The aim of this report is to review a theoretical approach that has been proposed recently to describe dynamic fluctuations in glassy systems (work in collaboration with H.E. Castillo, C. Chamon, J. L. Iguain, M. Kennett and M. Sellitto). Firstly, I summarize some of the main features of the averaged and global non-equilibrium relaxation of glassy systems, weakly sheared viscous liquids and weakly tapped granular matter, and how these results have been successfully reproduced with a mean-field-like analytic approach. Secondly, I explain the outcome of more refined experimental and numerical measurements that point at examining the dynamics at a mesoscopic scale, and the role of noise measurements in this respect. Finally, I discuss how our theoretical approach can be confronted to new experimental and numerical tests.

We present the first experimental determination of the time auto-correlation of magnetization in the non-stationary regime of a spin glass, and its quantitative comparison with the corresponding response, the magnetic relaxation function. These measurements were performed in a new experimental setup working as an absolute thermometer. Clearly, we observe a non-linear fluctuation-dissipation relation between correlation and relaxation: at large correlation (short observation times) fluctuation dissipation theorem is obeyed, while the fluctuation dissipation relation is driven by an effective temperature higher than the bath temperature in the aging regime (small correlation and large observation times). In the aging regime, the relaxation vs. correlation curves depend weakly on the waiting time. According to theoretical developments on mean field models, and lately on short range ones, in the limit of very large waiting times, the relation between relaxation and correlation in the aging regime becomes temperature independent for a given system. A scaling procedure allows us to extrapolate to the limit of long waiting times by separating stationary and non-stationary regimes and to check the validity of the temperature independence of the fluctuation dissipation relation in the non-stationary regime.

A number of recent experiments and simulations give strong support for the idea that dynamics vary with position in glassy materials. Relaxation times appear to be correlated over a few nanometers, supportive of the notion of cooperatively rearranging regions (CRR). But details of the local cooperative dynamics are still mysterious, and certain issues, such as the heterogeneity lifetime, remain controversial. I will describe experiments in which molecular cooperativity was directly observed near the glass transition, through nanometer-scale probing of dipolar noise in polymer glasses. The dynamics and evolution of individual CRR was studied. The CRR were found to revisit a handful (2-4) of configurations up to hundreds of times. Statistical analysis of the noise give information about the lifetime of the CRR, the local shape and evolution of the energy landscape, and the evolution from exponential to nonexponential response. * E. Vidal Russell and N. E. Israeloff, Nature 408, 695 (2000).

Flunctuation microscopy is a hybrid diffraction-imaging technique that yields information about higher-order correlations between structural units in materials. It has been shown to be well suited for detecting medium rangeorder in atomic positions in amorphous materials. This article presents a review of flunctuation microscopy as employed in a transmission electron microscope for the study of amorphous tetrahedral semiconductors. Possible extensions of the technique to other radiations such as x-rays, and for other structurally noisy materials such as polymers and starches, are discussed.

We report measurements of conductance noise of a-Si_1-xGe_x:H in two different geometries; one where the current flow is transverse to the surface and the other longitudinal to it. Because of the large increase in sample resistance in going from transverse to longitudinal conduction, it was not possible to measure both geometries at the same temperature. However, the temperature trends are compatible with a common noise source. For both geometries, alloying with up to 40% Ge reduces the noise magnitude by a factor of 50 over that found in a-Si:H.

Measurements of the second spectra that characterize the non-Gaussian statistical nature of conductance fluctuations are reported for a series of hydrogenated amorphous silicon thin films. The deposition conditions used to synthesize the films were systematically varied in order to observe the effect that differing amounts of disorder have on the noise statistics. One series of n-type films were deposited at varying substrate temperatures, another n-type series was grown at varying rf powers, and a third series of compensated films was synthesized with varying ratios of phosphine to diborane. None of these series shows any significant change in the non-Gaussian noise statistics as the long-range disorder and deposition properties are changed. Measurements of the second spectra for a film synthesized in an inductively coupled plasma thermal growth system, which yields nano-particles of ~ 150 nm in diameter, are also reported. These results are discussed in terms of models for the non-Gaussian noise properties in amorphous silicon.

