2 Surface anisotropy and thin films magnetism

Table 1.1: Experimental data for magnetic surface anisotropy of ferromagnetic transition metals. Data obtained of Ref. [54]

System	Temperature[K]	$\mathbf{ K_{s}}$ $\mathbf{[erg/cm^{2}]}$	Ref.
$UHV/Ni(111)$	$300$	$-0.48$	[58]
Cu, $Pd/Ni(111)$	$300$	$-0.22$	[58]
$Re/Ni(111)$	$300$	$-0.19$	[58]
$O_{2}/Ni(111)$	$300$	$\cong 0$
$UHV/Fe(100)$	$293$	$+1$
$Ag/Fe(100)$	$293$	$+0.6$
$UHV/Fe(100)/Ag(100)$	$293$	$\cong 0$
$UHV/Fe(100)/W(110)$	$293$	$-0.5$
$Ag/Fe(100)/Ag(111)$	$77-293$	$\cong 0$
$Au/Fe(100)/Au(111)$		$> 0$
$UHV/Fe/Cu(100)$	$100$	$+1$
$Cu/Fe(100)/Cu(100)$		$+0.5$
$Au/Co/Au(111)$	$293$	$+0.5$
	$5$	$+0.7$
$Pd/Co/Pd(111)$	$293$	$+0.26$
$UHV/Co/Cu(100)$	$293$	$\geq 0$

The experimental results show different values of the surface anisotropy in different systems: pure transition metals Ni [59], Fe [55], Co [46,54,56,60] on various substrates, orientations and overlayers or alloys such as MnSb [61]. The data are shown in Table 1.1.

In general, the easy axis of the magnetization in thin film is determined by the competition between the magnetocrystalline anisotropy, the magnetostatic energy and the surface anisotropy. The experimental progress in growing epitaxial magnetic thin films and multilayer down to monolayer thickness has revealed a wealth of interesting phenomena, such as the perpendicular magnetic anisotropy (PMA), which consist of a preference for the magnetization to lie along the normal to the plane of the magnetic film. The use of a magnetic system that presents PMA as a magnetic storage media has been shown as a good strategy to improve the storage density.

Figure 1.7: $K^{eff}\cdot t_{Co}$ of a Co thin film layer in a Co/Pd multilayer as a function of the Co thickness $t_{Co}$. ( from Ref. [62]).

The balance between different anisotropies can be changed as the temperature or global thickness of a thin films are varied [63,56,64], leading to a re-orientation of the global anisotropy axis. A change from perpendicular orientation of the easy axis for film thickness (t) below a few monolayers to an in-plane orientation for larger t has been reported, for example in Fe/Ag(001) [65] and Fe/Cu(001) etc. [66]. A contrary crossover from in-plane to perpendicular orientation of the easy axis has been reported for example in Ni/Cu(001) [63]. A detailed analysis of the magnetization near the re-orientation transition in ultrathin films has shown that the surface magnetization pattern can be very complex, consisting, for example, of perpendicularly magnetized stripes [67,68,69] or ripple structures [70].

In order to illustrate the spin reorientation transition we present in Fig. 1.7 the case of Co/Pd multilayer. This system shows a shape anisotropy with in-plane easy axis and a surface anisotropy with an easy axis perpendicular to the surface. The system shows a reorientation transition of its global easy axis from perpendicular to the surface to in-plane as the thickness of the Co layer is increased [62]. In Fig. 1.7 we show the values of the $K^{eff}\cdot t_{Co}$ as a function of $t_{Co}$ (the thickness of the Co layer). The reorientation transition is indicated in the figure by the change of $K^{eff}$ sign. If $K^{eff}>0$ the easy axis of the system is perpendicular to the surface, and the easy axis of the system is in plane if $K^{eff}<0$.