3.4 Simulations of one grain of FePt/FeRh

The switching field of the soft/hard bilayer depends on various microscopic and morphological parameters such as the saturation magnetization of soft layer, the exchange parameter at the interface or the thickness of soft and hard phases. We can appreciate this dependence in the formulae of Section 3.2. Since those formulae deal only with ideal and limiting cases, we have modeled a grain based on FePt/FeRh parameters to investigate the switching behavior of the composite media in different ranges of the parameters: thicknesses and interfacial exchange. The grain has a size of $6 nm \times 6 nm \times L nm$ consisting of an FePt grain above FeRh one with exact grain matching. We have used the atomistic model I with the following parameters: $K^{FePt} = 7 \cdot 10^7\; erg/cm^3$ and $K^{FeRh} = 0$. The calculation finishes when the following condition is met $\epsilon <10^{-5}$ for the error (see Section 2.2.3).

Figure: Magnetization as a function of the applied field for a singular grain of FePt/FeRh and two FePt thicknesses with $J_s/J=0.4$.

Figure: Domain wall center position as a function of the applied field for $J_s/J=0.4$. The solid line represents the interface between FePt and FeRh.

Figure: Domain width as a function of the applied field for $J_s/J=0.4$.

Fig. 3.8 represents a hysteresis cycle of FePt/FeRh magnetic grain calculated for two different thicknesses of FePt. The nucleation process starts in FeRh grain, which is softer but has an additional shape anisotropy due to the grain elongation. The domain wall (exchange spring) of the Néel-type propagates and gets pinned at the FePt/FeRh interface. An additional field is necessary to push the center of the domain wall into the FePt (see Fig. 3.9). Associated with the movement of the domain wall, there is a change of the domain wall width illustrated in Fig. 3.10. The initial process is a compression of the domain wall against the interface [Dobin 06] that is reflected in the reduction of its width. Once the center of the domain wall penetrates inside the hard medium, this produces the complete magnetization reversal in FePt.

Fig. 3.11 represents the coercivity reduction in the case of the exchange spring medium as a function of the FePt thickness. For a thinner ($3 nm$) FePt layer, the domain wall could not be completely formed in the hard magnetic material (with the domain wall thickness $4 nm$) as can be observed in Fig. 3.12. This is important since the total domain wall formation is an implicit assumption of some analytical models [Asti 06,Loxley 06,Kronmüller 02] that consider infinite thickness, included the one used to obtain the pinning field Eq. (3.4). This reduces the coercivity because the pinning is less effective. A remarkable reduction of the switching field (more than $5$ times) than that of the pure FePt grain could be obtained even with small interfacial exchange value for thin FePt layer.

Figure 3.11: Coercivity reduction in an exchange spring medium with 12 nm FeRh, calculated in one-grain model as a function of FePt thickness for different reduced interfacial exchange parameters.

Figure: Domain wall in an exchange spring medium with 3 nm FePt/12 nm FeRh and $J_s/J=0.4$ for different values of the applied field.

Fig. 3.13 represents the coercive field reduction as a function of the thickness of FeRh. It is clearly seen that the exchange spring formation (thick soft layer) is more efficient in decreasing the coercive field value than the case of thin soft layer. The coercivity saturates when the length of soft material is larger than its domain wall width. Fig. 3.14 represents the coercivity reduction as a function of interfacial exchange in grains with different thicknesses. Substantial reduction of the switching field could be achieved with interfacial exchange of the order of $10\%$ of the bulk value. However, more interfacial exchange is necessary for thicker FePt layer as compared to a thinner one to get the same reduction.

Figure: Coercivity reduction calculated in one-grain model as a function of FeRh thickness for two different thickness of FePt and the value of the interfacial exchange parameter $J_s/J=0.4$.

Figure 3.14: Coercivity reduction as a function of reduced interface parameter for grains with different FePt and FeRh thicknesses.