Introduction

Ferromagnetic Co2-Heusler compounds with the chemical formula Co2YZ, where Y is a transition metal and Z is a main group element such as Si and Ge, are candidate materials for half-metals with a fully spin-polarized (100% spin polarization) density of states (DOS) at the Fermi level.1,2,3 For spintronic memory and sensor applications,4,5 a number of high-performance Co2-Heusler compounds have already been reported as ferromagnetic electrodes in magnetic tunnel junctions (MTJs),6,7,8,9 current-perpendicular-to-plane giant magnetoresistive (CPP-GMR) devices,10,11,12,13 and lateral spin-valve (LSV) devices.14,15,16

In the field of semiconductor spintronics,17,18,19,20,21,22,23,24,25,26,27 the use of Co2YZ has been proposed for spin injector and detector contacts in spin-based light-emitting diodes (LEDs) and field-effect transistors (FETs).28,29,30 Figure 1a–b shows schematics of a spin FET, proposed by Datta and Das,31 and a spin metal–oxide–semiconductor (MOS) FET, proposed by Sugahara and Tanaka,32,33 respectively. Here, the source/drain (S/D) contacts are composed of a ferromagnetic (FM) material and FM/semiconductor heterojunctions. Although the device structures of both types of spin transistors are almost the same, quite different operating principles have been proposed, involving spin transport in III–V semiconductor channels with a large spin–orbit interaction31 or in Group-IV semiconductor channels with a small spin–orbit interaction.32,33 For the Datta and Das spin FET, because electrons’ spins are controlled by an electric field via the Rashba spin–orbit coupling in the III–V semiconductor channels, it is not necessary to change the magnetization direction of the FM materials at the SD contacts.31 For the Sugahara and Tanaka spin MOSFET, on the other hand, the output signal is related to the spin-dependent transport through the Group-IV semiconductor channels, depending on the magnetization direction of the FM materials at the SD contacts.32,33 In particular, if one can realize a high-performance spin MOSFET on a Si platform, nonvolatile memory devices can be integrated into CMOS transistors.33,34 To achieve highly efficient spin-dependent transport in these FETs, electrical spin injection, transport, and detection in III–V or Group-IV semiconductor channels with Co2YZ S/D contacts should be explored.

Figure 1
figure 1

Conceptual illustrations of (a) Datta-Das-type spin field-effect transistor (FET)31 and (b) Sugahara-Tanaka-type spin metal–oxide–semiconductor FET,32,33 where the metallic source/drain (S/D) materials are ferromagnets. Both types are composed of Schottky-tunnel S/D contacts for spin injection and detection. 2DEG and BOX stand for two-dimensional electron gas and buried oxide layer, respectively.

Full size image

One of the most important parameters for Co2YZ is the structural order. The top illustration in Figure 2a–b is the crystal structures of L21-ordered Co2YZ. When the Y-site atoms are randomly replaced by the Z-site atoms, it is a so-called B2-ordered structure. If Co, Y, and Z atoms occupy all the sites randomly, it is not an ordered structure but is an A2 structure. In general, B2- or L21-ordered structures are required to obtain high-performance spintronic devices.2,3 For MTJs and CPP-GMR devices, high-temperature annealing treatments (~550°C) are generally performed to promote the formation of B2- or L21-ordered structures.6,7,8,9,10,11,12,13 However, because these high-temperature annealing treatments are not compatible with the formation of heterostructures consisting of Co2YZ and semiconductors, low-temperature formation techniques are required. Thus, crystal growth of Co2YZ films with B2- or L21-ordered structures on semiconductors has been explored. In particular, because the lattice parameters for Co2YZ compounds such as Co2MnSi and Co2FeSi are nearly equivalent to those for GaAs and Ge, low-temperature growth methods by molecular beam epitaxy (MBE) are attractive for achieving B2- or L21-ordered structures without forming magnetic dead layers and/or atomic interdiffusion layers at Co2YZ/GaAs or Co2YZ/Ge heterojunctions.28,29,30

Figure 2
figure 2

Schematics of crystal structures of L21-ordered Co2YZ and GaAs (a) and Ge (b). Surface crystal orientations of GaAs(001) and Ge(111) are ideal for epitaxial growth of Co2YZ films. (c) In situ reflection high-energy electron diffraction patterns of the surface of Co2FeAl0.5Si0.5 during molecular beam epitaxy growth (top) and of a Ge(111) surface after surface cleaning (bottom).