We describe a mechanism, which links the long-range potential fluctuations induced by charged defects to the low frequency resistance noise widely known as 1/f noise. This mechanism is amenable to the first principles microscopic calculation of the noise spectrum, which includes the absolute noise intensity. We have performed such a calculation for the thin films of hydrogenated amorphous silicon (a-Si:H) under the condition that current flows perpendicular to the plane of the films, and found a very good agreement between the resulting theoretical spectra and the spectra obtained in our own experiments. The mechanism described is quite general. It should be present in a broad class of systems containing poorly screened charged defects. For a given defect, the rate of charge fluctuations depends on the activation barrier, which an electron should overcome in order to escape from that defect. This rate, in turn, depends on the local random potential. Therefore, our study also introduces a new experimental method of characterizing the random potential landscapes in the vicinity of deep defects.

The conductance noise of Anderson-insulating amorphous and crystalline indium-oxide films exhibits a number of intriguing features. In the linear-response regime (small applied fields), the power spectrum (PS) in these systems is 1/f-like and does not exhibit saturation down to f approx 103 Hz. A sharp transition in the character of the noise occurs when the conductance is measured some distance into the non-Ohmic regime, and when the sample is immersed in liquid He. The PS acquires a strong component that is flat up to frequency f*, above which it declines sharply with f (faster than a power-law), and eventually is masked by the 1/f noise. Measurements in the time domain reveal that this anomalous noise is due to downward-going spikes in the conductance G, which start to appear once the drive current exceeds a threshold value. The average frequency of the occurrence of spikes increases monotonically with the current density. The spikes shape varies somewhat from sample to sample but it is usually asymmetric with a faster attack-edge and a slower trailing-edge. The characteristic duration of each spike τ in a given sample increases with the drive-current (causing f* in the PS to increase). More importantly, t depends on the carrier concentration n. For high-density systems (n greater-than-or-equal-to 10²¹ cm^-3) τ may be as high as 200mS near threshold. As n goes down τ decreases and for n less-than-or-equal-to 10¹⁹ cm^-3 τ is of order of 1mS. The detailed way τ depends on n correlates with the relaxation times in these systems, which are known to be electron-glasses. The anomalous noise is heuristically interpreted as an out-of-equilibrium phenomenon associated with two ingredients: A congested current-flow situation developing at some bottleneck resistor in the percolation network, which in turn results in a short-lived local field across a bottleneck resistor. This field may nucleate a cavity at the sample-helium interface that produces as thermal shock, which is converted by the sample to exhibit a current spike.

Studies of low-frequency resistance noise demonstrate that glassy freezing occurs in a two-dimensional electron system in silicon in the vicinity of the metal-insulator transition (MIT). The width of the metallic glass phase, which separates the 2D metal and the (glassy) insulator, depends strongly on disorder, becoming extremely small in high-mobility (low-disorder) samples. The glass transition is manifested by a sudden and dramatic slowing down of the electron dynamics, and by a very abrupt change to the sort of statistics characteristic of complicated multistate systems. In particular, the behavior of the second spectrum, an important fourth-order noise statistic, indicates the presence of long-range correlations between fluctuators in the glassy phase, consistent with the hierarchical picture of glassy dynamics.

Quench-condensed ultrathin granular Al films, with normal-state sheet resistance close to 10 kΩ/square, are superconducting below 2.5 K in zero magnetic field. Above a critical field, they are only weakly insulating at mK temperatures. However, in this field-driven normal state, the films demonstrate a glassy electronic behavior such as strong hysteresis and ultraslow, non-exponential relaxation in film resistance when the temperature is varied below 300 mK. The hysteresis is nonlinear and can be suppressed by a dc bias voltage. The relaxation time does not obey the Arrhenius form, indicating the existence of a broad distribution of low energy barriers. Furthermore, large resistance fluctuations, having a 1/f-type power spectrum with a low-frequency cut-off, are observed at low temperatures. With decreasing temperature, the amplitude of the fluctuation increases and the cut-off frequency decreases. We argue that the fluctuation power spectrum reveals a growing correlation length with decreasing temperature in the electron glass.

