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ISRN Condensed Matter Physics

Volume 2012 (2012), Article ID 198590, 25 pages

http://dx.doi.org/10.5402/2012/198590

## Magnetic Mn-Doped Ge Nanostructures

Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011, USA

Received 4 December 2011; Accepted 9 January 2012

Academic Editors: A. Dinia, K. Haenen, E. Liarokapis, and C. Trallero-Giner

Copyright © 2012 Faxian Xiu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

With the seemly limit of scaling on CMOS microelectronics fast approaching, spintronics has received enormous attention as it promises next-generation nanometric magnetoelectronic devices; particularly, the electric field control of ferromagnetic transition in dilute magnetic semiconductor (DMS) systems offers the magnetoelectronic devices a potential for low power consumption and low variability. Special attention has been given to technologically important group IV semiconductor based DMSs, with a prominent position for Mn doped Ge. In this paper, we will first review the current theoretical understanding on the ferromagnetism in Mn_{x}Ge_{1−x} DMS, pointing out the possible physics models underlying the complicated ferromagnetic behavior of Mn_{x}Ge_{1−x}. Then we carry out detailed analysis of Mn_{x}Ge_{1−x} thin films and nanostructures grown by molecular beam epitaxy. We show that with zero and one dimension quantum structures, superior magnetic properties of Mn_{x}Ge_{1−x} compared with bulk films can be obtained. More importantly, with Mn_{x}Ge_{1−x} nanostructures, such as quantum dots, we demonstrate a field controlled ferromagnetism up to 100 K. Finally we provide a prospective of the future development of ferromagnetic field effect transistors and magnetic tunneling junctions/memories using dilute and metallic Mn_{x}Ge_{1−x} dots, respectively. We also point out the bottleneck problems in these fields and rendering possible solutions to realize practical spintronic devices.

#### 1. Introduction

Dilute magnetic semiconductors (DMSs) attract tremendous interest as emerging candidates for the microelectronics industry due to their uniqueness in exhibiting spin-dependent magneto-electro-optical properties. Their distinctive material characteristics such as spin-dependent coupling between semiconductor bands and the localized states promises magnetoelectric effect—the modulation of magnetic properties by an applied electric field—in semiconductors [1, 2]. Thus, a wide variety of semiconductor devices can be envisaged [3], such as spin polarized light-emitting diodes, lasers [4, 5] and spin transistor logic devices [2, 6, 7]. The development of these devices is considered as a possible route for extending the semiconductor scaling roadmap to spin-added electronics [8].

DMS materials can be developed by alloying semiconductors with several percentages of magnetic transition elements (with 3-*d* orbitals), such as Fe, Mn, Co, Ni, and V [9]. The anticipated outcome due to this doping is the fact that the transition elements occupying substitutional sites hybridize with the semiconductor host via the *sp-d* exchange interaction and help to enhance the spin-dependent transport, which in turn increase both the magnetization and the Curie temperature () of the semiconductor system [10]. This means that the transition metal doping can generate strong spin-dependent coupling states in semiconductor systems, which may be further modulated by an electric field [2]. Since the band gap engineering and crystal structures of a DMS material are compatible with other semiconductors, they offer significant integration advantages as well [3].

The dependence of the transition temperature on the density of mobile carriers is considered as a good evidence for a genuine DMS. However, the key challenge for the growth of DMS materials is the ability to control synthesis of transition metals in semiconductors, aimed at increasing the doping concentration in order to realize room-temperature ferromagnetism. Thus, achieving both semiconducting and ferromagnetic property at room temperature has become a great challenge. Unfortunately, this is hampered by low solubility of transition metal species with a strong tendency to form metallic clusters or heterogeneous regions within the matrix. So the primary research on DMS growth is to produce samples with uniform doping and being free of metallic precipitates.

Substantial theoretical and experimental work were carried out in the past two decades, either to predict or to measure the magnetic properties on a variety of semiconductor materials, including binary and ternary compounds such as III-V, II-VI, IV-VI, VI oxides, III nitrides, and group IV systems. Among them, (Ga, Mn)As became the first and the mostly studied DMSs since 1996 [11]; but to our knowledge, some studies lacked the threshold doping profile to push its curie temperature to room temperature and above (currently around 190 K [12–15]). Since then, substantial research has been carried out in III-V and II-VI semiconductors to improve the by increasing the solubility limit and meanwhile minimizing self-compensation effect of magnetic structures, using radical techniques such as delta doping of modulation-doped quantum structures [16–19]. Another approach to achieve high- DMS is to use transition metal-doped wide bandgap nitrides and oxides, such as GaN, AlN, ZnO, and TiO_{2}. In these materials, high magnetic impurity concentrations are needed due to the lack of long-range interaction among magnetic spins. However, there have been only limited reports on the carrier mediated effect in the wide band gap materials at room temperature [20–22]. Though considerable amount of work has been done on III-V and II-VI DMSs [2, 23], the lack of high and the difficulty in achieving electric field modulated ferromagnetism (carrier-mediated ferromagnetism) at or above room temperature deters them from being considered for semiconductor integration.

Group IV semiconductors are of particular interest to the spintronics technology because of their enhanced spin lifetime and coherent length due to their low spin-orbit coupling and lattice inversion symmetry [24, 25]. There is also considerable interest for transition metal-doped group IV semiconductors [26–36] to the semiconductor industry, owing in part to their excellent compatibility with silicon process technology. Several transition metals—including the use of single and codoping of elements such as Mn, Cr, Co, Fe, Co-Mn, and Fe-Mn—have been used as magnetic dopants in both Si and Ge either through blanket implantation or through *in situ* doping during epitaxial growth process. Both these materials are reported to be ferromagnetic [33, 37, 38]. The reported experimental results also clearly showed the presence of carrier-mediated ferromagnetism in DMS Ge [39, 40]. A recent study predicted that the could be increased by enhancing the substitutional doping of Mn in Ge and Si, via codoping—by adding conventional electronic dopants such as As or P during the Mn doping process [41]. Theories [42] and experiments [29, 43] further suggest that the ferromagnetic transition temperature is related to the ratio of interstitial to substitutional Mn similar to that in the group III-V system [10].

Considering the fact that, nanosystems such as nanowires and quantum dots (QDs) are the versatile building blocks for both fundamental studies in nanoscale and the assembly of present day functional devices, low-dimensional Ge DMS systems such as Mn_{x}Ge_{1−x} nanowires [13, 30, 44, 45] and QDs [46] have also been reported to have room temperature ferromagnetism. The above results are supported by modeling results [47] although carrier-mediated exchange has not yet to be experimentally verified in nanowires. Similarly, high Curie temperatures have been observed in other transition metal-doped semiconductor nanostructures such as II-VI (including ZnO [48–50], ZnS [51, 52], CdS [52]), and III-V (including GaN [52, 53], GaAs [54]), but only inconclusive reports have been published on the magnetoelectric transport in these nanostructures. It could be attributed to the complicated ferromagnetic properties caused by precipitates, second-phase alloys and nanometer-scale clusters. Therefore, it is important and indispensable to differentiate their contributions. Unfortunately, there is still a lack of fundamental understanding of the growth process and spin-dependent states in these systems that gives an impetus to extensive investigations into these and related material systems.

In this paper, we will first introduce the state-of-art theoretical understanding of ferromagnetism in group IV DMSs, particularly pointing out the possible physics models underlying the complicated ferromagnetic behavior of MnGe. Then, we primarily focus on the magnetic characterizations of epitaxially grown Mn_{x}Ge_{1−x} thin films ranging from three-dimensional thin films to zero-dimensional QDs. It is found that when the material dimension decreases (to zero), it evidences a change of material structures being free of precipitates and a significant increase of over 400 K. The preliminary explanation on these behaviors can be attributed to the carrier confinement in the DMS nanostructures which strengthens hole localization and subsequently enhances the thermal stability of magnetic polarons, thus giving rise to a higher than those of bulk films.

