Difference between revisions of "Quantum Entanglement"
(Created page with "Relaxonomy --> here ---- Most muon spin relaxation is caused by '''R'''andom '''L'''ocal '''M'''agnetic '''F'''ields ['''RLMF'''] due to the magnetic moments of nearby pa...") |
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Most muon spin relaxation is caused by '''R'''andom '''L'''ocal '''M'''agnetic '''F'''ields ['''RLMF'''] due to the magnetic moments of nearby particles, either nuclei or electrons. (I count atomic orbitals with nonzero angular momentum as "electrons".) But this description ignores the fact that whatever spin hamiltonian operates on the muon spin due to the other spins also acts on the other spins due to the muon spin. In reality, all the coupled spins evolve together until interrupted by fluctuations or |
Most muon spin relaxation is caused by '''R'''andom '''L'''ocal '''M'''agnetic '''F'''ields ['''RLMF'''] due to the magnetic moments of nearby particles, either nuclei or electrons. (I count atomic orbitals with nonzero angular momentum as "electrons".) But this description ignores the fact that whatever spin hamiltonian operates on the muon spin due to the other spins also acts on the other spins due to the muon spin. In reality, all the coupled spins evolve together until interrupted by fluctuations or muon hopping. |
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The result is most vividly obvious when the muon captures a single electron to form the [[Muonium]] atom, which see. |
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But it is also clearly evident in cases where the muon couples to a small number of spin-1/2 nuclei, as in fluoride insulators, where the <math>\mu^+</math> takes up a position between two <SUP>19</SUP>F nuclei and the 3-spin system exhibits oscillations at three characteristic frequencies in ZF: |
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Characteristic "FµF" signals in a variety of insulating fluorides.|} |
Characteristic "FµF" signals in a variety of insulating fluorides.|} |
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The role of <SUP>19</SUP>F in such coupled evolution can be played by any spin-1/2 nucleus, but few have a large enough magnetic moment or are sufficiently near the µ<SUP>+</SUP> to show themselves so vividly. |
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However, even a system as complicated as the µ<SUP>+</SUP> surrounded by 8 copper nuclei in the octahedral site exhibits enhanced relaxation when the muon's Zeeman splitting matches the electric quadrupolar splitting of the Cu nuclei in the muon's electric field. This phenomenon is known as [[Resonant Relaxation]], which see. |
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Latest revision as of 14:49, 17 September 2022
Relaxonomy --> here
Most muon spin relaxation is caused by Random Local Magnetic Fields [RLMF] due to the magnetic moments of nearby particles, either nuclei or electrons. (I count atomic orbitals with nonzero angular momentum as "electrons".) But this description ignores the fact that whatever spin hamiltonian operates on the muon spin due to the other spins also acts on the other spins due to the muon spin. In reality, all the coupled spins evolve together until interrupted by fluctuations or muon hopping.
The result is most vividly obvious when the muon captures a single electron to form the Muonium atom, which see.
But it is also clearly evident in cases where the muon couples to a small number of spin-1/2 nuclei, as in fluoride insulators, where the <math>\mu^+</math> takes up a position between two 19F nuclei and the 3-spin system exhibits oscillations at three characteristic frequencies in ZF:
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Characteristic "FµF" signals in a variety of insulating fluorides.|} The role of 19F in such coupled evolution can be played by any spin-1/2 nucleus, but few have a large enough magnetic moment or are sufficiently near the µ+ to show themselves so vividly. However, even a system as complicated as the µ+ surrounded by 8 copper nuclei in the octahedral site exhibits enhanced relaxation when the muon's Zeeman splitting matches the electric quadrupolar splitting of the Cu nuclei in the muon's electric field. This phenomenon is known as Resonant Relaxation, which see. |
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