Magnetic domain dynamics in an insulating quantum ferromagnet

The statistics and form of avalanches in a driven system reveal the nature of the underlying energy landscape and dynamics. In conventional metallic ferromagnets, eddy-current back action can dominate the dynamics. Here, we study Barkhausen noise in Li(Ho,Y)${\mathrm{F}}_4$, an insulating Ising ferromagnet that cannot sustain eddy currents. For large avalanches at temperatures approaching the Curie point, we find a symmetric response free of drag effects. In the low-temperature limit, drag effects contribute to the dynamics, which we link to enhanced pinning from local random fields that are enabled by the microscopic dipole-coupled Hamiltonian (the Ising model in transverse field).

Figure 1

Measurement of Barkhausen events in $\mathrm{LiH}{\mathrm{o}}_{0.44}{\mathrm{Y}}_{0.56}{\mathrm{F}}_4$. (a) Schematic of the experimental setup. A pickup coil is wound around a single-crystal sample (inset) and placed on the cold finger of a helium dilution refrigerator inside a superconducting solenoid magnet. The induced voltages are amplified at low temperature by a high-frequency transformer, at room temperature by a low-noise voltage preamp, and then digitized to a computer. (b) Typical magnetization hysteresis loops, measured using a GaAs Hall magnetometer, at $T=80$ and 700 mK. The overall behavior of the magnetization in the low-field regime $(\left|H\right|<1$ kOe) is essentially temperature-independent (c) Voltage time series showing an individual, single-polarity Barkhausen event. (d) Voltage time series showing a long-duration event with an opposing-polarity precursor stage.

Figure 2

Statistical distribution of events for a series of temperatures. (a) Probability distribution of event area (integral of V×time) and energy $\left({\mathrm{V}}^2\times \mathrm{time}\right)$. (b) Probability distribution of event duration and power spectral density of events (c) Bivariate histograms of event probability versus area and duration at $T=80$ mK and 600 mK, showing an approximately linear relationship with no well-defined crossover. Lines are best-fit power laws (offset for clarity). For events with opposing-polarity precursors [Fig. 1], only the forward-polarity portion is included in the histogram analyses. Since these precursors are both rare and considerably smaller than the associated forward event, incorporating them into the histograms would have minimal effect.

Figure 3

Evolution of line shape as a function of temperature and event duration, showing the onset of drag effects. [(a) and (b)] Average scaled event shape vs scaled duration (see text for details on averaging and scaling process) for short $\left(<150\mu \mathrm{s}\right)$ and long $\left(>500\mu \mathrm{s}\right)$ events, respectively. Dashed line is a fit at $T=700$ mK to the ABBM model incorporating shape demagnetization and a phenomenological skew term [14].