Room-temperature spin injection from a ferromagnetic semiconductor

Spin injection using ferromagnetic semiconductors at room temperature is a building block for the realization of spin-functional semiconductor devices. Nevertheless, this has been very challenging due to the lack of reliable room-temperature ferromagnetism in well-known group IV and III-V based semiconductors. Here, we demonstrate room-temperature spin injection by using spin pumping in a BiSb/(Ga,Fe)Sb heterostructure, where (Ga,Fe)Sb is a ferromagnetic semiconductor (FMS) with high Curie temperature (TC) and BiSb is a topological insulator (TI). Despite the very small magnetization of (Ga,Fe)Sb at room temperature (45 emu/cc), we detected spin injection from (Ga,Fe)Sb by utilizing the large inverse spin Hall effect (ISHE) in BiSb. Our study provides the first demonstration of spin injection at room temperature from a FMS.

[(Ga,Fe)Sb (50 nm)], respectively, measured at 5 K with a perpendicular magnetic field of 0.2 T, 0.5 T, and 1 T, normalized by the intensity of the E1 peak at 1 T. As shown in Figs. S1(a) and (b), the MCD spectra have the E1 peak around ~ 2.4 eV, reflecting the band structure of zinc-blende (Ga,Fe)Sb in both samples. In Figs. S1(a) and (b), normalized MCD spectra which were measured at various magnetic fields are overlapped on one spectrum, indicating that the ferromagnetism in (Ga,Fe)Sb comes from a single phase, that is the zinc-blende (Ga,Fe)Sb.
Also, Figs. S1(c) and (d) show the magnetic-field (0H) dependence of the MCD intensity at E1 of both the samples, which show clear hysteresis even at room temperature. Thus, the ferromagnetism and the related magnetic properties are maintained in the (Ga,Fe)Sb before and after depositing BiSb without destroying the intrinsic ferromagnetism of zinc-blende (Ga,Fe)Sb. We note that the coercive force of the BiSb/(Ga,Fe)Sb (sample A) is smaller than that of the (Ga,Fe)Sb (sample B) at 5 K, probably due to over-etching of the cap layer before depositing the BiSb layer. The coercive force is caused by domain wall pinning at crystal defects, such as defects at the cap layer/(Ga,Fe)Sb interface. By slightly over-etching the cap layer, such defects may be removed and the coercive force of (Ga,Fe)Sb in sample A became smaller.
S-3 Figure S1. (a) and (b) MCD spectra of the (a) BiSb (7nm) / (Ga,Fe)Sb (50 nm) heterostructure (sample A) and (b) (Ga,Fe)Sb (50 nm) reference (sample B) at 5 K with a magnetic field of 0.2 T, 0.5 T, and 1 T applied perpendicular to the film plane. The MCD spectra measured at 0.2 T and 0.5 T are normalized to that at 1 T by the intensity of the E1 peak. (c) and ( indicating that the ferromagnetism of (Ga,Fe)Sb did not change before and after depositing BiSb. From Fig. S2, the estimated saturation magnetization 0MS is 0.056 ± 0.002 T. We used this 0MS value for the estimation of spin current and magnetic anisotropy.   Fig. S4(a).

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Next, we have used the fitting equations which were derived from the Smith-Beljers relation S1  ( Here, 0 is the vacuum permeability, ω = 2f is the angular frequency of magnetization precession where f is the microwave frequency, γ = gµB/ħ is the gyromagnetic ratio where g is the Landé g-factor, µB is the Bohr magneton, and ħ is the reduced Planck constant. 0HR, 0H2⊥, 0H2//, and 0MS are the resonance field, perpendicular uniaxial magnetic anisotropy, in-plane uniaxial magnetic anisotropy, and saturation magnetization, respectively. H and M are the out-  S4 (b)]. M and M are given by: S-7 Using 0MS (= 0.056 ± 0.002 T), which was obtained from the SQUID result, together with 0H2⊥, 0H2// and γ values, we reproduced the experimental angular dependence of FMR fields very well, as shown in Fig. S4 (c) and (d). The estimated values of 0H2⊥ and 0H2// are 0.026 ± 0.002 T and 0.004 ± 0.002 T, respectively; and γ(= gµB/ħ) after substituting g = 2.09 ± 0.03 is (1.84 ± 0.02)  10 11 (T -1 s -1 ).

Spin pumping measurement
In spin pumping experiments, we used a JEOL electron spin resonance (ESR) spectrometer whose cavity resonates in the transverse electric (TE011) mode with a microwave frequency f of 9.14 GHz (X-band). We cut the samples into a 3 × 1 mm 2 piece with edges along 0H is superimposed to obtain the FMR spectrum in its derivative form. The voltage between the indium contacts is detected by a nano-voltmeter. We have measured the FMR signal and the voltage signal V between the indium contacts simultaneously by sweeping the magnitude of H. When the FMR condition is satisfied, a pure spin current with the spin polarization parallel to the magnetization precession axis in the (Ga,Fe)Sb layer is injected into the BiSb layer by spin pumping. This injected spin current is converted to a charge current by ISHE, which generates a voltage signal between the edges in the BiSb layer. As discussed in the main manuscript, this voltage signal sometimes contains galvanomagnetic effects, which is originated due to the shift in the sample alignment from the center position inside the cavity.
As a result, the microwave electric field produces galvanomagnetic effects. These galvanomagnetic effects can be separated from the inverse spin Hall effect (ISHE) signal by S-9 decomposing the voltage signals into symmetric and asymmetric components using Eq. (1) (110) plane. l is the distance between the two gold wires connected to the indium contacts.
Next in order to detect the spin current from the (Ga,Fe)Sb layer using spin pumping, we first tried to use heavy metal such as Pt with spin Hall angle (SHA) = 0.056 S3 , as a spin detector of (Ga,Fe)Sb. We grew a 10 nm-thick Pt layer by sputtering over a 50 nm-thick S-10 (Ga,Fe)Sb film grown by molecular beam epitaxy. Figure S6 shows

