Phys. Rev. B 76, 165122 (2007)
Spin and orbital magnetic response in metals: Susceptibility and NMR shifts
Mayeul d'Avezac, Nicola Marzari, and Francesco Mauri
(Received 12 July 2007; published 23 October 2007)
A DFT-based method is presented which allows the computation of all-electron NMR shifts of metallic compounds with periodic boundary conditions. NMR shifts in metals measure two competing physical phenomena. Electrons interact with the applied magnetic field (i) as magnetic dipoles (or spins), resulting in the Knight shift, and (ii) as moving electric charges, resulting in the chemical (or orbital) shift. The latter is treated through an extension to metals of the gauge-invariant projector augmented wave developed for insulators. The former is modeled as the hyperfine interaction between the electronic spin polarization and the nuclear dipoles. NMR shifts are obtained with respect to the computed shieldings of reference compounds, yielding fully ab initio quantities which are directly comparable to experiment. The method is validated by comparing the magnetic susceptibility of interacting and noninteracting homogeneous gas with known analytical results, and by comparing the computed NMR shifts of simple metals with experiment.
Phys. Rev. B 76, 155201 (2007)
Long-lived spin echoes in a magnetically dilute system: An NMR study of Ge single crystals
A. M. Panich, N. A. Sergeev, and I. Shlimak
(Received 22 March 2007; revised 1 August 2007; published 1 October 2007)
Owing to the well-developed technology, isotopic engineering of Si and Ge semiconductors permits one to control the density of nuclear spins and vary the spin coherence time, a crucial parameter in spintronics and quantum computing where nuclear spin is used as a qubit. In the present paper, we report on the NMR study of 73Ge nuclear spin decoherence in germanium single crystals with different abundances of the 73Ge isotope. Our measurements of Hahn- and solid-echo decays show that they are well fit by a superposition of two exponentials; at that, the deviation from the single exponential is more pronounced in the more spin-diluted sample, causing long-lived echoes. We show that the decay of these echoes becomes slower with the reduction of 73Ge abundance and is therefore caused by dipole-dipole interaction, reflecting the fundamental decoherence process in the spin system. The fast decay at the beginning of the relaxation process is shown to be mainly caused by the quadrupole interaction. Our experimental findings are supported by the calculations of Hahn- and solid-echo decays in the germanium crystals under study. Quite good agreement between the theory and experiment is demonstrated.