Whenever you see anomalous Hall effect resistivity/conductivity vs. external magnetic field curves, there is always some low-field part with a greater slope that changes to a lesser slope at some characteristic field. In magnets, this low-field region is usually attributed to magnetic domains aligning to the direction of the external field, and the point where the slope changes is called the "saturation magnetization"--this is where all the domains are aligned.

What causes this characteristic field in non-magnetic systems that show the AHE (topological semimetals)?

"Liang, T. et al. Anomalous Hall effect in ZrTe5. Nat. Phys. 14, 451–455 (2018)."

I.e., What causes the "shoulder" to be at ~1.5 T in this plot of the AHE in ZrTe5--a Dirac semimetal--since it is not magnetic and are therefore no magnetic domains?


1 Answer 1


In this case, the slope is not just "lesser", it is zero at high fields. This is because the high field linear resistance has been subtracted off of the total Hall resistivity to isolate the anomalous component (i.e. this plot does not show the true Hall resistivity that would be measured directly).

There is evidence that this anomalous contribution is Berry curvature induced (see reference by Sun et. al. below), in which case the vanishing of the anomalous contribution would be indicative of a topological phase transition (Chern insulator -> trivial insulator). The Hall resistivity above 1.5 T becomes linear with negative slope, as the charge carriers of $\text{Zr}\text{Te}_5$ are holes.


Sun, Z., Cao, Z., Cui, J. et al. Large Zeeman splitting induced anomalous Hall effect in ZrTe5. npj Quantum Mater. 5, 36 (2020). https://doi.org/10.1038/s41535-020-0239-z

For completeness, the source article citation for this image is:

Liang, T., Lin, J., Gibson, Q. et al. Anomalous Hall effect in ZrTe5. Nature Phys 14, 451–455 (2018). https://doi.org/10.1038/s41567-018-0078-z

  • $\begingroup$ Right, I forgot to mention the subtracted linear background. However, I am still confused. Are you saying that the "shoulder" at 1.5 T is where the magnetic field induces the topological phase transition? Also, what do you mean by "Chern insulator ->trivial insulator?" Certainly, ZrTe5 is not a Chern insulator, nor a trivial insulator. $\endgroup$
    – Nick Quirk
    Commented Sep 11, 2020 at 18:51
  • $\begingroup$ @NickQuirk The nature of the AHE in this material is still not well understood. That being said, I am repeating what the first reference says, please read it for a more detailed explanation. Also, how do you know it is not an insulator at high fields? $\endgroup$
    – Alex
    Commented Sep 11, 2020 at 22:06

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