Muon-Fluorine Entangled States in Molecular Magnets

The information accessible from a muon-spin relaxation experiment can be limited due to a lack of knowledge of the precise muon stopping site. We demonstrate here the possibility of localizing a spin polarized muon in a known stopping state in a molecular material containing fluorine. The muon-spin precession that results from the entangled nature of the muon spin and surrounding nuclear spins is sensitive to the nature of the stopping site. We use this property to identify three classes of sites that occur in molecular magnets and describe the extent to which the muon distorts its surroundings.

Figure 1

(a) Linear chain structure of ${\mathrm{CuF}}_2({\mathrm{H}}_2\mathrm{O}{)}_2(\mathrm{pyz})$. The circled regions show sample fluorine atoms near which muons are expected to localize. (b) Crystal packing viewed parallel to the chain axis. Dotted lines show $\mathrm{OH}··\mathrm{F}$ hydrogen bonds. (c) Example ZF ${\mu }^{+}\mathrm{SR}$ spectrum measured at $T=3.4\mathrm{K}$ with a fit to the $\mathrm{F}–{\mu }^{+}$ dipole interaction described in the text. Inset: $\mathrm{F}–{\mu }^{+}$ configuration: the resulting energy levels (top right) with allowed transitions and the calculated frequency spectrum (bottom left).

Figure 2

(a) Structure of $[\mathrm{Cu}({\mathrm{NO}}_3)(\mathrm{pyz}{)}_2]{\mathrm{PF}}_6$ in the $a\mathrm{\text{−}}b$ plane showing 2D sheets of $[\mathrm{Cu}(\mathrm{pyz}{)}_2{]}^{2+}$ and $\mathrm{PF}_6{}^{-}$ anions occupying the pores in the structure [14]. The circled region shows sample fluorines near which the muon is expected to localize. (b) Example ZF spectra measured at $T=5.7\mathrm{K}$ with a fit described in the text. Inset: proposed $\mathrm{F}–{\mu }^{+}$ configuration: (top right) the resulting energy levels with allowed transitions and (bottom left) the calculated frequency spectrum.

Figure 3

(a) Structure of $[\mathrm{Cu}({\mathrm{HF}}_2)(\mathrm{pyz}{)}_2]Y$, with $Y$ molecules omitted for clarity. The circled region shows a sample fluorine and proton near which the muon is expected to localize. (b) Example ZF spectra measured at $T=11\mathrm{K}$ with a fit described in the text. Inset: proposed $\mathrm{F}–{\mu }^{+}–p$ configuration: (top right) the resulting energy levels with allowed transitions and (bottom left) the calculated frequency spectrum.