SQUID Results

In this section the results from the SQUID measurements are presented. The investigated samples are; A789c, Mn136, Mn137 and Mn381. For all of the samples the magnetic hysteresis loops were measured at three different temperatures, i.e. 5 K, 130 K and 298 K. In addition to the sample’s thickness, which was known from the growers’ specifications, the sample’s width wsampleand length ℓsamplewere measured to calculate the sample’s volume Vsample (see table 6.1).

100 200 300 400 500

Figure 6.2: Diamagnetic background of the SQUID.

Measurement conducted using the Mn381 sample.

Prior to the hysteresis measurements, the diamag-netic background has been measured as function of temperature, to calculate the magnetization values of each sample. The calibration for the diamagnetic background is shown in Fig. 6.2. As one can see, the diamagnetic background is linear as function of applied field and only deviates (slightly) for very low temperatures. For calculations on the magnetization, we have used the average linear fit for all curves of Fig. 6.2, which is

M= −6.77 · 10⁻⁸× B + 2.17 · 10⁻⁶ . (6.6) The results of the SQUID measurements are pre-sented in Fig. 6.3. The magnetization has been mea-sured as function of temperature. This is shown in the top left inset of each of the hysteresis loops in Fig. 6.3. For each sample, the magnetization curves have been taken under ‘saturation’ conditions mean-ing that an external B field of 100 mT was applied to enhance the sample’s magnetic moment. The values for saturation magnetization MS, the remanent magne-tization or remanence MR, the saturation field HS and the coercive field or coercitivity HC of each sample were determined from the hysteresis loop (also see chapter 1, Fig. 1.5a) by using the following relations

-400 -300 -200 -100 0 100 200 300 400

Figure 6.3: Hysteresis curves for various samples as function of magnetic field at different temperatures. The left inset shows the magnetization curve as function of temperature. (a) A789c sample. Note the different scaling for the magnetic field. (b) Mn136 sample. (c) Mn137 sample. (d) Mn381 sample. This sample is not ferromagnetic for temperatures above ±110 K.

The results are listed in table 6.2 for the four samples under investigation. As one can see, sample A789c (Fig. 6.3a) shows ferromagnetic behavior up to room temperature [15]. Also the other three samples were expected to show ferromagnetic behavior at room temperature, but due to the small thickness τlayer of the Ga1−xMnxAs layer, the magnetic moment of these samples was beyond the SQUID detection limit. The first order phase transition of the GaMnAs layer as function of temperature is not observed for this sample. We expect this to be a result of the ferromagnetic contribution of the MnAs rather than the GaMnAs layer to the overall ferromagnetic behavior. The samples Mn136 and Mn137 (Fig. 6.3b and 6.3c) show ferromagnetic

Table 6.2: Magnetization values for the four (Ga,Mn)As samples.

Name Temp. ±MS ±MR ±HS +HC −HC

[K] [emu/cm³] [emu/cm³] [emu/cm³] [emu/cm³] [emu/cm³] A789c

5 19.9 ± 0.2 8.7 ± 0.3 600 ± 10 46.5 ± 0.3 47 ± 0.3

130 19.6 ± 0.2 4 ± 1 600 ± 10 25 ± 2 5 ± 2

298 13.9 ± 0.2 × 600 ± 10 × ×

Mn136 5 55.1 ± 0.2 12.4 ± 0.2 1160 ± 10 49 ± 0.3 50.4 ± 0.3 130 18.0 ± 0.2 3.3 ± 0.3 990 ± 10 12.9 ± 0.5 10 ± 0.5 Mn137 5 39.7 ± 0.2 7.5 ± 0.2 1170 ± 10 50 ± 0.3 45 ± 0.3

130 10.1 ± 0.2 × 926 ± 10 × ×

Mn381 5 24 ± 1 × 1000 ± 10 × ×

behavior up to temperatures TC ∼ 250 K, which is agreement with theoretically predicted values [12] and experimentally observed properties [10]. Based on these observations, we expect the Mn concentration of these samples to be x ∼ 0.06. The magnetization temperature dependence clearly shows second phase transition around temperatures ∼ 80 K, which is also comparable to results reported in literature [10]. The fourth sample (Mn381, Fig. 6.3d) only shows ferromagnetic behavior up to temperatures of T = 110 K, which is in good agreement with the theoretically estimated value TC= 115 K for comparable concentrations of Mn [88].

