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Mesoscopic, Non-equilibrium Fluctuations of Inhomogeneous Electronic States in Manganites

By using the dark-field real-space imaging technique of transmission electron microscopy (TEM), we have observed slow 200 A-scale fluctuations of charge-ordered (CO) phase in mixed-valent manganites under a strong electron beam irradiation. In addition to these unusual fluctuations of the CO phase, we observed the switching-type fluctuations of electrical resistivity in the same sample, which were found to be as large as several percents. Systematic analysis indicates that these two different types of fluctuations with a similar time scale of the order of seconds are interconnected through a meta-stable insulating charge-disordered state. Current dependence of the fluctuations suggests a non-equilibrium nature of this slow dynamics.

the standard four-probe method over the temperature range T = 4.2-300 K. The long-term stability of T in our transport measurement was better than ~ 1 mK at T ~ 10-300 K. A bias current I = 10 -8 -10 -6 A was driven through the sample by a low-noise current source with the output resistance much greater than the sample resistance.
The temperature dependence of ρ is shown in Fig. 1. With cooling below the CO transition (T CO ~ 210 K), ρ increases sharply until the system undergoes the M-I transition at T C ~ 40 K. Below 40 K, ρ remains almost constant. Previous studies have demonstrated that the M-I transition is of a percolation type, and that the large value of ρ at low T is due to coexistence of metallic and insulating phases. A signature of the percolative M -I transition in low-T C manganites is a strong thermal hysteresis of ρ in the interval T ~ 15-100 K. Slow monotonic 4 relaxation of the resistivity from a meta-stable h igh-ρ (solid line) to a more stable low-ρ state (dashed line) is typical when T is fixed in this interval [16].
We observed discrete discontinuities superimposed on the monotonic relaxation of ρ at fixed T in the range of thermal hysteresis T ~ 35-75 K (see the insets in Fig. 1). The stepwise drops of ρ (inset 1) were found to be more typical for the high-ρ state (the solid line). Another type of discontinuities, switching of ρ back and forth, is typical when the sample is in the stable Switching has been found to be very sensitive to the measuring current (inset 4). Neither steps nor switching of ρ have been found outside of the thermal hysteresis interval.
In order to gain further insight into the origin of fluctuating ρ, we have investigated the local structural properties of the same sample by the dark field imaging technique of TEM. In this technique, the most intense electron diffraction superlattice spot from the charge ordering is used to form a real-space image of the sample. Since only the superlattice reflections are used, not the main Bragg peaks, the bright contrast in this imaging mode is directly associated with the charge ordered domains. The dark field images reveal coexistence of CO and charge-disordered (CD) domains at low temperatures, consistent with previous investigations. Under low electron beam intensity, it is found that the domains of different types are stable with time at a fixed T= 90 K. However, as the incident beam intensity gradually increases, the CO domains are found to break up into smaller CD domains as shown in Fig. 2. At low beam intensity (~ 50 mA/cm 2 at the sample), the CO domains exhibit relatively uniform contrast with the exception of the curvy anti-phase boundaries (Fig. 2a). Small isolated CD clusters (~ 200 Å) with dark contrast start to appear at intermediate beam intensities ~ 500 mA/cm 2 (Fig. 2b). With further increase of the 5 beam intensity to ~ 20 A/cm 2 , more CD clusters are nucleated and, eventually, a continuous path of the CD phase is established (Fig. 2c). Note that CD-insulating and CD-metallic phases cannot be distinguished in the dark field TEM studies: both appear as dark regions. The typical CD cluster size is ~ 200 Å with no significant further growth after its nucleation. The whole process is found to be reversible with the change of the electron beam intensity. After reducing the beam intensity to the initial level, we found that most of the CD clusters have reverted back to the CO state except for a few that are strongly pinned (Fig. 2d). Given enough time, even the strongly pinned CD clusters eventually are transformed back to the CO state. Similar behavior of the coexisting CO and CD domains has been observed at other temperatures within the entire hysteresis loop. These observations directly show that the transition from CO to CD states can be induced by a strong electron beam irradiation [17]. It should be emphasized that the fluctuations between CO and CD phases in the TEM experiment were not detected at low electron beam intensities, and were observed only when the 6 electron beam intensity was high enough. In other words, these fluctuations are a nonequilibrium process, induced by the electron beam of a high enough intensity. Heating by the electron beam can be neglected since the microstructural changes associated with the phase transitions observed by TEM occur at the same temperatures as determined by the transport and magnetic susceptibility measurements. To prevent inelastic scattering and electrons trapping, the sample in TEM experiment was thinned from bulk to its final thickness about 50 nm, and the problem of sample charging was avoided. In the transport measurements, the observed discrete fluctuations of ρ also exhibit a very strong dependence on the measuring current, which suggests a current-driven non-equilibrium nature of this process. In the measurements of ρ at fixed T, a small variation of the measuring current δI = 5-20 % results in changes of the switching rates or could lead to steps in ρ(t) or even a complete fade-out of switching (Fig. 1, inset 4). With restoring the initial value of I, switching usually recovers. Note that I in our transport measurements was well below the level at which heating of the entire bulk sample occurs (I ∼ 1 µA).
This non-equilibrium, oscillatory behavior of ρ can be induced by local heating of a small region of the percolation cluster without changing the average temperature of the sample.
Significant local heating can occur due to highly non-uniform current in an electronically inhomogeneous sample. Indeed, near the percolation threshold, the local current density in a percolation link can be very high. Due to the local increase of T, the link undergoes a transition from a low-T conducting to a high-T insulating state, reducing the local current and temperature and, hence, undergoing the transition back to the low-T conducting state. This self-oscillation process causes periodic fluctuations of ρ. The frequency of such oscillations depends on the electrical conductivity of the metallic domains and the thermal conductivity κ of the insulating 7 domains. Two-level switching in a spherical particle of radius r can be modeled by the heat balance equation: The first term represents the Joule energy released in the particle during time τ. The second term is the energy removed from the particle due to heat conduction. The right-hand side of the equation is the energy necessary to increase the temperature of a particle with the density p and specific heat C V by ∆T = T local -T average . Typical values for κ, C V and p for manganites at T ~ 50 K correspond to 10 -2 W/cmK, 20 J/moleK and 7 g/cm 3 , respectively [18]. In summary, we found that slow fluctuations observed in the resistivity and d ark-field images in TEM occur as a result of non-equilibrium processes in a system involving two stable phases -insulating charge-ordered and conducting ferromagnetic, and a meta-stable chargedisordered insulating phase. The meta-stable CD-I phase, which retains much of the characteristics of the high temperature paramagnetic phase, also plays an important role in the CMR effect. 9 This work was partially supported by the NSF Grant No. 9802513. We thank M. Uehara for sample preparation, Lixin He for computer analysis and V. Kiryukhin and M. Weissman for helpful discussions.