Supplemental material for the Applied Physics Letter Hysteretic anomalous Hall effect in a ferromagnetic, Mn-rich Ge:Mn nanonet Danilo Bürger, Shengqiang Zhou, Marcel Höwler, Xin Ou, György J. Kovacs, Helfried Reuther, Arndt Mücklich, Wolfgang Skorupa, Manfred Helm, and Heidemarie Schmidt Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, P. O. Box 51119, 1314 Dresden, Germany Various results are not presented in the 4-page limited APL format. To overcome this issue, in the following important measurement results are presented. Transmission electron microscopy (TEM) First, TEM images are presented to confirm the etching rate of the Ar-ion etching. The image shown in Fig. 1 has been taken on the same sample that was also used for the magnetotransport measurements (Fig. 3+4 in the paper, Fig. 9 in the suppl. material). It is clearly visible in the crosssection TEM (XTEM) that after etching 1 nm away the tadpole shaped precipitates are still present. Because of removing 1 nm from the top, the average length of the precipitates is decreased. Fig 1: Tadpole-shaped, Mn-rich precipitates after Ar-ion etching of 1 nm in cross-section view. The film is relatively smooth and the tadpole-shaped precipitates are still present. In Fig. 2 the plan-view HAADF image is shown. The HAADF technique visualizes elemental contrast between elements with low and high atomic number Z. The signal is proportional to Z 2 and the thickness of the sample. Germanium with an atomic number of 32 is heavier than manganese with an atomic number of 25. If one assume a similar thickness of the plan-view image, which is clearly visible in Fig. 1 for etching from the top, than normally a higher intensity (more brightness) of the HAADF signal can be correlated with the element with the higher atomic number. In our case, the regions between the cells are brighter. 1
Probing two separate points with energy dispersive X-ray analysis (EDX) allows us to determine the elemental concentration of individual points. Point 1 was measured between two cells and Point 2 within one cell. The EDX results do not show manganese in a cell (point 2), whereas between two cells a clear manganese signal exists. This contradicts with the theory mentioned above, but the reason for that is that from amorphous structures no conclusions can be made for the HAADF signal. ( critical problems concerning surface amorphous films adhering to a crystal and amorphous materials remain completely unresolved due to the lack of a reliable simulation of amorphous materials, although it would be considered that an amorphous film which is produced either during specimen preparation or by contamination causes noise and/or reduces image contrast. (T. Yamazaki et al., Ultramicroscopy 99, Issue 2-3, 125 (24)). Therefore, the bright nanonet in the HAADF image cannot be interpreted as a region with a low amount of Mn. For this heterogeneous structure the reverse is true. Fig 2: Mn-rich nanonet after Ar-ion etching of 1 nm in plan-view. The film clearly shows a contrast between the amorphous nanonet and the crystalline Ge. 2
In Fig. 3 a conventional plan-view image (a) and the corresponding electron-diffraction image (b) is shown. From the electron-diffraction image one can clearly see that no Ge 2 Mn 5 phases are left. Only two weak points indicate a lattice spacing of.142 nm. Inverse Fourier transformation shows that a weak crystalline structure of the cell in Fig. 3(b) is responsible for that. The thickness or the thin amorphous layer on top of the film makes it difficult to recognize these crystalline structures. Probably, a near range order of the thin amorphous-like layer on top of the film makes it difficult to identify a certain reflection of the Ge-crystal. (a) (b) Fig. 3: (a) High resolution TEM image of the sample after Ar-ion etching of 1 nm in plan-view. (b) The corresponding electron-diffraction image. The two marked points can be correlated with a lattice spacing of.142 nm. Ge 2 Mn 5 is an orthorhombic phase with the following lattice parameters after the JCPDS pattern -24-448: a = 9.656 b = 1.149 c = 1.854 a/b =.95142 c/b = 1.6946 3