Full size image

Epitaxial growth of Co2YZ films on GaAs and Ge

Figure 2a–b shows structural models illustrating the orientations for epitaxial crystal growth of Co2YZ films on GaAs and on Ge, respectively. Because there is almost no lattice mismatch between some of the Co2YZ compounds (0.564–0.570 nm) and GaAs or Ge (~0.566 nm), it is possible to realize epitaxial growth of the Co2YZ films. For the GaAs(001) surface highlighted by the blue square in Figure 2a, the growth of Co2YZ films has been explored by low-temperature MBE methods.28,29 Thus far, epitaxial growth of Co2MnGe,35 Co2FeSi,36,37,38,39 Co2FeAl,40,41,42 Co2CrAl,40,43 and Co2MnSi39,44,45 films has been reported. The B2- or L21-Co2YZ/GaAs heterostructures formed at low temperatures from 100ºC to 487°C enable electrical spin injection into GaAs through the Co2YZ/GaAs Schottky-tunnel barrier.35,37,38,39,44,45 Owing to highly efficient spin injection and detection through the B2- or L21-ordered Co2YZ/GaAs interface, room-temperature spin transport was observed even in GaAs-based channels,39,45,46 which are influenced by D'yakonov-Perel' spin relaxation due to the broken space inversion symmetry in the crystal structure. Progress in spin injection is described in the next section.

For Ge, on the other hand, we explored the epitaxial growth of Co2YZ films on the (111) surface shown by the blue triangle in Figure 2b using low-temperature MBE.47,48,49,50,51 If we look at the (111) planes, we find that there is good matching between the atomic arrangements of Co2YZ and Ge.30 The Ge(111) plane has also been utilized for the epitaxial growth of Fe-based Heusler compounds52,53,54,55,56 and all-Heusler-compound trilayers.57 Epitaxial growth of Ge(111) layers on Heusler-compound structures was also demonstrated using low-temperature MBE methods.58,59

Figure 2c displays a reflection high-energy electron diffraction (RHEED) pattern observed during the growth of a Co2FeAl0.5Si0.5 film on a Ge(111) surface, where the growth temperature is less than 100°C.51 The symmetrical streak patterns show that two-dimensional epitaxial growth of the Co2FeAl0.5Si0.5 film occurs on Ge(111). Structural and magnetic characterization revealed the formation of B2-ordered Co2FeAl0.5Si0.5/Ge(111) heterointerfaces despite the low growth temperature.51,60 Through these efforts, we have demonstrated the epitaxial growth of Co2FeAlxSi1−x films on Ge(111) at growth temperatures less than 100°C.51

Atomic-resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) analyses of the Co2FeAl0.5Si0.5 film grown on Ge(111) were also performed,60,61 where the contrast in the HAADF-STEM image provides information on the mass distribution in the matrix and is related to the atomic number of each element. As shown in Figure 3a, the different crystallographic structures of Co2FeAl0.5Si0.5 and Ge indicate the structural abruptness of the interface and the epitaxial relationship between the layers. However, there are some fluctuations in the atomic composition in the Co2FeAl0.5Si0.5 layer near the interface, as denoted by arrows. These fluctuations are attributed to Ge out-diffusion during growth.60,61 To suppress Ge out-diffusion near the interface, we recently developed a new method for improving the quality of the Co2FeAl0.5Si0.5 layer. By inserting a very thin (~0.7 nm) Fe layer between Co2FeAl0.5Si0.5 and Ge,62 the compositional fluctuation due to out-diffusion of Ge atoms into the Co2FeAl0.5Si0.5 layer is markedly suppressed (Figure 3b). As a result, B2-ordered Co2FeAl0.5Si0.5 was formed near the interface on top of the Fe-terminated Ge layer (Figure 3c).62 Recent progress in this effort on spin transport in Ge is also described later.

