Modeling and characterization of irreversible switching and viscosity phenomena in perpendicular exchange-spring Fe-FePt bilayers

A numerical model has been developed for simulating magnetic domain configurations, remanence, and viscosity curves in systems with strong perpendicular anisotropy and strong disorder, starting from internal switching field distributions for pinning and nucleation processes in the slow dynamics regime. In the considered systems, the domains expand in a percolationlike manner and domain configuration displays fractal properties. The simulations show that even in the case of pinning not governed by nucleation an abrupt avalanche propagation of reversed domains occurs. It is moreover evidenced that a decrease of viscosity coefficients can coexist with lowered energy barrier heights. The model has been applied to perpendicular FePt thin films with granular morphology and corresponding exchange-coupled Fe/FePt bilayers, by exploiting magnetic force microscopy, dc demagnetization (DCD), isothermal remanence, and viscosity data. The comparison between magnetic viscosity phenomena in thin films and exchange-coupled bilayers has been achieved by the definition of an adimensional viscosity coefficient. The addition of the Fe layer causes a decrease of the maximum viscosity coefficient, thus demonstrating that viscosity measures can be utilized to verify the coupling of hard/soft layers. From experiments it is inferred that our samples are mainly influenced by the pinning energy barrier law, the linearity of which allows reconstructing universal viscosity curves starting from DCD data. The calculated activation volumes are comparable to the average grain volume of the FePt layer. The obtained results also demonstrate that the addition of the Fe layer leads to a widening and a shift to lower fields of the pinning field distribution, determining a decrease of both the maximum viscosity and the pinning energy barrier heights and an increase of the demagnetizing effective field.

Figure 1

(Color online) Hysteresis loops, measured by the SQUID magnetometer, (a) for the FePt (10 nm), (b) for the Fe (2 nm)/FePt (10 nm), and (c) for the Fe (3.7 nm)/FePt (10 nm) samples in the temperature range 100–300 K; SQUID (open circles) and AGFM (thin solid lines) room-temperature recoil curves for the Fe (3.7 nm)/FePt (10 nm) bilayer are also reported in (c).

Figure 2

Room-temperature hysteresis loops for the exchange-coupled and the fully decoupled Fe (3.7 nm)/FePt (10 nm) bilayer: $H_{c1}$ and $H_c$ are the nucleation and the coercive fields, respectively, of the exchange-coupled bilayer, while $H_d$ is the nucleation field of the fully decoupled bilayer. The vertical axis reports the magnetic moment per unit area.

Figure 3

(Color online) Scanning probe microscopy observations of the FePt (10 nm) film. (a) Topographical AFM image $\left(0.8\times 0.8\mu {\text{m}}^2\right)$. (b) MFM domain configuration image $\left(50\times 50\mu {\text{m}}^2\right)$ in the remanent state after application of a reverse magnetic field of 3.5 kOe.

Figure 4

Room-temperature normalized DCD and IRM curves, measured by the AGFM, for the FePt (10 nm) film and the Fe (2 nm)/FePt (10 nm) and the Fe (3.7 nm)/FePt (10 nm) bilayers.

Figure 5

Normalized viscosity curves with different external fields, measured by the AGFM at room temperature for the FePt (10 nm) film.

Figure 6

Field dependence of the adimensional viscosity coefficient $s\left(H\right)$ as defined by Eq. (2): (a) for the FePt (10 nm) film and the Fe (2 nm)/FePt (10 nm) and the Fe (3.7 nm)/FePt (10 nm) bilayers at 300 K; (b) for the FePt (10 nm) film at different temperatures. The lines are guides to the eyes.

Figure 7

Simulations obtained for different processes utilizing a $512\times 512$ rectangular grid. (a) Comparison among normalized DCD curves for pure pinning in the case of site and bond percolation and pure nucleation; the boundary of the gray area represents the effective switching volume in terms of the number of switched units (right scale); inset shows the domain configuration in the state evidenced on the DCD curve. (b) Normalized IRM curves for pure pinning in the case of site and bond percolation; inset shows the domain configuration in the demagnetized state. (c) Comparison among normalized DCD curves for pure pinning with and without effective fields and $\text{pinning}+\text{nucleation}$ with effective field; inset shows the domain configuration in the state evidenced on the DCD curve.

Figure 8

Simulation of normalized viscosity curves, obtained for the case of a pure pinning process with uniform energy barrier distribution, in the field range 5.1–6.1 kOe with a 100 Oe field step.

Figure 9

(Color online) (a) Comparison between the room-temperature experimental (open symbols) and simulated (solid lines) normalized DCD curves, and (b) “true” pinning switching field distributions expressed in terms of internal field, for the FePt (10 nm) film and the Fe (2 nm)/FePt (10 nm) and the Fe (3.7 nm)/FePt (10 nm) bilayers. Inset: simulation on a $2500\times 2500$ grid of the domain configuration (external reverse field $H=3.5\text{kOe}$).

Figure 10

(Color online) Room-temperature plot of the FePt (10 nm) universal viscosity curve compared to the corresponding DCD curve transformed by the $H\to \text{ln}t$ substitution of Eq. (4).

Figure 11

(Color online) Room-temperature experimental (open symbols) and simulated (lines) maximum viscosity curves of the FePt (10 nm) film and the Fe (2 nm)/FePt (10 nm) and the Fe (3.7 nm)/FePt (10 nm) bilayers. The corresponding external reverse fields are 3.6, 3.1, and 2.5 kOe, respectively.