In accordance with was expected, this as–grown sample does not show any ferromagnetic behavior behavior for higher temperatures. For future research, these as–grown samples should be annealed at 180^◦C for 24 hrs and measured again.

In conclusion, the four (Ga,Mn)As samples that have been analyzed show little to no ferromagnetic behavior for temperatures above 200 K, apart from the A789c sample. Even at low temperatures, the magnetization of the samples is very small (MS≤ 200 µemu). This constitutes a problem in terms of resolution and sensitivity for MFM measurements. But, as we have shown in the previous chapter, the sensitivity and resolution of the MFM have been optimized. Furthermore, by using hard magnetic high Q cantilevers with super–sharp tips and by applying a magnet field at low temperatures to enhance the sample’s magnetic moment, we expect to present low temperature magnetic force microscopy measurements in the (very) near future.

Conclusions

In this thesis, the sensitivity and resolution of the magnetic force microscope present in the PSN group have been investigated and optimized. In order to achieve an optimal operation of the magnetic force microscope, we have improved many facets of the setup such as the tip and sample mounting, the optical detection path, the electronics, the measurement procedures and so on. In order to test the improvements we have exten-sively performed atomic force and magnetic force microscopy measurements at ambient and low temperature conditions. This work has resulted in a reduction of the phase noise level of the setup by a factor of 5 and an increased magnetic spatial resolution from ∼ 700 nm to ∼ 50 nm. From a magnetic force microscopy point of view, the specs have now reached a state of art level. The performance of high Q magnetic cantilevers has been studied in order to further increase the spatial resolution and sensitivity of our microscope. In view of our future objectives to apply this microscope for study of nanomagnetism in semiconductors we have already analyzed several magnetic nanostructured (III,Mn)V semiconductor samples by means of magnetometry.

Although strong progress has been obtained unfortunately, due to experimental problems beyond our control, we have not yet been able to conduct magnetic force microscopy measurements on these samples with the improved setup. Although our setup is not yet perfect and fully reliable at the moment, we are convinced that with the reduction of the overall noise level, the improved resolution in combination with the use of dedicated cantilevers, will allow for a better understanding of local magnetism in semiconductor nanostructures. In future research, the setup will be applied for studies of the formation of magnetic domains in diluted (III,V) based semiconductor nanostructures, the properties of small magnetic MnAs inclusions in GaMnAs layers and granular magnetic semiconductor materials.

My deepest gratitude goes out to my family and friends for their love and support, without them this work would not have been completed. I would like to thank Prof. dr. Paul Koenraad for given me the confidence, the opportunity and the support to work in the PSN group under his supervision. My appreciation also goes out to M.Sc. Juanita Bocquel for her guidance and support in the past year and also to all of the members of the PSN group. It has been a great year! I would like to thank the FNA group, in particular Reinoud Lavrijsen, Gerrie Baselmans and Jürgen Kohlhepp, for their guidance with the SQUID measurements.

Fourier analysis

A.1 Fourier transformation

In chapter 3 we use Fourier analysis to map the time dependent quantities from the time into the frequency domain. For AFM applications, the Fourier transformation used for the time average deflection ∆z²_rmsdefines

ˆ

z(ω) = 1 2π

+∞

ˆ

−∞

z(t)e^−iωtdt (A.1a)

z(t) =

+∞

ˆ

−∞

ˆ

z(ω)e^−iωtdω (A.1b)

hz²i =

+∞

ˆ

−∞

ˆ

z(ω)²dω. (A.1c)

In the frequency domain, the cantilever’s displacement can be calculated from the applied force, by using the compliance ˆC(ω) (or response function | ˆC(ω) |²) of the damped oscillator system

ˆ

z(ω) = ˆC(ω) ˆF(ω) (A.2a)

C(ω) =ˆ 1/m

q

(ω²− ω0²)²+ (ωω0/Q)²

. (A.2b)