In one of the most celebrated examples of the theory of universal critical phenomena, the phase transition to the superfluid state of $^{4}$He belongs to the same three dimensional $mathrm{O}(2)$ universality class as the onset of ferromagnetism in a
lattice of classical spins with $XY$ symmetry. Below the transition, the superfluid density $rho_s$ and superfluid velocity $v_s$ increase as power laws of temperature described by a universal critical exponent constrained to be equal by scale invariance. As the dimensionality is reduced towards one dimension (1D), it is expected that enhanced thermal and quantum fluctuations preclude long-range order, thereby inhibiting superfluidity. We have measured the flow rate of liquid helium and deduced its superfluid velocity in a capillary flow experiment occurring in single $30~$nm long nanopores with radii ranging down from 20~nm to 3~nm. As the pore size is reduced towards the 1D limit, we observe: {it i)} a suppression of the pressure dependence of the superfluid velocity; {it ii)} a temperature dependence of $v_{s}$ that surprisingly can be well-fitted by a powerlaw with a single exponent over a broad range of temperatures; and {it iii)} decreasing critical velocities as a function of radius for channel sizes below $R simeq 20$~nm, in stark contrast with what is observed in micron sized channels. We interpret these deviations from bulk behaviour as signaling the crossover to a quasi-1D state whereby the size of a critical topological defect is cut off by the channel radius.
We have developed a pulsed magnet system with panoramic access for synchrotron x-ray diffraction in magnetic fields up to 31T and at low temperature down to 1.5 K. The apparatus consists of a split-pair magnet, a liquid nitrogen bath to cool the puls
ed coil, and a helium cryostat allowing sample temperatures from 1.5 up to 250 K. Using a 1.15MJ mobile generator, magnetic field pulses of 60 ms length were generated in the magnet, with a rise time of 16.5 ms and a repetition rate of 2 pulses/hour at 31 T. The setup was validated for single crystal diffraction on the ESRF beamline ID06.
We report the first direct observation of the influence of high magnetic fields on the Jahn-Teller (JT) transition in TbVO4. Contrary to spectroscopic and magnetic methods, X-ray diffraction directly measures the JT distortion; the splitting between
the (311)/(131) and (202)/(022) pairs of Bragg reflections is proportional to the order parameter. Our experimental results are compared to mean field calculations, taking into account all possible orientations of the grains relative to the applied field, and qualitative agreement is obtained.
