DOI: 10.1126/science.1089408. The Anomalous Hall Effect and Magnetic Monopoles in Momentum Space

The Anomalous Hall Effect and Magnetic Monopoles in Momentum Space

10.1126/science.1089408

Crossref journal-article

American Association for the Advancement of Science (AAAS)

Science (221)

Abstract

Efforts to find the magnetic monopole in real space have been made in cosmic rays and in particle accelerators, but there has not yet been any firm evidence for its existence because of its very heavy mass, ∼10 16 giga–electron volts. We show that the magnetic monopole can appear in the crystal momentum space of solids in the accessible low-energy region (∼0.1 to 1 electron volts) in the context of the anomalous Hall effect. We report experimental results together with first-principles calculations on the ferromagnetic crystal SrRuO 3 that provide evidence for the magnetic monopole in the crystal momentum space.

Bibliography

Fang, Z., Nagaosa, N., Takahashi, K. S., Asamitsu, A., Mathieu, R., Ogasawara, T., Yamada, H., Kawasaki, M., Tokura, Y., & Terakura, K. (2003). The Anomalous Hall Effect and Magnetic Monopoles in Momentum Space. Science, 302(5642), 92â95.

Authors 10

Zhong Fang (first)
Naoto Nagaosa (additional)
Kei S. Takahashi (additional)
Atsushi Asamitsu (additional)
Roland Mathieu (additional)
Takeshi Ogasawara (additional)
Hiroyuki Yamada (additional)
Masashi Kawasaki (additional)
Yoshinori Tokura (additional)
Kiyoyuki Terakura (additional)

References 25 Referenced 901

P. A. M. Dirac, Proc. R. Soc. London133, 60 (1931). / Proc. R. Soc. London (1931)
G.'t Hooft, Nucl. Phys. B79, 276 (1974). (10.1016/0550-3213(74)90486-6) / Nucl. Phys (1974)
A. M. Polyakov, JETP Lett.20, 194 (1974). / JETP Lett. (1974)
10.1098/rspa.1984.0023
It has been recognized in the original paper by Berry ( 25 ) that the degeneracy point in the parameter space acts as a MM where the gauge field is enhanced.
10.1126/science.281.5379.951
R. Karplus, J. M. Luttinger, Phys. Rev.95, 1154 (1954). (10.1103/PhysRev.95.1154) / Phys. Rev. (1954)
J. Smit, Physica24, 39 (1958). (10.1016/S0031-8914(58)93541-9) / Physica (1958)
W. Kohn, J. M. Luttinger, Phys. Rev.108, 590 (1957). (10.1103/PhysRev.108.590) / Phys. Rev. (1957)
J. M. Luttinger, Phys. Rev.112, 739 (1958). (10.1103/PhysRev.112.739) / Phys. Rev. (1958)
L. Berger, Phys. Rev.B2, 4559 (1970). (10.1103/PhysRevB.2.4559) / Phys. Rev. (1970)
M. Onoda, N. Nagaosa, Phys. Rev. Lett.90, 206601 (2003). (10.1103/PhysRevLett.90.206601) / Phys. Rev. Lett. (2003)
10.1103/PhysRevLett.88.207208
10.1126/science.1058161
J. Sinova, T. Jungwirth, J. Kucera, A. H. MacDonald, Phys. Rev. B67, 235203 (2003). (10.1103/PhysRevB.67.235203) / Phys. Rev. B (2003)
Materials and methods are available as supporting material on Science Online.
A. Shapere F. Wilczek Geometric Phases in Physics (World Scientific Singapore 1989). (10.1142/0613)
10.1103/PhysRevLett.49.405
R. M. Martin, Phys. Rev. B5, 1607 (1972). / Phys. Rev. B (1972)
R. D. King-Smith, D. Vanderbilt, Phys. Rev. B47, 1651 (1993). (10.1103/PhysRevB.47.1651) / Phys. Rev. B (1993)
This gauge field is distinct from that of the magnetic field B ( r ) in real space although they are analogous to each other. In the presence of B ( r ) the covariant momentum operator π μ is given by π μ = – i δ zμ + eA μ ( r ) where B = ∇ × A . This leads to the commutation relation [π x π y ] =– ie (∂ x A y –∂ y A x ) =– ieB z etc. and to the Lorenz force due to the magnetic field B . Therefore these two gauge fields b μ ( k ) and B ( r ) are dual to each other and the presence of the one does not necessarily mean that of the other.
More Ca-doped samples with different concentrations have been measured. They all follow the same trend and are not shown here because of space limitations.
T. T. Wu, C. N. Yang, Phys. Rev. D12, 3845 (1975). / Phys. Rev. D (1975)
S. Murakami, N. Nagaosa, Phys. Rev. Lett.90, 057002 (2003). (10.1103/PhysRevLett.90.057002) / Phys. Rev. Lett. (2003)
M. Shikano, T. K. Huang, Y. Inaguma, M. Itoh, T. Nakamura, Solid State Comm.90, 115 (1994). (10.1016/0038-1098(94)90942-3) / Solid State Comm. (1994)

Dates

Type	When
Created	21 years, 10 months ago (Oct. 2, 2003, 4:43 p.m.)
Deposited	1 year, 7 months ago (Jan. 9, 2024, 10 p.m.)
Indexed	2 days, 1 hour ago (Aug. 23, 2025, 9:20 p.m.)
Issued	21 years, 10 months ago (Oct. 3, 2003)
Published	21 years, 10 months ago (Oct. 3, 2003)
Published Print	21 years, 10 months ago (Oct. 3, 2003)

Funders 0

None

BibTeX

@article{Fang_2003, title={The Anomalous Hall Effect and Magnetic Monopoles in Momentum Space}, volume={302}, ISSN={1095-9203}, url={http://dx.doi.org/10.1126/science.1089408}, DOI={10.1126/science.1089408}, number={5642}, journal={Science}, publisher={American Association for the Advancement of Science (AAAS)}, author={Fang, Zhong and Nagaosa, Naoto and Takahashi, Kei S. and Asamitsu, Atsushi and Mathieu, Roland and Ogasawara, Takeshi and Yamada, Hiroyuki and Kawasaki, Masashi and Tokura, Yoshinori and Terakura, Kiyoyuki}, year={2003}, month=oct, pages={92–95} }

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      [
        2003,
        10,
        3
      ]
    ]
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  "journal-issue": {
    "issue": "5642",
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        [
          2003,
          10,
          3
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      ]
    }
  },
  "alternative-id": [
    "10.1126/science.1089408"
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  "URL": "http://dx.doi.org/10.1126/science.1089408",
  "relation": {},
  "ISSN": [
    "0036-8075",
    "1095-9203"
  ],
  "subject": [],
  "container-title-short": "Science",
  "published": {
    "date-parts": [
      [
        2003,
        10,
        3
      ]
    ]
  }
}