Another important aspect of DMS research lies in the electric-field-controlled ferromagnetism. We emphasize the existing experimental efforts and achievement in this direction and provide a detailed description on the field-controlled ferromagnetism of the Mn_{x}Ge_{1−x} nanostructures. We show that the ferromagnetism for the Mn_{x}Ge_{1−x} nanostructures, such as QDs, can be manipulated via the control of gate voltage in a gate metal-oxide-semiconductor (MOS) structure (up to 100 K). These experimental data suggest a hole-mediated ferromagnetism as controlled by a gate bias and promise a potential of using Mn_{x}Ge_{1−x} nanostructures to achieve spintronic devices. Beyond the scope of DMSs, we will present the metallic Mn_{x}Ge_{1−x} with *x* ~ 20%, in which a constant Curie temperature was observed. The emphasis, however, is the manipulation of these metallic dots into self-assembled periodic arrays for potential device applications. Finally, we render general comments on the development of the Mn_{x}Ge_{1−x} system and possible research schemes to develop spintronics devices based on this material system.

#### 2. Theories of Ferromagnetism in Group IV DMS

As in other popular dilute magnetic semiconductors such as (Ga, Mn)As, the formation of magnetic order and the origin of ferromagnetism in Mn_{x}Ge_{1−x} can be described (within the parametric limits) either using complementary mean field approximation models such as the Zener-Kinetic exchange [55], the Ruderman-Kittel-Kasuya-Yoshida (RKKY) [56] interaction, and percolation theory [57] or using density functional theory such as *ab initio* full-potential augmented plane wave (FLAPW) [58] electronic calculations. Interestingly, the Zener-kinetic exchange model proposed in 1950 could be used for interpreting many of the experimental results in transition metal-doped semiconductors [59–61] besides the transition metals themselves. All the above theoretical approaches have tried to address and to a certain extent successfully answered chemical, electronic, and magnetic properties of the transition metal-doped group IV semiconductors within the context of (1) the nature of transition metal impurities, (2) the origin of ferromagnetism, (3) the influence of dopants on the , (4) the solubility limits of carrier density on the chemical nature, (5) the influence of carrier density on the electronic structure, and (6) the influence of different hosts on the electronic structure. Within the above theoretical approaches, these models assume that the ferromagnetism in transition metal-doped Ge system is mediated through exchange coupling between the carriers and the interacting lattice. This means that, the interaction is through *p-d* orbital hybridization between the levels and the valence band states of Ge. According to these models, as the number of dopant carriers increases both the electronic mobility and the ferromagnetic ordering of the system also increases along with the . Thus, the assumption is that the strong exchange coupling between the and orbitals leads to strong kinetic exchange coupling between the spin-polarized holes and spin polarized TM substitutional vacancies. Among all the 3-*d* TM impurities, [TM = V, Cr, Mn, Fe, Co, Ni], Mn is the most favored dopant. This is because compared to other dopants, Mn favors less clustering, low nonuniform doping distribution and higher substitutional doping over interstitials. The *ab initio* electronic structure calculations within density functional theory show that such doping behaviors could result in relatively higher carrier hole concentrations and increased magnetic moments [27, 58]. Complementary theoretical work using the frozen-magnon scheme also shows that the ferromagnetism is produced only through holes and Mn is a good source for generating holes in Ge system [62].

In addition, some of the other factors that determine the ferromagnetic strengths in Ge are (1) disorder of Mn site locations, (2) distance between Mn-Mn atoms, (3) solid solubility limits and preferential surface orientation for interstitial and substitution site formation [63–65], and (4) codoping of Co or Cr with Mn. (They were found to reduce cluster formation but not to significantly contribute to the ferromagnetism in the system [66, 67].) According to full potential linearized augmented plane wave (FLAPW) calculations made on the RKKY model, the coupling between the Mn atoms could be ferromagnetic (FM) or antiferromagnetic (AFM) in nature but the interaction is very localized to Mn sites and depends on the distance between Mn atoms: the density of states decreases rapidly as the Ge atom moves away from Mn [58]. However, disorder of Mn site locations is found to influence the ferromagnetic strength and the transition temperature. In addition, the impact of inherent disorder is also confirmed both by experiments and by the mean field approximation [57, 68, 69]. Some of the above models found themselves hard to explain the long-range exchange interaction and coupling strength when there is varying dopant concentration and disorder ranging from high resistive state to half metallic state. On the other hand, there are attempts to find solutions for disorder-dependent magnetic variation using Percolation theory-based mean field approximation calculation [57, 70]. Percolation theory provides possible explanations for the experimentally observed low values of saturation magnetization in low carrier density Mn_{x}Ge_{1−x} because the infinite cluster of percolating bound magnetic polarons triggering the long-range ferromagnetic order leaves out a large number of Mn moments at temperatures less than . However, the role of disorder with respect to insulating and conductive metallic phases and their effects on mobility is still not well understood. Conversely, the FLAPW calculations using the density functional theory shows that Mn favors long-range ferromagnetic alignment over short-range antiferromagnetic alignment and this increases with the increase of Mn content which is in agreement with many of the experimental results [58]. The estimated Curie temperature is within the range of 134–400 K and is in agreement with experimental and theoretical results [47].

However, there are also conflicting reports that long-range FM order could only happen at low temperature (12 K) and that at low temperature MnGe could show only spin glass behavior due to the intercluster formation between the FM Mn-rich clusters [42, 71]. With these reports, it is understood that the magnetic phases are more favored over paramagnetic phases by an energy difference of 200 meV/Mn atom [58]. The report also states that the Mn_{x}Ge_{1−x} system is very close to half metallicity irrespective of the amount of doping concentration [58, 72]. Electronic band structure calculations using density of states (DOSs) show that the binding energy of the Ge 4*s *states are basically unaffected by the exchange splitting of Mn states and the valence band maximum of the minority spin channel in Mn_{x}Ge_{1−x} reaches at Gamma () such that the spin gap becomes zero [58, 72]. In other words, the DOS shows a valley around and is strictly zero at in the minority spin channel. On the other hand, the energy gap is indirect and the bands around in the majority spin channel arise from Mn and Ge hybridizations so as to give rise to hole pockets closer to the gamma point with a localized magnetic moment of about 3 *μ*_{B}. This could also be explained using chemical and structural configurations of Mn in Ge. The different chemical species determine the relative positions of the anion and cation atomic energy levels in the Mn_{x}Ge_{1−x} while the different anion size dictates essentially the equilibrium lattice constants [58]. This essentially explains the carrier-mediated effect in Mn_{x}Ge_{1−x} even though the system is closer to half metallic. The aim of all these theoretical works is to build foundation for achieving carrier-mediated ferromagnetism at temperatures above room temperature. It is understood that this can be achieved only by growing cluster-free and uniformly doped Mn_{x}Ge_{1−x} samples. Experimental reports show that as high as 400 K is obtained for cluster-free Mn_{x}Ge_{1−x} samples grown (1) using subsurfactant epitaxial method [73], (2) epitaxial QDs [40], and (3) nanowire structures [13, 30, 44]. However, there are only very few theoretical studies depicting the relation between the quantum confinement and its influence on the origin of ferromagnetism in low-dimensional DMS structures [74–76]. It apparently lacks of systematic theoretical study particularly on Mn_{x}Ge_{1−x} QDs. Therefore, it will be interesting to understand the ability of the quantum confinement phenomenon to retain spin polarization in Mn_{x}Ge_{1−x} QDs structure. Studies on III-V QDs using LSDA approximation show that, unlike in the bulk structures, adding a single or multiple carriers in a magnetic QD can both strongly change the total carrier spin and the temperature of the onset of magnetization and this can be modulated by modifying the quantum confinement and the strength of coulomb interactions. These theoretical results must have ramification in the high Curie temperature Mn_{x}Ge_{1−x} QDs as well since our studies also reveal similar characteristics. But, all of the effects including high that we observe cannot be explained without invoking tiny defects either at the interface or on the surface although the conventional transmission electron microscopy (TEM) cannot reveal their existence due to the limited resolution. All of the above material and electronic properties have been studied in order to understand how feasible a DMS material is for carrier-mediated ferromagnetism.

