Electric-Field Modulation of Damping Constant in a Ferromagnetic Semiconductor (Ga,Mn)As

The modulation of the Gilbert damping constant $\alpha$ in (Ga,Mn)As by the application of an electric field is detected by ferromagnetic resonance measurements, where $\alpha$ increases with decreasing hole concentration. The smaller modulation of other magnetic parameters, such as magnetic anisotropy fields and Landé $g$ factor, suggests that the modulation of $\alpha$ is governed by other effects rather than the spin-orbit coupling. Comparison of the conductivity dependence of $\alpha$ with that of the magnetization indicates that the magnetic disorder induced by carrier localization plays a major role in determining the magnitude of $\alpha$ in (Ga,Mn)As.

Figure 1

Schematic of metal-insulator-semiconductor (MIS) structure for ferromagnetic resonance and magnetization measurements. Capacitance area is $1.0\times 2.3{\mathrm{mm}}^2$. Right panel shows crystal orientations of (Ga,Mn)As and the definition of angles of magnetic field ${\theta }_H$ and magnetization ${\theta }_M$.

Figure 2

Ferromagnetic resonance spectra as a function of (a) magnetic-field angle ${\theta }_H$ at 15 K, and as a function of gate voltages $V_G$ at 20 K at magnetic-field angles (b) ${\theta }_H=0°$ and (c) ${\theta }_H=90°$. Gate-voltage $V_G$ dependence of resonant fields $H_R$ at (d) ${\theta }_H=0°$ and (e) ${\theta }_H=90°$ and that of linewidths $\mathrm{\Delta }H$ at (f) ${\theta }_H=0°$ and (g) ${\theta }_H=90°$.

Figure 3

(a) Magnetic-field angle dependence of resonant fields $H_R$ at 20 K as a function of gate voltages $V_G$. Symbols represent experimental results, and the solid line is the fit by Eq. (1). Gate-voltage dependence of (b) magnetic anisotropy fields, $H_K$, $H_B$, and $H_U$, and (c) Landé $g$ factor $g$.

Figure 4

(a) Magnetic-field angle dependence of linewidths $\mathrm{\Delta }H$ at 20 K as a function of gate voltages $V_G$. Symbols represent experimental results, and solid lines are fittings by using Eq. (4). (b) Gate-voltage dependence of damping constants $\alpha$.

Figure 5

(a) Temperature dependence of resistivity $\rho$ at gate voltages $V_G$ of $-24$, 0, and $+24\mathrm{V}$. (b) Temperature dependence of in-plane magnetization $M$ for zero-field cooled state and state under magnetic field ${\mu }_{0}H$ of 200 mT at gate voltages $V_G$ of $-23$, 0, and $+23\mathrm{V}$. $T_C$ is modulated by $\sim 6\mathrm{K}$.

Figure 6

Temperature dependence of magnetization $M$ of zero-field cooled state and state under magnetic field ${\mu }_{0}H=200\mathrm{mT}$ for (a) a 200-nm-thick insulating sample with $x=0.075$ and (b) a 20-nm-thick metallic sample with $x=0.068$. (c) Damping constant $\alpha$ (closed symbols) and ratio of superparamagneticlike component $M_{\mathrm{SP}}$ to total magnetic component $M_{\mathrm{tot}}$ (open symbols) as a function of resistivity $\rho$. Circles (triangles) are for the sample with $x=0.075$ (0.068), whose $\rho$ is changed by annealing. Squares are for the MIS structure, whose $\rho$ is change by applied gate voltage. The results for the samples with $x=0.075$ and 0.068 are taken at 10 K except for one $\alpha$ value obtained at 45 K as indicated, and those for the MIS structure are taken at 20 K. (d) $\alpha$ as a function of $M_{\mathrm{SP}}/M_{\mathrm{tot}}$. Circles and triangles are for (Ga,Mn)As with $x=0.075$ and 0.068, respectively. Squares are for (Ga,Mn)As in the MIS structure.