Effect of an applied magnetic field on the relaxation time of single-chain magnets

Single-chain magnets (SCMs) are one-dimensional systems in which the relaxation of the magnetization becomes very slow at low temperature. This singular behavior is due to the vicinity of the critical point located at vanishing temperature (T=0) and applied magnetic field (H=0). In order to optimize the properties of these nano-objects, detailed studies of the observed critical behavior are necessary. However, previous works on the SCM relaxation have essentially analyzed experimental data in the absence of applied magnetic field. We discuss in this paper the effect of applying a magnetic field on two different examples of single-chain magnets. These samples have been previously described in the absence of magnetic field and considered as model systems since their chains are composed of a regular one-dimensional (1D) arrangement of anisotropic trimer units. These magnetic trinuclear motifs can be described at low temperature as effective spins coupled ferromagnetically. Theoretical results relevant to analyze our data in the presence of an applied magnetic field are first described. We also present a simple numerical approach to discuss finite-size effects relevant in SCM systems. Experimental data, including ac and dc data on powder samples and single crystals, are then presented. These results are analyzed and compared with the theoretical predictions deduced for the 1D Ising model. At low field, for h xi << 1 (where xi is the correlation length normalized to the unit cell parameter and h=mu H/k(B)T is the dimensionless applied field) or for hL << 1 when finite-size effects are relevant (L being the chain length normalized to the unit cell parameter), we show that experimental data reproduce the critical behavior expected from the theory. Moreover, the obtained values of xi or L are in excellent agreement with the estimation deduced from susceptibility data. At higher fields, for h xi >> 1 or hL >> 1, we show that the field dependence of the relaxation time is drastically different for the two samples. This difference is understood taking into account the field dependence of the relaxation time of the effective spins located inside a domain wall.