#### 3. Growth and Characterizations of Group IV DMS and Nanostructures

##### 3.1. Overview of the Mn-Doped Ge

As mentioned above, the Ge-based DMS has attracted extensive attention due to its possibility to be integrated with the mainstream Si microelectronics, in which they may be used to enhance the functionality of Si-integrated circuits [27]. In particular, the hole-mediated effect discovered in Mn_{x}Ge_{1−x} DMS opens up tremendous possibilities to realize spintronic devices with advantages in reducing power dissipation and increasing new functionalities, leading to perhaps normally off computers. To date, there are many reports on the Mn_{x}Ge_{1−x} growth and characterizations by molecular beam epitaxy (MBE) [27, 28, 31, 33, 43, 77–85], ion implantation [86–93], and bulk crystal growth [37, 94]. We can divide them here, for an easier orientation, into two groups: those that cover fundamental studies of phase formation, ferromagnetism, and transport properties [26, 27, 29, 31, 33, 35–37, 43–45, 64, 77–85, 94–115], and those that aim to minimize cluster formation and enhance Curie temperatures via codoping methods [28, 32, 34, 116–118].

Experimental results show that the Mn-doping process in Mn_{x}Ge_{1−x} is complex. Both the and the saturation magnetization depend on the interplay of a variety of factors, which are ultimately determined by growth conditions and postannealing process [33]. The concentration and distribution of Mn dopants, the carrier density, the presence of common defects such as Mn interstitials and Mn clusters significantly influence the magnitude and interactions of the magnetic coupling [94]. In early 2002, Park et al. [27] demonstrated ferromagnetic Mn_{x}Ge_{1−x} thin films by low-temperature MBE. It was found that the Mn_{x}Ge_{1−x} films were *p*-type semiconductors in character with hole concentration of 10^{19}~10^{20} cm^{−3} and exhibited pronounced extraordinary Hall effect. The of the Mn_{x}Ge_{1−x} thin films increased linearly with Mn concentration from 25 to 116 K (Mn ≤ 3.5%). Field-controlled ferromagnetism was also observed in a simple gated structure through application of a gate voltage (±0.5 V), showing a clear hole-mediated effect at 50 K. Such a small gate voltage presents an excellent comparability with conventional low voltage circuitry. The origin of ferromagnetic order was understood in the frame of local-spin density approximation (LSDA), where strong hybridization between Mn states of T_{2} symmetry with Ge states leads to the configuration , with a magnetic moment of 3 *μ*_{B}. However, the LSDA calculations gave overestimated which was attributed to the incomplete activation of Mn in experiments and the absence of hole compensation in the simulation [27].

Since then, various preparation techniques were employed in order to produce Mn-doped Ge DMS, including aforementioned MBE [28, 31, 33, 43, 77–85], single-crystal growth [37, 94], and ion implantation [86–93], aiming to further increase and to obtain the electric field controllability at room temperature [94]. Among these efforts, Cho et al. [37] reported the synthesis of Mn-doped bulk Ge single crystals with 6% of Mn and a high ferromagnetic order at about 285 K via a vertical gradient solidification method. The origin of the high was found to be complex because of the presence of dilute and dense Mn-doped regions. Jaeger et al. [77], however, pointed out that the magnetic properties of these samples were clearly dominated by the presence of the intermetallic compound Mn_{11}Ge_{8}. This was indeed observed by Biegger et al. [94], where similar Mn_{x}Ge_{1−x} crystals were produced via Bridgman’s crystal growth technique and intermetallic compounds were found in both Mn-rich and Mn-poor regions. These experiments suggest that the bulk Mn_{x}Ge_{1−x} crystals produced at over 1000°C may not be an appropriate method for the Mn_{x}Ge_{1−x} DMS preparation [94].

Apart from the bulk crystal growth, MBE has been widely recognized as a power tool for DMS growth since it can provide nonequilibrium conditions to enhance the incorporation of Mn dopant [27]. Via this technique, Mn doping was found to be extremely sensitive to growth conditions, particularly to the growth temperature. Excellent work on this aspect can be found in references [32, 33, 43, 79, 81, 83, 85]. In general, at low growth temperatures (), the diffusion of Mn atoms leads to the formation of Mn-rich nanostructures, such as nanocolumns [82] and nanodots [81] with irregular shapes. These nanostructures could contain a high Mn concentration up to 38% 33, while the surrounding matrix remains a low Mn concentration less than 1%. A perfect lattice coherence was found in the proximity of the nanostructures, indicative of a strong compression for coherent nanostructure and a large tension for the surrounding matrix [82]. These observations are in good agreement with theoretical predictions of a spinodal decomposition [119], which occurs under a layer-by-layer growth mode with strong pairing attraction between Mn atoms and a tendency of surface diffusion of Mn atoms. These theoretical calculations successfully explained the formation of nanostructures in (Ga, Mn)N and (Zn, Cr)Te) [82, 119], which can be also readily applied to the Mn_{x}Ge_{1−x} system [82]. The magnetic properties, however, exhibit various characteristics depending on the nanostructure size and the Mn concentration. In most cases, zero-field-cooled (ZFC) and field-cooled (FC) magnetizations show superferromagnetic properties with a blocking temperature of ~15 K. It is now clear that such a low blocking temperature is originated from the coherent nanostructures with a diameter below several nanometers. Curie temperatures of these nanostructures were also identified to be below 170 K and varied with different Mn concentration. No Mn_{5}Ge_{3} metallic phases were observed at low temperature regime ().

Bougeard et al. [81] also found that when the dimension of the nanostructures further reduced, the films showed no overall spontaneous magnetization down to 2 K. TEM results were interpreted in terms of an assembly of superparamagnetic moments developing in the dense distribution of nanometer-sized clusters. In addition to the single crystalline Mn_{x}Ge_{1−x}, homogeneous nanoclusters were also observed under certain growth conditions and contributed to ferromagnetic order below 100 K [82, 107]. To render a general understanding of the Mn_{x}Ge_{1−x} magnetic properties, Jaeger et al. [77] presented a detailed study on Mn_{0.04}Ge_{0.96} and Mn_{0.20}Ge_{0.80} thin films grown at low temperatures and related their magnetic behavior to spin-glass. A frozen magnetic state at low temperatures was observed and attributed to the formation of nanostructures. This is in a good agreement with Devillers et al. [82]. Therefore, it can be concluded that the Mn_{x}Ge_{1−x} magnetic semiconductor is not a conventional ferromagnet since its magnetic properties are significantly complicated by the formation of nanostructures and metallic clusters.

When the growth temperature falls into 120~145°C, the Mn_{5}Ge_{3} nanoclusters start to develop and dominate the magnetic property with a Curie temperature of 296 K [33, 82]. This phase, frequently observed at high-temperature growth, is the most stable (Mn, Ge) alloy. The other stable compound Mn_{11}Ge_{8} was also observed in nanocrystallites surrounded with pure Ge [83]. Although they are ferromagnetic, the metallic character considerably jeopardizes their potential for spintronic applications. Under a narrow growth window around 130°C, another phase MnGe_{2} nanocolumns could be developed with a ~33% of Mn and a beyond 400 K [33]. A remarkable feature of these clusters is the large magnetoresistance due to geometrical effects. Further increasing the growth temperature leads to the dominating magnetic behavior from the Mn_{5}Ge_{3} clusters. As the coherent nanostructures grow larger at high temperature growth, higher blocking temperatures (~30 K) were also obtained [82].

