Understanding the interplay between spin and heat is a fundamental and intriguing subject. Here we report thermal spin injection and accumulation in CoFe/MgO/n-type Ge contacts with an asymmetry of tunnel spin polarization. Using local heating of electrodes by laser beam or electrical current, the thermally-induced spin accumulation is observed for both polarities of the temperature gradient across the tunnel contact. We observe that the magnitude of thermally injected spin signal scales linearly with the power of local heating of electrodes and its sign is reversed as we invert the temperature gradient. A large Hanle magnetothermopower (HMTP) of about 7.0% and the Seebeck spin tunneling coefficient of larger than 0.74 meV K−1 are obtained at room temperature.
The tremendous power consumption and accompanying heat generation in current electronic devices requires alternative technologies to provide a solution for the energy issues and to realize the energy efficient electronics. Spintronics is a viable route for it, using the spin degree of freedom in addition to the conventional charge transport1. Recently another important ingredient, namely heat, appears on the stage. It has been reported that the temperature gradient and heat flow in ferromagnetic structures gives rise to a variety of spin related phenomena2. Understanding the interplay between heat and spin transport is a fundamental and intriguing subject but also offers unique possibilities for emerging electronics based on the combination of thermoelectrics and spintronics.
Especially in SC-based spintronics, the functional use of heat provides a new route to inject and control of spin in semiconductors (SCs)3. The generation of non-equilibrium spin populations (i.e. spin accumulation) in non-magnetic SC is a central issue of SC-based spintronics1,3,4,5. Significant progress has been made on the spin accumulation in various SC systems by means of circularly polarized light4,6, spin-polarized tunneling7,8,9,10,11,12,13, hot-electron spin filtering14,15, spin-orbit interaction16,17, or magnetization dynamics18,19.
Intriguingly, Le Breton et al.20 have reported a rather different mechanism for the spin accumulation, in which temperature difference across a ferromagnet (FM)/oxide/SC tunnel contact can induce the spin accumulation () in SC via Seebeck spin tunneling (SST). It was found that the SST effect, involving thermal transfer of spin angular momentum from FM to SC without a tunneling charge current, is a purely interface-related phenomenon of the tunnel contact and governed by the energy dependence of its tunnel spin polarization (TSP)20. This provides a conceptually new mechanism for the generation of in SC as well as for the functional use of heat in spintronic devices20. The SST and thermal spin accumulation () in p-type SC (e.g., p-type Si) have been intensely studied, using a Ni80Fe20/Al2O3/SiO2/p-SC contact with the asymmetry in TSP of tunneling holes20. However, the counterpart of n-type SC still needs to be explored21.
Here we report the thermal spin injection and accumulation in n-type Ge by employing CoFe/MgO/Ge contacts with the asymmetry in TSP of tunneling electrons. The Joule heating of Ge by electrical current or local heating of CoFe electrode by a laser beam gives rise to a temperature gradient across the tunnel contact and a consequent thermal spin injection into Ge. The thermally-induced spin accumulation was detected by means of the Hanle effect. The sign and magnitude of Hanle signals are analyzed using spin-dependent tunneling theory.
Principle of the approach
Figures 1a and 1b illustrate the thermal spin injection and accumulation process in a FM/oxide/SC tunnel contact for the case that the temperature of SC () is higher than the temperature of FM ()20. The temperature difference results in the unequal electron distributions in the FM and SC; the hot SC has a relatively larger number of filled (empty) states above (below) the Fermi-level (EF) than those of the cold FM (see Fig. 1b). Consequently, the electrons above EF mainly tunnel from the SC into FM (forward tunneling, indicated as (i) in Figs. 1a and 1b) and the electrons below EF flow in the opposite direction (reverse tunneling, indicated as (ii) in Figs. 1a and 1b). The important feature of the SST process is that the numbers of electrons tunneling in the opposite direction are the same and there is no net charge current. Nevertheless, if the energy dependence of TSP are different for the forward and reverse tunneling (in other words, the Seebeck tunnel coefficient for majority and minority spin electrons are different), a spin accumulation (or ) can be induced in the SC20. Obviously, the sign of can be reversed when the temperate gradient is inverted; the cold SC has a relatively smaller number of filled (empty) states above (below) the Fermi-level (EF) than those of the hot FM.
Figure 1c shows the device geometry and measurement scheme used in the present study. We fabricated a symmetric device consisting of three epitaxial CoFe(5 nm)/MgO(2 nm)/n-Ge tunnel contacts (a–c,) where the n-Ge channel is composed of a heavily P-doped surface layer ( at 300 K) and a moderately Sb-doped substrate ( at 300 K). These contacts are separated by about from each other, which is much longer than the spin diffusion length. The magnetic easy axis of the CoFe contacts are along the  direction of Ge in parallel to the long axes of the contacts. Details of the structural and electrical characterizations can be found elsewhere22,23.
