Theory of the location and associated hyperfine properties of the positive muon in ${\mathrm{La}}_2$${\mathrm{CuO}}_4$

The location of the positive muon, used as a tool for probing the magnetic properties of high-${\mathit{T}}_{\mathit{c}}$ systems, is investigated for ${\mathrm{La}}_2$${\mathrm{CuO}}_4$. Our calculations, using the unrestricted Hartree-Fock cluster procedure, indicate that the muon is located in the a-c plane, at a distance of 1.08 Å from the apical oxygen, with the ${\mathrm{\mu }}^{+}$-O(a) direction making an angle of 25° with the O(a)-Cu direction. The magnitude and direction of the hyperfine field at the equilibrium position are determined. Our results, which are in reasonable agreement with μSR data in powdered samples and single crystals, show the importance of including the local contact and dipolar contributions to the hyperfine field associated with the unpaired spin distribution in the neighborhood of the muon. Possible additional factors that could lead to a bridging of the remaining quantitative differences with experimental hyperfine data will be discussed.