3 Spin and orbital moments on $Co\setminus Ag_{1}$ interface

Unfortunately, a perfect free layer of a Co is difficult to obtain at ambient condition due to oxidation, lattice imperfection, etc. With the purpose of exploring its experimental properties it is often covered by another protective layer. "A-priori" the orbital and spin moments could be affected by this protective capping. We have analyzed how the Ag capping over the Co semi-infinite system can affect the orbital and spin moment.

Figure 6.6: The layered resolved spin and orbital magnetic moments, top and bottom graphics respectively, for a $Co(100)\setminus Ag_{1}$ and $Co(111)\setminus Ag_{1}$, where the interface between de Co and Ag is the atomic layer number 5.

In Fig. 6.6 we show the layered resolved values of the spin and orbital moments for a semi-infinite Co capped by a monolayer of Ag: $Co(100)\setminus Ag_{1}$ and $Co(111)\setminus Ag_{1}$. It is seen that both the spin and orbital moments are affected by the existence of the Ag capping. The orbital and spin moments of Co experience a variation with respect to the volume one, such modification depends on the orientation of the interface of $Co\setminus Ag$. We can observe that the spin magnetic moment in the case of Co with a monolayer capping of silver presents a reduction of its value with respect to the Co bulk one, on both (100) and (111) interfaces. In contrast to the spin moment, the orbital magnetic moment is increased in the same systems.

With the aim to summarize our results, we present in Tab. 6.2 the spin and orbital atomic moments of Co in several systems. We can observe that Co presents different spin and orbital moments depending on the chemical environment or the existence of a surface. This effect has been reported in the literature, both in theoretical [162,163] and experimental studies [164,165,9]. For example, in Co overlayer on Cu(100) an increment about the double of the bulk value of the Co orbital moment has been observed by Tischer et.al. The authors suggested that this increment could have its origin in an increased spin moment or an increased value of DOS at the Fermi level [161].

Table 6.2: The $\mu _{s}$ and $\mu _{L}$ values (in Bohr magneton $\mu _{B}$) obtained in the self-consistent calculations. In the second column we can find the value of the orbital and spin moment of a Co(bulk), in the third column we present the value at a free surface Co(100) and Co(111), in the last column there are the results of $\mu _{S}$ and $\mu _{L}$ at the interface $Co(100)\setminus Ag_{1}$ and $Co(111)\setminus Ag_{1}$.

Quantity	Co(fcc(100), bulk)	Co(fcc, surface(100))	$\mathbf{Co(100)\setminus Ag_{1}}$
$\mu _{L}$	0.078	0.11	0.094
$\mu _{s}$	1.663	1.821	1.643
Quantity	Co(fcc(111), bulk)	Co(fcc, surface(111))	$\mathbf{Co(111)\setminus Ag_{1}}$
$\mu _{L}$	0.078	0.091	0.091
$\mu _{s}$	1.658	1.705	1.639

The Ag has nearly filled $4d^{10}$ bands and it is diamagnetic in the absence of hybridization, nevertheless we have observed an appearance of a small orbital moment of the Ag layer, see Tab. 6.3. This result suggests us that the Ag layer has become polarized by Co layer, similar to the result reported by N. Joauen et. al for Fe/Ag multilayers [166]. On the other hand, we have observed that Ag spin magnetic moment is practically zero.

Table 6.3: The orbital magnetic moment of Ag, obtained in the self-consistent calculation for $Co(100)\setminus Ag_{1}$ and $Co(111)\setminus Ag_{1}$ systems.

System	Interface	$\mathbf{\mu_{L}/\mu_{B}}$
Ag monolayer on Co(fcc)	$(100)$	0.0089
Ag monolayer on Co(fcc)	$(111)$	0.0057