3.3 Atomistic models

Figure 3.6: Lattice of FePt and FeRh and interface structure of FePt/FeRh as observed in the paper [Goto 04].

We will describe our atomistic model including the interface, the exchange interactions, the lattice structure, the saturation magnetization and the anisotropy constants. We consider only Fe sites possessing the total magnetic anisotropy and saturation magnetization in a similar way to the effective one-ion Hamiltonian presented in Ref. [Mryasov 05] and in Section 2.2.4. In our implementation the arrangement of the FeRh lattice with respect to FePt one was taken from Ref. [Goto 04] so that the fct FePt lattice is rotated $ 45$ degrees with respect to bcc FeRh lattice and displaced half an FeRh lattice constant as shown in Fig. 3.6, with the c axis of the FePt lattice normal to the interface. Due to this rotation, it is more convenient to represent the FePt with a bct cell as shown in Fig. 3.7. Considering the bct lattice, the parameters for FePt are $ a=0.272  nm$ and $ c=0.385 nm$ and the lattice of the FeRh is matched according to the observed structure [Thiele 04b].

We have developed two models for exchange interaction in the FePt material. The first model (I) was developed to compare with the micromagnetic simulations. In this case we considered a model for FePt with exchange parameters $ J_{\bot}=J_{\Vert}=7.7\cdot10^{-14}
 erg$ calculated from Eqs. (2.23) and (2.24) and the corresponding micromagnetic exchange constant $ A$. In the second model (II), used in the Section 3.8, we used a representation of exchange interactions based on the first-principle calculations [Mryasov 05] but with an exchange interaction only until first neighbors. The exchange interaction has been renormalized in order to obtain the same thermal properties (i.e Curie temperature). This gives different exchange values perpendicular to the plane $ J_{\bot}=3.139\cdot10^{-14} erg$ and in-plane $ J_{\Vert}=7.8476\cdot10^{-14} erg$, according to the layered structure of FePt .

For the simulations in the Section 3.8 the generic soft magnetic material was simulated using a generic model with cubic lattice with $ a=0.272  nm$, exchange parameter $ J=7.696\cdot10^{-14} erg$ and varying saturation magnetization value. The interface in this simulation is such that in the Z direction there is a hard material atom just above the position of a soft material atom.

The saturation magnetization corresponding to the FeRh $ M_s^{FeRh} = 1270 emu/cm^3$ is extracted from the experimental work of J. Thiele [Thiele 03]. In the case of the FePt anisotropy we have used the value measured in the perfectly ordered alloy, $ K^{FePt} = 7 \cdot 10^7 erg/cm^3$, and that for an FePt epitaxial film with a chemical order parameter of $ 0.7$, $ K^{FePt} = 2 \cdot 10^7 erg/cm^3$. This parameter represents the number of atoms that occupy its proper position in the alloy and the magnetic anisotropy of the FePt alloy is strongly dependent on it [Okamoto 02]. The anisotropy axis of the hard material was directed perpendicular to the plane. The saturation magnetization of FePt $ M_s^{FePt} = 1270 emu/cm^3$ was obtained from the last reference.

Figure: Relation between the unit cells of the fct and bct cells in $ L1_0$ phase.