To effectively generate the temperature difference () in the tunnel contact a, we used two different heating methods. For the SC heating (top panel of Fig. 1c), we applied a heating current (Iheating) through the SC channel using two contacts b and c, which causes Joule heating and raises TGe with respect to TCoFe (). For the FM heating (bottom panel of Fig. 1c), the Au bond pad was heated using a laser beam with a wavelength of 532 nm and a maximum power of 200 mW (note that the results obtained with the Joule heating of FM are shown in the Supplementary Information Note I). The laser beam spot (with a diameter of 5–10 μm and a skin depth of ~3 nm) on the 100 nm-thick Au pad is located at around 300 μm from the one edge of the tunnel contact. The size of the Au pad is large enough to prevent the direct illumination of the Ge layer. A part of heat generated from the laser beam passes through the contact, resulting in ().
In an open-circuit geometry, where the tunneling charge current (Itunnel) is zero, the measured voltage between the contact a and d is given by 20. The first term is the thermovoltage maintaining zero net charge current (Itunnel = 0) and the second term is the SST voltage due to the induced in the SC. The can be detected by means of the Hanle effect24,25. When we apply magnetic fields (Bz) transverse to the spins in the SC, the is suppressed via spin precession. This results in a voltage change (), directly proportional to , with a Lorentzian line shape as a function of the Bz. These two measurement schemes (Fig. 1c) using the Hanle effect24,25 provide a concrete means of demonstrating the SST and resultant in the SC.
Energy dependence of tunnel spin polarization in the CoFe/MgO/n-Ge contact
Before conducting the thermal spin injection experiments, we have estimated the form of TSP as a function of E, which determine the sign and magnitude of induced , using the conventional three-terminal Hanle (TTH) measurement7,20,26. Instead of applying Iheating, a non-zero Itunnel (or Iac) is applied across the contact a and c of the CoFe/MgO/n-Ge contact while the V is measured using the contact a and d in an applied magnetic field (see Fig. 1c).
Figure 2a shows the results obtained from the TTH measurements (up to 4 kOe) under perpendicular (Bz, closed circles) and in-plane (Bx, open circles) magnetic fields at RT. Clear electrical Hanle signals () with a Lorentzian line shape are detected at RT. It should be noted that the full spin accumulation () consists of the inverted Hanle signal () in Bx and the normal Hanle signal () in Bz27,28. As shown in Figs. 2a and 2b, the electrical Hanle signals () are significantly asymmetric with respect to the bias polarity, which is consistent with the previous work23. Both the and increase linearly with increasing the reverse bias current (, electron spin injection), but change slightly with increasing the forward bias current (, electron spin extraction). This asymmetry can also be seen in the middle panel of Fig. 2c, where the spin-RA products () is plotted as a function of the electrical voltage (). It should be mentioned here that the obtained spin-RA value () is several orders of magnitude larger than the expected value from the existing spin injection and diffusion theory5. This discrepancy between experiment and theory in the TTH measurement has been consistently observed with many types of tunnel barrier and SC, as discussed in the Ref. 3. The origins of this discrepancy, other enhancement factors not yet incorporated in the existing theory, are still under investigation29.
According to the spin injection and diffusion theory5, the is proportional to at a given temperature (T), which depends on Vel (note that, although the existing theory does not provide the quantitative agreement with the experiment, it provides the qualitative description of the TSP2 variation with E). Here, the is the TSP corresponding to the detection of induced spin accumulation at the Ge interface, the is the TSP of the injected/extracted electrons and the is the spin lifetime. Using the values (Fig. 2c) and effective values (not shown) extracted from the Lorentzian fit (black line in Fig. 2a), we plotted the TSP2 ( normalized) vs. in Fig. 2d. With the assumption of , the variation of TSP () with E is then obtained as for (gray line in Fig. 2d) and for (black line in Fig. 2d). The estimated profile of TSP vs. E is indeed similar to the schematically illustrated one on the middle panel of Fig. 1b. This asymmetry in the TSP of CoFe/MgO/n-Ge contacts is essential to induce the large in Ge via the SST20.
Detection of thermal spin accumulation in Ge
The SST and resultant in Ge were detected in the measurement geometry shown in the top panel of Fig. 1c. While heating the Ge side () as described above, the voltage change () is measured as a function of the applied magnetic field ().
As shown the plots in Figs. 3a and 3b, significant normal Hanle signals () with the Lorentzian line shape similar to that of (see Fig. 2a) were observed at 300 K. The inverted Hanle signals ()27,28 in (Figs. 3c and 3d), roughly half the magnitude of the , were also clearly measured.
