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Polaron

< Hypothesis on an ideal molecular magnet | Index

Following Dehn PRL Fe2O3 and Shenton-supplemental-Muons_in_Fe2O3-7a41fb6.zip? with https://github.com/Shenton-supplemental/Muons_in_Fe2O3

Ingredients: two or more spin, {$I$}, the muon, {$s$} the polaron, in a wider sense (the electron, for Mu), and {$S$}, the nn cation spin.

They interact through a hyperfine spin Hamiltonian {$\cal H$} made of contact, dipolar and Zeeman terms.

However, {$S, s$} may (or do) interact also through Coulomb terms. This is either explicit in {$\cal H$}, or in a statistical mechanics sense, hence it is effective as long as the relaxation time {$\tau$} (Drude, for a metal, electron T1, for a diamagnetic environment) is short wr to the muon window. The Coulomb energy is much larger than {$\cal H$}. This has distinct consequences in two extreme regimes.

• {$\tau\ll \tau_\mu$} motional narrowing of {$\cal H$}, stat mech determines electron density matrix (i.e. Coulomb interaction prevail )
• {$\tau\gg \tau_\mu$}, Coulomb interactions only if explicitly present in {$\cal H$}. This is the case for magnets, where {$S$} is also subject to Heisenberg, Hubbard etc (Coulomb scale)

So, typically

• Mu, assume {$\tau\gtrsim \tau_\mu$}, {$\cal H$} alone with unpolarized electron density matrix, each {$s$} state is coherent;
• F-{$\mu$}-F, as above
• typical muon site in a metal, assume {$\tau<< \tau_\mu$}, extreme narrowing regime of {$\cal H$}, only {$\chi_P H$} survives, negligible, and vanishing in {$H=0$};
• positive muon in Fe2O3, {$S$} part of {$\cal H$} acts as a local field, because its density matrix is {$S_z$}, can be absorbed in Zeeman, keeping tensor into account.
• polaron, same, also {$ s$} density matrix is polarized, both {$S, s$} fall into Zeeman (tensors)

< Hypothesis on an ideal molecular magnet | Index