Nuclear Spin Exchange in Solids:Tl203andTl205Magnetic Resonance in Thallium and Thallic Oxide

Abstract

The line width of the ${\mathrm{Tl}}^{203}$ and ${\mathrm{Tl}}^{205}$ nuclear magnetic resonance in thallium and thallium oxide greatly exceeds the dipolar width, and is a function of the abundance of the other isotope. The results can be interpreted in terms of an exchange interaction $A{\mathrm{I}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{I}}_{2}$ between a pair of nuclear spins which exceeds the normal dipolar interaction. The exchange between different isotopes leads to broadening. Exchange between like nuclei should lead to narrowing, but it was found that samples containing 98.7 percent ${\mathrm{Tl}}^{205}$ still exhibit lines broader than the dipolar interaction. Two causes are shown to exist: anisotropy of the chemical shift and pseudodipolar exchange interaction. Analysis with the method of the moments gives for the exchange interaction constant $A{h}^{\ensuremath{-}1}=17.5$ kc/sec with a 30 percent anisotropic pseudo-dipolar character in the hexagonal metal, and $A{h}^{\ensuremath{-}1}=12$ kc/sec with less than 10 percent pseudo-dipolar character in thallic oxide. The oxide has a chemical shift of +0.55 percent with an anisotropy of 34 percent of this amount. The metal exhibits a shift of 1.56 percent with 16 percent anisotropy.Ramsey's theory of the nuclear spin exchange via excited electron states in molecules, is extended to solids. Most heavy isotopes in metals and insulators should exhibit exchange effects. From the anisotropy of the exchange, information about the relative amount of $p$ or $d$ character of the electron wave function in the solid can be obtained.It is predicted that thallic oxide has a nuclear Curie point at 3.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ \ifmmode^\circ\else\textdegree\fi{}K. Whether it will become nuclear ferromagnetic or antiferromagnetic depends on details of the electronic band structure.