Nuclear Magnetic Resonance of Indium Metal at 4.2°K

Abstract

143only slightly in structure from each other and having no polarization effects in the substitution. These results are consistent with the dependence of the octahedral cubic field splitting on small variations of lattice spac ing, as obtained from pressure data in MgO. 12 They also indicate that the variations of some of the param eters among different hosts are sufficiently large to ex plain discrepancies between the measured anisotropy constant in YIG and that obtained, assuming that the anisotropy originates in the crystalline field but using spin-Hamiltonian parameters obtained for YGaG. Such results should, hopefully, motivate theoretical calcula tions of crystal field splitting for the Fe 3+ ground state in order to elucidate the mechanisms responsible for their existence, thus permitting resonance results on such impurities to be used more efficiently in the study of their environment. ACKNOWLEDGMENTWe wish to thank Miss W. Doherty for her very able assistance with the diagonalization program for the spin-Hamiltonian matrices.The nuclear magnetic resonance spectrum of indium metal power has been measured at twelve magneticfield points in the range of 17.0 to 30.5 kG at 4.2°K. The analysis of this spectrum gives the isotropic Knight shift as +0.80±0.02%, the anisotropic Knight shift as -0.05±0.02%, and the nuclear quadrupole spliting parameter v q as 1.884±0.002 Mc/sec. All three of these quantities were determined at each of the twelve field points, and no field dependence has been observed in this range.

A simple proof that third-order quadrupole perturbations of the NMR central transition of half-integral spin nuclei are zero

“…In this paper, we show that the third-order correction to the position of the central transition is exactly zero, which partly explains this observation. This is a well-known result in the literature [10,11,18,19], but we present a new, clear, and simple derivation.This result is based on a recently published selection rule [25]. The calculation uses the principle that the NMR transitions can be calculated directly, by setting up and diagonalizing the Liouvillian [26].…”

“…In this paper, we show that the third-order correction to the position of the central transition is exactly zero, which partly explains this observation. This is a well-known result in the literature [10,11,18,19], but we present a new, clear, and simple derivation.…”

“…Higher-order corrections to the wavefunctions have been published [14][15][16][17][18][19], as have a number of exact solutions [10,[20][21][22][23][24][25]. In practice, we find that second-order perturbation theory works remarkably well.…”

Φασματοσκοπικές Μελέτες Πυρηνικού Μαγνητικού Συντονισμού (NMR) Σε Συστήματα Περοβσκιτών Μαγγανίου Κολοσσιαίας Μαγνητοαντίστασης

“…Οη όξνη ηεο ηεηξαπνιηθήο δηαηαξαρήο ζε αλάιπζε πξώηεο θαη δεπηέξεο ηάμεο είλαη κε κεδεληθνί[407] θαη νδεγνύλ ζε ηππηθέο κνξθέο θάζκαηνο όπσο θαίλεηαη ζην ζρήκα 25. Ζ ζεσξία δηαηαξαρώλ δεύηεξεο ηάμεο πεξηγξάθεη ηθαλνπνηεηηθά ηα πεηξακαηηθά επξήκαηα ελώ νη όξνη ηξίηεο ηάμεο ζηελ θεληξηθή κεηάβαζε είλαη κεδεληθνί[408][409][410][411]. Απηό απνδεηθλύεηαη αθόκε θαη κε ηε ρξήζε ησλ ηειεζηώλ Liouville[412].…”

“…Απηό απνδεηθλύεηαη αθόκε θαη κε ηε ρξήζε ησλ ηειεζηώλ Liouville[412]. Μειέηεο πνπ αθνξνύλ δηνξζώζεηο αλώηεξεο ηάμεο ζηηο θπκαηνζπλαξηήζεηο βξίζνπλ ζηε βηβιηνγξαθία[408,411,[413][414][415][416] θαη πνιιέο θαηαιήγνπλ ζε αθξηβείο ιύζεηο[417][418][419][420][421][422].…”