## 1 Introduction  
Fe-Co alloys have attracted theoretical and technological interest due to their magnetic features. The atomic magnetic moment of the Fe\({}_{\mathrm{x}}\)Co\({}_{\mathrm{1-x}}\) alloys shows variations with composition following the known Slater-Pauling curve [1], which presents a maximum at \(x\) = 0.65 with a magnetic moment \(\mu\sim\) 0.45 \(\mu_{\mathrm{B}}\) per atom (\(\sim\)240 emu/g), at constant temperature. This magnetization is larger than pure metallic Fe or Co, and this behavior is determined by its electronic band structure, _i.e.,_ the average concentration of the 3d electrons in the alloy.  
On the other hand, magnetic nanoclusters have received much attention since the effect of nanoscale confinement leads to a different magnetic behavior from the bulk [2, 3]. These effects lead to novel properties and possibly new technological applications. It is known that as the particle size decreases, a finite-size effect dominates the magnetic properties due to surface effects. It is expected that the decrease in the coordination number induces a weakening of the exchange interactions between surface atoms. In this case, the picture of a magnetic single-domain particle where all spins are pointing in the same direction, thus leading to a coherent relaxation process, is no longer valid if one considers the effect on the global magnetic properties of the particle of misaligned spins on the surface [4]. Some experiments have shown that the hysteresis loops of very small nanoparticles display high irreversibility fields and do not saturate [5, 6, 7] even at high magnetic fields, which indicates that the anisotropy fields cannot be the only responsible mechanism for the magnetization reversal. Usually, these phenomena can be ascribed to intrinsic properties of the particle itself, _i.e.,_ spin-glass state of the surface which creates an exchange field on the core of the particle [5, 7] or a collective behavior induced by interparticle interactions [8, 9, 10], and has been the object of controversy [11]. Some core-shell models have been developed to describe the behavior of these nanoparticles [12, 13, 14, 15, 16, 17, 18, 19]. In metallic nanoparticles also, the band structure must be modified by the finite size leading to a confinement of the conduction electron band [20]. These confinement and surface effects can modify the behavior of the Fe-Co alloys, developing the effective magnetic moment and shifting the alloy composition where the maximum of the magnetization is observed. The presence of magnetic interactions between particles can also modify the surface configuration of spins, and the problem becomes more complex.  
Previous studies on (Fe\({}_{\mathrm{x}}\)Co\({}_{\mathrm{1-x}}\))\({}_{\mathrm{0.6}}\)B\({}_{\mathrm{0.4}}\) nanoparticles show a sharp maximum of the saturation magnetization at room temperature as a function of composition at \(x\) = 0.69 against the broad maximum present in the bulk materials [21]. In this work, we present magnetization results on (Fe\({}_{\mathrm{0.69}}\)Co\({}_{\mathrm{0.31}}\))\({}_{\mathrm{0.6}}\)B\({}_{\mathrm{0.4}}\) nanoparticles, where confinement effects contribute significantly to the magnetic properties of these samples.