In Fig. 4 the XTEM after 4 nm ion etching is shown. After etching, a thin amorphous layer remains on top of the film. The thickness of this layer is increasing from 1-2 nm after 1 nm etching to 3-4 nm after etching away 4 nm (inset of Fig. 4 b). Nearly all of the Mn-rich precipitates were removed. Only some of the deeply buried precipitates are left. That means the percolation of the nanonet should be destroyed. Fig 4: Mn-rich precipitates after Ar-ion etching of 4 nm. The film becomes rough and nearly all of the tadpole-shaped precipitates were removed. Only the deeply buried precipitates are left. In general, their density decreased dramatically compared to the 1 nm etched sample. That means that the percolation of the nanonet should be destroyed. The inset shows the film after Ar-ion etching of 4 nm with higher resolution. The amorphous film originates from the ion etching. Its thickness increases from 1-2 nm after etching away 1 nm and to 4 nm after etching away 4 nm. 4
To identify the role of the embedded Mn-rich nanonet, also Mn sensitive etching was performed. We used an etching recipe already reported by P. Gambardella et al. in PRB 75, 125211 (27). Dilute solutions (1:1) of HF:H 2 O and HCl:H 2 O were prepared and 3 s etching was performed in each solution. At first, the HF:H 2 O solution removed the oxide from the surface and after that the HCl:H 2 O solution removed the segregated Mn and Mn oxide. After that etching process the samples were rinsed in de-ionized water. In Fig. 5 the XTEM of the chemical etched sample is presented. It is clearly visible that the Mn-rich regions were successfully removed. The sample presented below was annealed with 5% instead of 75% modal overlap between adjacent laser stripes. That means smaller regions are melted twice during annealing and a large part of the Mn-rich material seems to be still below the surface. The peak in the AES spectra in Fig. 1 of the paper seems to be from such a local area, where the sample was molten once. Repeated melting and resolidification leads to an accumulation of Mn near the surface. Fig. 5: Remaining tadpole-shaped voids after chemical etching. PLA has been performed with 5% modal overlap between adjacent laser stripes. Therefore, a large part of the Ge:Mn was only molten once. 5
Fig. 6 presents the chemically etched sample in higher resolution. Especially, in Fig. 6 (b) it is visible that no Mn-rich phase is left on the surface. No amorphous top layer like after Ar-ion etching is formed. (a) (b) Fig. 6 (a) and (b): Removed Mn-rich precipitates after chemical etching. Tadpole-shaped voids after chemical etching (a) are filled with glue. (b) The 4 nm thick polycrystalline layer has also been removed by chemical etching. On the next page three images from the same local area are of an unetched sample are presented. Fig. 7 (a) presents a XTEM picture, Fig. 7(b) and (c) represent the energy filtered TEM (EFTEM). In Fig. 7(b) the germanium is displayed with the green color. One can clearly see that Fig. 7(c) is nearly complementary to Fig. 7 (c) which shows the Mn-rich regions in the green-red color. EFTEM is the direct evidence that the precipitates contain a lot of Mn. 6
(a) (b) (c) Fig. 7: (a) Unetched sample after implantation and PLA. (a) TEM image, (b), (c) EFTEM image of the same part. (b) The green color corresponds to the element Ge. (c) The green-red color indicates Mn-rich regions. 7
EDX-measurements On the next three pages the results from EDX-measurements are presented. A linescan shows the Mn depth distribution. Measurements at several points reveal that below (points 2, 4 and 6) and beside (point 3) a tadpole-shaped precipitate no Mn is detected (detection limit ~ 3 %). 8
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1
MR (%) MR (%) MR (%) MR (%) MR (%) MR (%) Magnetotransport Fig. 8 and Fig. 9 present the magnetoresistance on the unetched and 1 nm etched sample at 5, 1, 15, 2, 3, 5, 1, 2, and 3 K..6.4.2 (a). -.2 -.4 -.6 -.8 MR 5K MR 1K MR 15K MR 2K MR 3K -8-6 -4-2 2 4 6 8 15 1 5 MR 5K MR 1K MR 2K MR 3K (b). -.2-8 -6-4 -2 2 4 6 8-8 -6-4 -2 2 4 6 8 Fig. 8: (a) Magnetoresistance of the unetched samples in the temperature range from 5 K to 3 K. The inset shows the weak field region. A clear negative magnetoresistance is visible. (b) At higher temperatures the spin coherence in the Mn-rich nanonet is lost and the MR becomes positive..2. -.2 -.4 -.6 -.8-8 -6-4 -2 2 4 6 8 (a) MR 2.5K MR 5K 25 MR 5K MR 1K 2 (b) MR 15K MR 2K MR 25K 15 MR 3K 1 5 -.1.4 MR 1K MR 15K.2 MR 2K. MR 3K -.2 -.4 -.6-6 -4-2 2 4 6 Fig. 9: (a) Magnetoresistance after Ar-ion etching of 1 nm in the temperature range from 2.5 K to 3 K. A clear negative magnetoresistance is visible up to 3 K. (b) It seems that at higher temperatures the spin coherence in the nanonet is lost and the MR becomes positive. -.8 -.1-8 -6-4 -2 2 4 6 8 11
