Evidence for Two-Dimensional Spin-Glass Ordering in Submonolayer Fe Films on Cleaved InAs Surfaces

Magnetotransport measurements have been performed on two-dimensional electron gases formed at InAs(110) surfaces covered with a submonolayer of Fe. Hysteresis in the magnetoresistance, a difference in remanent magnetoresistance between zero-field-cooling procedures and field-cooling procedures, and logarithmic time-dependent relaxation after magnetic field sweep are clearly observed at 1.7 K for a coverage of 0.42 monolayer. These features are associated with spin-glass ordering in the Fe film.

Figure 1

In-plane magnetic field dependence of $\rho$ at $T=1.7\mathrm{K}$. (a),(b) Results for $\Theta =0.42\mathrm{ML}$. The electron density and mobility of the 2DEG are $N_s=3.54\times {10}^{12}{\mathrm{cm}}^{-2}$ and $\mu =7.9\times {10}^3{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$, respectively. Solid triangles represent the data obtained during the initial excitation up to $+9\mathrm{T}$. Open (solid) circles represent the data obtained during subsequent sweeps from $+9\mathrm{T}$ ($-9\mathrm{T}$) to $-9\mathrm{T}$ ($+9\mathrm{T}$). (c) Results for $\Theta =0.17\mathrm{ML}$ ($N_s=4.10\times {10}^{12}{\mathrm{cm}}^{-2}$ and $\mu =1.04\times {10}^4{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$). No hysteresis was observed.

Figure 2

(a) Remanent magnetoresistivity observed at $B=0\mathrm{T}$ and $T=1.7\mathrm{K}$ for different cooling and magnetizing procedures. The solid and open symbols represent the data obtained after ZFC procedures and FC procedures, respectively. The magnetic field was applied at different angles of $\phi =0°$ (circles), 45° (diamonds), and 90° (triangles) with respect to the surface normal. The data at $\phi =0°$ (45°) are offset by $-0.10\Omega$ ($-0.22\Omega$) for clarity. Solid lines represent ${\rho }_0(B_{\max })={\rho }_0(0)-\Delta \rho /[1+(B_0/B_{\max }{)}^2]$, where ${\rho }_0(0)=223.02\Omega$, $\Delta \rho =1.58\Omega$, and $B_0$ is a fitting parameter for each curve. (b) ZFC procedures. After cooling the sample, the magnetic field was applied up to a maximum value $B_{\max }$. (c) FC procedures.

Figure 3

Time evolution of $\rho$ after magnetic field sweep at $\phi =90°$. (a) Data obtained at 4.0 K (upper curve) and 1.7 K (lower curve) after a sweep from 9 to 0 T. (b) Data obtained at $T=1.7\mathrm{K}$ and $B=1.5\mathrm{T}$ after a down sweep from 2.0 T (upper curve) and an up sweep from 0.9 T (lower curve).