We show that 1/f noise is produced in a 3D electron glass by charge fluctuations due to electrons hopping between isolated sites and a percolating network at low temperatures. The low frequency noise spectrum goes as ω^-α with α slightly larger than 1. This result together with the temperature dependence of \alpha and the noise amplitude are in good agreement with the recent experiments. These results hold true both for a noninteracting electron glass with a flat density of states and for a Coulomb glass. In the latter case, the density of states has a Coulomb gap that fills in with increasing temperature. For a large Coulomb gap width, this density of states gives a dc conductivity with a hopping exponent of ≈ 0.75 which has been observed in recent experiments. For a small Coulomb gap width, the hopping exponent ≈ 0.5. At low temperatures the noise amplitude of a noninteracting electron glass increases linearly with temperature while the noise amplitude of a Coulomb glass increases quadratically.

Epitaxial thin films and bulk crystals of the colossal magnetoresistance (CMR) material La_2/3Ca_1/3MnO₃ (LCMO) exhibit large discrete equilibrium resistance fluctuations in the region of phase space where the magnetoresistance effects are strongest. Strongly inhomogeneous current paths allow us to observe the random telegraph signals of individual mesoscopic regions of material fluctuating between the paramagnetic-semiconductor phase and the ferromagnetic-conductor phase. Temperature and field dependences of the Boltzmann factors of individual fluctuators yield measurements of the magnetic moment and entropy differences between these phases, and of the fluctuator volumes. These measurements provide some of the first quantitative thermodynamic information about the locally-homogeneous CMR phase transition in an otherwise strongly inhomogeneous system. Careful analysis of the field- and temperature-dependences allows us to discriminate between fluctuations across the (first-order) CMR phase boundary and fluctuations of magnetic domain orientation deep in the ferromagnetic state. Similar measurements of the closely-related CMR material La_2/3Sr_1/3MnO₃ (LSMO) show almost no noise associated with the CMR transition, consistent with a second-order phase transition in this material.

We have investigated the dynamics of co-existing phases in the Charge Ordered (CO) manganite Pr_0.63Ca_0.37MnO₃ using the technique of conductance noise spectroscopy. We note that close to the CO transition temperature T_co the spectral power of S_v(f)/V² deviates significantly from the 1/f frequency dependence for f≤0.12Hz. Our analysis shows that this deviation can be described by a single frequency Lorentzian with corner frequency f_c in addition to the usual broadband 1/f noise. Such a Lorentzian contribution to S_v(f)/V² can come from a two level system (TLS). In the time serioues this shows up as RTN. For T≤T_co the system shows the onset of a non-linear conduction close to a threshold value J_dc = J_th the noise spectra is mainly 1/f in nature. For J > J_th a large low frequency component of noise (characterized again by a frequency f_c) appears. We associate f_c with the relaxation time tc of the TLS fluctuator so the tc = 1/f_c. For thermal activation of the TLS the temperature dependence of f_c will follow f_c=f_oexp(-E_a/k_BT) where E_a is an energy barrier. The value of f_c shows an increase with J_dc showing that the value of the activation energy E_a is being lowered by the applied bias.

Resistance fluctuations of low strain thin film La_0.7Ca_0.3MnO₃grown on NdGaO₃ show no dependence on low magnetic fields above T_c. At T_c, small volume local phase fluctuations are probed using the variance of the resistance noise power to give an upper bound fluctuator size scale of 100nm. The resistance noise peak at T_c is seen to broaden with magnetic field. Below T_c, comparison of the thermodynamics with the transport effects of large two state resistance fluctuations indicate large current inhomogeneity. Their behavior is similar to local phase fluctuations seen on higher strain films. The sample resistance below T_c is shown not to be a unique function of the bulk sample magnetization through a fluctuation-dissipation argument. Evidence for low temperature aging in the resistance noise power is also presented.