MR (%) MR (%) Hall resistance (k ) Fig. 1 (a) presents the detailed magnetoresistance of the sample after 4 nm etching. Fig. 1 (b) shows that no hysteretic anomalous Hall resistance is present anymore. Implantation and annealing were performed up to a depth of around 18 nm. A fabricated diluted magnetic semiconductor should keep the observed magnetotransport properties also after etching away of 4 nm. 12 1 8 6 4 2 (a) MR 2.5K MR 5K MR 1K MR 15K MR 2K MR 3K MR 5K MR 1K MR 15K MR 2K MR 25K MR 3K -8-6 -4-2 2 4 6 8-8 -6-4 -2 2 4 6 8 Fig. 1: (a) Magnetoresistance after Ar-ion etching of 4 nm in the temperatures range from 2.5 K to 3 K. A clear positive magnetoresistance is visible in the entire temperature range and no hysteresis in the Hall resistance (b) in the temperature range from 5 K to 5 K is visible. 2 1-1 -2 5K 1K 15K 2K 3K 5K (b) Fig. 11 (a) presents the positive magnetoresistance of the sample after chemical etching. Also the Hall resistance presented in Fig. 11 (b) has the same order of magnitude and no hysteretic anomalous Hall effect. Both samples (chemical etching, 4 nm Ar-ion etching) show similar magnetotransport properties. 3 2 1 (a) MR 2.5K MR 5K MR 1K MR 2K MR 3K MR 5K MR 1K MR 15K MR 2K MR 25K MR 3K -6-4 -2 2 4 6 Hall resistance (k ) 6 5 4 3 2 1-1 -2-3 -4-5 -8-6 -4-2 2 4 6 8 Fig. 11: (a) Magnetoresistance after chemical etching in the temperatures range from 2.5 K to 3 K. A clear positive magnetoresistance is visible in the entire temperature range. (b) Zoom-in of the Hall resistance in the temperature range from 5 K to 5 K. Similar to the Ar-ion etching there is no anomalous Hall resistance visible. 5K 1K 2K 3K 5K (b) 12
After Ar-ion etching, Mn implanted and pulsed laser annealed Ge:Mn with 5 at. % Mn in (1)-Ge or 1 at. % in (111)-Ge were investigated by TEM to obtain morphology-dependent Hall resistance data. These samples show only hysteretic Hall resistance up to 1...15 K and no direct evidence for the formation of a Mn-rich nanonet exists. However, its existence cannot be excluded. Near the temperature where the hysteretic Hall resistance is lost, giant Hall resistances between 6 Ω (5 at. % Mn in (1)-Ge) and 13 Ω (1 at. % Mn in (111)-Ge) at magnetic fields of approximately 1 kg and temperatures of around 2 K have been observed. For these samples a slope inversion occurs up to 5 kg...9 kg. A qualitative description for such behavior was presented by Yu et al. (JAP 19,12396, (211)) for granular ferromagnetic Ge. In general, for material systems near the percolation threshold between an embedded conductive phase in an isolating matrix (APL 67, 3497, (1995)) or for nonmagnetic material systems, there exists no conclusive model about Hall resistance effects near the percolation threshold (Rep. Prog. Phys. 43, 1263 (198); PRB 38, 11639 (1988); J. Stat. Phys. 58, 1 (199)). Here, the temperature dependent spin-diffusion length plays also a significant role. It seems that due to the percolating highly conductive Mn-rich nanonet giant Hall resistances are suppressed and the temperature where hysteretic Hall resistance can be observed increases. 13 Hall resistance ( ) Hall resistance ( ) Hall resistance ( ) 6 4 2-2 -4-6 1 5-5 -1 2.5K 5K 1K 2K 3K 5K 1K 15K 2K 25K 3K -8-6 -4-2 2 4 6 8 2.5K 5K 1K 15K 2K 3K 5K 1K 15K 2K 25K Hall resistance 5-5 -1 1 Fig. 12: Hall resistance for a sample after physical Ar-ion etching implanted with 5 at% Mn in (1)-Ge. A clear inverse slope of the Hall resistance is visible for higher fields above the temperature where the hysteresis is vanishing. -1 1 3K -8-6 -4-2 2 4 6 8 1 5-5 -1 Fig. 13: Hall resistance for a sample after physical Ar-ion etching implanted with 1 at% Mn in (111)-Ge. A clear inverse slope of the Hall resistance is visible for higher fields above the temperature where the hysteresis is vanishing. The reason for that behavior may be the complete different morphology during recrystallization in (111)-Ge.
