BaFe12O19 is a popular M-type hexaferrite with a Néel temperature of 720 K and is of enormous commercial value ($3 billion/year). It is an incipient ferroelectric with an expected ferroelectric phase transition extrapolated to lie at 6 K but suppressed due to quantum fluctuations. The theory of quantum criticality for such uniaxial ferroelectrics predicts that the temperature dependence of the electric susceptibility χ diverges as 1/T3, in contrast to the 1/T2 dependence found in pseudo-cubic materials such as SrTiO3 or KTaO3. In this paper we present evidence of the susceptibility varying as 1/T3, i.e. with a critical exponent γ = 3. In general γ = (d + z – 2)/z, where the dynamical exponent for a ferroelectric z = 1 and the dimension is increased by 1 from deff = 3 + z to deff = 4 + z due to the effect of long-range dipole interactions in uniaxial as opposed to multiaxial ferroelectrics. The electric susceptibility of the incipient ferroelectric SrFe12O19, which is slightly further from the quantum phase transition is also found to vary as 1/T3.
We demonstrate significant cooling of electrons in a nanostructure below 10 mK by demagnetisation of thin-film copper on a silicon chip. Our approach overcomes the typical bottleneck of weak electron-phonon scattering by coupling the electrons directly to a bath of refrigerated nuclei, rather than cooling via phonons in the host lattice. Consequently, weak electron-phonon scattering becomes an advant- age. It allows the electrons to be cooled for an experimentally useful period of time to temperatures colder than the dilution refrigerator platform, the incoming electrical connections, and the host lattice. There are efforts worldwide to reach sub-millikelvin electron temperatures in nanostructures to study coherent electronic phenomena and improve the operation of nanoelectronic devices. On-chip magnetic cooling is a promising approach to meet this challenge. The method can be used to reach low, local electron temperatures in other nanostructures, obviating the need to adapt traditional, large demagnetisation stages. We demonstrate the technique by applying it to a nanoelectronic primary thermometer that measures its internal electron temperature. Using an optimised demagnetisation process, we demonstrate cooling of the on-chip electrons from 9 mK to below 5 mK for over 1000 seconds.
Here we review recent progress in cooling micro-/nanoelectronic devices significantly below 10 mK. A number of groups worldwide are working to produce submillikelvin on-chip electron temperatures, motivated by the possibility of observing new physical effects and improving the performance of quantum technologies, sensors and metrological standards. The challenge is a longstanding one, with the lowest reported on-chip electron temperature having remained around 4 mK for more than 15 years. This is despite the fact that microkelvin temperatures have been accessible in bulk materials since the mid-twentieth century. In this review, we describe progress made in the last 5 years using new cooling techniques. Developments have been driven by improvements in the understanding of nanoscale physics, material properties and heat flow in electronic devices at ultralow temperatures and have involved collaboration between universities and institutes, physicists and engineers. We hope that this review will serve as a summary of the current state of the art and provide a roadmap for future developments. We focus on techniques that have shown, in experiment, the potential to reach sub-millikelvin electron temperatures. In particular, we focus on on-chip demagnetisation refrigeration. Multiple groups have used this technique to reach temperatures around 1 mK, with a current lowest temperature below 0.5 mK.
Hexagonal ferrites do not only have enormous commercial impact (£2 billion/year in sales)due to applications that include ultra-high density memories, credit card stripes, magnetic bar codes, small motors and low-loss microwave devices, they also have fascinating magnetic and ferroelectric quantum properties at low temperatures. Here we report the results of tuning the magnetic ordering temperature in PbFe12-xGaxO19 to zero by chemical substitution x. The phase transition boundary is found to vary as ~ − ⁄ / with xc very close to the calculated spin percolation threshold which we determine by Monte Carlo simulations, indicating that the zero-temperature phase transition is geometrically driven. We find that this produces a form of compositionally-tuned, insulating, ferrimagnetic quantum criticality.Close to the zero temperature phase transition we observe the emergence of an electric-dipole glass induced by magneto-electric coupling. The strong frequency behaviour of the glass freezing temperature Tm has a Vogel-Fulcher dependence with Tm finite, or suppressed below zero in the zero frequency limit, depending on composition x. These quantum-mechanical
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