Magnetic momentum density, Fermi surface and directional magnetic Compton profiles in LaSr$_{2}$Mn$_{2}$O$_{7}$ and La$_{1.2}$Sr$_{1.8}$Mn$_2$O$_7$

We have carried out first principles, all-electron computations of the magnetic momentum density $\rho_{mag}({\mathbf p})$ and magnetic Compton profiles (MCPs) for momentum transfer along the [100], [001], and [110] directions in LaSr$_2$Mn$_2$O$_7$ and La$_{1.2}$Sr$_{1.8}$Mn$_2$O$_7$ [1]. Parallel measurements of these three MCPs from a single crystal of La$_{1.2}$Sr$_{1.8} $Mn$_2$O$_7$ at 5 K in a magnetic field of 7 T are also reported. Here, we discuss details of the FS-related signatures in the first and higher BZs in the MCPs and show that high resolution magnetic Compton scattering experiments with a momentum resolution of 0.1 a.u. FWHM (full-width-at-half- maximum) or better will be necessary to observe this fine structure. We comment also on the feasibility of using positron annihilation spectroscopy in this connection. Work supported by the USDOE.\\ \mbox{[1]} Yinwan Li, P. A. Montano, J.F. Mitchell, B. Barbiellini, P. E. Mijnarends, S. Kaprzyk, and A. Bansil, Phys. Rev. Lett. 93 (2004) 207206.