Direct-current voltages in (Ga,Mn)As structures induced by ferromagnetic resonance

Abstract

Spin pumping is the phenomenon that magnetization precession in a ferromagnetic layer under ferromagnetic resonance produces a pure spin current in an adjacent non-magnetic layer. The pure spin current is converted to a charge current by the spin–orbit interaction, and produces a d.c. voltage in the non-magnetic layer, which is called the inverse spin Hall effect. The combination of spin pumping and inverse spin Hall effect has been utilized to determine the spin Hall angle of the non-magnetic layer in various ferromagnetic/non-magnetic systems. Magnetization dynamics of ferromagnetic resonance also produces d.c. voltage in the ferromagnetic layer through galvanomagnetic effects. Here we show a method to separate voltages of different origins using (Ga,Mn)As/p-GaAs as a model system, where sizable galvanomagnetic effects are present. Neglecting the galvanomagnetic effects can lead to an overestimate of the spin Hall angle by factor of 8, indicating that separating the d.c. voltages of different origins is critical.

Introduction

The introduction of spin polarization to non-magnetic semiconductors is an important step for realizing novel spintronics devices¹. So far, various schemes have been demonstrated to generate and detect spin current in non-magnetic semiconductors, which include electrical and optical means^{2,3,4,5,6,7,8,9,10}. Spin pumping is known as a method to generate a pure spin current without a net flow of charge current in non-magnetic materials adjacent to a ferromagnetic layer under ferromagnetic resonance (FMR). When the FMR condition for the ferromagnetic layer is fulfilled, precession of magnetization creates excess spin-polarized carriers in the ferromagnetic layer due to damping caused by the exchange interaction between magnetic spins and carriers^11,12. The excess spin polarization of carriers in the ferromagnetic layer penetrates into the adjacent non-magnetic layer, which generates spin current in the vicinity of the interface but no charge current under zero bias. The pure spin current can be detected electrically as a d.c. electromotive force induced by the inverse spin Hall effect (ISHE), which converts spin current J_s to charge current J_c through the spin–orbit interaction: J_cθ_SHEJ_s × σ, where θ_SHE is the spin Hall angle and σ is the spin polarization unit vector^13,14. Thus, by measuring the d.c. electromotive force, one can determine the value of θ_SHE. Spin injection and detection based on spin pumping and the ISHE have been applied to a variety of material systems^{13,14,15,16,17,18,19,20,21,22,23}. Recent work showed that it may be a promising tool for the generation and investigation of spin current in semiconducting materials, such as Si (refs 16,17), Ge (refs 18,19) and GaAs with n-type as well as p-type conduction²⁰.

Magnetization dynamics under FMR also produces d.c. voltage in the ferromagnetic layer through galvanomagnetic effects, that is, anisotropic magnetoresistance and anomalous Hall effect (AHE)^24,25,26. These effects have often been neglected in the quantitative analyses on the observed d.c. voltage generated in a non-magnetic layer next to a ferromagnetic layer under FMR; the non-negligible contribution of these effects was pointed out only recently^22,23,27. It is known that a ferromagnetic (Ga,Mn)As, which can be grown seamlessly on GaAs²⁸, shows sizable galvanomagnetic effects^29,30, and thus we expect that (Ga,Mn)As/p-GaAs bilayer structure is a suitable system to investigate the d.c. voltage observed under FMR. In this work, we systematically investigate d.c. voltages generated in a p-GaAs layer beneath an epitaxially grown (Ga,Mn)As layer under FMR, which are measured as functions of the magnitude of external magnetic field, magnetic field direction, microwave power and temperature. The results are analyzed by a phenomenological transport model in combination with the Landau–Lifshits–Gilbert (LLG) equation, which shows that the observed d.c. voltage is induced by the ISHE in p-GaAs accompanied by spin pumping as well as transverse galvanomagnetic effects, that is, the planar Hall effect (PHE, which is the transverse component of anisotropic magnetoresistance, and not a genuine Hall effect in the strict sense) and AHE in (Ga,Mn)As. We show both the ISHE and PHE result in a symmetric lineshape of d.c. voltage in their magnetic field dependence, while AHE has an anti-symmetric lineshape. The analysis of the magnetic field angle dependence of d.c. voltages enables us to deduce the ratio of the d.c. voltage by the ISHE to that by the PHE, because the voltages brought about by the two effects have different angle dependence. This analysis shows that the magnitude of d.c. voltage induced by the ISHE is about eight times smaller than that by the PHE. The spin Hall angle of p-GaAs is determined to be 0.006 from the magnitude of d.c. voltage induced by the ISHE, which is also about eight times smaller than that obtained by neglecting the presence of the PHE, indicating the importance of separating the d.c. voltages of different origins.

