Effect of the location of Mn sites in ferromagnetic GaMnAs on its Curie temperature

We report a strong correlation between the location of Mn sites in ferrromagnetic Ga 1-x Mn x As measured by channeling Rutherford backscattering and by particle induced x-ray emission experiments and its Curie temperature. The concentrations of free holes determined by electrochemical capacitance-voltage profiling and of uncompensated Mn ++ spins determined from SQUID magnetization measurements are found to depend on the concentration of unstable defects involving highly mobile Mn interstitials. This leads to large variations in T C of Ga 1-x Mn x As when it is annealed at different temperatures in a narrow temperature range. The fact that annealing under various conditions has failed to produce Curie temperatures above ~110K is attributed to the existence of an upper limit on the free hole concentration in low-temperature-grown Ga 1-x Mn x As.

In recent years, there is a growing interest in the possibility of using electron spins in electronic devices for the processing, transferring, and storing of information [1].
Many of such applications would require a combination of semiconducting and magnetic properties in the same material. The prospects for the practical realization of such "spintronic" devices increased significantly when it was discovered that alloys of GaAs with Mn (specifically, Ga 1-x Mn x As with x ≈ 0.07) could be made ferromagnetic with a Curie temperature T C as high as 110 K [2,3].
It was established experimentally that T C in Ga 1-x Mn x As increases with increasing Mn concentration x (as long as MnAs precipitates are not formed) and with the hole concentration [3]. These observations are consistent with the Zener model of ferromagnetism proposed by Dietl et al. [4], which predicts that where x is the mole fraction of substitutional Mn ++ ions, p is the hole concentration, and C is a constant specific to the host material. Alternatively, it has been proposed that the ferromagnetic coupling between Mn ++ ions is mediated by holes localized on adjacent ions [5].
It should be noted that Mn atoms can occupy three types of sites in the Ga 1-x Mn x As lattice. Mn atoms can occupy the Ga lattice sites to form the Ga 1-x Mn x As alloy.
They can occupy interstitial sites commensurate with the zinc-blende lattice structure.
Finally, Mn atoms can also precipitate out to form different phases (e.g., MnAs inclusions). In the latter case Mn resides at random sites and therefore it is incommensurate with the zinc blende lattice. In Ga 1- is not sensitive in measuring the coordination numbers (~20%) and distinguishing the chemical nature of the neighbors with small difference in atomic number (e.g. Ga and As). Lattice site location of impurities can only be indirectly inferred from multiparameter fitting of the EXAFS spectra using calculated model structures.
In this paper we report a study of the lattice sites occupied by Mn atoms in thin Ga 1-x Mn x As films using channeling Rutherford backscattering (c-RBS) and particle induced x-ray emission (c-PIXE) experiments. The results are combined with measurements (on the same samples) of the free hole concentration, carried out by the electrochemical capacitance-voltage (ECV) profiling; and of magnetization, carried out by SQUID measurements. These studies clearly establish the correlation between the arrangement of Mn sites in Ga 1-x Mn x As and its Curie temperature.
The Ga 1-x Mn x As films were grown on semi-insulating (001) GaAs substrate in a Riber 32 R&D molecular beam epitaxy system. Fluxes of Ga and Mn were supplied from standard effusion cells, and As 2 flux was produced by a cracker cell. Prior to Ga 1- x Mn x As deposition we grew a 450 nm GaAs buffer layer at 590ºC (i.e., under normal GaAs growth conditions). The substrate was then cooled down to 265ºC for the growth of a 3 nm thick low-temperature (LT) GaAs, followed by a 110 nm GaMnAs layer using an As 2 :Ga beam equivalent pressure ratio of 20:1. Mn concentration in the sample was estimated to be 8 ± 2% from the change in the growth rate monitored by RHEED oscillations. After the growth, three adjacent 7x7 mm pieces of the wafer were cut for 4 further study. One of these was used as-grown, the other two were annealed at 282ºC and 350ºC, respectively, for 1 hr in flowing N 2 . The locations of Mn sites in the Ga 1-x Mn x As lattice were then studied by directly comparing the Mn K α x-ray signals (c-PIXE) with the c-RBS signals of GaAs from the Ga 1-x Mn x As film simultaneously obtained using a 1.95MeV 4 He + beam.
The T C of the as-grown Ga 1-x Mn x As film was 67K. Annealing at 282°C (i.e. at temperature only slightly higher than the growth temperature) increased the T C to 111K.
Annealing at 350°C, however, resulted in a lower T C of 49K. It has been shown previously that varying the temperature [8] or the duration [9] of the low temperature annealing has produced similar changes of T C .
RBS and PIXE measurements on the as-grown Ga 1-x Mn x As sample reveal that the film has a Mn concentration x = 0.09, in good agreement with the value from RHEED oscillations. Figure 1 compares the PIXE spectra from the as-grown Ga 1-x Mn x As film when the crystal is not aligned (random), and when it is aligned in the <110> and <111> directions. The greatly reduced Mn K α x-ray yields in the aligned spectra indicates that a dominant fraction of the Mn atoms are shadowed by the lattice site host atoms, and therefore are not visible to the beam along the axial channel direction. The fact that for certain axial channeling projections the Mn atoms are shadowed by the Ga or As atoms indicates that the Mn atoms are in specific (non-random) sites commensurate with the lattice, but does not necessarily imply that the Mn atoms are in substitutional positions.
