Ultrasound attenuation and aP−B−Tphase diagram of superfluidH3ein 98%

Abstract

Longitudinal sound attenuation measurements in superfluid 3 He in 98% aerogel were conducted at pressures between 14 and 33 bar and in magnetic fields up to 0.444 T. The temperature dependence of the ultrasound attenuation in the A-like phase was determined for the entire superfluid region by exploiting the field-induced metastable A-like phase at the highest field. In lower fields, the A-B transition in aerogel was identified by a smooth jump in attenuation on both cooling and warming. Based on the transitions observed on warming, a phase diagram as a function of pressure ͑P͒, temperature ͑T͒, and magnetic field ͑B͒ is constructed. We find that the A-B phase boundary in aerogel recedes in a drastically different manner than in bulk in response to an increasing magnetic field. The implications of the observed phase diagram are discussed.

Optical conductivity of iron-based superconductors

“…For instance, the authors of Ref. 130 have assigned the smaller and the larger gaplike features in EuFe 2 As 2 , similar to those discussed above, to two different sets of opti-cal transitions: related to transitions within the spin-minority bands formed by Fe ions with the same spin and, therefore, sensitive to the long-range magnetic order and between the spin-majority and the spin-minority bands formed by Fe sites with opposite spins, respectively. The latter is mostly defined by the exchange splitting of the local magnetic moment due to Hund's coupling and thus less sensitive to the long-range order.…”

Ultrasonic interferometer for first-sound measurements of confined liquidHe4

“…The leading techniques for exploring acoustic properties of quantum liquids ( 3 He and 4 He) include measurements of the acoustic impedance [38][39][40] and propagation of ultrasonic pulses 41 . Neither of these are well suited to our measurement setup, because of the disruptive effects of the glass microfluidic cavity.…”

Frequency-dependent ultrasound attenuation in superfluidH3ein aerogel

“…For the case of 3 He, the nanometer scale aerogel structure presents a dilute concentration of elastic scattering centers in the system and the effects of impurities are unmistakably demonstrated in the low-temperature phase diagram of 3 He in 98% aerogel 3 as manifested by the substantial suppression of superfluid transition from the pure liquid, 1,2 the appearance of the disorder-driven quantum phase transition, 4 and the markedly different A-B transition. 5 In addition to the Fermi wavelength, f Ϸ 0.3 nm, and the bulk coherence length, o = បv f / 2T c Ӎ 20-80 nm in the pressure range of 34-0 bar ͑v f ϵ Fermi velocity and T c ϵ bulk superfluid transition temperature͒, aerogel introduces a few other important length scales in the system. More specifically, the size of the aerogel strand, ␦ a Ӎ 3 -5 nm, the porosity-dependent structural correlation length, a ͑Ӎ40 nm for 98% porosity͒, and the geometric mean free path, ᐉ a ͑Ӎ130 nm for 98% porosity͒ are important parameters.…”

“…Our experimental scheme is described in detail elsewhere. 5 With the 9.5 MHz transducers used in our earlier experiment, 11 we were able to resolve the multiple echoes in the received signal from which the absolute attenuation was extracted. However, long ringing in the transducers used in this work prevented us from resolving the echoes.…”

“…where d is the path length and A͑T͒ is the acoustic amplitude at temperature T. 5 The relative attenuation measured on warming at 3.69, 6.22, and 11.30 MHz for the sample pressure of 33 bar is displayed in Fig. 1͑a͒.…”