Results

Sample

A bilayer structure studied here consists of a 20-nm Ga_0.935Mn_0.065As and a 20-nm p-GaAs on a semi-insulating GaAs (001) substrate with a 100-nm undoped GaAs buffer layer all grown epitaxially by molecular beam epitaxy (see Methods, we also grow a single (Ga,Mn)As for reference). The p-GaAs layer is Be-doped GaAs with hole concentration p of 9.5 × 10¹⁸ cm⁻³. We cleave the grown epitaxial wafer into a 1 × 3 mm² piece with a longer side along the [110] orientation. The top (Ga,Mn)As layer except for a central area with 1 × 2 mm² is etched away, and two In ohmic contacts are formed at the two ends of bare GaAs:Be surface by annealing at 250 °C for 30 min. This heat treatment increases the Curie temperature T_C of (Ga,Mn)As from 79 K to 118 K (ref. 31). The schematic of the sample is shown in Fig. 1a. We confirm that linear current–voltage characteristics between the ohmic contacts and (Ga,Mn)As/p-GaAs junction at reduced temperature T of 30 K. Figure 1b compares the temperature T dependence of magnetization M of (Ga,Mn)As on p-GaAs with that on undoped GaAs (reference sample) after the same heat treatment, in which one can see that both (Ga,Mn)As layers have virtually identical magnetic properties.

Figure 1: d.c. voltage measurements and temperature dependence of magnetization.

(a) Schematic of measurement configuration for d.c. voltage, which is measured simultaneously with FMR spectrum. The Cartesian coordinate systems used in analyses are also presented. (b) The temperature T dependence of in-plane magnetization for (Ga,Mn)As/p-GaAs (triangles) as well as (Ga,Mn)As/undoped GaAs (circles).

FMR spectra and d.c. voltages

The sample is mounted on a quartz sample rod and put in a TE₀₁₁ microwave cavity, in which a magnetic (electric) field of the microwave is maximized (minimized). Microwave with frequency f₀=9.0 GHz is introduced to the cavity in a cryostat. Twisted Cu wires are bonded to the ohmic contacts and are connected to a d.c. voltmeter. We measure FMR (microwave absorption) spectrum and d.c. voltage V between the two ohmic contacts simultaneously by sweeping the magnitude of an external magnetic field H. The ac modulation field H_ac (1 mT, 100 kHz) parallel to H is superimposed to obtain FMR spectrum in its derivative form. To measure the angle (θ_H between H and [001] orientation) dependence of spectra, the sample is rotated about [110] axis, while keeping the (110) plane parallel to H (Fig. 1a). The same measurements are done for (Ga,Mn)As/undoped GaAs reference sample with two In ohmic contacts at the two edges of the (Ga,Mn)As surface (Supplementary Fig. S1b).

Figure 2 shows a typical result of (a) FMR spectrum and (b) V curve (offset voltage V_offset is subtracted) under microwave power P=20 mW at T=30 K and θ_H=89^o. The V_offset is due to electromagnetic induction by the application of H_ac. One can see a characteristic V signal in the vicinity of ferromagnetic resonant field H_R. To describe the lineshapes of spectra, we introduce symmetric (L_sym=ΔH²/[4(H−H_R)²+ΔH²]) and anti-symmetric Lorentzian (L_a-sym=−4ΔH(H−H_R)/[4(H−H_R)²+ΔH²]), where H=|H| and ΔH is the linewidth (FWHM)^14,32. As shown by dashed lines in Fig. 2a, the FMR absorption spectrum (Fig. 2a) is fitted well by −(2I/πΔH)dL_sym/dH, where I is the absorption coefficient³³, and V−V_offset (Fig. 2b) is fitted well by the sum of V_symL_sym and V_a-symL_a-sym where V_sym and V_a-sym are the magnitudes of symmetric and anti-symmetric voltage components. The fits show that the FMR spectrum and two components (symmetric and anti-symmetric components) of the measured d.c. voltage have identical H_R as well as identical ΔH, indicating a strong correlation between FMR in (Ga,Mn)As and V in p-GaAs. Fig. 2c show FMR spectra and V curves as a function of θ_H measured at T=45 K and P=20 mW. The θ_H dependence of H_R and ΔH obtained from FMR spectra is summarized for (Ga,Mn)As/p-GaAs and (Ga,Mn)As/undoped GaAs in Fig. 2e, respectively. While H_R is identical for both samples, a larger ΔH for (Ga,Mn)As/p-GaAs is observed. This increase in ΔH is known to be caused by spin pumping, which produces additional damping by the diffusion of spin angular momentum into the adjacent layer¹¹. (The θ_H dependence of H_R and ΔH for (Ga,Mn)As/undoped GaAs can be explained well by conventional analyses, which are shown in Fig. 2e by solid lines^34,35,36, see Supplementary Note 1).

