We have performed first-principles calculations to study the interfacial exchange coupling and magnetocrystalline anisotropy (MCA) energy in a SmCo₅/Sm₂Co₁₇ multilayer model systems. The phase of SmCo₅ and Sm₂Co₁₇ stacking along (0001) direction are structurally well matched. The atomic structure, including the alignment and the separation between layers, were firstly optimized. Then the non-collinear magnetic structures were calculated to explore the exchange coupling across the interface and the variation of MCA energy. We found that the inter-phase exchange coupling strength, rotating behavior and MCA energy are strongly dependent on the atomic thickness of the SmCo₅ and Sm₂Co₁₇ phase.

The perpendicular exchange bias effect is observed in the ferromagnetic Co/Ni multilayers adjacent to the antiferromagnetic FeRh layer. It is found that as the antiferromagnetic FeRh thickness increases from 10 Å to 50 Å, the hysteresis loop is gradually changed from the symmetric shape to the asymmetric shape shifted by some amount corresponding to the exchange-biased field at the thickness of 25 Å. Also, the magnetic domain observation experiment confirms that the domain reversals in the increasing and the decreasing field regions of the sample with the thickness of 50 Å exhibit the same single domain wall motion even though they have the different coercivities.

In atomic GdFe$_2$ films capped by 4$d$ and 5$d$ transition metals, we show that skyrmions with diameters smaller than 12 nm can emerge. The Dzyaloshinskii--Moriya interaction (DMI), exchange energy, and the magnetocrystalline anisotropy (MCA) energy were investigated based on density functional theory. Since DMI and MCA are caused by spin--orbit coupling (SOC), they are increased with 5$d$ capping layers which exhibit strong SOC strength. We discover a skyrmion phase by using atomistic spin dynamic simulations at small magnetic fields of $\sim$1 T. In addition, a ground state that a spin spiral phase is remained even at zero magnetic field for both films with 4$d$ and 5$d$ capping layers.