A1 Refereed original research article in a scientific journal
Spin-lattice relaxation via limited jumps in NH4 compounds
Authors: Punkkinen M, Ylinen EE
Publisher: ELSEVIER SCIENCE BV
Publication year: 2003
Journal:: Physica B: Condensed Matter
Journal name in source: PHYSICA B-CONDENSED MATTER
Journal acronym: PHYSICA B
Volume: 337
Issue: 1-4
First page : 111
Last page: 121
Number of pages: 11
ISSN: 0921-4526
DOI: https://doi.org/10.1016/S0921-4526(03)00386-7
Abstract
Nuclear spin-lattice relaxation of hydrogens in some ammonium hexachlorometallates at low temperatures is driven by small-angle or limited jumps of the NH4+ tetrahedra about the [111] equilibrium orientations of the high-temperature cubic phase. Usually, the low-temperature equilibrium orientations are not known and they vary most likely with the sample. Here they are defined by symmetry in such a way that each N-H bond of an NH4+ ion makes the same angle Delta with the nearest [I 1 1] direction. This assumption defines the six possible equilibrium orientations of NH4+ and also the directions of the intra-ion proton-proton vectors in terms of Delta. At low temperatures, when the rate of the 1200 rotations about the threefold axes of ammonium groups (with the correlation time tau(c)) has slowed down sufficiently, the limited jumps between the six equilibrium orientations dominate the proton spin-lattice relaxation. The time-dependent perturbation theory is used to calculate the transition rates, related to these limited jumps, between the various energy levels of the NH4+ rotational ground state, shifted by the rotational tunnelling and the interaction of the hydrogen atoms with the external magnetic field (the resonance frequency omega(0)). An expression is derived for the initial relaxation rate of the proton magnetization. A comparison with the relaxation rate at the normal minimum corresponding to omega(0)tau(c) approximate to 1 provides the angle Delta. The model is applied to the available experimental data on (NH4)(2)TeCl6 and the result Delta = 5.3degrees is obtained. (C) 2003 Elsevier B.V. All rights reserved.
Nuclear spin-lattice relaxation of hydrogens in some ammonium hexachlorometallates at low temperatures is driven by small-angle or limited jumps of the NH4+ tetrahedra about the [111] equilibrium orientations of the high-temperature cubic phase. Usually, the low-temperature equilibrium orientations are not known and they vary most likely with the sample. Here they are defined by symmetry in such a way that each N-H bond of an NH4+ ion makes the same angle Delta with the nearest [I 1 1] direction. This assumption defines the six possible equilibrium orientations of NH4+ and also the directions of the intra-ion proton-proton vectors in terms of Delta. At low temperatures, when the rate of the 1200 rotations about the threefold axes of ammonium groups (with the correlation time tau(c)) has slowed down sufficiently, the limited jumps between the six equilibrium orientations dominate the proton spin-lattice relaxation. The time-dependent perturbation theory is used to calculate the transition rates, related to these limited jumps, between the various energy levels of the NH4+ rotational ground state, shifted by the rotational tunnelling and the interaction of the hydrogen atoms with the external magnetic field (the resonance frequency omega(0)). An expression is derived for the initial relaxation rate of the proton magnetization. A comparison with the relaxation rate at the normal minimum corresponding to omega(0)tau(c) approximate to 1 provides the angle Delta. The model is applied to the available experimental data on (NH4)(2)TeCl6 and the result Delta = 5.3degrees is obtained. (C) 2003 Elsevier B.V. All rights reserved.
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