# Magneto-Optical Kerr Effect Driven by Spin Accumulation on Cu, Au, and Pt
## 3 Results  
I create a transient spin current from FM to NM by depositing a photon energy on FM. Around 30% of the pump fluence is absorbed by the samples, and the electrons of FM are thermally excited. The heat transfer from the electrons of FM to the magnons of FM leads to the bulk spin generation on the electrons of FM through ultrafast demagnetization [9],  
\[g_{\mathrm{s}}=-\frac{dM}{dt} \tag{1}\]  
where \(M\) is the magnetization of FM. I obtain d\(M\)/d\(t\) from the time derivative of the ultrafast demagnetization data measured with the probe on the sap side of the samples (Figure 2a,b). In order to convert the unit of the Kerr rotation (rad) to the unit of magnetization (A m\({}^{-1}\)), the Kerr rotation from the ultrafast demagnetization is divided by the static Kerr rotation of \(-440\)\(\upmu\)rad of the full magnetization, then multiplied by the saturation magnetization of 6 \(\times\) 10\({}^{5}\) A m\({}^{-1}\). Note that although the sign of the \(\Delta\theta\) from the ultrafast demagnetization of FM is positive, I plot the demagnetization signal to be negative in Figure 2a by adding a negative sign on the \(y\)-axis. This is because it is conventional to draw the demagnetization data as negative. The heat transfer from the electrons of FM to the electrons of NM leads to the interfacial spin generation at the FM/NM interface by the SDSE [18],  
\[G_{\mathrm{s}}=-\left(\frac{H_{\mathrm{B}}}{e}\right)\left(\frac{S_{\mathrm{s} }}{LT}\right)I_{q} \tag{2}\]  
where \(e\) is the elementary charge, \(S_{\mathrm{s}}\) is the effective spin-dependent Seebeck coefficient of \(-12\)\(\upmu\)V K\({}^{-1}\) for [Co/Ni], \(L\) is the Lorenz number of 2.45 \(\times\) 10\({}^{8}\) W \(\Omega\) K\({}^{-2}\), and \(J_{\mathrm{q}}\) is the electronic heat current at the FM/NM interface [18]. I obtain \(J_{\mathrm{q}}\) at the FM/Cu interface by analyzing the temperature evolution of the Cu surface with a thermal conductivity of 300 W m\({}^{-1}\) K\({}^{-1}\) and an electron-phonon coupling of 7 \(\times\) 10\({}^{16}\) W m\({}^{-3}\) K\({}^{-1}\) of Cu [18] (Figure 2c,d). Next, I measure the Kerr rotation on the NM side, where NM is Cu, Cu/Au, or Cu/Pt. In addition to the real part, an imaginary part of the MOKE is measured by inserting a quarter wave plate in the probe path. The Cu/Au layer produces about 2.3 times larger of a MOKE signal than does the Cu layer (Figure 3a,b). In both the Cu and Cu/Au layers, the real part of the MOKE is dominant, and the imaginary part is about thirty times smaller than the real part. The Pt capping layer suppresses the real part of the MOKE while it enhances the imaginary part (Figure 3c). Figure 3: Detection of the spin accumulation on NM. The Kerr rotation due to the spin accumulation on NM with the probe on the cap side of the sap/Pt(10)/[Co/Ni](3.8)/Cu(100)/cap sample, where cap is (**a**) MgO(3), (**b**) Au(10), and (**c**) Pt(2). Black squares and red circles are the real and imaginary parts of the Kerr rotation, respectively. Figure 2: The spin generation on FM. (**a**) The Kerr rotation due to the ultrafast demagnetization of FM with the probe on the sap side of the sap/Pt(10)/[Co/Ni](3.8)/Cu(100)/MgO(3) sample. The ultrafast demagnetization data is nearly identical with either Au or Pt capping on top of Cu. (**b**) The bulk spin generation rate on FM obtained from the time derivative of the demagnetization data of (**a**) (black circles). The red line is a fitting with a Gaussian function. (**c**) The temperature increase of the Cu surface of the sap/Pt(10)/[Co/Ni](3.8)/Cu(100)/MgO(3) sample. Black circles are data points obtained from time-domain thermoreflectance (TDTR), and the red line is the result of the thermal modeling. (**d**) The black line is the heat current at the FM/Cu interface estimated from the thermal modeling of (**c**). The red line is the interfacial spin generation rate at the FM/Cu interface obtained by the Equation (2) in the main text. I calculate the spin accumulation on Cu, Au, and Pt by performing spin diffusion modeling.