Glauber dynamics in a single-chain magnet: From theory to real systems

Abstract

The Glauber dynamics is studied in a single-chain magnet (SCM). As predicted a single relaxation mode of the magnetization is found. Above 2.7 K, the thermally activated relaxation time is mainly governed by the effect of magnetic correlations and the energy barrier experienced by each magnetic unit. This result is in perfect agreement with independent thermodynamical measurements. Below 2.7 K, a crossover towards a relaxation regime is observed that is interpreted as the manifestation of finite-size effects. The temperature dependences of the relaxation time and of the magnetic susceptibility reveal the importance of the boundary conditions. PACS numbers: 75.10. Pq, 75.40.Gb, 76.90.+d The design of new slow-relaxing magnetic nanosystems is a very challenging goal for both applications (as information storage) and fundamental research. A wellknown example of such systems is the single-molecule magnet (SMM) that shows slow reversal of the magnetization due to the combined effect of a high spin ground state and uniaxial anisotropy producing an energy barrier between spin-up and spin-down states [1]. When a magnetic field is initially applied to magnetize this system and then removed, the magnetization decays with a material-inherent relaxation time depending on the temperature. The corresponding relaxation time, τ , follows an Arrhenius law at high temperatures and the activation energy is equal to the barrier height, being roughly |D|S 2 , where D is the negative uniaxial anisotropy constant and S is the spin ground state of the molecule. At lower temperatures, τ may saturate when quantum tunneling through the barrier becomes relevant [2].Another research route of metastable magnetism has recently been explored with the synthesis of single-chain magnets (SCMs) [3,4,5]. In these materials, the slow relaxation of magnetization is not solely the consequence of the uniaxial anisotropy seen by each spin on the chain but depends also on magnetic correlations. The effect of the short-range order becomes more and more important when the temperature is reduced until a critical point is reached at T = 0 K for 1D systems. In fact, the relaxation time is found to be exponentially enhanced at low temperatures in agreement with the pioneer work of R. J. Glauber devoted to the dynamics of the 1D Ising model [6]. Although it seems that there is a reasonable agreement between the experimental data and the Glauber's theory [3,4,5], we show in this communication that several other arguments should be considered to fill the gap between the theory and the experimental results. Firstly, it should be mentioned that the experimental sys- tems are not strictly Ising-like. In the simplest case, they are rather described by an anisotropic Heisenberg model:where J is the ferromagnetic exchange constant between the spin units and D is the single-ion anisotropy. Secondly, the relaxation time of each magnetic unit, introduced phenomenologically in Glauber's study, is a priori temperature dependent [7] and this argument should also be consid...

Magnetization-based assessment of correlation energy in canted single-chain magnets

“…For ferromagnetic systems, this scenario is well confirmed 9,14,15 and has been exploited for a number of compounds 16,17 , but for antiferromagnetic chains with non-collinear anisotropy axes 11,18 the situation is much less clear. The problem was revealed 11 for the compound of formula [Mn(TPP)O 2 PHPh]·H 2 O considered a textbook example of SCM (TPP = mesotetraphenylporphyrin and PHPh = phenylphosphinate) and referred to as Mn-CAF (canted antiferromagnet).…”

Neutral Low-Dimensional Assemblies of a Mn(III) Schiff Base Complex and Octacyanotungstate(V): Synthesis, Characterization and Magnetic Properties

“…They show significant maxima for HDC=2 kOe which concurs with the value of the spin-flip field. As slow magnetic relaxations in such systems can be enhanced by applying sufficient DC field [30], AC measurements were conducted with DC field of 2 kOe applied as well. In these conditions, the frequency dependence became more visible, which is shown in Figures S8 and S10 (SI).…”

“…Taking into account that an interaction between adjacent spin carriers is −2JS1·S2, Δξ = 4|J|S 2 , for an isotropic model when |D/J| > 4/3 (Ising limit), while when |D| << |J|, Δξ = 4S 2 |JD| 1/2 (Heisenberg limit) [2,7]. Therefore, for an infinite magnetic chain the total spin reversal barrier can be written as Ueff = ΔA + 2Δξ [28][29][30]. However, in a finite-length spin chain the contribution of the correlation energy to the Ueff is twice smaller (Ueff = ΔA + Δξ) due to a nucleation effect of the chain ends.…”

Transition rates for aS≥1spin model coupled to ad-dimensional phonon bath

“…͑1͒ is known as the Blume-Capel model, 23,24 which was introduced to describe features of the phase diagram of He 3 -He 4 mixtures as well as to understand a phase transition in UO 2 . The S Ն 1 spin model can be applied to the following magnetic systems: arrays of weakly interacting magnetic nanoparticles, 4,5 nanoscale single-molecule magnets such as Mn 12 and Fe 8 , 6-8 a Mn͑III͒ 2 Ni͑II͒ single-chain magnet, 10,11 and a Co ferrimagnetic compound. 9 To understand spin relaxation in the S Ն 1 spin model, we assume that the spin system is weakly linearly coupled to a surrounding phonon bath in d dimensions.…”