The magnitude of thermal Hanle signals () as a function of the Iheating (up to ) is summarized in Figs. 3e–3h. In these figures, we can clearly see that the and also scale quadratically with the Iheating and scale linearly with the heating power density (Pheating). The Pheating is proportional to , where the is the resistance of the Ge heating layer and the is its volume. These results strongly support that the observed signals mainly come from the thermally driven spin accumulation, which scales linearly with the 20,30, in Ge.
The sign of has been determined by a direct comparison with that of obtained from the TTH measurements for the same tunnel contact a20. The sign of is negative for negative (, electron spin injection) and positive for positive (, electron spin extraction) in Figs. 2(a) and (b). The in Figs. 3a and 3b has the same sign with the former (), which means that the produced by the thermal spin injection has the same sign as the induced by the electrical spin injection. Given the positive TSP of epitaxial bcc FM/MgO(001) tunnel interfaces31,32, the induced by the SST for corresponds to the majority spin accumulation () in the Ge. This is in agreement with the expected from the SST mechanism20: when the TSP of FM/oxide/SC contacts (with positive sign) is constant below EF but decay above EF, as shown in Figs. 1b and 2d, majority spins accumulate in the SC () for (see Figs. 1a and 1b). We have calculated that the induced is ()0.26 meV with the maximum Pheating (667 nW μm−3) from 3,5,20, using the measured of (–)0.09 mV and the assumed TSP (γ) of (+)0.7 for the epitaxial CoFe/MgO tunnel interface31,32. This value should be considered as a lower limit for the , since we used the highest value of TSP. The SST theory20 based on the free-electron model predicts the value of ~10 μeV for the ΔT of ~1 K. Considering the possible range of ΔT across the tunnel contact is from 0.15 mK to 350 mK (see the Supplementary Information Note II), the obtained signal is at least one order of magnitude larger than the predicted value, which was also observed in the Ni80Fe20/Al2O3/SiO2/p-Si contact20. It is probably due to the limitation of the free-election model, the lack of detailed information about the energy dependence of TSP near the EF and the ignorance of inelastic (magnon-assisted) spin tunneling20.
It should be mentioned that our system requires about 100 times larger Pheating to obtain a similar magnitude of compared to the silicon-on-insulator (SOI) wafer based system20. This is mainly attributed to the different device structure. In our device structure, the across the tunnel contact is small because a large part of the Joule heat produced in the heavily-doped Ge layer can flow away to the substrate. The calculated heat flow ratio () across the tunnel barrier in our device is more than one order of magnitude smaller than that in the SOI wafer based device20 (see the Supplementary Information Note II).
Sign reversal of thermal spin signal by reversing the temperature difference
Another important feature of SST and is that the sign of the thermal spin signal is reversed when ΔT is reversed. To demonstrate this, we employed a laser beam for heating the FM instead of the Joule heating method. This approach allows us to heat the FM () effectively and exclude the contribution of spurious effects such as the current-in-plane (CIP) tunneling and anisotropic magnetoresistance (AMR) on the Hanle signal (see the Supplementary Information Note I).
Figures 4a and 4b show the obtained thermal spin signals as a function of perpendicular (Bz, Fig. 4a) and in-plane (Bx, Fig. 4b) magnetic fields with varying the laser power density (Plaser) at RT (). It should be noticed that we used the same contact a (see Fig. 1c) in both cases of the SC and FM heating. Clear normal and inverted Hanle signals are observed and the amplitudes of both Hanle signals are gradually increased with increasing the Plaser. As shown in the plots (Figs. 4c and 4d), the obtained Hanle signals ( and ) scale almost linearly with the Plaser, indicating that the obtained signal is from the thermal spin injection and accumulation in Ge.
We can see that the sign of is apparently reversed with respect to the SC heating case: the () is positive (negative) for (see Figs. 4c and 4d) whereas it is negative (positive) for (see Figs. 3g and 3h). This result clearly demonstrates another key feature of the SST and that the thermal spin signal reversed when is reversed.
In addition, this sign of the Hanle signal allows us to exclude other possible origins for the spin signal, for example, due to the spin-polarized hot-electron injection and conventional Seebeck effect, in the laser-heating experiment. The thermal excitation by the laser heating can result in a current flow in the Au pad and FM layer. Nevertheless, this electrical current cannot be an origin of the observed Hanle signal, since the sign of the observed (positive sign, see Fig. 4a) for the FM heating (TCoFe > TGe) by the laser beam is opposite to that (negative sign) expected by the injection of spin-polarized hot-electron current into the Ge (see the bottom panel of Fig. 2a). This strongly suggests that the observed Hanle signal does not come from the electrical current in the injector.
