3.8 Generic Soft/Hard material: one grain simulation

The potential usage of the exchange spring media for magnetic recording applications requires the evaluation of both coercive field reduction and thermal energy barrier. The parameters of the system have to be chosen with the goal of maximizing both quantities. However, the number of such parameters, including the intrinsic material ones, does not allow the systematic search to obtain the best choice. Other parameters, as for example the grain size, are limited by the current growing techniques. In this section we will consider a generic soft/hard grain and study the effect of several combinations of saturation magnetization in the overall exchange spring performance. We considered the grain sizes $ 6 nm \times 6 nm$ with the grain height $ 7.5 nm$ soft and $ 7.5 nm$ hard material. The anisotropy constants are $ K_{Hard}=2\cdot10^7 erg/cm^3$ and $ K_{Soft}=0$. The exchange interactions were taken from the models I and II for the FePt described in Section 3.3. For the saturation magnetization in the hard material we used the value of FePt, $ M_{Hard}=1100 emu/cm^3$, and alternatively, a low value $ M_{Hard}=250 emu/cm^3$, representing an hypothetical magnetic recording media. Accordingly, in the soft material we varied the saturation magnetization, starting from that of FeRh, $ M_{Soft}=1270 emu/cm^3$, and decreasing it up to a low value $ M_{Soft}= 200 emu/cm^3$.

Figure: Coercivity of a soft/hard grain in model I as a function of the interfacial exchange $ J_s$ for different values of $ M_{Soft}$ corresponding to: (a) $ M_{Hard}=1100 emu/cm^3$ and (b) $ M_{Hard}=250 emu/cm^3$
Figure: Hysteresis loops in a soft/hard grain simulated with the model I for $ M_{Hard}=1100 emu/cm^3$ and $ M_{Soft}=350 emu/cm^3$.

First, we will use the model I for the exchange interactions. Fig. 3.30 presents the coercivity field reduction as a function of interfacial exchange parameter $ J_s$. First of all, we note that changing the saturation magnetization value in the soft magnetic material, we change its domain wall width since it is determined by the magnetostatic interaction. Consequently, the coercivity mechanism undergoes a transition between two types of behavior. In the first case (high $ M_s^{soft}$) the exchange spring is formed. In the second case (low $ M_s^{soft}$), the magnetization reversal is homogeneous in each grain and can be represented by two-macrospins. The same type of transition was observed in Section 3.4 changing the thickness of the soft layer (see Fig. 3.13). In the low $ M_s^{soft}$ case we can distinguish also two types of behaviors. For low interfacial exchange the soft magnetic moment rotates and exerts an additional torque to the hard magnetic moment. For larger values of $ J_s$ the soft material will eventually be so coupled to the hard material that will be unable to rotate independently and the behavior will be collective. The corresponding demagnetization curves are shown in Fig. 3.31. This crossover of behaviors in the two-macrospins mechanism results in a minimum and, posteriorly, larger coercivity with increasing interfacial exchange as in Ref. [Richter 06]. This minimum has been observed experimentally in an exchange spring medium based on FeSiO(Soft) and CoPd(Hard) in Refs. [Wang 05a,Wang 05b]. In these experiments the variation of interfacial exchange is achieved through the interposition of a non magnetic material of different thicknesses, resulting in reduction of interfacial exchange with increasing thickness. From Fig. 3.30 it is clearly seen that the exchange spring formation is much more efficient in the coercive field reduction than the two macro-spins mechanism. In the exchange spring the coercivity reduction is saturated for the value of the interfacial exchange higher than $ 10\%$. This situation is favorable for an experiment since the field reduction is achieved for low exchange value and no tuning of the coupling parameter is necessary. In the opposite situation, the coercive field reduction is less, presents a narrow minimum for interfacial exchange values below $ 10\%$ and the coercivity reduction experiences slight increase for higher $ J_s$ values. To have an optimum coercivity reduction, the value of the exchange should be tuned to this value which is experimentally hardly affordable. The qualitative behavior does not change, if in the hard material we consider large or low magnetization, Fig. 3.30(a) and Fig. 3.30(b) respectively, although the minimum in the coercivity for small $ M_s^{soft}$ becomes less pronounced. Finally, Fig. 3.32 shows the calculation in model II. The two mechanisms are also present, but the interfacial exchange needed for saturation is $ 20-40\%$ of the bulk exchange, which is more difficult to reach. Additionally, the minimum, although present, is very shallow.

Figure: Coercivity of a soft/hard grain, normalized to the anisotropy field ( $ 2 K_{hard}/M_{Hard}$) of the hard magnetic phase, in model II as a function of the interfacial exchange $ J_s$ for different values of $ M_{Soft}$ and $ M_{Hard}$.
Figure: Energy barrier dependence on the interfacial exchange for different values of $ M_{Soft}$ and $ M_{Hard}$ in model I (a) and in model II (b)