One striking feature shown in Fig. 1 is that the Mn K α x-ray yields observed in the <110> alignment are much higher than those in the <111> spectrum. This immediately suggests that the non-random Mn atoms in this sample reside in more than one non-equivalent   (100) and (110) planar directions, but are exposed in the <110> axial channel at two equivalent interstitial 6 positions parallel to the (110) plane and in the (111) planar direction [10,11,15]. This gives rise to a double-peak feature in the <110> angular scan due to the flux peaking effect of the ion beam in the channel. A double-peak feature is indeed observable in the <110> scan for the as-grown sample (indicated by the arrows) shown in Fig. 3. The fraction of these intersititial Mn can be roughly estimated to be ~ 17%, assuming that flux peaking in the <110> channel of GaAs is ~1.5 [10,11,15]. The presence of interstitials in the as-grown film is further confirmed in (110) and (111)  It is well known that the determination of the hole concentration in ferromagnets is complicated by the so-called anomalous Hall effect (AHE), characteristic of conducting ferromagnets [3,16]. To circumvent this problem, we have used the electrochemical capacitance voltage (ECV) profiling method to measure the depth distribution of uncompensated Mn acceptors in the Ga 1-x Mn x As layers [17]. This method provides information on the distribution of the net space charge in the depletion region.
The ECV profiling showed an increase of the net acceptor concentration from 6x10 20 cm -3 observed in the as-grown sample to 1x10 21 cm -3 for the Ga 1-x Mn x As film annealed at 282°C [18]. The sample annealed at 350°C, on the other hand, showed practically no change in the hole concentration. We have verified the validity of the ECV method by comparing ECV and Hall measurements on (non-magnetic) heavily Be-doped LT-GaAs.
The ECV results are consistently within 10% of the Hall values of free hole concentration [19]. We can therefore assume that there are no donor levels close to the valence band and the ECV measurements reflect the free hole concentration in the Ga 1-x Mn x As films.
The ion channeling and ECV results show that out of ~2x10 21  Annealing the sample at 282ºC (only slightly above the growth temperature) breaks the relatively weak Mn I -Mn Ga pairs, releasing the highly mobile Mn I to diffuse to available substitutional sites or to form precipitates and/or clusters, thus leaving behind the substitutional Mn Ga , which can then become electrically-active acceptors.
Consequently the 282ºC annealing leads to a higher hole concentration, p = 1x10 21 cm -3 and a higher concentration of Mn atoms occupying random sites. The very high hole concentration, about an order of magnitude higher than the concentration limits in p-type GaAs [20,21] indicates that the sample annealed at 282ºC is still far from thermodynamic equilibrium. This is confirmed by the annealing at 350ºC that drives the system towards equilibrium by removing the Mn from the electrically active Mn Ga sites, to form random precipitates and/or clusters. Such mechanism has already been shown to be a driving force that limits the free hole concentration in heavily Zn doped GaAs [21]. It should be noted here that, contrary to earlier suggestions, [9] the arsenic antisite (As Ga ) defects are not expected to play a significant role in the annealing-induced changes, since these latter defects have been shown to remain stable up to 450ºC [22]. Our results show that the large changes in the electronic and magnetic properties induced by the annealing at temperatures so close to the growth temperature can be attributed to the lattice site rearrangement of highly unstable Mn I . The fact that our maximum T C of 111 K is so close to the maximum T C of 110 K reported by other groups [2,3,9] suggests the possibility that this could be a fundamental limit on T C in Ga 1- x Mn x As alloy system. If so, this may be the reason why similar maximum values of T C were found in Ga 1-x Mn x As with rather different values of x, ranging from 0.053 to 0.091 [3,9].
It is well known that the formation energies and thus also the concentrations of charged defects such as Mn I donors or Mn Ga acceptors are to a large extent controlled by the Fermi energy [20]. To maximize T C one strives to increase the concentration of electrically active Mn Ga acceptors, and thus also the concentration of uncompensated Mn spins. This, however, leads to a downward shift of the Fermi energy, that in turn increases the formation energy of negatively charged defects, thus making the incorporation of new Mn Ga acceptors energetically unfavorable. It is therefore reasonable to expect that there is a hole concentration limit, beyond which additional Mn can only be incorporated in the form of Mn I donors and/or electrically inactive precipitates. Our results indicate that in the low-temperature-grown materials the maximum T C is achieved for the hole concentration limit p max = 10 21 cm -3 , which requires Ga 1-x Mn x As with x > 0.045. While this value is quite large, we note that a similar hole concentration limit (p = 8x10 20 cm -3 ) has been also found in a nonmagnetic Be doped, low temperature grown GaAs [19,23]. It should be emphasized that any detailed description of the microscopic mechanism limiting the maximum Curie temperature will have to consider the role of As antisites donors [24,25].
In conclusion, we have shown that the location of Mn sites in the Ga 1-x Mn x As lattice plays a crucial role in determining its magnetic properties. The concentrations of free holes and of uncompensated Mn spins, both of which underlie the ferromagnetic properties in the III 1-x Mn x V alloys, are thus seen to be controlled by the behavior of unstable defects involving highly mobile Mn interstitials. In particular, the Curie temperature of Ga 1-x Mn x As is clearly affected by the rearrangement of the Mn atoms in the crystal lattice. The relationship of T C to the behavior of Mn interstitials thus leads to wide variations of this parameter for annealing even in a narrow temperature window.
Finally, we note that the observed limit for maximum Curie temperature can be attributed to the limit on the free hole concentration attainable in low temperature grown Ga 1- x Mn x As.