A giant and nonlinear Zeeman splitting in diluted magnetic semiconductors (DMS) offers a unique opportunity to examine quantum Hall ferromagnetism (QHF) since crossing of Landau levels (LL) can be achieved in moderately strong (B_tot ≈ 1 T) total magnetic fields. We carried out magnetoresistance studies on modulation-doped, gated heterostructures of Cd_1-xMn_xTe/Cd_1-yMg_yTe:I. We put into evidence the formation of ISing quantum Hall ferromagnet with Curie temperature T_c as high as 2 K. QHF in our device is manisfested by anomalous magnetoresistance maxima, their hysteretic behavior, and time-dependent resistance, similar to earlier observations in III-V heterostructures. However, in our system these phenomena are much stronger, especially when either 2^- or 1^-, and 0⁺ LL are brought into coincidence. The magnitude of the QHF spikes depends dramatically on the history of the sample, shows hysteresis when either magnetic field or gate voltage are swept, stretched exponential-time evolution characteristic of glassy systems, and strong Barkhausen noise reflecting the dynamics of ferromagnetic domains. Our study indicates that these metastabilities stem from the electronic systems itself as an effect of slow dynamics of ferromagnetic domains, while the nuclear spin polarization plays a rather minor role.

We present theory for a current shot noise in mesoscopic diffusive superconductor-normal metal-superconductor (SNS) junctions. The current shot noise is tremendously enhanced at small applied voltage, V < Δ/e, due to the mechanism of multiple Andreev reflection (MAR), which creates long correlated trains of transmitted electrons. The central result for the MAR regime is a universal value for the noise power in the limit of small voltage and at zero physical temperature, which corresponds to the effective noise temperature of the order of superconducting energy gap Δ. At very small voltage, MAR is destroyed by inelastic relaxation, consequently, the level of noise reduces and approaches at V = 0 the thermal noise value. We investigate the suppression of MAR by inelastic scattering processes and analyze the crossover from the MAR regime to a hot electron regime.

Tunnel barriers play a key role in current applications of superconducting tunnel-devices for THz frequency heterodyne mixing and for magentic tunnel junctions for data-storage applications. Shot noise in the tunnel current limits the sensitivity of tunnel junctions as high frequency detectors. The observed voltage dependence has proven to be a valuable probe to evaluate the quality of the tunnel barrier, in particular for inhomogeneities in thickness or at least for a distribution of transmissivities. It is an open question whether similar measurements can be made informative for magnetic tunnel junctions as well.

We consider quantum fluctuations in a current biased overdamped Josephson junction in the regime when the bias current is larger than the critical current. The fluctuations of the voltage and phase across the junction are assumed to be initiated by equilibrium current fluctuations in the shunting resistor. This corresponds to low enough temperatures, when fluctuations of the normal current in the junction itself can be neglected. Quantum effects are important when the resistor temperature is low compared to the Josephson frequency, even in the case when noise is measured at frequencies lower than the temperature. We used the quantum Langevin equation in terms of random variables related to the limit cycle of the nonlinear Josephson oscillator. This allows to go beyond the perturbation theory and calculate the widths of the Josephson radiation lines.

The relatively large and linear magnetoresistance found in nonstoichiometric silver chalcogenides makes them attractive candidates for studying the mechanisms of linear magnetoresistance and for field sensing applications. After a brief review of the magnetoresistive properties of these materials, we report on the intrinsic electrical noise in bulk, polycrystalline Ag_2+δTe. Low-frequency noise is due to resistance fluctuations having a 1/f-like power spectrum. The temperature dependence of the noise magnitude and its spectral slope indicate thermally activated kinetics which we attribute to some form of charge trapping-detrapping process occurring in or near the intergranular regions. The effective magnetic field noise in Ag_2+δTe is also compared to other materials systems used in field sensing applications.