To minimize the phase separation, Mn codoping with Co was attempted to stabilize structures at high Mn-doping concentration [28, 34, 116]. It showed that codoping with Co can dramatically reduce phase separation and diffusion of Mn within the Ge lattice while it magnetically complements Mn. The measured strain states indicate the critical role played by substitutional Co with its strong tendency to dimerize with interstitial Mn [34]. The highest achieved so far is about 270 K [28]. Similarly, Gareev et al. [118] reported on the codoping of Fe to achieve a of 209 K. Recent polarized neutron reflectivity measurements provided evidence to show no segregation and lower clustering tendencies for higher Fe doping [117], which further supported codoping approach in Mn_{x}Ge_{1−x}.

Ion implantation was also attempted due to its efficiency of Mn incorporation [92]. However, extensive experiments revealed that Mn-rich precipitates were developed and buried in a crystalline Ge matrix [86–93] in a much similar manner to that of the thin films grown by MBE [32, 43, 81, 83].

Although there has been much progress in producing high-quality Mn_{x}Ge_{1−x} thin films, the formation of uncontrollable metallic clusters yet remains a challenge. High DMS thin films without any precipitations seem to be a critical obstacle for the fabrications of practical spintronic devices functioning at room temperature, not to mention the room-temperature-controlled ferromagnetism. Table 1 provides a brief summary of the current status of Mn_{x}Ge_{1−x} on the growth method, the , and the field controllability of ferromagnetism.

##### 3.2. Mn_{x}Ge_{1−x} by Molecular Beam Epitaxy

To gain further insight into the complex growth of this material system, we have performed detailed structural and magnetic characterizations of Mn_{x}Ge_{1−x} grown by MBE with different thickness. Our experiments showed that the Mn-doping behavior and magnetic properties are dramatically different when the material dimension becomes smaller. Bulk Mn_{x}Ge_{1−x} films always tend to form clusters no matter what growth conditions are. When it comes to one and zero dimensions, however, the cluster formation may be possibly limited because the Mn concentration cannot accumulate enough and the strain can be easily accommodated to minimize the metallic clusters [84, 93]. We further show that self-assembled Mn_{x}Ge_{1−x} DMS QDs can be successfully grown on Si substrate with a high in excess of 400 K. Finally, the electrical-field-controlled ferromagnetism was also demonstrated in MOS structures using these QDs as the channel layers, as elaborated in Section 4.

###### 3.2.1. Mn_{x}Ge_{1−x} Thin and Thick Films

Mn-doped Ge films were grown on Si substrates by a Perkin-Elmer solid source MBE. Si substrates were cleaned by H_{2}SO_{4} : H_{2}O_{2} (5 : 3) and 10% HF with a final step of HF etching. The native oxide was removed by a 10 min flash at 800°C in the vacuum chamber. After that, a direct growth of 80 nm thick Mn_{x}Ge_{1−x} on Si was carried out at 250°C. A 5 nm Ge capping layer was deposited on the surface in order to prevent Mn_{x}Ge_{1−x} from oxidizing. To probe the annealing effect, identical Mn_{x}Ge_{1−x} thin films were grown repeatedly and followed by *in situ* annealing process at 400°C for 30 min. All as-grown and annealed samples were characterized by high-resolution TEM (HR-TEM, FEI Tecnai F30 operating at 200 keV) and superconducting quantum interference device (SQUID, Quantum Design MPMS XL 5). Cross-section HR-TEM specimens along were prepared by using a tripod technique, followed by a final thinning using a Gatan precision ion polishing system.

Figures 1(a) and 1(b) show cross-sectional TEM images of the as-grown and annealed 80 nm thick Mn_{0.04}Ge_{0.96}. Nonuniform and discontinued rough films were observed in both cases. Figures 1(c) and 1(d) are their corresponding Mn elemental maps, respectively. Mn is seen to concentrate on top for both samples. Mn-containing clusters are confirmed near the top of the crystalline layer as indicated by the white arrow in Figure 1(a). A HR-TEM image clearly indicates that a Mn-containing cluster is formed on top of the Ge lattice as shown in Figure 1(e). Using the lattice constant of Ge as the reference, the lattice spacings of the Mn-containing cluster can be determined as 0.62 and 0.25 nm, which are matched with the distances of (100) and (002) atomic planes of the hexagonal Mn_{5}Ge_{3} phase. Fast Fourier transformation (FFT) map shown in the inset of Figure 1(e) also indicates that the cluster belongs to the hexagonal Mn_{5}Ge_{3} phase. Mn_{5}Ge_{3} clusters may be formed when the Mn concentration is sufficiently high for the nucleation of clusters [84].

Figure 2 shows the TEM cross-section of as-grown and 400°C annealed samples. Stacking faults along atomic planes are clearly observed in both cases. The annealing process does not dramatically affect the stacking-faults. However, the magnetic properties have a noticeable change. Figures 3(a) and 3(d) show clear hysteresis loops at 298 K for both the as-grown and annealed samples. Before annealing, the film shows a clear hysteresis at 10 K while a very small magnetic moment is observed at room temperature. After annealing, the hysteresis showed a significant change and the coercive field at 10 K decreased from 430 Oe to 92 Oe. For the as-grown film, Mn_{5}Ge_{3} formed on the surface gave the of around 298 K as shown in Figure 3(b). The blocking temperature was estimated to be about 250 K. After annealing, both Mn_{5}Ge_{3} and Mn clusters led to a complex magnetic behavior, showing multiple phase transitions at different temperatures in Figure 3(e). The increased from 298 to over 400 K. Further investigation is needed to understand the change of the magnetic property. The Arrott’s plots were made to confirm the in Figures 3(c) and 3(f). The estimated Curie temperatures for the as-grown and annealed samples were obtained to be 298 K and above 400 K, respectively.

To understand the magnetic behavior of Mn in an ultrathin Ge, a Mn_{x}Ge_{1−x} film with a thickness of about 15 nm was grown directly on Si substrate by following the same growth procedure as that for the 80 nm thick film. Figures 4(a) and 4(b) show typical cross-sectional TEM images and general morphologies of the as-grown and annealed samples. From these figures, a relative uniform crystalline layer, adjacent to the Si substrates topped with an amorphous layer, can be seen in both cases. The formation of amorphous layers is not clear yet, but it could be attributed to the growth conditions and the sample preparation for TEM when exposing to the air.

To understand the structural variation for the two cases, high-resolution TEM was carried out and typical zone-axis HR-TEM images are shown in Figures 4(b) and 4(e) for the two cases, respectively, where the amorphous layers can be clearly seen. From these HR-TEM images, stacking faults in the crystalline layers can also be seen in both cases. No structural clusters were found through our extensive HR-TEM investigations and no secondary phases were detected by our XRD measurements (not shown here). To further understand the Mn distribution in the Mn_{x}Ge_{1−x} film (crystalline and amorphous), energy-filtered TEM was preformed. Figures 4(c) and 4(f) give the EF-TEM elemental maps of Mn that correspond to Figures 4(a) and 4(d), respectively. It is of interest to note that, in the as-grown case, a higher Mn concentration is found in the amorphous layer when comparing Figures 4(a) with 4(c). The overall concentration of Mn is low, so that the contrast in the Mn maps tends to be faint. Nevertheless, the distribution of Mn in the entire film can be clearly observed. In contrast, the Mn map (Figure 4(f)) in the annealed case shows some Mn distribution in the entire film, suggesting that the annealing has not only promoted crystallization, but also redistribute Mn in the entire Mn_{x}Ge_{1−x} film. Nevertheless, a higher Mn concentration can still be observed in the surface region in the annealed sample (refer to Figure 4(f)). The fact that, for the as-grown sample, most of Mn was found in the topmost layer suggests that, during the growth of the Mn_{x}Ge_{1−x} film, a dynamic Mn diffusion has taken place, even at a relatively low growth temperature of 250°C as in our case; Mn tends to diffuse towards the top surface.