BixSb1-x thin films with metallic surface states and insulting bulk states
To characterize the properties of Bi1-xSbx, we have grown Bi1-xSbx thin films on semiinsulating GaAs(111)A substrates by molecular beam epitaxy (MBE). The growth procedure is as follows: After desorption of the surface oxide layer of the GaAs (111) S5. Note the metallic behavior in the 10 nm-thick Bi0.93Sb0.07 (see Fig. S7(a)), and 10 nm-thick Bi0.89Sb0.11 (see Fig. S7(c)) thin films. These results indicate that surface-state transport becomes dominant in BiSb when the film thickness is less than 10 nm. In section 6, we show how we estimate the contribution of the surface-state transport.

Estimation of surface-state contribution
We estimate the band gap Eg of Bi1-xSbx thin films from the temperature dependence of the resistivity, using the surface and bulk parallel conduction model S5 . Here, the total includes the semiconducting bulk conductance  We observed similar behavior for sputtered BiSb thin films, and confirmed that the surface conduction is dominant at t ≤ 10 nm S7 . Figure S9 shows the conductivity BiSb of sputtered BiSb thin films, grown on a Sapphire substrate, as a function of the BiSb thickness t from 28 nm to 4 nm measured at 300 K. For 28 nm  t  7 nm, the conductivity keeps increasing as t decreases, consistent with the dominant surface conduction. Below 7 nm (t < 7 nm), the conductivity abruptly decreases; we believe that this is due to the quantum interference of the top and bottom surface. This quantum interference leads to band gap opening of the surface states S8 . The surface states become less metallic and slightly semiconducting with a small band gap, thus the conductivity decreases. Because the band gap opening is not suitable for our purpose of measuring the inverse spin Hall effect coming from the topological surface states, we have chosen the thickness of 7 nm, where the surface conduction is maximum and thus the conductivity is maximum.
Next, the surface conductance Gs can be obtained by The contribution of the surface states to the total conductivity at room temperature is then given by = S ~ 97% for the 7 nm-thick Bi0.85Sb0.15 thin film (estimated in Sec 7).

Surface state conduction in the 7-nm-thick BiSb layer (this work)
To show that the surface conductance is dominant in our BiSb layer, we demonstrate the same conductance of two layers of BiSb grown on the same substrate [semi-insulating (SI) GaAs (001) substrates] in two different samples. By fitting our model described in Sec 6, to the measured transport data of the BiSb layers of different samples, we show that surface state conduction is dominant in our 7-nm-thick BiSb layer. Next, we measured the temperature dependence of electrical conductivity (T) of the S-18 BiSb layer in sample A [BiSb/(Ga,Fe)Sb] and sample C [BiSb/GaAs]. Because Bi and Sb both belong to the same group-V elements, BiSb is free from doping effects due to off-stoichiometry issues and unintentional enhancement of conductivity is unlikely. Thus, the surface conductivity and bulk conductivity can be modeled using the surface and bulk parallel conduction model S5 (see Sec 6). Figure S11 shows the measured temperature dependence of the normalized resistivity /  300K , where  is the resistivity at different temperatures and  300K is the resistivity at room temperature of the 7-nm-thick BiSb layer in sample C [BiSb/GaAs] and the whole layers [BiSb(7nm)/ GaFeSb(50nm)/ AlSb(100nm)/ AlAs(10nm)/ GaAs (50nm) conductivity of the BiSb layers (we will show this later by using Eq. (S5)). Moreover, the estimated value of the BiSb conductivity in our work is also in agreement with that (~ 2  10 5  -1 m -1 ) in ref S7.
Next, we determine the surface state contribution to the total conductivity, , of the BiSb layer, defined by using the following equation where ISurface and IBulk are the currents flowing in the surface states and the bulk states, respectively. We found that  is ~ 97% for both samples. Moreover, the experimental data S-19 and estimated  values in this study also agree with the results in Sec 6 ( Fig. S8(a)), which showed temperature dependence of the / 300K of BiSb films with various thicknesses (t = 10 nm, 41 nm, and 92 nm). As shown in Sec 6 that Γ rapidly increases with decreasing the BiSb thickness and reaches nearly 90% for the samples thinner than 20 nm. This means that the topological surface state conduction in BiSb becomes dominant when the BiSb thickness t ≤ 10 nm. We note that both the bulk and surface states are 2D in nature. Therefore, the "bulk" term in this work means trivial QW states (i.e. quantized bulk states). Because of the strong quantum size effect in BiSb, the "bulk" band gap (the energy separation between the first level of the trivial QW electron state and hole state) increases up to about 200 meV at t = 10 nm from our transport measurement S7 . Also, very recently, Xing et al. S9 successfully showed that BiSb is a topological insulator by observing quantum well states by scanning tunneling microscopy (STM) and detected a clear bandgap ~ 0.39 eV (much larger than the 20 meV for bulk BiSb) for 5.5-nm-thick BiSb, which is explained by the quantum confinement effect S5 . Furthermore, they found that the Fermi level lies in the bandgap of BiSb. Since we are using 7-nm-thick BiSb with Γ = ~97%, nearly all the current flows in the surface states of BiSb at room temperature.
These results verify our conclusion that almost all the electrical transport occurs in the topological surface states of BiSb. S-20