Magnetic properties and domain structure of (Ga,Mn)As films with perpendicular anisotropy

The ferromagnetism of a thin ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ layer with a perpendicular easy anisotropy axis is investigated by means of several techniques that yield a consistent set of data on the magnetic properties and the domain structure of this diluted ferromagnetic semiconductor. The magnetic layer was grown under tensile strain on a relaxed ${\mathrm{Ga}}_{1-y}{\mathrm{In}}_y\mathrm{As}$ buffer layer using a procedure that limits the density of threading dislocations. Magnetometry, magnetotransport, and polar magneto-optical Kerr effect (PMOKE) measurements reveal the high quality of this layer, in particular, through its high Curie temperature $\left(130\mathrm{K}\right)$ and a well-defined magnetic anisotropy. We show that magnetization reversal is initiated from a limited number of nucleation centers and it develops by easy domain-wall propagation. Furthermore, MOKE microscopy allowed us to characterize in detail the magnetic domain structure. In particular, we show that the domain shape and wall motion are very sensitive to some defects, which prevents a periodic arrangement of the domains. We ascribed these defects to threading dislocations emerging in the magnetic layer, inherent to the growth mode on a relaxed buffer.

Figure 1

Thermal dependence of the longitudinal resistivity for the as-grown (Ga,Mn)As film (dashed line, left), and for the annealed sample (full line, right).

Figure 2

Magnetic hysteresis loops measured by the Hall resistivity at low temperatures: (a) as-grown film; (b) annealed film. Sweeping rate of the magnetic field is $17\mathrm{Oe}∕\mathrm{s}$.

Figure 3

Hysteresis loop measured by (SQUID) magnetometry at $4\mathrm{K}$ for the annealed sample. The magnetic field was applied along the growth axis.

Figure 4

Temperature dependence of the magnetization (open circles) of the annealed sample measured by SQUID magnetometry under $H=250\mathrm{Oe}$ applied along the growth axis, compared to that of the remnant PMOKE signal (closed squares). For each curve, the data were normalized to their low temperature value, and plotted as a function of the reduced temperature $T∕T_c$. For comparison, the mean-field $S=\frac{5}{2}$ Brillouin function is also plotted (dashed line).

Figure 5

(a) PMOKE hysteresis loops measured at different temperatures for the annealed (Ga,Mn)As film; (b) in the vicinity of $T_c=130\mathrm{K}$.

Figure 6

Magnetic after-effect relaxation curves for the annealed (Ga,Mn)As film and for different field values. (a) $T=1.8\mathrm{K}$; (b) $T=77\mathrm{K}$; (c) $T=113.5\mathrm{K}$.

Figure 7

ac-demagnetized state of the annealed (Ga,Mn)As film at $77\mathrm{k}$, obtained from saturation, after a slow decrease of the amplitude of an alternative magnetic field parallel to the [001] axis down to zero. Up (down)-magnetized domains are appearing in black (white). Image size: $135\mu \mathrm{m}\times 176\mu \mathrm{m}$.

Figure 8

Successive snapshots of the magnetization reversal at $77\mathrm{K}$, observed by PMOKE microscopy, after having applied a field of $H=-20.5\mathrm{Oe}$ during $1\min$. The lag time between successive images is, $10\mathrm{s}$ between (a) and (b), and (b) and (c). It is $30\mathrm{s}$, 2 and $15\min$ between (c) and (d), (d) and (e), (e) and (f), respectively. The image size is $135\mu \mathrm{m}\times 176\mu \mathrm{m}$.

Figure 9

Remnant domain structure after applying a field $H=-50\mathrm{Oe}$, and switching it to zero. Image size: $135\mu \mathrm{m}\times 176\mu \mathrm{m}$. Stable nonreversed filamentary domains (360° domain walls) are clearly observed.

Figure 10

Successive PMOKE snapshots of the magnetic domain structure on another part of the annealed (Ga,Mn)As film. (a) The sample is first saturated in a positive field (black up-magnetized domains), and subsequently submitted to a negative field $H=-140\mathrm{Oe}$ for a few seconds, and switched to zero. Up-magnetized filamentary domains are frozen in the remnant state. (b) A negative field $(H=-112\mathrm{Oe})$ is applied. The filamentary structure is shrinked, since the field tends to reduce their width. (c) Switching again the field back to zero, a remnant state similar to the previous one (a), is observed, except for a few branches that have disappeared under the field due to their depinning on defects. (d) Finally, a positive field $(H=53\mathrm{Oe})$, close to the coercive value, has been applied during $5\mathrm{s}$. The snapshot is obtained after switching off the field. The image size is $135\mu \mathrm{m}\times 176\mu \mathrm{m}$.