Figure 3
figure 3

© 2018 American Physical Society. (b) and (c) Adapted from Reference 62.

High-angle annular dark-field scanning transmission electron microscope (HAADF-STEM) images of Co2FeAl0.5Si0.5/n-Ge (a) and Co2FeAl0.5Si0.5/Fe(~0.7 nm)/n-Ge (b) interfaces, viewed along the \([\overline{1}10]\) zone axis in lateral spin-value devices. (c) High-resolution HAADF-STEM image at the Co2FeAl0.5Si0.5/Fe(~0.7 nm)/n-Ge interface. (a) Reprinted figure with permission from Reference 61.

Full size image

Thus far, it has been difficult to form B2- or L21-ordered Co2MnSi on Ge(111) even by low-temperature MBE methods.48,49 To obtain a sufficient magnetic moment in Co2MnSi films on Ge(111), postannealing treatments were required.49,63,64 While B2- or L21-ordered Co2MnSi was formed on Ge(111) after postannealing, it was still difficult to obtain high-quality and smooth Co2MnSi/Ge(111) heterojunctions due to atomic interdiffusion between Co2MnSi and Ge.49,63,64 Although the contact resistance between Co2MnSi and Ge was relatively high, the insertion of an MgO tunnel-barrier layer at the interface was employed to obtain L21-ordered Co2MnSi on Ge.65 Very recently, we predicted the formation of energetically stable Co2MnSi–Ge(111) heterointerfaces with Fe atomic layers.66 As expected, we demonstrated L21-ordered Co2MnSi films on Ge(111) using low-temperature MBE (~ 80°C). Owing to this effort and phosphorus (P) δ-doping techniques,30,67 we decreased the contact resistance area product (RA) of the Co2MnSi/Ge Schottky-tunnel barrier down to ~ 0.1 kΩµm2,66 resulting in a reduction of the parasitic resistance in the device structure.

Spin injection into GaAs and Ge with Co2YZ contacts

To evaluate electrical spin injection from FMs into nonmagnets (NMs), four-terminal nonlocal voltage measurements of lateral spin-valve (LSV) devices have been utilized in the research field of spintronics,68,69,70 where charge-related magnetoresistance such as anisotropic magnetoresistance (AMR) and/or local Hall effects can be neglected. Figure 4 shows a schematic illustration of the principles of the detection scheme for the nonlocal spin signal. A typical structure of an FM1–NM–FM2 LSV device is depicted in Figure 4a. If electrical spin injection can be realized under the application of a negative direct current (I), nonequilibrium splitting of electrochemical potentials, Δµ = µ↑ − µ↓, beneath the spin-injector contact (FM1) can be created. Here the created Δµ is termed spin accumulation in NMs. As a result, the spin accumulation created in NMs can be detected as a pure spin current, a flow of spin angular momentum without charge currents, at the side of the spin-detector contact (FM2). Figure 4b shows a schematic illustration of Δµ in the FM1-NM-FM2 structure. Along the lateral direction x, the exponentially decayed Δµ is detected electrically as a difference in the nonlocal voltage (ΔVNL) between parallel and antiparallel magnetization states. By sweeping the in-plane external magnetic field along the long axis of the FM1 and FM2 contacts, hysteretic nonlocal resistance changes (ΔRNL = ΔVNL/I) are observed depending on the magnetization states between FM1 and FM2 (Figure 4c). In addition, by applying an out-of-plane external magnetic field to the LSV devices, the Hanle effect, which corresponds to Larmor spin precession in NMs, is also detected electrically. For both parallel and antiparallel magnetization states, precessional decay of the nonlocal resistance is seen, as shown in Figure 4d. Based on fitting with the one-dimensional spin drift–diffusion model,69,71 the spin relaxation mechanism in NMs can be roughly investigated.

