Coherent phonon control via electron-lattice interaction in ferromagnetic Co/Pt multilayers

The manipulation of coherent phonons in condensed systems has attracted fundamental interest, particularly for its applications to future devices. We demonstrate that a coherent phonon in Co/Pt nano-multilayer can be quantitatively controlled via electron-lattice coupling, specifically by changing the multilayer repeat number. To that end, systematic measurement of the time-resolved reflectivity and magneto-optical Kerr effect in Co/Pt multilayers was performed. The coherent phonon frequency was observed to be shifted with the change of the multilayer repeat number. This shift could be clearly explained based on the two-temperature model. Detailed analysis indicated that the lattice heat capacity and electron-lattice coupling strength are linearly dependent on the repeat number of the periodic multilayer structures. Accessing the control of coherent phonons using nanostructures opens a new avenue for advanced phonon-engineering applications.

The Co/Pt multilayer has been fabricated with well-defined interface structures, which are confirmed with the X-ray reflection measurement as shown in the figure for the case of n = 5.
Minor peaks from the multilayer interfaces are clearly distinguishable, providing the best fitting result of t Co = 6.3 Å and t Pt = 9.3 Å. The corresponding static magnetic hysteresis loop for n = 5, measured by the vibrating sample magnetometer along the out-of-the plane of the sample is plotted as in the inset, clearly showing that the film has a perpendicular magnetic anisotropy It guarantees that each layer of the Co is ferromagnetically ordered along the easy axis out of the film plane. The perpendicular magnetic anisotropy is found in all the sample in the present study.   Hence, it is concluded that this oscillation is of magnetic origin, It is observed that spin precessional motion is in a frequency range of a few GHz. Indeed this is consistent with recent MOKE experimentation with Pt/8-Å Co/Pt film in Mizukami's work, where the precession frequency was reported to be lower than 10 GHz. 2 We have further analyzed the damping of spin precessional motions. The effective damping constant α is achieved from the relation α = 1/2πfτ D , where τ D is determined from the analysis of spin precession signals ( Figure S3

(4) Characteristic behavior of demagnetization with respect to change of source term and electron-and lattice-specific heat and electron-lattice interaction strength
The two-temperature model by Bigot et al. `has often been employed to quantitatively analyze the time-resolved MOKE signals where T e (t) and T l (t) are the time-dependent electron and lattice temperatures, respectively, C e (t) the temperature-dependent electron-specific heat, G el the electron-lattice interaction strength, C l the lattice-specific heat, and  l the thermal conductivity.
We performed a series of simulations to determine how the specific heat coefficient and the electron-lattice interaction strength would change electron and lattice temperature as well as magnetization. In our simulations, the thermal diffusion term was neglected due to the lateral uniformity, and we assumed that C e (t) is proportional to T e (t). Hence, Eq. S(1) can be

dT C T t G T t T t P t dt dT C G T t T t dt
where C e0 is the electron-specific heat coefficient.
The time-resolved remanence signal, M(T e (t)), can be calculated using the equation where M s is the spin magnetization and T c is the Curie temperature (1645 K for Cobalt). We assume here that the electron temperature is the same as the spin temperature. In the present work, we also applied a three-temperature model, wherein almost no difference was found between the spin and the electron temperature; therefore, we simply adopted the twotemperature model to focus on coherent phonon behavior.  where i =1, 2, and 3 corresponds to the multilayer samples with 5, 10, and 15 bi-layers, respectively. C l is assumed not to be a function of the lattice temperature, since it has only a weak temperature dependence at high temperatures.
We used the two-temperature model to globally fit all of the remanent magnetization signals with the constraints given in Eq. S(5). In all of the fittings, we also included the numerical convolution between S M (t) and a normalized Gaussian function, G(t), to account for the pulse duration of the probe beam:

S(6)
All of the experimental remanence signals were fit using Eq. S(6).