Inverse Laplace Transformation Analysis of Stretched Exponential Relaxation

Abstract

We investigate the effectiveness of the Inverse Laplace Transform (ILT) analysis method to extract the distribution of relaxation rates from nuclear magnetic resonance data with stretched exponential relaxation. Stretched-relaxation is a hallmark of a distribution of relaxation rates, and an analytical expression exists for this distribution for the case of a spin-1/2 nucleus. We compare this theoretical distribution with those extracted via the ILT method for several values of the stretching exponent and at different levels of experimental noise. The ILT accurately captures the distributions for $\beta \lesssim 0.7$, and for signal to noise ratios greater than $\sim 40$; however the ILT distributions tend to introduce artificial oscillatory components. We further use the ILT approach to analyze stretched relaxation for spin $I>1/2$ and find that the distributions are accurately captured by the theoretical expression for $I=1/2$. Our results provide a solid foundation to interpret distributions of relaxation rates for general spin $I$ in terms of stretched exponential fits.

arXiv comment10 pages, 10 figures

References in corpus (20)

• Electronic Liquid Crystal Phases of a Doped Mott Insulator
• Rheology of Soft Glassy Materials
• Defects in correlated metals and superconductors
• Stretched Exponential Relaxation Arising from a Continuous Sum of Exponential Decays
• Commensurate Itinerant Antiferromagnetism in BaFe2As2: 75As-NMR Studies on a Self-Flux Grown Single Crystal
• Stripe glasses: self generated randomness in a uniformly frustrated system
• Inhomogeneous Low Frequency Spin Dynamics in La_{1.65}Eu_{0.2}Sr_{0.15}CuO_4
• Interacting Antiferromagnetic Droplets in Quantum Critical CeCoIn_5
• Disorder in a Quantum Critical Superconductor
• Similar glassy features in the NMR response of pure and disordered La1.88Sr0.12CuO4
• Coexistence of cluster spin glass and superconductivity in Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ for $0.060\le x\le 0.071$
• Coexistence of antiferromagnetic order and unconventional superconductivity in heavy fermion compounds CeRh_{1-x}Ir_xIn_5: nuclear quadrupole resonance studies
• Uniaxial strain control of spin-polarization in multicomponent nematic order of BaFe${}_2$As${}_2$
• Spontaneous formation of a superconducting and antiferromagnetic hybrid state in SrFe2As2 under high pressure
• NMR imaging of the soliton lattice profile in the spin-Peierls compound CuGeO_3
• NMR evidence for inhomogeneous nematic fluctuations in BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$
• NMR evidence for inhomogeneous glassy behavior driven by nematic fluctuations in iron arsenide superconductors
• ${}^{139}$La NMR investigation of the interplay between the lattice, charge, and spin dynamics in charge ordered high $T_c$ cuprate La${}_{1.875}$Ba${}_{0.125}$CuO${}_4$
• Distribution of the magnetic environment in charge ordered La${}_{1.885}$Sr${}_{0.115}$CuO${}_4$
• Uncovering the Hidden Order in URu2Si2 by Impurity Doping

Cited by in corpus (3)

• From spin liquid to magnetic ordering in the anisotropic kagome Y-Kapellasite Y3Cu9(OH)19Cl8: a single crystal study
• Field evolution of magnetic phases and spin dynamics in the honeycomb lattice magnet Na2Co2TeO6: 23Na NMR study
• Competition between spin ordering and superconductivity near the pseudogap boundary in La2-xSrxCuO4: insights from NMR