### Abstract

Phenomenological equations describing the hyperfine splitting of a localized electron resonance in a metal are studied. The transverse susceptibility χ^{+}(ω) is obtained for the case of nuclear spin I=1/2, and its poles and residues are displayed. The corresponding eigenvectors are determined, enabling a physical generalization to arbitrary nuclear spin. The validity of the generalization procedure is verified by an examination of the generalized susceptibility. The conditions for the observation of the hyperfine splitting in a dilute magnetic alloy are detailed. Three distinct regions are found to be important, depending on the strength of the exchange coupling. Region (1), corresponding to a very weak exchange coupling, exhibits hyperfine splittings of the same character as in an insulator. The linewidth of each hyperfine component equals Δ _{se}+Δ_{sL}, where Δ_{se} is the second-order localized-conduction electron exchange relaxation rate, and Δ_{sL} the localized spin lattice relaxation rate. Region (2) corresponds to sufficiently larger values of the exchange coupling for a magnetic resonance bottle-neck to obtain, but for which ω_{hf}/ Δ_{se}≫1, where ω_{hf} is the electronic hyperfine splitting frequency. In region (2) the hyperfine splitting is the same as in region (1), but the width of each component equals [2I/(2I+1)] ·[Δ_{se}+Δ_{sL}]. Region (3) corresponds to yet larger values of the exchange coupling, such that ω_{hf}/ Δ_{se}≪1. In this more strongly bottlenecked region the hyperfine split resonance is narrowed into a single line, and the resonance properties are those one would derive in the complete absence of a hyperfine interaction. Recent successful observations of the hyperfine splitting of a localized moment resonance for rare-earth alloys belong to category (1). Unsuccessful measurements in transition metal alloys indicate their character is appropriate to region (3). It is suggested that lower temperature measurements may shift some of these materials into region (2) (because Δ_{se} ∝T), allowing for a direct determination of the magnitude of the exchange coupling constant, even though the resonance system is still in the bottlenecked regime.

Original language | English (US) |
---|---|

Pages (from-to) | 1659-1665 |

Number of pages | 7 |

Journal | Journal of Applied Physics |

Volume | 42 |

Issue number | 4 |

DOIs | |

State | Published - 1971 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Journal of Applied Physics*,

*42*(4), 1659-1665. https://doi.org/10.1063/1.1660388

**Hyperfine splitting in a metal of a localized moment.** / Barnes, Stewart; Dupraz, J.; Orbach, R.

Research output: Contribution to journal › Article

*Journal of Applied Physics*, vol. 42, no. 4, pp. 1659-1665. https://doi.org/10.1063/1.1660388

}

TY - JOUR

T1 - Hyperfine splitting in a metal of a localized moment

AU - Barnes, Stewart

AU - Dupraz, J.

AU - Orbach, R.

PY - 1971

Y1 - 1971

N2 - Phenomenological equations describing the hyperfine splitting of a localized electron resonance in a metal are studied. The transverse susceptibility χ+(ω) is obtained for the case of nuclear spin I=1/2, and its poles and residues are displayed. The corresponding eigenvectors are determined, enabling a physical generalization to arbitrary nuclear spin. The validity of the generalization procedure is verified by an examination of the generalized susceptibility. The conditions for the observation of the hyperfine splitting in a dilute magnetic alloy are detailed. Three distinct regions are found to be important, depending on the strength of the exchange coupling. Region (1), corresponding to a very weak exchange coupling, exhibits hyperfine splittings of the same character as in an insulator. The linewidth of each hyperfine component equals Δ se+ΔsL, where Δse is the second-order localized-conduction electron exchange relaxation rate, and ΔsL the localized spin lattice relaxation rate. Region (2) corresponds to sufficiently larger values of the exchange coupling for a magnetic resonance bottle-neck to obtain, but for which ωhf/ Δse≫1, where ωhf is the electronic hyperfine splitting frequency. In region (2) the hyperfine splitting is the same as in region (1), but the width of each component equals [2I/(2I+1)] ·[Δse+ΔsL]. Region (3) corresponds to yet larger values of the exchange coupling, such that ωhf/ Δse≪1. In this more strongly bottlenecked region the hyperfine split resonance is narrowed into a single line, and the resonance properties are those one would derive in the complete absence of a hyperfine interaction. Recent successful observations of the hyperfine splitting of a localized moment resonance for rare-earth alloys belong to category (1). Unsuccessful measurements in transition metal alloys indicate their character is appropriate to region (3). It is suggested that lower temperature measurements may shift some of these materials into region (2) (because Δse ∝T), allowing for a direct determination of the magnitude of the exchange coupling constant, even though the resonance system is still in the bottlenecked regime.

AB - Phenomenological equations describing the hyperfine splitting of a localized electron resonance in a metal are studied. The transverse susceptibility χ+(ω) is obtained for the case of nuclear spin I=1/2, and its poles and residues are displayed. The corresponding eigenvectors are determined, enabling a physical generalization to arbitrary nuclear spin. The validity of the generalization procedure is verified by an examination of the generalized susceptibility. The conditions for the observation of the hyperfine splitting in a dilute magnetic alloy are detailed. Three distinct regions are found to be important, depending on the strength of the exchange coupling. Region (1), corresponding to a very weak exchange coupling, exhibits hyperfine splittings of the same character as in an insulator. The linewidth of each hyperfine component equals Δ se+ΔsL, where Δse is the second-order localized-conduction electron exchange relaxation rate, and ΔsL the localized spin lattice relaxation rate. Region (2) corresponds to sufficiently larger values of the exchange coupling for a magnetic resonance bottle-neck to obtain, but for which ωhf/ Δse≫1, where ωhf is the electronic hyperfine splitting frequency. In region (2) the hyperfine splitting is the same as in region (1), but the width of each component equals [2I/(2I+1)] ·[Δse+ΔsL]. Region (3) corresponds to yet larger values of the exchange coupling, such that ωhf/ Δse≪1. In this more strongly bottlenecked region the hyperfine split resonance is narrowed into a single line, and the resonance properties are those one would derive in the complete absence of a hyperfine interaction. Recent successful observations of the hyperfine splitting of a localized moment resonance for rare-earth alloys belong to category (1). Unsuccessful measurements in transition metal alloys indicate their character is appropriate to region (3). It is suggested that lower temperature measurements may shift some of these materials into region (2) (because Δse ∝T), allowing for a direct determination of the magnitude of the exchange coupling constant, even though the resonance system is still in the bottlenecked regime.

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U2 - 10.1063/1.1660388

DO - 10.1063/1.1660388

M3 - Article

AN - SCOPUS:33744556559

VL - 42

SP - 1659

EP - 1665

JO - Journal of Applied Physics

JF - Journal of Applied Physics

SN - 0021-8979

IS - 4

ER -