### Abstract

We present new and refined data for the magnetic field (H) and temperature (T) dependence of the proton spin-lattice relaxation rate (1/T_{1}) 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/T_{1})/(Tχ(T)), given by R(H,T)=Aω_{c}(T)/(ω_{c}
^{2}(T) + ω_{N}
^{2}), where χ=(∂M/∂H)_{T} is the differential susceptibility, A is a fitting constant, and ω_{N} is the proton Larmor frequency, and (2) a temperature-dependent correlation frequency ω_{c}(T) which at low T is given by ω_{c}(T) ∝T^{α}, 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 T_{0}(H) for which ω_{c}(T) = ω_{N}; (2) for low T a scaling formula applies, R(H,T)/R(H,T_{0}(H))=2t^{α}/(1+t ^{2α}), where t≡T/T_{0}(H). Both results are confirmed by our experimental data for the choice α=3.5±0.5.

Original language | English |
---|---|

Article number | 134434 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 70 |

Issue number | 13 |

DOIs | |

Publication status | Published - Oct 2004 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*70*(13), [134434]. https://doi.org/10.1103/PhysRevB.70.134434

**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.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 70, no. 13, 134434. https://doi.org/10.1103/PhysRevB.70.134434

}

TY - JOUR

T1 - Scaling behavior of the proton spin-lattice relaxation rate in antiferromagnetic molecular rings

AU - Baek, S. H.

AU - Luban, M.

AU - Lascialfari, A.

AU - Micotti, E.

AU - Furukawa, Y.

AU - Borsa, F.

AU - Van Slageren, J.

AU - Cornia, A.

PY - 2004/10

Y1 - 2004/10

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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U2 - 10.1103/PhysRevB.70.134434

DO - 10.1103/PhysRevB.70.134434

M3 - Article

AN - SCOPUS:42749098569

VL - 70

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 13

M1 - 134434

ER -