Figure 4
figure 4

(a) Typical structure of a lateral spin-valve (LSV) device with a nonmagnetic (NM) spin-transport channel and four-terminal nonlocal voltage measurement.68,69,70 (b) Schematic diagram of electrochemical potential (µ↑, µ↓) in the FM1–NM–FM2 structure along z1–x–z2. (c) A nonlocal spin-valve signal is expected to be observed on sweeping with an in-plane external magnetic field. (d) Typical shapes of nonlocal Hanle-effect curves observed by application of out-of-plane external magnetic field. The magnetization states between FM1 and FM2 are depicted as black arrows.

Full size image

The four-terminal nonlocal spin signals are recognized as evidence of the electrical detection of a pure spin current in the field of semiconductor spintronics. In 2007, Lou et al. simultaneously observed nonlocal spin signals and Hanle-effect curves at low temperatures in n-type GaAs (n-GaAs) LSV devices with epitaxial Fe Schottky-tunnel contacts.71 Since this development, electrical spin injection from Co2FeSi or Co2MnSi into GaAs has been investigated in LSV devices.38,39,44,45 In particular, room-temperature nonlocal spin signals were observed in n-GaAs by using Co2FeSi/GaAs and Co2MnSi/CoFe/GaAs Schottky-tunnel contacts,39,45 although nonlocal Hanle curves were not exhibited at room temperature. Because the magnitude of the nonlocal Hanle signal with a parallel or an antiparallel magnetization state is less than half the magnitude of the nonlocal spin signal (∣ΔRNL∣) (Figure 4c–d), it is generally difficult to detect the nonlocal Hanle curves with both parallel and antiparallel magnetization states at room temperature in the case of small ΔRNL values.

For n-GaAs, it is particularly important to understand the influence of Co2YZ/GaAs Schottky-tunnel contacts and/or the D'yakonov-Perel' spin relaxation mechanism on the spin-transport signals. In 2014, Ebina et al. reported that insertion of a 1.3-nm-thick CoFe layer suppresses the diffusion of Mn atoms into GaAs during the growth of Co2MnSi films, leading to improved spin injection properties.45 Then, Uemura et al. demonstrated nuclear-spin-based qubits in GaAs without using a large magnetic field because the efficient spin injection from Co2MnSi/CoFe contacts enabled dynamic nuclear polarization of Ga and As nuclei.72 In 2016, Peterson et al. clarified the strong influence of D'yakonov-Perel' spin relaxation in n-GaAs in LSV devices with Co2FeSi and Co2MnSi contacts from low temperatures up to room temperature.39 However, in 2018, Rath et al. proposed that interfacial Mn segregation in Co2MnSi/GaAs(001) induces the loss of half-metallicity for the Co2MnSi film, leading to degradation of the performance of LSV devices.73 Namely, it is inferred that the interfacial quality of Co2YZ/GaAs heterojunctions influences the ability to study room-temperature spin transport with nonlocal Hanle curves in both the parallel and antiparallel magnetization states. In 2019, Lin et al. used AlGaAs/GaAs-based two-dimensional electron gas (2DEG) systems with Co2MnSi contacts. Although they observed nonlocal spin signals up to room temperature, the spin relaxation mechanism could not be explained clearly.46 These efforts have revealed the effectiveness of the use of Co2YZ/n-GaAs Schottky-tunnel contacts to study spin injection, transport, and detection in n-GaAs.