Figure 5(a) shows the hysteresis loops at 298 K and 10 K. A clear hysteresis at 298 K indicates room-temperature ferromagnetism. Figure 5(b) shows that the plot of the magnetic moment as a function of temperature at a magnetic field of 100 Oe. The moment in the FC curve decreases very marginally as the temperature increases from 10 to 298 K, showing that the is above the room temperature. The separation of the ZFC data from that of the FC shows a spin glass phase. Before and after annealing, there is no clear difference observed in magnetic properties. The can only be inferred to be above 400 K as shown in Figure 5(b).

The difference of structural and magnetic properties between the 80 nm thick and the 15 nm thick Mn_{x}Ge_{1−x} thin films suggest that when it comes to the nanostructures, the strain and the Mn distribution could be different from that of the bulk films. There might be a threshold thickness for a certain Mn concentration, beyond which the nucleation of metallic clusters (such as Mn_{5}Ge_{3} and Mn_{11}Ge_{8}) takes place and accounts for the RT ferromagnetism ( K) [84, 108]. It is therefore of great interest to further investigate Mn_{x}Ge_{1−x} nanostructures to explore their magnetic properties. Mn_{x}Ge_{1−x} nanodots may be formed by ion implantation process of Mn into Ge and by a self-assembling process with MBE. Since the Mn ion implantation induces metallic clusters and defects [92], we will only focus on the Mn_{x}Ge_{1−x} DMS QDs fabricated via MBE.

###### 3.2.2. Self-Assembled DMS Mn_{x}Ge_{1−x} QDs

Mn_{0.05}Ge_{0.95} QDs were grown on *p*-type Si substrates. Cross-section TEM was carried out to determine the structural characteristics and the Mn composition. HR-TEM image reveals that a QD has a dome shape with a base diameter of about 30 nm and a height of about 8 nm (Figure 6(a)) The interface between the dot and the Si substrate has excellent lattice coherence. A careful inspection reveals that the dot is single crystalline without evidence of pronounced dislocations or stacking faults. However, because of the heavy Mn doping it is possible that some amount of point defects (such as Mn interstitials) may be present inside the dot, which is beyond the detect capability of conventional TEM.

Directly underneath the Mn_{0.05}Ge_{0.95} QD, Mn diffuses into Si substrate and forms a strained MnSi area, which has the same diameter as the top Mn_{0.05}Ge_{0.95} QD, but a height of about 16 nm (Figure 6(a)). This diffusion behavior is not unusual as it was also observed in (In, Mn)As and (In, Cr)As QDs systems [120, 121]. However, the migrations of Mn into the substrate make it difficult to accurately determine Mn concentration inside the dot. To address this challenge, we have performed energy dispersive X-ray spectroscopy (EDS) experiments (in a scanning TEM mode) to analyze the Mn composition at nanoscale (Figure 6(b)). When the EDS was performed, electron probes with several nanometers in diameter were illustrated on the Mn_{0.05}Ge_{0.95} QDs and their underlying Si substrate. Consequently, Si peaks are constantly observed in the EDS spectra. To estimate the Mn concentrations, we performed a quantitative analysis of atomic percentages of Mn and Ge and artificially discounted the Si peak. The EDS analysis over many QDs reveals a Mn/Ge atomic ratio of about 0.144 : 1. Since approximately 1/3 volume fraction of Mn is distributed in the Mn_{x}Ge_{1−x} QD [40], the average Mn concentration can be estimated to be 4.8 ± 0.5%. Note that the deviation was determined by a thorough study of many Mn_{0.05}Ge_{0.95} QDs. Both the HR-TEM investigations and the composition analysis suggest that each individual QD is a single crystalline DMS system.

Magnetic properties were studied using a superconducting quantum interference device (SQUID) magnetometer at various temperatures. Figure 7(a) and two corresponding insets show the temperature-dependent hysteresis loops when the external magnetic field is parallel to the sample surface (in-plane). The field-dependent magnetization indicates a strong ferromagnetism above 400 K. The saturation magnetic moment per Mn atom is roughly estimated to be 1.8 *μ*_{B} at 5 K. A fraction of roughly 60% of Mn is estimated to be activated assuming that each Mn has a moment of 3 *μ*_{B} [27, 58]. The Arrott plots were also made in order to evaluate the (Figure 7(b)). By neglecting the high-order terms, the magnetic field can be expressed in the following equation [122]:
where is the external magnetic field, is the magnetic moment from the sample, is the susceptibility, and is a material dependent constant.

According to (1), can be plotted as a function of . When is extrapolated to , the intercept on the axis gives . The for this material can be obtained when vanishes. Figure 7(b) shows the Arrott plots at several temperatures. It can be seen that even at 400 K the intercept () on the axis does not vanish, which means that the susceptibility still has a finite value and the has not been reached yet. By using the slope obtained at 400 K, a dashed line can be drawn as shown in Figure 7(b), in which a is projected to be beyond 400 K. This is in a good agreement with the data from the hysteresis loops showing the magnetic order above 400 K. Figure 7(c) and corresponding inset show the temperature-dependent saturation and remnant moments per Mn ion, respectively. Both of them demonstrate weak temperature dependences and substantial amount of magnetization moments remain even at 400 K.

ZFC and FC magnetizations were measured with a magnetic field of 100 Oe as shown in Figure 7(d). The magnetic moments do not drop to zero, suggesting a high beyond 400 K, which is in a good agreement with the Arrott plots in Figure 7(b). From these two curves, one can also infer the formation of a single phase in this material system, that is, DMS QDs. The wide separation of the ZFC and FC curves in the temperature range of 5 to 400 K shows the irreversibility of susceptibilities, possibly arising from strain-induced anisotropy as a large lattice mismatch exists between Si and Ge [61]. The temperature-dependent coercivity is shown in Figure 7(d) inset. The coercivity decreases from 170 Oe (at 5 K) to 73 Oe (at 400 K). The small coercivity in the entire temperature range measured features a soft ferromagnetism which originates from Mn ions diluted in the Ge matrix [30]. The above magnetic properties support the fact that the Mn_{0.05}Ge_{0.95} QDs exhibit a DMS-type ferromagnetic order.

It is well known that the direct interaction (superexchange) between *d*-shells of the adjacent Mn atoms leads to an antiferromagnetic configuration of the *d*-shell spins [8]. Therefore, the presence of Mn-Mn clusters would lead to the antiferromagnetism; but when this pair is surrounded by other Mn atoms, the ferri- or ferromagnetic coupling may appear. However, the extensive high-resolution TEM did not reveal observable Mn clusters although such a possibility cannot be completely excluded (Figure 6). Thus, the origin of strong ferromagnetism possibly comes from the Mn_{0.05}Ge_{0.95} QDs via the hole mediation process. In general, when Mn dopants are introduced into Ge, they produce two acceptor levels, that is, 0.16 eV and 0.37 eV above the valence band [123]. When the doping concentration becomes high, the impurity bands could be developed (instead of being separate acceptor levels). However, theoretically the formation of such impurity bands may not affect the physics of ferromagnetism [124]. In the following, we will analyze the Mn-doping behavior by considering a single acceptor level of 0.16 eV in an approximate form. At a sufficiently high temperature, Mn acceptors can be activated to generate holes. These holes are itinerant among a number of Mn ions and align Mn local spins along one direction via the *p-d* exchange coupling to reduce the total energy of the system, resulting in the hole-mediated ferromagnetism [125]. Experimentally this phenomenon has been widely observed in several material systems, such as group III-V (GaAs and InAs) [2, 126], group II-VI (ZnO) [127], and group IV (Ge) [27, 39]. While most of research focuses on bulk DMS, of particular interest is to study the ferromagnetism origin in quantum structures such as (In, Mn)As and Mn_{x}Ge_{1−x} QDs. Previously, Chen et al. [39]and others [120] have suggested that the carrier confinement in a DMS QD can strengthen hole localization and subsequently enhance the thermal stability of magnetic polarons giving rise to a higher than bulk films.