Magnetization (µemu) Magnetization (µemu) SQUID As mentioned in the paper, after longtime annealing the Curie temperature is increased from 22 K to 25 K. This is shown in Fig. 14 for the unetched sample. It is also visible that the remanence is decreasing up to around 8 K 9 K before the remanence increases again. This behavior is due to small residual field in the SQUID system caused by trapped magnetic flux in the SQUID coils. This leads to a very sensitive behavior of the slope of the remanence curve. A similar magnetic behavior is also observed after 1 nm Ar-ion etching. That means that the polycrystalline phase Ge 2 Mn 5 does not significantly contribute to the observed magnetic properties. The non-zero magnetization of the sample after PLA is caused by slightly higher residual fields in the SQUID that lead to a small diamagnetic contribution of the substrate. The slight difference in the residual field is not responsible for the observed higher Curie temperature of the sample after PLA + post annealing because measurements with different compensating fields higher than the typical residual fields show no significant shifts of the Curie temperature at 25 K. 2 1 3 25 2 15 1 5 5 1 15 2 25 Temperature (K) after PLA+post annealing after PLA 14 16 18 2 22 24 26 28 Temperature (K) Fig. 14: Remanence of the unetched sample directly after PLA and after PLA+post annealing without etching. The post annealing was performed at 18 C for 35 minutes under flowing Ar-atmosphere. The Curie temperature of the magnetic phase with the low magnetization is increased from 22 K to 25 K. 14
Magnetization (µemu) Because of the laser energy distribution, there exists the possibility to incorporate magnetic anisotropy in the Ge:Mn material system. In Fig. 15 the hysteresis of the unetched sample (implanted with 1 at. % Mn in (1)-Ge, after PLA) were measured along the three principal axes of the coordinate system with respect to the sample. Geometry 1 shows the measurement perpendicular to the plane. Geometry 2 and 3 are measured in-plane parallel and perpendicular to the 2 mm long laser stripes, respectively. The two visible lines on the samples have a distance of 2 mm and result from the overlapping of the annealing lines. As a result of this measurement we can see that there is no significant difference between the different geometries. The nanonet induces no visible magnetic anisotropy in the sample. This effect was also measured at higher temperatures. 4 2 sample geometry correlated with the magnetic field direction 1 2 3 1-2 2 3-4 -8-6 -4-2 2 4 6 8 Fig. 15: Magnetic anisotropy of the sample for different geometries to the magnetic field. The hysteresis loops were measured at 1 K. No significant magnetic anisotropy is observed. 15
Counts X-ray photoelectron spectroscopy (XPS) Chemical analysis after 1 nm Ar-ion etching reveals three different binding energies. The mentioned data have to be corrected by a value of -1,3 ev (estimated from the shift of the carbon C1s-peak =284.6 ev). A database for the binding energies of different chemical bondings can be found under http://srdata.nist.gov/xps/energytypevalsrch.aspx Unfortunately, no GeMn compositions are listed in the database and we found no other literature sources which correlate the peaks in the spectra with certain types of bonding. Three relatively broad peaks at 641.3 ev, 645.3 ev and 653.3 ev in Fig. 16 are visible. They indicate no clear bonding type. The integral intensities between the peaks at 641.3 ev and 645.3 ev is 78% and 22%, respectively. The peaks at 641.3 ev and 653.3 ev belong to the 2p 3/2 and 2p 1/2 oxidized state of Ge, respectivley. For the peak at 645.3 ev no clear literature values exists. Most probably this peak can be correlated with the bonding of Ge and Mn. 84 642.6 ev - 1.3 ev = 641.3 ev 654.6 ev - 1.3 ev = 653.3 ev 82 646.6 ev - 1.3 ev = 645.3 ev 8 78 (a) Fitting Mn2p A Fitting Mn2p B Fitting Mn2p C Envelope 76 64 645 65 655 66 Binding energy (ev) Fig. 16: (a) X-ray photoelectron spectroscopy (XPS) recorded on the Mn-rich percolating nanonet after Ar-ion etching of 1 nm. 16