from the magnetization data for T < ∼ 3 K and the magnetic field B < ∼ 2 T, in β-YbAlB 4 it has been discovered that the magnetic susceptibility χ shows the following T/B scaling behavior over four decades of T/B:where µ B and k B are the Bohr magneton and Boltzmann constant, respectively, and ϕ is the function ϕ(x) = Λ(Γ 2 + x 2 ) 1/4 with Λ and Γ being constants. 7) Namely, χ −1 /(µ B B) 1/2 is expressed as a single scaling function of the ratio T/B.This striking behavior of Eq. (1) calls for theoretical explanation, and it has so far been proposed that anisotropic hybridization between f and conduction electrons is the key origin

YbMgGaO4: A Triangular‐Lattice Quantum Spin Liquid Candidate

“…[115][116][117] Conversely, YbMgGaO 4 does not show any sharp magnetic transitions at any applied magnetic field up to a value where the spin-1/2 system is fully polarized, [60,79] only except that a weak constant anomaly is observed in the low-T susceptibility curve between 1.6 and 2.8 T. [60] The above points should indicate stronger quantum fluctuations in YbMgGaO 4 than those in NaYbO 2 . Therefore, the bond randomness caused by the sitemixing of nonmagnetic Mg 2+ and Ga 3+ may play a "positive" role in enhancing the quantum fluctuations of the spin system of YbMgGaO 4 , and thus in supporting the observed gapless QSL behavior, [50] despite the differences of the spin-orbit couplings.…”

“…[44] It also triggers extensive theoretical and numerical studies on trying to understand the observed QSL behavior, in the presence of the spatial anisotropy (J'/J < 1), [45] second-neighbor interaction, [46,47] multiple-spin [48] /ring [49] exchanges, and (or) bond randomness. [50] Similarly, the organic EtMe 3 Sb[Pd(dmit) 2 ] 2 also has a nearly regular-triangular lattice (J'/J ≈ 1) of S = 1/2 spins, with J = 220-250 K, and does not undergo any conventional freezing at low temperatures. [51,52] A linear temperature dependent behavior of the low-T heat capacity was also reported suggesting the possible gapless QSL GS.…”

Topological basis for understanding the behavior of the heavy-fermion metalβ−YbAlB4under application of magnetic field and pressure

“…Recent measurements on the heavy-fermion (HF) metal β − YbAlB 4 have been performed under the application of both a magnetic field B and hydrostatic pressure P , with results that have received considerable theoretical analysis [1][2][3][4][5][6][7][8][9][10] . Measurements of the magnetization M (B) at different temperatures T reveal that the magnetic susceptibility χ = M/B ∝ T −1/2 demonstrates non-Fermi liquid (NFL) behavior and diverges as T → 0, implying that the quasiparticle effective mass m * diverges as m…”

Origin of Quantum Criticality in Yb–Al–Au Approximant Crystal and Quasicrystal

“…8,9) On the other hand, a new theoretical framework for critical Yb-valence fluctuation under magnetic field has been developed recently. 10) The theory has succeeded in explaining novel scaling discovered in β-YbAlB 4 where the magnetic susceptibility χ is expressed as a single scaling function of the ratio of temperature to magnetic field T/B over four decades. 5) Surprisingly, recent measurement of magnetic susceptibility in the quasicrystal Yb 15 Al 34 Au 51 has revealed that the same T/B-scaling behavior appears over six decades of T/B.…”

“…3 [see the (i, ξ) = (1, 13) data]. Then, we apply the recently-developed mode-coupling theory for critical valence fluctuations under magnetic field 10) to the present system, which starts from the Hamiltonian…”