Atomic force microscopy (AFM) and magnetic force microscopy (MFM) measurements were carried out to investigate the morphology and ferromagnetism of Mn_{0.05}Ge_{0.95} QDs at 320 K, respectively. The average dot size is 50 nm in base diameter and 6 nm in height. The dot density is about 6 × 10^{9} cm^{−2} (Figure 8(a)). The corresponding MFM image was taken by lifting up the MFM probe 25 nm above the topographic height of the sample in a phase detection mode (Figure 8(b)). The appearance of bright-and-dark areas in the MFM image clearly shows the formation of magnetic domains in the Mn_{0.05}Ge_{0.95} QDs, which is similar to (In, Mn)As DMS QDs [128]. Figures 8(c)–8(f) show enlarged MFM images of several individual Mn_{0.05}Ge_{0.95} QDs. By reversing the tip magnetization, opposite contrast was observed for each dot, indicating that the magnetic signals originated from the top Mn_{0.05}Ge_{0.95} QDs. Note that each QD is a single domain “particle.” During the magnetization process, the domain would rotate preferentially along the magnetic field to produce net magnetization moments. Since the experiments were performed at 320 K, the formation of metallic phases such as Mn_{5}Ge_{3} and Mn_{11}Ge_{8} can be easily ruled out because they have low Curie temperatures of 296~300 K. Overall, the above MFM results agree well with the TEM observations and the ferromagnetic order at high temperature obtained in the SQUID measurements.

##### 3.3. Discussions

We have reviewed the growth of Mn_{0.05}Ge_{0.95} by MBE, ion implantation, and bulk sintering, emphasizing the growth temperature effect on the phase formation and magnetic properties. While the current motivation is driven by the prospect of enhancing Curie temperatures, the experiments show a strong tendency of metallic precipitates developed in bulk and relatively thick Mn_{x}Ge_{1−x} crystals. The fundamental understanding here points to a spin-glasslike feature in Mn_{x}Ge_{1−x} due to the formation of various lattice coherent nanostructures and metallic precipitates, which exhibit magnetic blocking behaviors under different temperature regimes. The challenge to eliminate these clusters seems to be overwhelming and nearly impossible. However, when the material dimension decreases, it evidences a change of material structures being free of precipitates and a significant increase of Curie temperatures over 400 K. The preliminary explanation on these behaviors can be attributed to the carrier confinement in a DMS QD which strengthens hole localization and subsequently enhances the thermal stability of magnetic polarons giving rise to a higher than those of bulk films. Nevertheless, the experimental data suggest that with nanoscale structures, the quantum confinement effect comes into being which significantly influences the exchange coupling between the confined holes and the localized Mn^{2+}. Future progress in this direction will involve a detailed theoretical treatise to understand the quantum confinement effect on magnetic properties in a quantitative picture.

#### 4. Electric-Field-Controlled Ferromagnetism

##### 4.1. Introduction

Electric field control of ferromagnetism has a potential to realize spin field-effect transistors (spin FETs) and nonvolatile spin logic devices via carrier-mediated effect [129, 130]. With the manipulation of carrier spins, a new generation of nonvolatile (green) computing systems could be eventually developed for many low-power-dissipation applications in all fields, including sensor network, health monitoring, information, and sustainable wireless system. Since Datta and Das [131] first introduced the concept of spin FETs in 1990, enormous efforts were dedicated to creating a device wherein the carrier transport is modulated by electrostatic control of carrier spins [2, 20, 22, 23, 132–136]. To understand and exploit this controllability, several theoretical models were proposed to explain the ferromagnetic coupling in DMS on a microscopic scale (also elaborated in the theoretical section): the Zener Kinetic-exchange [10], double-exchange [137], and the RKKY interaction [138, 139]. These models share a common feature that a spontaneous ferromagnetic order is carrier-mediated through the increase of carrier concentrations. One of major challenges, however, is to search an ideal material with room-temperature controllable spin states [21, 22, 140]. In recent years, emerged DMSs became one of the promising candidates since they could possibly offer high in excess of 300 K [137]. The demonstration of the carrier-medicated ferromagnetism involving correlated electron/hole systems leads to a para- to ferromagnetism phase transition [27, 39, 130, 137]. In principle, the collective alignment of spin states in these DMSs can be manipulated by the modulation of carrier concentrations through gate biasing in a FET structure [2, 140]. For this kind of spin FETs, the “source” and “drain” may be completed through “nanomagnet,” which are in turn controlled by the gate; and no carrier transport is needed. Clearly, one may also involve the control of source-drain conductance by gate-voltage-induced precession of injected spins (from the source). Since early 2000s, a significant progress was achieved [2, 23, 130, 135], in which the ferromagnetism of a (In, Mn)As channel layer could be effectively turned on and off via electric fields in a gated FET. Such extraordinary field-modulated ferromagnetism immediately rendered the development of future spintronic devices. However, the manipulation of ferromagnetism was limited because of low of the Mn-doped III-V materials [141]. Therefore, a search for new DMS materials with K and carrier-mediated ferromagnetism becomes a current global challenge [10, 140].

##### 4.2. Electric-Field-Controlled Ferromagnetism in Mn-Implanted Ge Dots

In parallel with the experimental efforts on field controlled ferromagnetism in III-V material system, we have previously investigated the magnetic properties of Mn_{x}Ge_{1−x} nanostructures by ion implantation of Mn [39]. We demonstrated the hole-mediated effect in Mn-implanted nanodot structures and the modulation of their ferromagnetism by applying gate biases in MOS capacitors at a low temperature of 10 K. Figure 9 shows the magnetic properties of samples with Mn implantation into Ge via the nanopatterned SiO_{2} mask on different doped substrates. It is observed that the Mn-implanted Ge (10^{19} cm^{−3}) has stronger ferromagnetic signals than that *n*-type Ge (10^{17} cm^{−3}), which may indicate a hole-mediated effect. Note that we cannot completely exclude the possibility of the formation of dopant complexes, such as B-Mn and Sb-Mn in the and *n*-type Ge, respectively. Taking advantage of this effect, we further fabricated a MOS capacitor device with Mn-implanted Ge as the channel layer. Figure 10 shows the magnetic moment versus applied field for the MOS structure on the *n*-type substrate under various gate biases at 10 K. When the voltage is applied from −6 to −30 V, the hole concentration in the Mn_{x}Ge_{1−x} channel increases and the magnetic hysteresis becomes larger. At 0 V bias, only a line with a small slope and a small negligible loop are seen; this is because a low density of excess holes is present. When a positive voltage is applied to the gate, holes are partially depleted, resulting in a decrease of the channel magnetization and in the disappearance of magnetic hysteresis. These experimental results demonstrated the hole-mediated effect in Mn_{x}Ge_{1−x}, consistent with the finding by Park et al. [27]. However, the metallic precipitates such as Mn_{5}Ge_{3} and Mn_{11}Ge_{8} and implantation damages were found in these nanostructures, which made the system rather complex and might have partly jeopardized the hole-mediated effect.

