Molecular Magnets by Juan Bartolomé Fernando Luis & Julio F. Fernández

Author:Juan Bartolomé, Fernando Luis & Julio F. Fernández
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

If the Landau’s argument is rephrased for DW excitations of finite thickness , the counting of equivalent configurations with the same energy needs to be modified and—in turn—the entropy contribution S 2−S 1=kln(N/w). In this case, splitting the uniform configuration into domains becomes convenient as soon as the number of spins exceeds the product . The latter threshold gives an estimate of the average number of consecutive spins that can be found aligned at a given temperature. To the leading order, the correlation length scales in the same way at low temperature: . The energy represents the natural “unit” which controls the divergence of the correlation length. Thus, in classical spin chains with uniaxial anisotropy the characteristic exponential divergence of ξ is closely related to the fact that ferromagnetism is destroyed by thermally excited DWs.

In contrast to the Ising model [33], the classical spin Hamiltonian (8.1) can also host spin-wave excitations, besides DWs. Due to the interaction between spin waves and broad DWs an additional temperature-dependent factor appears in front of the exponential in the low-temperature expansion of the correlation length [35]. Moreover, spin waves renormalise the DW energy at intermediate temperatures. The net result of the complicated interplay between thermalised spin waves and DWs is that the energy barrier controlling the divergence of ξ (usually called Δ ξ in SCM literature [6–9]) is generally smaller than and takes different values depending on the temperature range in which it is measured [34]. A similar effect was reported for the activation energy of 2π sine-Gordon solitons in Mn2+-radical spin chains [36]. Figure 8.2 highlights how Δ ξ is constant and equal to for sharp DWs, while it varies significantly for broad DWs. However, the correlation length in units of w keeps depending only the ratio , i.e., . The inset shows that the curves corresponding to broad DWs indeed collapse onto each other when the ratio ξ/w is plotted as a function of .

Fig. 8.2Log-linear plot of ξ in lattice units computed with the transfer-matrix technique as function of the ratio for different values of D/J. For D/J=0.1 (red crosses), 0.3 (green crosses), 0.5 (blue stars) DWs are broad and has been computed numerically on a discrete lattice. For D/J=5 (open squares) DWs are sharp and has been used. The two solid lines give the “reference” behaviour which is indeed followed when DWs are sharp (D/J=5) but not when DWs broaden. Inset: Λ=ξ/w is plotted as a function of for the values of D/J consistent with broad DWs. The universality of Λ is highlighted by the data collapsing. Solid lines evidence the decrease of Δ ξ with increasing temperature [34]

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