Figure 1 - uploaded by Giovanni Manfredi
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Illustration of the two generic geometries coresponding to a 1D nanowire (left) and a 2D nanolayer (right)
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... possible limitation of the LLG approach is that the amplitude of the local magnetic moment |m(t, x)| remains constant in time, which is not necessarily true at high temperatures, notably near T C . Chubykalo-Fesenko et al. [4] have investigated this issue using an atomistic time-dependent model and indeed they found that the modulus of the magnetization varies in time (see figure 1 in [4]). However, this variation is limited to a dip during an initial transient, after which |m(t, x)| recovers approximately its initial value. ...
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... mimic a 2D nanolayer, the 3D domain is taken with a small thickness in the Figure 1 illustrates those two geometries. All numerical parameters are listed in Table 2. Discretization. ...
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... for the following Sec. 4.2 -where the independence of the results on the space and time discretizations are tested on a 3D cube -all numerical simulations are preformed on three ferromagnetic materials (cobalt, iron and nickel) and two geometries (see Figure 1): ...
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... type of power-law has been observed in many experiments [31,17,24,32,36,34] and numerical simulations [1,28]. Experimental works yielded correlation length ξ 0 of the order of a few In the analysis of our simulation results, the Curie temperature of the bulk T C (∞) is in fact replaced by the Curie temperature of the largest structure that we consider T C (d max ), that is d max = 41 nm, see Table 3. Figure 10 (for nanowires) and Figure 11 (for nanolayers) illustrate this powerlaw behaviour for the three materials considered here, both on a linear scale (left panels) and on a logarithmic scale (right panels). Blue circles correspond to the numerical results T C (d) extracted from Table 3. ...
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... type of power-law has been observed in many experiments [31,17,24,32,36,34] and numerical simulations [1,28]. Experimental works yielded correlation length ξ 0 of the order of a few In the analysis of our simulation results, the Curie temperature of the bulk T C (∞) is in fact replaced by the Curie temperature of the largest structure that we consider T C (d max ), that is d max = 41 nm, see Table 3. Figure 10 (for nanowires) and Figure 11 (for nanolayers) illustrate this powerlaw behaviour for the three materials considered here, both on a linear scale (left panels) and on a logarithmic scale (right panels). Blue circles correspond to the numerical results T C (d) extracted from Table 3. ...
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... the tolerance parameter ε fixed to 0.1. Figure 12 illustrates schematically this convergence time t conv , and also shows the transient time τ , which is the time used to compute the average magnetization, see Eq. (10). Figure 13 shows the convergence time, as a function of the temperature, for nanowires of size 6000 × d × d nm 3 and nanolayers of size 600 × 600 × d nm 3 , for two values of d. First, we note that the convergence time t conv is always smaller than the transient time τ taken to compute the average M tot (t conv has a maximum value around 20 ps, which is always smaller than τ = 40 ps). ...
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... 12 illustrates schematically this convergence time t conv , and also shows the transient time τ , which is the time used to compute the average magnetization, see Eq. (10). Figure 13 shows the convergence time, as a function of the temperature, for nanowires of size 6000 × d × d nm 3 and nanolayers of size 600 × 600 × d nm 3 , for two values of d. First, we note that the convergence time t conv is always smaller than the transient time τ taken to compute the average M tot (t conv has a maximum value around 20 ps, which is always smaller than τ = 40 ps). ...