Because of the space inversion symmetry in Ge, the influence of the D'yakonov-Perel' mechanism on spin relaxation is negligibly small in Ge channels. If highly efficient spin injection from Co2YZ films into Ge is demonstrated, efficient spin transport can be expected even in Ge-based LSV devices. Thus far, for n-type Ge (n-Ge), a modified Elliott–Yafet spin relaxation mechanism including the spin–orbit interaction of host materials and donor atoms has been verified theoretically74,75 and in experiments.51,76,77,78 To explore the lateral spin transport, we prepared LSV devices with an n-Ge spin-transport channel and two ferromagnetic Co2YZ contacts,51,62,76,77,78,79,80 as shown in Figure 5a. The detailed growth and fabrication processes for the LSV device were as follows: First, an undoped Ge(111) buffer layer (~28 nm) (LT-Ge) was grown at 350°C on a commercial undoped Si(111) substrate (ρ ~ 1000 Ω cm), followed by an undoped Ge(111) buffer layer (~70 nm) grown at 700°C (HT-Ge), where we utilized a two-step MBE growth technique.81 Next, as the spin-transport layer, a 140-nm-thick P-doped Ge(111) layer (doping concentration ~1019 cm−3) was grown on top by MBE at 350°C. Here, the room-temperature carrier (electron) concentration of the spin-transport layer is 6.0−7.0 × 1018 cm−3,62,66,80 estimated from Hall effect measurements. To eliminate the large conductivity mismatch82,83,84,85 between Co2YZ and n-Ge, we developed a Schottky-tunnel contact consisting of Co2YZ and a P δ-doped Ge layer,30,67 where the P δ-doped Ge layer was terminated by a 0.7-nm-thick Fe layer.62,66,80 After that, a Co2YZ film was grown on top by MBE at a growth temperature of less than 100°C.30,51,66 Thus, the whole sample stack was prepared by MBE techniques. Finally, the formed Co2YZ/n-Ge Schottky-tunnel layer was patterned into two contacts with a width of 0.4 µm (FM1) or 0.5 µm (FM2), and a channel structure with a channel width (w) of 5.0 µm and an edge-to-edge distance (d) between the FM contacts of 0.45 µm. The detailed fabrication processes for the LSV device are presented in the literature.79

Figure 5
figure 5

adapted from Reference 62. The red and blue Hanle curves are measured in parallel and antiparallel magnetization configurations, respectively. (d) Comparison of the magnitude of ∆RNL at 8 K between Co2FeAl0.5Si0.5(8 nm)/n-Ge and Co2FeAl0.5Si0.5(8 nm)/Fe(0.7 nm)/n-Ge contacts.

(a) Schematic illustration of a lateral spin-valve (LSV) device fabricated with ferromagnetic (FM)/Ge Schottky-tunnel contacts and an n-Ge channel on Si, where FM is a Co2-Heusler compound. Nonlocal magnetoresistance (b) and Hanle-effect curves (c) at 8 K at I = −1.0 mA for an LSV device with Co2FeAl0.5Si0.5(8 nm)/Fe(0.7 nm)/n-Ge contacts, which are

Full size image

Figure 5b shows a representative ΔRNL signal as a function of the in-plane magnetic field (By) at I = −1.0 mA at 8 K for an LSV device with Co2FeAl0.5Si0.5(8 nm)/Fe(0.7 nm)/n-Ge Schottky-tunnel contacts as shown in Figure 3c. Here, a negative value of I (I < 0) indicates that the spin-polarized electrons are injected into n-Ge from Co2FeAl0.5Si0.5 (i.e., a spin injection condition via the Schottky-tunnel barrier). An evident nonlocal hysteresis curve is observed, which depends on the parallel and antiparallel magnetization states between Co2FeAl0.5Si0.5 contacts, depicted by the arrows in Figure 5b. Notably, the value of ΔRNL reaches ~400 mΩ. In four-terminal nonlocal measurements under an out-of-plane magnetic field (Bz), we also observe nonlocal Hanle curves, indicating spin precession in the channel (Figure 5c). We also note that, even in the antiparallel magnetization state under the application of Bz, the Hanle-effect signal is clearly observed, indicating reliable pure-spin-current transport in the n-Ge layer. Using a one-dimensional spin drift–diffusion model,69,71 the spin injection/detection efficiency and spin lifetime can be roughly estimated to be ~0.24 and ~0.76 ns, respectively, from the four-terminal nonlocal spin-transport data. For comparison, we explored four-terminal nonlocal spin-transport data for LSV devices with various FM Schottky-tunnel contacts.30,51,76 In Figure 5d, we give a simple comparison of the magnitude of ΔRNL at 8 K for LSV devices with Co2FeAl0.5Si0.5(8 nm)/n-Ge (blue) and Co2FeAl0.5Si0.5(8 nm)/Fe(0.7 nm)/n-Ge (red) Schottky-tunnel contacts. The magnitude of ΔRNL is significantly enhanced only by inserting a 0.7-nm-thick Fe layer between Co2FeAl0.5Si0.5 and n-Ge. This feature is strongly related to the interface quality as shown in Figure 3. For reference, if Co2FeAl0.5Si0.5 contacts were not used in the n-Ge-based LSV devices, we could not obtain such large ΔRNL values. For example, when we used epitaxial CoFe/n-Ge Schottky-tunnel contacts, the magnitude of ΔRNL was less than 4 mΩ, which is two orders of magnitude smaller than that in Figure 5b. Therefore, the use of Co2YZ is clearly effective even for Ge-based spintronic devices, but it is quite important to achieve a high-quality heterointerface between Co2YZ and Ge,30,51,61,62,66 as well as GaAs.45,73