Spectroscopy of Stochastic Signals (3S) has been used to study conduction behavior in electrochemically deposited conductive polymers (CP) using as example polyaniline and poly(3-methyl thiophene). Within the 3S approach, the conduction process is considered as a stochastic process in heterogeneous disordered system rather than as some classical conduction mechanisms like Schottky or Poole-Frenkel emission. We have been able to distinguish several modes of the conduction process in conducting polymers using the 3S methodology. Particularly, we have established that the transport of charge carriers in highly doped CPs is much less correlated than in non-doped ones, that is, at low doping levels elementary processes involved in the conduction are more correlated than in highly doped polymer. By increasing applied electric field we also achieve lower correlation in a sequence of elementary events contributing to the conductivity of CP. Apparently, the change in the correlation length corresponds to changing mechanism of the electrical conduction. The lower correlation in highly doped sample can be attributed to various factors including change in CP conformation, enhancement in inter-chain charge transfer and generation of polaron lattice. The obtained results show the high informative potential of the 3S method in studying conduction mechanism in conducting polymers.

The large increase in the flux-flow voltage noise, commonly observed in the vicinity of the peak-effect in superconductors, is ascribed to a novel noise mechanism. The mechanism consists of random injection of the strongly pinned metastable disordered vortex phase through the sample edges and its subsequent random annealing into the weakly pinned ordered phase in the bulk. This results in large critical current fluctuations causing strong vortex velocity fluctuations. The excess noise due to this dynamic admixture of two vortex phases is found to display pronounced reentrant behavior. In the Corbino geometry the injection of the metastable phase is prevented and, accordingly, the excess noise disappears. The excess flux-flow noise in the peak-effect regime is dominated by vortex velocity fluctuations while the density fluctuations, frequently considered in the conventional flux-flow noise models, are negligibly weak. Strong nongaussian fluctuations are associated with S-shaped current-voltage characteristics. The spectral properties of the noise reflect the form of the frequency characteristics of the dynamically coexisting vortex phases which is equivalent to the first order filter response. The cutoff frequency in the spectra corresponds to the time-of-flight of vortices through the disordered part of the sample.

We use particle dynamics simulations to probe the correlations between noise and dynamics in a variety of disordered systems, including superconducting vortices, 2D electron liquid crystals, colloids, domain walls, and granular media. The noise measurements offer an experimentally accessible link to the microscopic dynamics, such as plastic versus elastic flow during transport, and can provide a signature of dynamical reordering transitions in the system. We consider broad and narrow band noise in transport systems, as well as the fluctuations of dislocation density in a system near the melting transition.

The emergence of non-gaussian distributions for macroscopic quantities in nonequilibrium steady states is discussed with emphasis on the effective criticality and on the ensuing universality of distribution functions. The following problems are treated in more detail: nonequilibrium interface fluctuations (the problem of upper critical dimension of the Kardar-Parisi-Zhang equation), roughness of signals displaying Gaussian 1/f power spectra (the relationship to extreme-value statistics), effects of boundary conditions (randomness of the digits of π).

The low-frequency excess (1/f) noise of metal-oxide-semiconductor (MOS) devices has long been known to depend strongly on defects at or near the Si/SiO₂ interface. We discuss several defect microstructures for oxygen-vacancy-related defects that are found via density functional theory to have energy levels consistent with 1/f noise. These include two variations of the so-called E_γ' center, one of which includes a fivefold coordinated, puckered Si atom. A stretched dimer O vacancy defect ( the E_δ') is also found to potentially cause MOS 1/f noise. These defects appear to be sufficient to describe much of the noise in many kinds of nMOS and pMOS transistors. However, pMOS transistors that show latent interface-trap buildup and/or buried channel conduction may present a special challenge for these or otehr noise models. O-vacancy-related and hydrogen-related defects that cause 1/f noise in larger devices will cause other kinds of performance and reliability problems in highly scaled devices, such as random telegraph noise, enhanced tunnel current, stress or radiation induced leakage current, and/or dielectric breakdown.

