† Corresponding author. E-mail:
For static magnetic properties of the Co/Ni bilayers, macroscopic hysteresis loops and microscopic magnetic moment distributions have been determined by the object oriented micromagnetic framework (OOMMF). It is found that when the bilayer systems are fully decoupled, the magnetizations of the two phases reverse separately. The coercivity of the bilayers decreases to a valley value sharply with increasing interfacial exchange coupling and then rises slowly to a platform. On the other hand, we have carried out an atomistic simulation for the laser-induced ultrafast demagnetization of the Co/Ni bilayer. A larger damping constant leads to a faster demagnetization as well as a larger degree of demagnetization, which is consistent with the first-principle theoretical results. For the magnetization recovery process, the damping constant has different influences on the recovery time with various peak electron temperatures, which is ignored in previous atomistic simulations as well as the Landau–Liftshit–Bloch (LLB) micromagnetic calculations. Furthermore, as the interfacial exchange coupling increases, the ultrafast demagnetization curves for Co and Ni become coincident, which is a demonstration for the transition from two-phase phenomenon to single-phase phenomenon.
The Co/Ni magnetic multilayered thin films with perpendicular anisotropy have drawn a great deal of attention in the past several decades owing to their applications in the field of magnetic storage and spintronic devices.[1] The properties of interface induced large perpendicular magnetic anisotropy (PMA)[2] can be modified by controllable experimental conditions. The PMA with Ni as the capping layer increases linearly with the annealing temperature. It is in contrast to that in the case of the Pt capping layer.[3] The influence of the layer repetition numbers and film thickness on PMA has been studied by You et al.[4] The interfacial effect is very critical for obtaining the high quality thin film, and in turn it can affect both the static and dynamic properties of the bilayers. Up to now, the fast magnetization dynamics in GHz frequency has been discussed widely in Co/Ni systems. For instance, the relationship between Gilbert damping and magneto-crystalline was studied using an all-optical method.[5–7] Also, the dependence of the intrinsic Gilbert damping on the stack number as well as the layer thickness was reported for Co/Ni thin films.[8] However, the ultrafast demagnetization in Co/Ni bilayer on the sub-ps scale is rarely reported, which is helpful for understanding the terahertz emission in such thin films with large PMA.[9]
In this study, the hysteresis loops and magnetic reversal process of a Co/Ni bilayer system were calculated using the object oriented micromagnetic framework (OOMMF), in which the interfacial exchange coupling constant plays a major role. More importantly, we also investigated the interfacial effect on the laser induced ultrafast demagnetization dynamics in the Co/Ni bilayer based on the atomistic spin dynamics model. Our work can open a novel avenue to manipulate the ultrafast demagnetization via the interfacial exchange coupling constant in perpendicular magnetic anisotropic Co/Ni bilayers, and it has an immediate implication for the design of high frequency spintronic devices.
The three-dimensional (3D) micromagnetic calculation of the OOMMF code is based on the Landau–Lifshitz–Gilbert dynamic equations[10,11]
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![](cpb_27_5_057501/cpb_27_5_057501_ieqn1.gif)
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The average energy density E in Eq. (
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![](cpb_27_5_057501/cpb_27_5_057501_ieqn4.gif)
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In the 3D simulation carried out by OOMMF, the length and width of both the Co and Ni layers are set as 20 nm. The material is divided into small cells whose length and width are 2.0 nm. The height of each cell is set as 0.1 nm. The applied field varies from 3 T to −3 T in the simulation, starting from a positive saturation state, in which the magnetic moments in each cell are uniformly distributed with the initial magnetization parallel to the applied field.
In this work, both Co and Ni have a strong PMA with the following parameters:[13]
Figure
![]() | Fig. 1. (color online) Calculated major hysteresis loops of the Co/Ni bilayers with out plane easy axes based on OOMMF with various interface exchange energy constants. |
The interfacial exchange coupling constant plays an important role in determining the hysteresis loops, and consequently the intrinsic coercivity. Figure
The ultrafast demagnetization dynamics is simulated with an atomistic spin model using the Vampire software package.[13,18] In this atomistic simulation, the energetics of the systems are described by an extended Heisenberg spin model with the following form:
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![](cpb_27_5_057501/cpb_27_5_057501_ieqn20.gif)
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The dynamics of spin systems are determined by the Landau–Liftshit–Gilbert equation with Langevin dynamics
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![](cpb_27_5_057501/cpb_27_5_057501_ieqn22.gif)
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As shown in Fig.
It turns out that λ in the atomistic spin model can be defined by the microscopic spin-flip rate as done in LLB micromagnetic simulations.[24,25] As the material-specific intrinsic spin scattering rate, it is necessary to investigate its influence roughly in a large range of λ as shown in Fig.
![]() | Fig. 5. (color online) Ultrafast demagnetization curves with a large range of microscopic damping constant. |
In the ultrafast magnetization dynamics, the recovery time[26] is another critical parameter besides the above demagnetization time and demagnetization state. Figure
Up to now, we have investigated the effect of interactions among spins, electrons, and lattice in cobalt single layer thin film carefully. Though similar principles still hold for the Co/Ni bilayer system, the effect of the interfacial coupling constant on the ultrafast demagnetization is worth-investigating. In statics, the hysteresis loops present distinct magnetization reversal behaviors with various interfacial coupling. In dynamics, the ultrafast demagnetization curves for the Co and Ni phases in the Co/Ni bilayer on the timescale less than 1 ps are regulated by the interfacial exchange coupling as well. In Fig.
In this study, the static and dynamics properties of Co/Ni bilayers have been studied using 3D micromagnetic simulation and atomistic spin dynamics model, respectively. The coercivity of the bilayers decreases to a valley value sharply with increasing interfacial exchange coupling and then rises slowly to a platform. Also, the interfacial coupling between the Co and Ni layers affects the magnetic reversal in Co/Ni bilayers. The microscopic damping constant in the atomistic spin dynamics domains the ultrafast demagnetization mechanism in Co/Ni bilayers. The recovery time of the magnetization after the laser pulse shows a non-monotonic behavior with the increasing microscopic damping due to the coexistence influence from both the coupling constant between the spin and lattice and the final demagnetization state.
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