There are three major sources of the 'randomness' underlying noise phenomena.
These are the random outcomes of quantum 'measurement' processes, the random
ensembles of statistical mechanics, and the algorithmic complexity of many dynamical
processes. Here I dwell on the possible connections between the first two sources of
randomness. It is often held that the empirical irreversibility of quantum measurement
arises from statistical mechanics. I present somewhat speculative arguments that in fact
the irreversible approach to statistical ensembles may be rooted in an irreversible
quantum decoherence process.
Resistance fluctuations of low strain thin film La<sub>0.7</sub>Ca<sub>0.3</sub>MnO<sub>3</sub> grown on NdGaO<sub>3</sub> are examined. The appearance of two state resistance fluctuations are found to be correlated with the onset of remanent magnetization and not with the onset of percolation-like conduction. Their behavior with current, applied magnetic field, and temperature provide information on the nature of the fluctuation. In contrast to the magnetization at the putative T<sub>c</sub> of the thin film, the resistance fluctuations display memory of the applied magnetic filed history. An explanation involving a strain enhanced AF interaction is posited.
In previous work , which we recently reviewed in [2,3,4], we discovered a critical point in the behavior of hysteretic systems. Adding disorder to the system, we found a second order transition from hysteresis loops with a macroscopic jump or burst (roughly as seen in the supercooling of liquids) to smoothly varying hysteresis loops (as seen in most magnets). We have studied the critical point in the nonequilibrium zero temperature random field Ising model (RFIM) (which is a simple model for magnets, that has aplications far beyond magnetic hysteresis and associated Barkhausen Noise), using mean field theory, renormalization group techniques, and numerical simulations in 2,3,4, and 5 dimensions. In a large region near the critical disorder the model exhibits power law distributions of noise (avalanches), universal behavior, and a diverging length scale [5,6,7].
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.
Epitaxial thin films and bulk crystals of the colossal
magnetoresistance (CMR) material La<sub>2/3</sub>Ca<sub>1/3</sub>MnO<sub>3</sub> (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<sub>2/3</sub>Sr<sub>1/3</sub>MnO<sub>3</sub> (LSMO) show almost no noise associated with the CMR transition, consistent with a second-order phase transition in this material.
Resistance fluctuations of low strain thin film La<sub>0.7</sub>Ca<sub>0.3</sub>MnO<sub>3</sub>grown on NdGaO<sub>3</sub> show no dependence on low magnetic fields above T<sub>c</sub>. At T<sub>c</sub>, 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<sub>c</sub> is seen to broaden with magnetic field. Below T<sub>c</sub>, 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<sub>c</sub> 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.
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.