Electromigration in sub-micron conductors of Cu and CuAl was studied by 1/f noise measurements for the first time. 1/f noise can serve as a very sensitive indicator for electromigration damage: The 1/f noise level is increased by up to two orders of magnitude whereas the resistance of the damaged interconnects is enhanced by less than a factor of two only. The most striking advantage of the 1/f noise measurement technique compared to the methods frequently used at present for electromigration studies (e.g., the Median Time of Failure, MTF technique) is that it is possible to determine the distribution of the activation energies of the processes involved from a single sample at progressive electromigration damaging. In Cu interconnects a strong increase in the number of mobile defects is observed during electromigration damaging whereas the shape of the distribution of the activation energies (maximum between 0.8 and 0.95 eV) does not change much, except shortly before the failure of the interconnect lines where a shift to higher activation energies (maximum: 1.05 eV) is measured. Significantly higher activation energies observed in undamaged and electromigration damaged CuAl_0.5wt% interconnects indicate an advanced resistance of CuAl alloys to electromigration when compared to pure Cu lines.

We study the influence of periodical interference pulses on the 1/f fluctuations of variety of systems showing 1/f noise. We show that in some cases, when interference pulses 'reset' the slow evolving 1/f noise mechanism, the magnitude of the noise is suppressed. We demonstrate it on both mechanisms that fluctuate at quasi-equilibrium, as well as on a dynamically driven 1/f noise mechanisms. Furthermore: by using voltage as the interference pulses, we are able to set a new classification for the 1/f noise mechanism in resistive disordered systems. The technique can detect bias dependent current paths rearrangement. Although it is known that in resistive systems the 1/f noise comes from equilibrium local resistance fluctuations that are bias independent, we show that in some such systems, applying different bias changes the set of perculative current paths, resulting in a 1/f noise signature that comes from a new set of local fluctuators.

The theory of the fluctuations of the van der Waals (vdW) attractive force between macroscopic bodies is developed. A general equation for the spectral density of the fluctuating surface Maxwell stress (force per unit area) in vacuum near the surface of a body is derived under the assumption that, inside the bodies, the random Langevin sources of the electric and magnetic fields (charges, polarizations, currents) are Gaussian. This spectral density of stress is an integral over frequencies of a sum of terms each of which is a product of Fourier amplitudes of two field components' correlation functions. For metallic bodies, the contribution of free electrons to the vdW force (at frequencies up to the frequency of electron scattering) is calculated. This contribution to the force and its noise grows with temperature. Application of noiseless voltage to two interacting metals across the vacuum gap between them generates an additional force noise. This additional noise is proportional to the voltage squared and to the spectral density of the random electric field at the frequency of noise measurement. The theoretical qualitative conclusions are in good agreement with experiments.

Since its discovery by Barkhausen in 1919, the jerky motion of domain walls in bulk soft magnetic materials has represented a unique tool to study the microscopical processes responsible for the magnetic hysteresis. For long time, the description of this complex motion has been purely phenomenological, without any precise connection with the magnetization processes involved or the material microstructure. In the last years, using different approaches proper of mechanical statistics, new microscopical models has been introduced, offering the possibility to link the observed statistical properties of the noise to some material parameters. In particular, the Barkhausen jumps are found to exhibit universal properties, with the size and duration distributions showing extended scaling regions. Moreover, the properties of the noise of different materials can be grouped into two universality classes, depending only on the strength of long range interactions. We review all these aspects and peculiarities of the recent studies, with a particular emphasis of the still existing differences between the available experimental data and the theoretical predictions. We also show how this approach is useful to investigate the general properties of magnetic hysteresis, and the dynamics of domain walls in thin films, an important technological open problem strongly debated in the recent literature.

