Scaling behavior of the proton spin-lattice relaxation rate in antiferromagnetic molecular rings

S. H. Baek, M. Luban, A. Lascialfari, E. Micotti, Y. Furukawa, F. Borsa, J. Van Slageren, A. Cornia

Research output: Contribution to journalArticle

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Abstract

We present new and refined data for the magnetic field (H) and temperature (T) dependence of the proton spin-lattice relaxation rate (1/T1) in antiferromagnetic molecular rings as well as a new explicit scaling formula that accurately reproduces our data. The key ingredients of our formulation are (1) a reduced relaxation rate, R(H,T) = (1/T1)/(Tχ(T)), given by R(H,T)=Aωc(T)/(ωc 2(T) + ωN 2), where χ=(∂M/∂H)T is the differential susceptibility, A is a fitting constant, and ωN is the proton Larmor frequency, and (2) a temperature-dependent correlation frequency ωc(T) which at low T is given by ωc(T) ∝Tα, that we identify as a lifetime broadening of the energy levels of the exchange-coupled paramagnetic spins due to spin-acoustic phonon coupling. The main consequences are (1) R(H,T) has a local maximum for fixed H and variable T that is proportional to 1/H; the maximum occurs at the temperature T0(H) for which ωc(T) = ωN; (2) for low T a scaling formula applies, R(H,T)/R(H,T0(H))=2tα/(1+t ), where t≡T/T0(H). Both results are confirmed by our experimental data for the choice α=3.5±0.5.

Original languageEnglish
Article number134434
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume70
Issue number13
DOIs
Publication statusPublished - Oct 2004

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Spin-lattice relaxation
spin-lattice relaxation
Protons
scaling
protons
rings
ingredients
Temperature
Electron energy levels
temperature
energy levels
Acoustics
Magnetic fields
magnetic permeability
formulations
life (durability)
Hydrogen
acoustics
magnetic fields

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Scaling behavior of the proton spin-lattice relaxation rate in antiferromagnetic molecular rings. / Baek, S. H.; Luban, M.; Lascialfari, A.; Micotti, E.; Furukawa, Y.; Borsa, F.; Van Slageren, J.; Cornia, A.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 70, No. 13, 134434, 10.2004.

Research output: Contribution to journalArticle

Baek, S. H. ; Luban, M. ; Lascialfari, A. ; Micotti, E. ; Furukawa, Y. ; Borsa, F. ; Van Slageren, J. ; Cornia, A. / Scaling behavior of the proton spin-lattice relaxation rate in antiferromagnetic molecular rings. In: Physical Review B - Condensed Matter and Materials Physics. 2004 ; Vol. 70, No. 13.
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N2 - We present new and refined data for the magnetic field (H) and temperature (T) dependence of the proton spin-lattice relaxation rate (1/T1) in antiferromagnetic molecular rings as well as a new explicit scaling formula that accurately reproduces our data. The key ingredients of our formulation are (1) a reduced relaxation rate, R(H,T) = (1/T1)/(Tχ(T)), given by R(H,T)=Aωc(T)/(ωc 2(T) + ωN 2), where χ=(∂M/∂H)T is the differential susceptibility, A is a fitting constant, and ωN is the proton Larmor frequency, and (2) a temperature-dependent correlation frequency ωc(T) which at low T is given by ωc(T) ∝Tα, that we identify as a lifetime broadening of the energy levels of the exchange-coupled paramagnetic spins due to spin-acoustic phonon coupling. The main consequences are (1) R(H,T) has a local maximum for fixed H and variable T that is proportional to 1/H; the maximum occurs at the temperature T0(H) for which ωc(T) = ωN; (2) for low T a scaling formula applies, R(H,T)/R(H,T0(H))=2tα/(1+t 2α), where t≡T/T0(H). Both results are confirmed by our experimental data for the choice α=3.5±0.5.

AB - We present new and refined data for the magnetic field (H) and temperature (T) dependence of the proton spin-lattice relaxation rate (1/T1) in antiferromagnetic molecular rings as well as a new explicit scaling formula that accurately reproduces our data. The key ingredients of our formulation are (1) a reduced relaxation rate, R(H,T) = (1/T1)/(Tχ(T)), given by R(H,T)=Aωc(T)/(ωc 2(T) + ωN 2), where χ=(∂M/∂H)T is the differential susceptibility, A is a fitting constant, and ωN is the proton Larmor frequency, and (2) a temperature-dependent correlation frequency ωc(T) which at low T is given by ωc(T) ∝Tα, that we identify as a lifetime broadening of the energy levels of the exchange-coupled paramagnetic spins due to spin-acoustic phonon coupling. The main consequences are (1) R(H,T) has a local maximum for fixed H and variable T that is proportional to 1/H; the maximum occurs at the temperature T0(H) for which ωc(T) = ωN; (2) for low T a scaling formula applies, R(H,T)/R(H,T0(H))=2tα/(1+t 2α), where t≡T/T0(H). Both results are confirmed by our experimental data for the choice α=3.5±0.5.

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