Spin in Uniform Gravity, Hidden Momentum, and the Anomalous Hall Effect
DOI:
https://doi.org/10.15407/ujpe71.2.119Keywords:
spin Hall effect, gravitational field, anomalous spin Hall effectAbstract
We review the recent discussions concerning the absence of the spin Hall effect in a uniform gravitational field, pointing out differences from the anomalous spin Hall effect in ferromagnetic systems despite a similar form of the Hamiltonian.
References
1. R. Karplus, J. Luttinger. Hall effect in ferromagnetics. Phys. Rev. 95, 1154 (1954).
https://doi.org/10.1103/PhysRev.95.1154
2. Y. Yao, L. Kleinman, A. MacDonald, J. Sinova, T. Jungwirth, D.-s. Wang, E. Wang, Q. Niu. First principles calculation of anomalous Hall conductivity in ferromagnetic bcc Fe. Phys. Rev. Lett. 92, 037204 (2004).
https://doi.org/10.1103/PhysRevLett.92.037204
3. Z. Fang, N. Nagaosa, K. S. Takahashi, A. Asamitsu, R. Mathieu, T. Ogasawara, H. Yamada, M. Kawasaki, Y. Tokura, K. Terakura. The anomalous Hall effect and magnetic monopoles in momentum space. Science 302, 92 (2003).
https://doi.org/10.1126/science.1089408
4. I.V. Solovyev. Effects of crystal structure and on-site Coulomb interactions on the electronic and magnetic structure of A2 Mo2O7 (A = Y, Gd, and Nd) pyrochlores. Phys. Rev. B 67, 174406 (2003).
https://doi.org/10.1103/PhysRevB.67.174406
5. N. Nagaosa, J. Sinova, S. Onoda, A.H. MacDonald, N.P. Ong. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539 (2010).
https://doi.org/10.1103/RevModPhys.82.1539
6. D. Xiao, M.-C. Chang, Q. Niu. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959 (2010).
https://doi.org/10.1103/RevModPhys.82.1959
7. J. Sinova, S.O. Valenzuela, J. Wunderlich, C.H. Back, T. Jungwirth, Spin Hall effects. Rev. Mod. Phys. 87, 1213 (2015).
https://doi.org/10.1103/RevModPhys.87.1213
8. Z.-L. Wang. Gravitational spin Hall effect of Dirac particle and the weak equivalence principle. Phys. Rev. D 109, 044060 (2024).
https://doi.org/10.1103/PhysRevD.109.044060
9. A. Czarnecki, T. Gao. Hidden momentum and the absence of the gravitational spin Hall effect in a uniform field. Universe 11, 365 (2025).
https://doi.org/10.3390/universe11110365
10. W. Shockley, R.P. James. "Try Simplest Cases" discovery of "Hidden Momentum" forces on "Magnetic Currents". Phys. Rev. Lett. 18, 876 (1967).
https://doi.org/10.1103/PhysRevLett.18.876
11. D.J. Griffiths. Resource letter EM-1: Electromagnetic momentum. American J. Physics 80, 7 (2012).
https://doi.org/10.1119/1.3641979
12. D. Babson, S.P. Reynolds, R. Bjorkquist, D.J. Griffiths. Hidden momentum, field momentum, and electromagnetic impulse. American J. Physics 77, 826 (2009).
https://doi.org/10.1119/1.3152712
13. A. Hammerlindl, J. Bowman, T. Prince. Asymptote: the Vector Graphics Language (2025). https:// asymptote.ualberta.ca/.
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