We review the two main theoretical frameworks for understanding Barkhausen noise and other avalanche-like phenomena. We show that while the theories predict a response which is symmetric in time, various measurements show a persistent time-asymmetry. In the ABBM model, assuming Gaussian pinning field statistics guarantees time-symmetric Barkhausen noise. On the other hand, our recent experiments show non-Gaussianity in the effective pinning field of an amorphous soft metallic ferromagnet. We suggest a possible connection between the non-Gaussianity of the pinning field and the observed time asymmetries.

Relaxor ferroelectrics form a diverse class of materials which typically show cooperative freezing into a nonergodic glassy state without long-range ferroelectric order. We discuss Barkhausen noise techniques in the non-ferroelectric regimes of the relaxors as a probe of the types of glassy order present. Preliminary data on PMN/PT (10% and 32%) show dipole moment step sizes which shrink abruptly upon cooling into the relaxor regime. This is similar to previous results on PMN, but with interesting differences possibly due to the larger ferroelectric correlations in PMN/PT: namely, a history dependence of the noise and a smaller dynamic step size despite larger static ferroelectric correlations. In light of these noise results and aging behavior in PMN/PT and SBN:La, we discuss a tentative new picture we recently proposed of freezing in PMN and related relaxors (analogous to that in reentrant spin glasses) as well as constraints on theoretical models for the relaxors.

We present a set of experimental results concerning the power spectrum of current noise, detected on a granular high Tc superconductor submitted either to a slowly varying magnetic field or to a varying current intensity. Experiments were performed on a YBCO specimen suitably treated in order to weaken the weak links without affecting the oxygen content of grains. The weakening of the intergrain region allowed the use of very small magnetic fields and currents to induce the resistive transition of the specimen and to observe current noise. The induced noise is of the 1/f² type and will be interpreted in terms of two different models. One of the model is based on the enhancement of the noise due to the clustering of the resistive transition of the weak links, produced by correlation effects related to the strong nonlinearity of their Josephson type I-V characteristics. This model has been the object of a computer simulation based on a 3D-network of Josephson-like elements and seems suitable to explain the noise produced by current variation. The second model explains the excess noise as produced by discontinuous penetration of the magnetic flux inside the intergrain region. This discontinuity is related to the field screening effect of rings made of several superconducting weak links connecting different grains, which are alternatively broken and restored by the current induced during flux variation, and seems suitable to explain the larger noise produced by a varying magnetic field.

We have performed flux noise and AC-susceptibility measurements on two 400 nm thick MgB₂ films. Both measurement techniques give information about the vortex dynamics in the sample, and hence the superconducting transition, and can be linked to each other through the fluctuation-dissipation-theorem. The transition widths for the two films are 0.3 and 0.8 K, respectively, and the transitions show a multi step-like behavior in the AC-susceptibility measurements. The same phenomenon is observed in the flux noise measurements through a change in the frequency dependence of the spectral density at each step in the transition. The results are discussed and interpreted in terms of vortices carrying an arbitrary fraction of a flux quantum as well as in terms of different macroscopic regions in the films having slightly different compositions, and hence, different critical temperatures.

Recent advances in cantilever-based force detection have allowed detection of forces below an attonewton. We have applied this capability to the study of dissipation and fluctuations in nanometer-scale systems. Our work is largely motivated by our effort to extend magnetic resonance force microscopy (MRFM) to single-spin sensitivity, where we have been confronted with a variety of unanticipated noise issues. Phenomena that we have studied include magnetic moment fluctuations in nanoscale ferromagnets, non-contact friction and force fluctuations near surfaces, and increased electron spin relaxation rates observed when closely monitoring electron spins by MRFM. The enhanced spin relaxation rate is believed to be caused by Rabi frequency magnetic noise that is generated by thermal vibrations in high order cantilever modes. Overcoming these various noise issues will be key to achieving single-spin quantum readout. This work was performed in collaboration with H. J. Mamin, R. Budakian, B. Chui, B. Stipe and C. S. Yannoni. We thank ONR and the DARPA Mosaic program for financial support.