##### 4.3. Electric-Field-Controlled Ferromagnetism in Self-Assembled DMS Mn_{0.05}Ge_{0.95} QDs

Since the self-assembled Mn_{0.05}Ge_{0.95} QDs have a high above 400 K and are free of metallic phases (Mn_{5}Ge_{3} and Mn_{11}Ge_{8}), it can be potentially used as a channel layer in a MOS device to study the modulation of ferromagnetism by electric field. The device structure consists of a metal gate (Au, 200 nm), Al_{2}O_{3} (40 nm), Mn_{0.05}Ge_{0.95} QDs (6 nm), a wetting layer (<0.6 nm), a *p*-type Si substrate ( cm^{−3}), and a back metal contact (Au, 200 nm). A relative thick dielectric of Al_{2}O_{3} (40 nm) is employed to ensure a small leakage current to a level below 10^{−6} A/cm^{2}. Figure 11 shows the electric field controlled ferromagnetism performed at 50, 77, and 100 K, corresponding to (a)–(c), (d)–(f), and (g)–(i), respectively. Due to the similarity of the data, we take 77 K as an example to describe the device operation in Figures 11(d)–11(f). Figures 11(d) and 11(e) show the hysteresis loops by SQUID with negative and positive biases on the MOS gate at 77 K, respectively. Under a negative bias, the holes are attracted into the channel of the device (accumulation). In this circumstance, however, the hysteresis loop does not show a remarkable change (Figure 11(d)). This could be explained by the fact that even at 0 V, the QDs device is already accumulated with enough holes to induce ferromagnetism. In other words, the hole-mediated effect is sufficient to align a majority of the activated Mn ions along one direction in each individual QD. Further increasing negative bias does not change much on the hole concentrations. On the contrary, with the positive bias, a large amount of holes are depleted into the *p*-type Si so that hole-mediated effect is notably reduced. In fact, the surface of the device can have a high concentration of electrons if the leakage is limited (inversion). As a result, the Mn ions start to misalign because of the lack of holes. The saturation moment per Mn ion decreases more than 10 times as the gate bias increases from 0 to +40 V (Figure 11(e)). It should be noted that, at +40 V, the saturation and remnant moments of the Mn_{0.05}Ge_{0.95} QDs become fairly weak, resembling a “paramagnetic-like” state. Figure 11(f) summarizes the change of remnant moments as a function of gate voltage. A similar trend in the carrier density as a function of the gate bias was observed from CV curves (not shown here), suggesting a strong correlation between hole concentrations and the ferromagnetism, that is, the hole-mediated effect. The inset in Figure 11(f) displays an enlarged picture to clearly show the change of remnant moments with respect to the gate bias. By increasing the measurement temperature to 100 K (Figures 11(g)–11(i)), the modulation of the ferromagnetism becomes less pronounced compared to those at 50 and 77 K due to the increased leakage current in our MOS devices. The above results evidently demonstrate that the hole-mediated effect does exist in this material system.

##### 4.4. Discussions

Electrical-field-controlled ferromagnetism has been successfully demonstrated in Mn-doped III-V DMSs [2, 23, 130, 135, 140]. It is well established that the variation of hole concentrations renders such a controllability [2]. The low of III-V DMS, however, presents a challenge to further realize room-temperature-controlled ferromagnetism [141]. Alternatively, the recent experiments on Mn_{0.05}Ge_{0.95} QDs show a high above room temperature and gate-modulated ferromagnetism over 100 K [40]. While the leakage current suppressed the gate modulation, room-temperature-controlled ferromagnetism would not be impossible because of the high of this system. Research in this direction may open up a pathway for achieving room-temperature Ge-based (and other) spin-FETs and spin logic devices. These spintronic devices could potentially replace the conventional FETs with lower power consumptions and provide additional new device functionalities, which is beyond today’s mainstream CMOS technology of microelectronics.

#### 5. Metallic Mn_{x}Ge_{1−x} (*x* ~ 20%) Nanodot Arrays

##### 5.1. Introduction

There is also a need to develop ferromagnet/semiconductor hybrid structures for semiconductor spintronics since they have magnetic and spin-related functions and excellent compatibility with semiconductor device structures [142, 143]. By embedding magnetic nanocrystals into conventional semiconductors, a unique hybrid system can be developed, allowing not only utilizing the charge properties but also the spin of carriers, which immediately promises next-generation nonvolatile magnetic memories and sensors [144, 145]. On the other hand, spin injections into the semiconductor can be dramatically enhanced via coherent nanostructures, which considerably reduce undesired spin scatterings [146]. Although magnetic hybrid systems, such as MnAs/GaAs, have been extensively studied over several decades, the control (over the spatial location, shape and geometrical configuration) of the magnetic nanostructures (for instance MnAs) still remains a major challenge to further improve the performance of the related magnetic tunnel junctions (MTJs) and spin valves [147].

##### 5.2. Growth Methods

We employed a concept of stacked Mn_{x}Ge_{1−x} (*x* ~ 20%) (hereafter, we denote it as MnGe) nanodots by alternatively growing MnGe and Ge layers with designated thicknesses (nominal 3 nm thick MnGe and 11 nm thick Ge). It is well known that Mn doping in Ge induces compressive strain because of its larger atomic size [148], assuming that no lattice defects are generated during the doping process, that is, lattice coherence. Mn-rich MnGe nanodots induced by the spinodal decomposition should be strained if the lattice coherence between the nanodots and the matrix remains. Once the strained nanodots are developed, a thin Ge spacer layer, subsequently deposited with an optimized thickness, will retain the perfect lattice coherence with the underneath nanodots. This enables the existing nanodots to exert strain on the Ge spacer layer and produce “strained spots,” which, in turn, become preferred nucleation sites for successive nanodots. Eventually, multilayered and vertically aligned MnGe nanodot arrays can be produced, similar to the scenarios of stacked InAs/GaAs [149, 150] and Ge/Si [151] quantum dots. Indeed, by employing this innovative approach, we achieved the growth of coherent self-assembled MnGe nanodot arrays with an estimated density of 10^{11}~10^{12} cm^{−2} within each MnGe layer.

Ten periods of MnGe nanodots were epitaxially grown on Ge (100) and GaAs (100) substrates by the MBE system. TEM and EDS in the scanning TEM (STEM) mode were performed to understand the nanostructures and compositional variations of the resulting thin films. Figures 12(a) and 12(c) are typical plane-view and cross-sectional TEM images and show the general morphology of the MnGe nanostructures, viewed along the and directions, respectively. A high density of dark nanodots can be clearly seen in both cases. Based on the magnified cross-sectional image shown in Figure 12(d), the nanodot arrays are clearly observed with 10 stacks along the growth direction although not perfectly vertical. In order to determine the composition of the dark dots, EDS analyses in the STEM mode were carried out and typical plane-view and cross-sectional STEM images are shown in Figures 12(b) and 12(e), respectively. Figure 12(f) is the EDS result taken from a typical dot and shows clearly the Mn and Ge peaks. Figures 12(g) and 12(h) present EDS line scans using the Mn peak for the dots marked by G and H in Figures 12(b) and 12(e), respectively, indicating high concentrations of Mn inside the dots. Taking all these comprehensive TEM results into account, it is concluded that the nanodots are Mn rich when compared with the surrounding matrix.

Figure 13(a) shows a high-magnification TEM image taken from a thin area, where several aligned MnGe nanodots can be evidently observed. The distance between two vertically adjacent nanodots (along the growth direction) is measured to be 14 ± 1 nm, well matched with the designed period of a 11 nm thick Ge spacer layer and a 3 nm thick MnGe layer. It should be noted that these nanodots are uniform in size with an elliptical shape (a dimension of 5.5 ± 0.5 nm and 8 ± 0.3 nm in the horizontal and vertical directions, resp.), as demonstrated in Figure 13(a). Since the nominal thickness of the MnGe layer (3 nm) is far less than the dot vertical dimension (8 nm), it suggests that, during the growth of the MnGe thin film, Mn not only diffuses laterally (to form dots), but also migrates vertically into the adjacent Ge spacer layers, primarily in the proximity of the dot regions, resulting in ellipse-shaped nanodots.

