Frequency dependence of the anomalous Hall effect: possible transition from extrinsic to intrinsic behavior

John Cerne, University at Buffalo, SUNY, DMR 0449899

In metals, magnetic fields deflect moving charges to produce a voltage perpendicular to the flow of the charges. This phenomenon is known as the Hall effect and is critical to characterizing materials as well as fundamental science. Two Nobel prizes in the last few decades have been awarded for the integer and fractional quantum Hall effect in semiconductors. In some magnetized metals, the moving charges are deflected even when no magnetic field is present. This is known as the anomalous Hall effect (AHE). Two competing models are used to explain the AHE. The intrinsic model demonstrates that AHE can arise from the fundamental electronic structure of the material. The extrinsic model shows that impurity scattering (which depends on the purity of a particular sample) can produce the AHE. In many materials such as SrRuO3, it is not clear which model is more appropriate. The AHE effect remains a rich and challenging problem in condensed matter physics.

The AHE conductivity xy as a function of probe energy. The thin lines are from a calculation of the intrinsic AHE by Fang Science, 2003) From Kim PRB, 2010. Copyright (2010) by the American Physical Society.

Unlike conventional Hall measurements, which measure the static Hall voltage produced by a dc current at zero frequency, we have extended Hall measurements to higher frequencies by looking at the oscillating Hall voltage responding to an alternating current, which is produced by infrared light (wavelengths from 11 to 0.6 m). Instead of looking at just one point, our infrared Hall measurements map out the Hall response over a broad energy range. The frequency, temperature and magnetic field dependence of the infrared AHE conductivity xy in SrRuO3 (see figure) suggest that in fact both mechanisms are present, with the extrinsic dominating at low energy and the intrinsic accounting for the high energy behavior. These results have been published by Kim et al. in Physical Review B in June 2010. This tunable probe of the Hall effect provides new insights into SrRuO3 as well as many other materials such as magnetic semiconductors (Acbas PRL 2009) and high temperature superconductors (Zimmers PRB 2010).

Conceptual approach to waves: Phasors and ac circuits John Cerne, University at Buffalo, SUNY, DMR 0449899

We have created a web site, http://electron.physics.buffalo.edu/claw/ that explains many basic wave concepts using dynamic and interactive graphical simulations. One of the most conceptually challenging aspects of waves is learning how to add two or more waves together. One powerful, but often confusing, approach is to treat each wave as a two-component vector (amplitude and phase) and to add the waves vectorially. In the first applet, we see that a sine wave can be represented by mapping the vertical component of a vector as a function of time as it rotates counterclockwise. To add two waves, one simply adds the vertical components of the two vectors as they rotate. Note that the applet allows the student to change the magnitude and phase (shifting the wave left/right) of each wave/vector.

In the second applet (which automatically starts after 80 seconds), we see the application of this phasor technique to an ac electrical circuit. Here the voltages across an inductor (V_L), capacitor (V_C), and resistor (V_R) are added to obtain the total voltage that drives the circuit. Note that the phase of each voltage is critical, with the voltage across the inductor and capacitor tending to cancel each other out. The student can change the values for the capacitor, inductor, resistor, and driving voltage. Furthermore, the student can change the driving frequency, which shifts the contribution from the capacitor to the inductor as frequency increases and allows the students to observe a resonant enhancement of the electric current (I) when the voltages across the inductor and capacitor exactly cancel.