Potential for applications

Room-temperature pure-spin-current transport with Hanle curves was first observed in LSV devices with semiconducting graphene86,87,88 and Si89,90,91 channels because of the large spin diffusion lengths (λSC) of several microns even at room temperature. Then, progress in the crystal growth and formation of high-quality Co2YZ/Ge heterojunctions also enabled pure-spin-current transport with Hanle curves at room temperature even in Ge-based LSV devices,92 despite a relatively small λSC (~0.4 µm) compared to graphene and Si. In this section, we discuss the potential use of Co2YZ/Ge structures in practical applications.

It is generally important to observe a two-terminal local magnetoresistance (MR) effect, indicating spin-dependent transport of spin-polarized electrons or holes through semiconductors at room temperature (RT).31,32,33,34 The two-terminal MR ratio is defined as (∆RL/Rp) × 100, where ∆RL and Rp are the two-terminal local spin accumulation signal (∆VL/Ibias), shown in the inset (middle) of Figure 6a, and the resistance between the FM contacts through the semiconductor layer in the parallel magnetization state, respectively. In Si-based LSV devices,91,93,94,95,96 tunnel barriers consisting of insulators such as MgO were found to cause a large parasitic resistance component in Rp. As a result, to obtain an MR of 0.06% at room temperature, which is the largest value in Si LSV devices, quite high bias voltages (~2.3 V) must be applied, leading to a large S/D voltage and electric power of ~1.15 mW.96 Thus, the use of controllable Schottky-tunnel contacts should be explored to reduce the electric power required to obtain the two-terminal MR effect.

Figure 6
figure 6

(a) Nonlocal-(top) and local-(bottom) magnetoresistance (MR) curves measured at 296 K room temperature (RT) at I and Ibias = −1.0 mA, respectively, for an n-Ge lateral spin-valve (LSV) device with Co2FeAl0.5Si0.5 (8 nm)/Fe(0.7 nm)/n-Ge Schottky-tunnel contacts, which are adapted from Reference 62. The inset in the middle illustrates an LSV device in two-terminal MR measurements. (b) MR ratio (%) for LSV devices with Co2YZ/Fe/n-Ge (red, blue) and Co2YZ/n-Ge (gray) Schottky-tunnel contacts, together with theoretical curves with γ ~ 0.018 (gray-dashed curve), γ ~ 0.14 (red-solid curve), γ ~ 0.42 (blue-dashed curve), and γ ~ 0.75 (pink-dashed curve) based on Equations 1 and 2. The data in References 62, 66, and 100 are replotted.