##### 5.3. Magnetotransport Properties of Nanodot Arrays

The resistivity measurements were carried out to probe the carrier transport under different temperatures. It was found that the temperature-dependent resistivities rapidly increase with decreasing temperature due to the carrier freeze-out effect at low temperatures, which is typically observed in doped semiconductors [152]. Considering the embedded MnGe nanodots, the rise in resistivities at low temperatures also suggests a strong localization of carriers, which takes place at the Mn sites and/or at the MnGe/Ge interfaces, similar to the scenario of MnSb clusters in InMnSb crystals [153]. The temperature-dependent resistivity can be generally described by [154]
where is the temperature-dependent resistivity; and denote material parameters, is a dimensionality parameter: . For one-dimensional (1D), for 2-*d*, and for 3-*d* systems. In order to reveal the carrier transport mechanisms at different temperature regions, fittings were performed in the plots of as a function of (Figure 14(a)). The best fittings were found when equals 1 and 4 in the high-temperature and low-temperature regions, respectively, corresponding to the carrier transport via the band conduction [155] (thermal activation of acceptors) and the 3-*d* Mott’s variable range hopping processes [154]. According to the fitting results to (2), the obtained nanodot arrays show a dominated hopping process below 10 K. At such a low temperature, the majority of free holes are recaptured by the acceptors. As a result, the free-hole band conduction becomes less important and hole hopping directly between acceptors in the impurity band contributes mostly to the conductivity [155]. Above 100 K, the conduction is dominated by the thermal activation of the holes (the band conduction). A thermal activation energy () of 15 meV can be obtained from (2) with and where is the Boltzmann constant. This activation energy does not correspond to any known acceptor energy levels due to Mn doping in Ge, consistent with results shown in [156].

To explore practical applications for our extraordinary nanodot arrays, the MR measurements were performed from 2 to 300 K with an external magnetic field up to 10 Tesla. Figure 14(b) shows the plots of temperature-dependent MR at given magnetic fields (5 and 10 Tesla) for the nanodot arrays. Under a strong magnetic field, the MR in the region of variable range-hopping conduction can be described by [157, 158] where the magnetic length equals and C is a field- and temperature-independent constant. Note that (3) is only valid in a strong-field limit [157–159]. The inset in Figure 14(b) shows the best fitting results, in which a linear behavior of MR versus is obtained, further confirming the hopping conduction mechanisms ( K). Note that the absolute values of MRs were used for the fitting purpose. These fitting results are reasonably close to the obtained hopping regions determined from the zero-magnetic-field resistivity measurements (K, Figure 14(a)).

It is striking to observe that the coherent MnGe nanodot arrays present a large and positive MR up to 900% at 2 K (Figure 14(c)). Traditionally, the positive MR is attributed to the Lorentz force in the semiconductor matrix, which deflects the carriers during the transport process [159]. The resulting MR is positive and proportional to under low magnetic fields ( Tesla in our case) where is the semiconductor mobility (units m^{2}V^{−1}S^{−1} or T^{−1}) and is the magnetic field. However, with a simple calculation, the estimated orbital MR is too small to explain the large MR observed from the nanodot arrays. Instead, we anticipate that, besides the effect of orbital MR, the high-density magnetic nanodots could significantly contribute to the large MR ratios due to an enhanced geometric MR effect, from which the current path may be significantly deflected when external magnetic fields were applied to the magnetic nanostructures [57, 160]. To elucidate the underlying physics of the geometrical effect, we consider a thin Hall bar geometry with a measurement current applied in the -direction, a Hall voltage in the direction, direction normal to the sample surface, and an external magnetic field parallel to . For semiconductors, the current density and the total electric field can be described by , where the magnetoconductivity tensor is given by [57, 160]
Here, . At zero magnetic field, vanishes. The conductivity tensor is diagonal when lacking of the magnetic field; and the current density can be simply described by . Since the electric field is normal to the surface of a metallic inclusion and , the current flowing through the material is concentrated into the metallic region which behaves like a “short circuit” [35]. As a result, the inclusion of metallic clusters can lead to a higher conduction than that of a homogeneous semiconductor [57, 160]*.* However, at high magnetic fields (), the off-diagonal terms of dominate. Equivalently, the Hall angle between and approaches 90°; and the current becomes tangent to the nanodots. This further indicates that the current is deflected to flow around the nanodots, resembling an “open circuit” state [35]. The transition from the “short circuit” at the zero field to the “open circuit” at high fields produces an increase of resistance, that is, a positive geometrically enhanced MR [160].

##### 5.4. Discussions

The introduction of high percentage Mn (*x* ~ 20%) generates metallic behavior in Mn-doped Ge. Such heavily doped samples possess nanoscale MnGe dots. With a superlattice approach, we have successfully fabricated extraordinarily coherent and self-organized MnGe nanodot arrays embedded in the Ge and GaAs matrixes by low temperature MBE. A high yield of such aligned nanodot arrays was confirmed on different substrates, showing an ideal controllability and reproducibility. More importantly, giant positive magnetoresistances were obtained due to the geometrically enhanced effect. We anticipate that these studies will advance the development of MnGe magnetic semiconductors and/or other similar systems. The obtained coherent and self-assembled nanostructures could be potentially used as the building blocks in the high-density magnetic memories, sensors, MTJs, and other spintronic devices, enabling a new generation of low dissipation magnetoelectronic devices.

#### 6. Summary and Prospective

This paper is a review of theoretical and experimental progress that has been achieved in understanding ferromagnetism and related electronic properties in the Mn_{x}Ge_{1−x} DMSs, and MnGe metallic nanodots. Interest in DMS ferromagnetism is motivated by the possibility to engineer systems that combine many of the technologically useful features of ferromagnetic and semiconducting materials. This goal has been achieved to an impressive degree in (III, Mn)V DMSs, and further progress can be anticipated in the future. However, due to the low of (III, Mn)V DMSs, the spintronics research seemly reaches a critical bottleneck, where achieving a high DMS becomes an intriguing and challenging task. Fortunately, the Mn_{x}Ge_{1−x} material system offers a possible route towards higher . The structural and magnetic properties can be adjusted simply by modifying the system dimensions from 3-*d* thin films to 0D quantum dots. A high in excess of 400 K can be obtained and is presumably attributed to the quantum confinement effect, which strengthens the hybridation between the localized Mn impurities and iterant holes. Bound magnetic polarons may also exist since this system falls into a regime where Mn concentrations are much larger than that of holes. Nevertheless, the high in the low-dimensional system suggests that the quantum structure exibits extraordinary properties that significantly differ from these of bulk films. The future progress would rely on the precise theoretical understanding of the quantum confinement effect on ferromagnetism.

It is well known that in order to achieve functioning spintronic devices working at ambient temperatures, it requires the following criteria: (i) the ferromagnetic transition temperature should safely exceed room temperature, (ii) the mobile charge carriers should respond strongly to changes in the ordered magnetic state, and (iii) the material should retain fundamental semiconductor characteristics, including sensitivity to doping and light and electric fields produced by gate charges. For more than a decade, these three key issues have been the focus of intense experimental and theoretical research. Progress has been also made in achieving field-controlled ferromagnetism in (III, Mn)As system, even though the controllability remains at low temperatures because of low . Therefore, the critical challenge now is either to continue increasing in (III, Mn)As, or to look for a new DMS system with both high Curie temperature ( K) and the field-controlled ferromagnetism to satisfy all these three criteria. The experimental results of field-controlled ferromagnetism in the Mn_{0.05}Ge_{0.95} QDs suggest that the ferromagnetism in this system sensitively responds to the electrical field via the hole-mediated effect, similar to that in (III, Mn)As system. Therefore, with a much higher compared with III-V DMS, the Mn_{x}Ge_{1−x} nanostructures could become one of the most promising candidates to achieve room-temperature operation.

On the other hand, the metallic MnGe nanodots with a high percentage of Mn (~20%) show perfect lattice coherence with the Ge matrix. Such a ferrromagnet/semiconductor hybrid system is extremely useful owing to their high-quality defect-free interface, where a high efficient spin injection can be realized without a need of oxides such as MgO (spin filter). We also hope to encourage more research efforts in this direction because of the excellent compatibility of MnGe nanodots with the current CMOS technology.

#### Acknowledgments

F. Xiu would like to acknowledge startup funds from the Department of Electrical and Computer Engineering, Colleage of Engineering, and Microelectronics Research Center (MRC) at Iowa State University. F. Xiu thanks Professor Kang L. Wang (UCLA, USA), Professor Jin Zou (Queensland University, Australia), and Professor Yong Wang (Zhejiang University, China) for their contributions to this work.

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