Kerr rotation in Cu, Ag, and Au driven by spin accumulation and spin-orbit coupling

We measure transient spin accumulation in Cu, Ag, and Au by time-resolved magneto-optical Kerr effect. The transient spin current is generated by ultrafast demagnetization of a ferromagnetic [Co/Pt] layer, and spin accumulates in an adjacent normal metal, Cu, Ag, or Au by spin diffusion. The magnitude of the Kerr rotation is described by an off-diagonal conductivity tensor that is proportional to spin accumulation and spin-orbit coupling. From comparisons between observed Kerr rotations and calculated spin accumulations, we determine the strength of spin-orbit coupling of conduction electrons in Cu, Ag, and Au to be 0.02, 0.01, and $0.12\mathrm{eV}$, respectively.

Figure 1

(a) Demagnetization data measured on the Pt side of the Cu-100 (black squares), Ag-100 (red circles), and Au-100 (blue triangles) samples. (b) The −$dM/dt$ of the Cu-100 (black squares), Ag-100 (red circles), and Au-100 (blue triangles) samples. Data are obtained by multiplying the saturation magnetization $4\times {10}^5\mathrm{A}{\mathrm{m}}^{-1}$ by numerical differention of (a).

Figure 2

The Kerr rotations measured on the NM side of the (a) Cu-$h$, (b) Ag-$h$, and (c) Au-$h$ samples: black squares, red circles, and blue triangles are for NM thickness of 100, 150, and 200 nm, respectively.

Figure 3

The calculated spin accumulations at the NM surface of the (a) Cu-$h$, (b) Ag-$h$, and (c) Au-$h$ samples: black, red, and blue lines are for NM thickness of 100, 150, and $200\mathrm{nm}$, respectively.

Figure 4

The dependence of the peak spin accumulation on the (a) Cu, (b) Ag, and (c) Au thicknesses. (a) Black circles are experimental data from Fig. 2 and solid lines are from calculation [black, red, and blue lines are for $l_{\mathrm{S}}$ of Cu of $300\left({\tau }_{\mathrm{S}}=9\mathrm{ps}\right),400\left({\tau }_{\mathrm{S}}=16\mathrm{ps}\right),\mathrm{and}500\left({\tau }_{\mathrm{S}}=26\mathrm{ps}\right)\mathrm{nm}$, respectively]. (b) Black circles are experimental data from Fig. 2; solid lines are from calculation [black, red, and blue lines are for $l_{\mathrm{S}}$ of Ag of $100\left({\tau }_{\mathrm{S}}=0.7\mathrm{ps}\right),150\left({\tau }_S=1.5\mathrm{ps}\right),\mathrm{and}200\left({\tau }_S=2.7\mathrm{ps}\right)\mathrm{nm}$, respectively]. (c) Black circles are experimental data from Fig. 2; solid lines are from calculation [black, red, and blue lines are for $l_{\mathrm{S}}$ of Au of $50({\tau }_{\mathrm{S}}=0.3\mathrm{ps}),60\left({\tau }_{\mathrm{S}}=0.4\mathrm{ps}\right),\mathrm{and}70\left({\tau }_{\mathrm{S}}=0.5\mathrm{ps}\right)\mathrm{nm}$, respectively].

Figure 5

The raw Kerr rotation measured on the Au side of the Au-100 sample (black squares) and the demagnetization signal (red circles), which is scaled to match the Kerr rotation at $10\mathrm{ps}$. The $\Delta \theta$ by spin accumulation of the Au-100 sample in Fig. 2 is obtained by subtracting the demagnetization signal from the raw Kerr rotation.

Figure 6

The STT result with the [Co/Pt/Co/Ni] layer, grown at KIST. (a) The $-dM/dt$ of [Co/Pt/Co/Ni] (black circles), obtained from the demagnetization data of Ref. [9]. Solid line is a fit to a Gaussian function. (b) The calculated spin current that is absorbed by the CoFeB layer in the Pt (30)/[Co/Pt/Co/Ni] (6.4)/Cu (10)/CoFeB (2) (unit in nm) sample with ${\tau }_{\mathrm{S}}=0.02\mathrm{ps}$ of $\left[\mathrm{Co}/\mathrm{Pt}/\mathrm{Co}/\mathrm{Ni}\right]$. (c) The precession data (black circles) and simulation result (solid lines) of the CoFeB precession of the Pt (30)/[Co/Pt/Co/Ni] (6.4)/Cu (10)/CoFeB (2) sample: the data are taken from Ref. [9]; the simulation is based on Eq. (B1) with an input spin current of (b).

Figure 7

The comparison of the spin accumulation data of [Co/Pt/Co/Ni], grown at KIST, and [Co/Pt], grown at UIUC. (a) The Kerr rotation measured on the Cu side of the Pt (30)/[Co/Pt/Co/Ni] (6.4)/Cu (80) (unit in nm) sample (black squares): The $\Delta \theta$ by spin accumulation (blue triangles) is obtained by subtracting the demagnetization signal (red circles) from the raw Kerr rotation. (b) The Kerr rotation measured on the Cu side of the Pt (30)/[Co/Pt] (6)/Cu (100) (unit in nm) sample (black circles). All data are taken from Ref. [9].

Figure 8

The dependence of the spin accumulation on the spin relaxation time of Pt, [Co/Pt], and Cu in the Pt (20)/[Co/Pt] (6)/Cu (100) (unit in nm) structure. (a) The ${\tau }_{\mathrm{S}}$ of Pt is varied from 0 to $0.6\mathrm{ps}$ while ${\tau }_{\mathrm{S}}$ of [Co/Pt] and Cu are fixed at 0.01 and 16 ps, respectively. (b) The ${\tau }_{\mathrm{S}}$ of [Co/Pt] is varied from 0 to $0.02\mathrm{ps}$ while ${\tau }_{\mathrm{S}}$ of Pt and Cu are fixed at 0.3 and 16 ps, respectively. (c) The ${\tau }_{\mathrm{S}}$ of Cu is varied from 0 to 30 ps while ${\tau }_{\mathrm{S}}$ of Pt and [Co/Pt] are fixed at 0.3 and $0.01\mathrm{ps}$, respectively.