Anomalous relaxation in a quasi-one-dimensional fractal cluster glass

Abstract

The low-temperature spin glass state of the quasi-$1\mathrm{D}$ organic-based magnet ${[\mathrm{MnTPP}]}^{+}{[\mathrm{TCNE}]}^{\ensuremath{-}}\ifmmode\cdot\else\textperiodcentered\fi{}x(1,3\ensuremath{-}{\mathrm{C}}_{6}{\mathrm{H}}_{4}{\mathrm{Cl}}_{2})$ has unusually long relaxation times due to frustration induced by dipole-dipole interactions between fractal spin clusters. This long relaxation is investigated with in-field relaxation measurements. The extremely long relaxation process enables probing of time-dependent phenomena using conventional magnetic measurements, including sweep rate-dependent hysteresis curves, even for temperatures well above the spin glass transition temperature $({T}_{g})$. For a temperature of $\ensuremath{\sim}1.3{T}_{g}$, the coercive field increased by 170% for differing sweep rates, while below ${T}_{g}$ the change was less than 5%. A study of the temperature dependence of the coercive field reveals detailed information on the behavior of fractal spin clusters within the system. For temperatures above ${T}_{g}$, the largely single-chain spin clusters act independently during magnetic reversal. As the spin clusters branch out below ${T}_{g}$, magnetic reversal is more cooperative, reflecting an enhancement of the magnetic interaction in the interpenetrating fractal cluster system.