Magnetic irreversibility and relaxation in assembly of ferromagnetic nanoparticles

Abstract

Measurements of the magnetic irreversibility line and time-logarithmic decay of the magnetization are described for three F e2O3 samples composed of regular amorphous, acicular amorphous and crystalline nanoparticles. The relaxation rate is the largest and the irreversibility temperature is the lowest for the regular amorphous nanoparticles. The crystalline material exhibits the lowest relaxation rate and the largest irreversibility temperature. We develop a phenomenological model to explain the details of the experimental results. The main new aspect of the model is the dependence of the barrier for magnetic relaxation on the instantaneous magnetization and therefore on time. The time dependent barrier yields a natural explanation to the time-logarithmic decay of the magnetization. Interactions between particles as well as shape and crystalline magnetic anisotropies define a new energy scale that controls the magnetic irreversibility. Introducing this energy scale yields a self-consistent explanation of the experimental data.

Magnetic irreversibility and the Verwey transition in nanocrystalline bacterial magnetite

“…In order to compare different samples, we chose our measurements based on previous studies with various iron oxide nanoparticles [38][39][40][41][42][43] and report measurements of M͑T͒ and M͑H͒ dependencies as well as magnetic relaxation, M͑time͒, for a fixed set of parameters as described in detail in the following sections.…”

“…However, in assemblies of nanoparticles, relaxation is always time logarithmic, which we show is due to the collective nature of the barrier that now depends on the total magnetic moment, U͑M͒. 38,39 Alternative theories invoke size ͑hence barrier͒ distributions that supposedly lead to stretched exponential relaxation. Magnetotactic bacterial nanocrystalline magnetite provides useful insight into the problem because their size distribution is very narrow and their crystal structure is perfect ͑that excludes barrier variations due to the amorphous nature of the synthetic nanoparticles͒.…”

“…Very similar relaxation curves are observed in frozen ferrofluids 39 and dry powders. 38 Our previous work has shown, both experimentally and theoretically, that obvious time-logarithmic dependence of magnetization is due to the collective barrier for magnetic relaxation. Single-particle barrier does not depend on the total magnetic moment ͑of the surroundings͒ and results in time-exponential relaxation.…”

“…38,39 It is believed that this relaxation is a result of Arrhenius thermal activation, exp͑−U / k B T͒, where U is the barrier for magnetic moment reorientation. In a simple single-particle barrier, U depends only on magnetocrystalline anisotropy and the strength of the applied field, so the relaxation should be time exponential.…”

“…The low-temperature part, which is absent in the single crystal, is most likely related to dipolar interparticle interactions that lead to the enhancement of the collective barrier for magnetic moment reorientation. 38,39 Another aspect of temperature-dependent magnetization is the absolute value of the magnetic moment across the Verwey transition. Figure 3 shows a set of transition curves in a single crystal measured in different fields.…”