Full size image

To overcome the issue of limitations due to high bias voltages, we focused on achieving a high-quality Co2YZ/Fe/Ge heterointerface, shown in Figures 3 and 5, for the Schottky-tunnel contacts in the LSV devices with n-Ge. Thanks to P δ-doping techniques,30,67 the RA value could be reduced to ~0.1 kΩ µm2 at room temperature.62,66,80 The bottom of Figure 6a shows a two-terminal local spin signal (∆RL = ∆VL/Ibias) as a function of By at Ibias = −1.0 mA at 296 K. As a reference, the corresponding ΔRNL as a function of By at I = −1.0 mA at 296 K is also shown at the top. Positive changes in ∆RL with hysteretic behavior are clearly observed even at room temperature.62,66 The blue curve at the bottom represents a minor loop with abrupt magnetization switching between parallel and antiparallel states, implying that the observed positive ∆RL is derived from conventional spin-dependent transport of electrons through the n-Ge layer. From these data for various LSV devices, we have roughly estimated the MR ratio to be 0.04–0.1% at room temperature.62,66 Notably, the data were obtained at low applied bias voltages (~0.12 V), leading to a decrease in the electric power required to ~0.12 mW, one order of magnitude lower than that (~1.15 mW) for Si-based LSV devices with MgO tunnel barriers.96 Although the MR ratio for Co2YZ/Fe/n-Ge LSV devices is higher than that for Si-based LSV devices,91,93,94,95,96 there is still a great gap between this and the MR values required for logic/memory applications with a spin-MOSFET.34 We discuss a strategy for achieving high-performance Ge-based LSV devices, together with experimental results and theoretical predictions in the following section.

Given the definition of the MR ratio as (∆RL/Rp) × 100, we should separately determine the values of ∆RL and Rp. In general, on the basis of the one-dimensional spin drift–diffusion model developed by Fert and Jaffrès,84 the magnitude of ∆RL and Rp in FM–SC–FM with double tunnel barriers has been expressed as follows.84,94,97,98,99

$$\Delta {R}_{\text{L}}= \frac{8{\upgamma }^{2}{r}_{\text{b}}^{2}{r}_{\text{SC}}}{{S}_{\text{SC}}\left[{\left({2r}_{\text{b}}+{r}_{\text{SC}}\right)}^{2}{\text{exp}}\left(\frac{d}{{\uplambda }_{\text{SC}}}\right)-{r}_{\text{SC}}^{2}\mathrm{exp}\left(-\frac{d}{{\uplambda }_{\text{SC}}}\right)\right]},$$
(1)
$${R}_{\text{p}}= \frac{1}{{S}_{\text{SC}}}\left[{r}_{\text{SC}}\frac{d}{{\uplambda }_{\text{SC}}}+2\left(1-{\upgamma }^{2}\right){r}_{\text{b}}+2\frac{{\upgamma }^{2}{r}_{\text{SC}}{r}_{\text{b}}{\text{tanh}}(\frac{d}{{2\uplambda }_{\text{SC}}})}{{r}_{\text{b}}+{r}_{\text{SC}}{\text{tanh}}(\frac{d}{{2\uplambda }_{\text{SC}}})}\right],$$
(2)

where γ is the spin polarization of the FM/SC interfaces, rb is the value of RA for the FM/SC contacts, SSC is the cross-sectional area of the SC spin-transport channel, and rSC (= ρSC × λSC) is the spin resistance of the SC layer. Here, for our Ge-based LSV devices, d (= 0.35−0.45 µm) and SSC (= 0.98 µm2) are device parameters, and ρSC is the channel resistivity (1.59 mΩ cm ≦ ρSC ≦ 2.16 mΩ cm). The RA values (0.1−0.4 kΩ µm2) were directly measured by a three-terminal method, as described in previous work.62 Since the value of λSC has already been estimated at 8 K (= 0.84 ± 0.07 µm)62,77 and 296 K (= 0.44 ± 0.02 µm),92 we can roughly estimate the value of rSC at each temperature.

