Exchange-spring behavior below the exchange length in hard-soft bilayers in multidomain configurations

Exchange-coupled hard-soft biphase magnets are technologically relevant systems in that they enable tailoring the magnetization reversal process. Here, exchange-spring behavior is observed in $\mathrm{CoF}{\mathrm{e}}_2{\mathrm{O}}_4$/FeCo bilayers for soft thicknesses as thin as 2 nm, at least four times below the exchange length of the system. This result is in contrast with the accepted theory for spring magnets that states that the exchange length defines the critical thickness below which both magnetic phases should be rigidly coupled. In combination with micromagnetic calculations, this surprising observation is understood as a consequence of the dominance of domain-wall propagation in the soft phase during the reversal process, so far unaccounted for in theoretical descriptions. Our results emphasize the need to expand the existing spring theory from coherent rotation to domain-wall related processes in multidomain configurations in order to accurately design magnetic heterostructures with controllable reversal.

Figure 1

TEM characterization. (a) Low resolution STEM-HAADF image showing the multilayer arrangement sketched in (b). (c) EDXS maps for different elements present in the stack. (d) RBS data corresponding to a bilayer with soft FeCo thickness of 17 nm. A HRTEM image of the CFO/FeCo interface is shown in (e), with insets containing fast Fourier-transform patterns for each film. In (f), a filtered image using together the (10-1) in FeCo and (400) in CFO of the interface region delimited in red is presented.

Figure 2

(a) VSM magnetization curves measured at room temperature of a reference CFO film for a 2-nm (FC2) and a 4-nm soft bilayer (FC4). (b) Recoil loops of FC4, FC17, and CFO measured after saturating at $+5\mathrm{T}$. (c) $H_n$ and $H_{\mathrm{sw}}$ extracted from the magnetization curves as a function of soft thickness. (d) Polar plot of coercivity $\left(H_c\right)$ determined by MOKE as a function of the in-plane angle between the applied field and the (110) direction of the Si substrate for the FC4 sample.

Figure 3

(a) Profile corresponding to the magnetic domain wall indicated by the red line. Inset: XMCD-PEEM image obtained at the Fe L edge at remanence and RT showing magnetic domains in the pure CFO film. (b) First magnetization (virgin) curves for CFO and FC4.

Figure 4

(a) Simulated $dM/dH$ curve for four different exchange stiffness values for a 4-nm FeCo/77-nm $\mathrm{CoF}{\mathrm{e}}_2{\mathrm{O}}_4$ (CFO) bilayer. (b) Simulated magnetization curves corresponding to the highest and lowest stiffness values.