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This Letter reports measurements of the magnetic field dependence of the resistive critical temperature T c of a regular square network of superconducting aluminum. We find new effects of flux quantization corresonding to both integral (1,2,3,...) and fractional (T>T>T>T>T>T>T) numbers of flux quanta per unit cell of the network. The fractal fine structure of the upper critical-field line is identified as the edge of the Landau-level spectrum for a tight-binding problem on a square lattice.

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We have performed thermal conductance measurements on individual single crystalline silicon suspended nanowires. The nanowires (130 nm thick and 200 nm wide) are fabricated by e-beam lithography and suspended between two separated pads on Silicon On Insulator (SOI) substrate. We measure the thermal conductance of the phonon wave guide by the 3ω method. The cross-section of the nanowire approaches the dominant phonon wave length in silicon which is of the order of 100 nm at 1K. Above 1.3K the conductance behaves as T 3 , but a deviation is measured at the lowest temperature which can be attributed to the reduced geometry.

A particularly sensitive heat capacity measuring device has allowed us to measure the tunneling process of Mn 12 O 12 -acetate single crystals (mass: 1 and 20 mg) from the irreversible tunneling process below the blocking temperature T B to the reversible resonant tunneling process above T B . Above the T B (typically 3.5 K) we find specific heat anomalies at the magnetic field values that correspond to the crossing of spin up and spin down levels of different magnetic quantum numbers. Below T B , heat relaxation pulses at the crossing of crystal field levels are observed for fields applied antiparallel to the initial magnetization. These measurements give a new scope to Mn 12 O 12 -acetate investigations and show the great interest of nanocalorimetry for studies of big magnetic molecules. [S0031-9007(97)03794-0] PACS numbers: 75.45. + j, 61.46. + w, 07.20.Fw Crystals of Mn 12 O 12 -acetate clusters [1] are molecular spin systems that exhibit spectacular effects [2]. Twelve manganese ions (4 Mn 31 and 8 Mn 41 ) are coupled by ferromagnetic exchange to a S 10 macrospin. The Mn 12 O 12 clusters are embedded in an organic matrix and show no exchange coupling from one cluster to another.The crystals are regular parallelepipeds with a strong magnetocrystalline anisotropy (ϳ60 K) along the longitudinal axis. Once oriented, they present at low temperatures and zero magnetic field a very long relaxation time of the magnetization (two months at 2 K [3]). Recently, quantum tunneling of molecular spins through the anisotropy, at magnetic field values that correspond to the crossing of spin up and spin down levels of different magnetic quantum numbers, has been demonstrated [4][5][6].The anisotropy lifts the 2S 1 1 degeneracy of the magnetic levels in zero field, creating a double well configuration [5] as sketched in Fig. 1. The manganese system is superparamagnetic and can be described by a Hamiltonian of the form [7]where D 0.6 K is the anisotropy energy per cluster, H the magnetic field applied parallel to the easy axis of magnetization, g Ӎ 2 is the gyromagnetic factor, and S is the spin per cluster. H l is a term that does not commute with S z and is due to the demagnetizing field, dipole coupling, higher anisotropy terms, and/or hyperfine splitting. A great effort is underway to understand how it comes about [7,8]. Thermal measurements as a function of a magnetic field enlighten the interplay between the spin system and the lattice of the crystal, e.g., clarifying how the phonons influence the tunneling of the macrospins, therefore, giving a great deal of new information.We have performed two kinds of measurements on Mn 12 O 12 monocrystals, the heat capacity as a function of an applied static magnetic field (C[H]) and the temperature as a function of a slowly scanned magnetic field ͑T ͓H͔͒. The measure of very small single crystals promises a high quality of the sample and avoids the broadening found with powder samples due to the slightly different characteristics of every crystal. On the other side, it implies a gr...

The broadening of the resistive transition along the c axis of a YBa2Cu307 single crystal in the presence of strong magnetic fields (H )H& i) parallel to ab disappears below a well-defined line in the H-T phase diagram. Above this line, dissipation is Ohmic and field dependent.Below this line, a discontinuity appears in the resistivity curves, and the I-V behavior is strongly nonlinear. The shape of the resistive transition below the T"(H) line has a universal character, which remains unaff'ected by changes in the amplitude of the field. This unusual behavior contradicts any collective-Aux-pinning model that predicts a field-dependent activation energy, and suggests a phase transition related to the depinning line.The broadening of the superconducting transition of the high-T"compounds in high magnetic fields (H )H, i ) has been the subject of intensive investigation. 'The anisotropy of broadening phenomena is principally related to the orientation of the field with respect to the CuO planes because of anisotropic pinning forces. As a general rule, the width of the transition decreases with the angle between the field and the CuO planes. The relevance of the Lorentz force is not clear, since the broadening persists even in the absence of macroscopic Lorentz force. Giant fluctuations have been suggested in order to account for this feature, but it is difficult to understand how the superconducting fluctuations are enhanced by the magnetic field, which should act as a pair-breaking mechanism. When the nature of the mixed state is considered an interesting physical situation arises. In these high-x, high-T"materials a melting transition of the vortex lattice is possible well below T,. '' For a low density of pinning centers the flux liquid will not be pinned; instead, the vortex lattice will be pinned. If the melting transition indeed occurs, one expects entanglement of the flux liquid. ' This gives rise to a local Lorentz force even if the transport current flows parallel to the external applied field. In this case smooth resistivity curves are expected, with the resistivity decreasing continuously down to the solidification temperature where the flux liquid is disentangled. In contrast, when the external field is applied perpendicular to the transport current, the mean Lorentz force is independent of the local arrangement of the vortices and remains 6nite at the melting temperature. At this temperature, pinning forces increase abruptly with the formation of a Aux lattice, and one expects a discontinuity of the resistivity at T . In a weak pinning regime the melting transition should remain of first order' and one should be able to define the "melting" line in the phase diagram from a sharp transition in the resistivity curves. The dissipation for a given point in the 8-T diagram should then depend uniquely on the distance from this line. Kwok et al. reported a Lorentz force mechanism giving rise to a "kink" in the resistivity for H 1.5 Tllab, perpendicular to the current, whereas an unexplained resistive backgroun...

An innovative nanocalorimeter has been developed for measuring specific heats of thin films, multilayers (typical thickness: 1000 Å) and single crystals (mass: 1 μg) in the temperature range of 1.5–20 K. The addenda of the device are as small as 3 nJ/K at 4 K (0.5 nJ/K at 1.5 K), thus samples with a heat capacity of the order of nJ/K at 4 K can be measured. Heat capacity differences as a function of temperature or an external magnetic field (5 T) were determined with a resolution of ΔC/C≃10−4. This way we have seen heat capacity variations of less than a pJ/K. We present as an example measurements on very small Mn12O12 acetate single crystals and a measurement of a thin superconducting Pb layer. In the latter measurement we could evidence via specific heat a finite size effect.

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