Figure 6b shows plots of the MR ratio as a function of rb/rSC (= RA/ρSCλSC) for Co2YZ/n-Ge and Co2YZ/Fe/n-Ge LSV devices, and theoretical curves based on Equations 1 and 2. Here, the gray plots are data at 296 K for Co2FeAl/n-Ge LSV devices in Reference 100 and the red plots are examples for Co2MnSi/Fe/n-Ge (circles) at 297 K66 and for Co2FeAl0.5Si0.5/Fe/n-Ge (triangles) at 296 K.62 As references, we also show the data for Co2MnSi/Fe/n-Ge (circles) at 8 K and for Co2FeAl0.5Si0.5/Fe/n-Ge (triangles) at 8 K in blue. Furthermore, to discuss the present situation, we provide theoretical curves with γ ~ 0.018 (gray-dashed curve), γ ~ 0.14 (red-solid curve), γ ~ 0.42 (blue-dashed curve), and γ ~ 0.75 (pink-dashed curve) based on Equations 1 and 2. Comparison of experimental data and theoretical curves shows that the interface spin polarization γ is enhanced by an order of magnitude owing to the contribution from high-quality Co2YZ/Fe/Ge Schottky-tunnel contacts. Notably, the MR ratio can be enhanced up to ~1% at 8 K because of the increase in γ (~0.42). If a large γ (0.4–0.5) is demonstrated at room temperature, an MR ratio of more than 1% can be obtained even for LSV devices with n-Ge. Assuming γ ~ 0.75, the MR ratio can reach 10%. Thus, half-metallic Co2YZ is effective for obtaining sizable MR ratios in LSV devices with n-Ge. However, as with MTJs,7,8,9 the temperature dependence of the half-metallicity should be improved in Co2YZ/Fe/n-Ge Schottky-tunnel contacts.80,101

Even if we achieve γ ~ 0.9, the MR ratio could not reach a value greater than 100%, which is required to use a Ge-spin-MOSFET for spin-based logic/memory applications.34 In this case, the limitation of MR enhancement depends strongly on having a small value of λSC for n-Ge at room temperature. As previously mentioned, the present value of λSC for the n-Ge spin-transport channel used here is 0.84 ± 0.07 µm at 8 K77 and 0.44 ± 0.02 µm at room temperature.92 It should be emphasized that an increase in λSC to more than 2 µm at room temperature enables enhancement of the MR ratio of more than 100%. For n-Ge, intervalley spin-flip scattering of electrons between L valleys in the conduction band should be taken into account to increase λSC.51,74,75,76,77,78 Recently, impurity- and phonon-induced intervalley spin-flip scattering processes were partly suppressed by utilizing a strained n-Si0.1Ge0.9(111) layer,102,103 where the Ge-rich Si1−xGex exhibited a Ge-like electronic band structure with conduction-band minima at L points. In the future, researchers should explore the simultaneous utilization of high-quality Co2YZ/Fe/Ge Schottky-tunnel contacts with a large γ (≧ 0.8) and strained n-Ge-rich Si1−xGex channels with a large λSC (≧ 2.0 µm) at room temperature.

Conclusion

This article reviewed the progress of the GaAs- and Ge-based semiconductor spintronics with ferromagnetic Co2-Heusler compounds showing high spin polarization. The GaAs(001) and Ge(111) surface orientations have been utilized for epitaxial growth of Co2-Heusler films using low-temperature MBE. Experimental studies of electrical spin injection from Co2-Heusler contacts into GaAs and Ge through Schottky-tunnel barriers at room temperature have been reported, meaning that Co2-Heusler compounds are useful for realizing spin injection, transport, and detection in GaAs and Ge. However, to achieve highly efficient spin-transport properties, it is important to suppress the interfacial out-diffusion of GaAs or Ge into the Co2-Heusler layer near the heterojunctions. Recent progress in high-quality Co2-Heusler/Ge heterojunctions has demonstrated two-terminal magnetoresistance ratios of more than 0.1% at room temperature even for semiconductor spintronic device structures. This approach using Co2-Heusler compounds provides a powerful solution to the need for simultaneous achievement of highly efficient spin injection and low electric power at the source and drain contacts in semiconductor devices such as spin MOSFETs.