Blocking temperature in magnetic nanoclusters

Abstract

A recent study of nonextensive phase transitions in nuclei and nuclear clusters needs a probability model compatible with the appropriate Hamiltonian. For magnetic molecules a representation of the evolution by a Markov process achieves the required probability model that is used to study the probability density function (PDF) of the order parameter, i.e. the magnetization. The existence of one or more modes in this PDF is an indication for the superparamagnetic transition of the cluster. This allows us to determine the factors that influence the blocking temperature, i.e. the temperature related to the change of the number of modes in the density. It turns out that for our model, rather than the evolution of the system implied by the Hamiltonian, the high temperature density of the magnetization is the important factor for the temperature of the transition. We find that an initial probability density function with a high entropy leads to a magnetic cluster with a high blocking temperature.

Probability assignment in a quantum statistical model

“…For he spin model we will consider two cases, firstly we consider a system consisting of a single large spin, typically used in connection with nano-magnets, and indicated by LS. Secondly we will consider the many spin system, typically used to calculate the blocking temperature [3] or other phase-transitions [9,10,11,12], and indicated by MS. For the M/M/∞-queue we will use the maximum entropy principle to show that it is able to distinguish between different initial conditions. Furthermore we will calculate the Shannon entropy of the queue and of the "quantum" model equivalent to the queue and show that the entropies have completely different behavior with respect to β .…”

“…In ref. [3], we compared the PDF of magnetization based on the assignment (1) with the PDF based on the Markov representation and we found that they are different. In order to indicate the possible origin of this difference we briefly indicate the steps necessary to achieve the Markov representation.…”

“…The mapping and references to the physical origin of the model can be found in the paper: [3]. The second system is an M/M/∞ -queue.…”

“…When the Hamiltonian is rewritten in terms of spin lowering and raising operators, the generator Q for the continuous time Markov process can be calculated using the techniques which are documented in ref. [3]. Casting the Markov representation of ( 6) into a matrix equation: ∂ βK (β ) =QK(β ), and straightforward matrix methods can be used to obtain K m m ′ (β ).…”

Macrospin approximation and quantum effects in models for magnetization reversal

“…Since S > 1/2 there is an underscreened Kondo effect, the development of which is hampered by the anisotropy as has been shown by timedependent numerical renormalization group. 17 As the quantum character of the macrospin is not accounted for by simple Langevin dynamics, 7 different approaches [18][19][20] have been suggested to treat the macro-or many-spin dynamics in contact with bosonic baths by means of quantum master-equation approaches and to determine, e.g., the blocking temperature. The importance of a manyspin model, for example, is demonstrated by studies of the probability density function of the macrospin obtained by replacing thermal with Markov processes.…”