For a quantitative analysis, we have calculated the Hanle magnetothermopower (HMTP) (or Hanle magneto-Seebeck ratio ())30 defined as the relative change of charge Seebeck coefficient () due to spin accumulation as follows:
where is the electrical tunnel conductance, is the thermoelectric tunnel conductance, is the charge thermopower at zero and is the SST coefficient. Figure 5a shows the calculated HMTP (or ) as a function of the Plaser. The HMTP value of is and remains almost constant with varying the Plaser. It is important to note that these values are ~70 times larger than the maximum value (~0.1%) of Hanle magnetoresistance (HMR), defined as , obtained by the electrical spin injection using the same contact a (see Fig. 2). This experimental result supports the theoretical proposition30 that the thermal spin injection is more efficient than the electrical spin injection for the tunnel contacts with the strong asymmetry in TSP and the moderate thermal interface resistance.
To estimate the value of , defined as 30, the information of across the CoFe/MgO/Ge tunnel contact is required. We carried out the combined analyses using the one-dimensional (1-D) heat flow model20 and simulation using a commercial finite element software (COVERTOR) to determine (see the Supplementary Information Note II). Both the 1-D heat flow model and commercial finite element simulation provide a similar magnitude of ΔT.
Figures 5b and 5c show the representative results of the simulated temperature distribution in a two-dimensional (2-D) cross-section and temperature line-scan cross the tunnel contact when heating the Ge with the maximum of 667 nW μm−3. Here we used a reasonable value of 0.04 W m−1 K−1 (or a of 2×107 W m−2 K−1) for the 2 nm-thick MgO barrier. The possible range of ΔT across the tunnel contact is from 0.15 mK to 350 mK and a reasonable ΔT is an order of 10 mK (see the Supplementary Information Note II for the detailed discussion). Using and ΔT = 10 mK, the value is estimated to be 26 meV K−1 for the CoFe/MgO/n-Ge contact. If we use the largest ΔT of 350 mK, the goes down to 0.74 meV K−1. These values are comparable to those of the Ni80Fe20/Al2O3/SiO2/p-Si contact20 but they are at least two orders of magnitude lager than the spin Seebeck coefficient (−3.8 μV K−1) of the Co/Cu metallic system33, which may be attributed to the different spin injection/detection efficiency and the different measurement scheme.
In conclusion, we have observed the thermal spin injection and accumulation in CoFe/MgO/n-type Ge contacts using local heating of electrodes by laser beam or electrical current. We demonstrate that the magnitude of thermally injected spin signal scales linearly with the power of local heating of electrodes and its sign is reversed as we invert the temperature gradient. Based on the Seebeck spin tunneling theory, we have obtained a large Hanle magnetothermopower (HMTP) of about 7.0% and the Seebeck spin tunneling coefficient of larger than 0.74 meV K−1 in the CoFe/MgO/n-Ge contact at room temperature. This is attributed to the strong asymmetry in the TSP of the contact. Our experimental results demonstrate that the thermal spin injection is an efficient way of spin injection in SC.
The single crystalline CoFe(5 nm)/MgO(2 nm)/n-Ge(001) tunnel structures were prepared by molecular beam epitaxy (MBE) system with a base pressure better than 2×10−10 torr. Prior to the deposition of CoFe/MgO layers, the composite n-Ge consisting of a heavily P-doped surface layer ( at 300 K) and a moderately Sb-doped substrate ( at 300 K) was formed by ion implantation technique. All layers were deposited by e-beam evaporation with a working pressure better than 2×10−9 torr. The MgO and CoFe layers were grown at 125°C and RT, respectively and then the samples were subsequently annealed in-situ for 30 min at 300°C below 2×10−9 torr to improve the surface morphology and crystalllinity. Finally, the samples were capped by a 2 nm thick Cr layer at RT to prevent oxidation of the sample. The symmetric device (Fig. 1c) consisting of three tunnel contacts with lateral sizes of 100×300/100×300/100×300 μm2 was prepared by using micro-fabrication techniques (e.g., photo-lithography and Ar-ion beam etching) for the thermal spin accumulation experiments. For the electrical isolation at the sides of the tunnel contacts, about 120 nm-thick Ta2O5(115 nm)/Al2O3(2 nm) layers were grown by sputtering technique. For the contact pads, 110 nm-thick Au(100 nm)/Ti(10 nm) layers were deposited.
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This work was supported by the DGIST R&D Program of the Ministry of Education, Science and Technology of Korea (11-IT-01); by the KIST institutional program (2E22732 and 2V02720) and by the Pioneer Research Center Program (2011-0027905); and by the KBSI grant no.T32517 for S-YP.
The authors declare no competing financial interests.
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Jeon, KR., Min, BC., Park, SY. et al. Thermal spin injection and accumulation in CoFe/MgO/n-type Ge contacts. Sci Rep 2, 962 (2012). https://doi.org/10.1038/srep00962
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