Figure 2: FMR spectra and d.c. voltages.

Typical spectrum of (a) FMR and (b) d.c. voltage V obtained at temperature T=30 K and magnetic field angle θ_H=89^o, where offset voltage V_offset is subtracted. Solid lines are experimental results and dashed lines are fitting. In panel b, symmetric and anti-symmetric components of fitting are also shown by dashed lines. The θ_H dependence of (c) FMR spectra and (d) V–V_offset obtained at T=45 K and microwave power P=20 mW. The θ_H dependence of (e) FMR resonant fields H_R and (f) linewidths ΔH of (Ga,Mn)As/p-GaAs (triangles) as well as (Ga,Mn)As/undoped GaAs (circles). Solid lines show the fitting results. arb. units, arbitrary units.

Microwave power dependence of d.c. voltages

Figure 3a shows V−V_offset as a function of P at 30 K, and at θ_H=89^o and −89^o, respectively. The signal shows an opposite polarity with opposite θ_H. The V_sym and V_a-sym obtained from the fit increase in proportion to P as shown in Fig. 3c, showing that the both components are related to FMR.

Figure 3: Microwave power dependence of d.c. voltages.

(a) Magnetic field angle θ_H=89^o and (b) θ_H=−89^o at temperature T=30 K. (c) Microwave power dependence of magnitudes of symmetric (V_sym, squares) and anti-symmetric (V_a-sym, circles) components of d.c. voltages for θ_H=−89^o and 89^o at 30 K.

Temperature dependence of d.c. voltages

Figure 4a shows the T dependence of V−V_offset measured under P=100 mW at θ_H=89^o. The ΔH increases above 80 K, which is consistent with previous FMR results on (Ga,Mn)As³⁷. The T dependence of V_sym and V_a-sym at various P from 20–100 mW is presented in Fig. 4b, respectively, in which the signals decrease to zero as T approaches T_C, showing that the signals are indeed related to the magnetization dynamics in (Ga,Mn)As. The temperature at which FMR signal disappears is in good agreement with T_C determined by magnetization measurements, indicating that heating caused by microwave absorption is negligible. By changing the measurement configuration, we rule out possible contribution from transverse thermoelectric effect (Nernst-Ettingshausen effect) to V in the present structure (Supplementary Note 5). The magnitude of V_sym shows a monotonic decrease with the increase of T, while that of V_a-sym does not, suggesting that the two signals have different origins.

Figure 4: Temperature dependence of d.c. voltages.

(a) Spectra obtained at microwave power P=100 mW and magnetic field angle θ_H=89^o as a function of temperature T. The T dependence of (b) symmetric d.c. voltage V_sym and (c) anti-symmetric d.c. voltage V_a-sym as a function of P ranging from 20–100 mW (black 100 mW, red 90 mW, green 80 mW, dark blue 70 mW, light blue 60 mW, pink 40 mW, olive green 20 mW).

Discussion

There are three possible origins of the observed d.c. voltage induced by magnetization dynamics; one is the ISHE¹⁴, and the other two are transverse galvanomagnetic effects, i.e., PHE and AHE³⁸. We use the LLG equation, dM/dt=−γ M × μ₀H_eff+(α/|M|)M × dM/dt, to describe the magnetization dynamics, where M is the magnetization vector, dM/dt its time derivative, γ the gyromagnetic ratio, μ₀ the permeability in vacuum and α the damping constant³⁹. The first and second terms in the LLG equation correspond to precessional and damping torques, respectively. We use a Cartesian coordinate system with x along [110] and z along the precession axis of M as shown in Fig. 1a, and thus M=(m_xe^iωt, m_ye^iωt, M_z), where ω is the angular frequency of precession. The effective magnetic field vector H_eff is the sum of an external magnetic field, magnetic anisotropy fields, their dynamical components, and microwave field h=$e^{i{\omega }_{0}t}$(h, 0, 0) with ω₀=2πf₀. By solving the LLG equation, one can calculate the H dependence of complex susceptibility χ as well as the real (Re) and imaginary (Im) parts of m_x and m_y: Re(m_x), Im(m_x), Re(m_y), and Im(m_y) (see Supplementary Notes 1, 2 and 3).

The ISHE signal V_ISHE in p-GaAs results from the pure spin current with spin polarization along in-plane z′ direction ([] orientation) generated by spin pumping, which flows perpendicular direction to the interface between (Ga,Mn)As and p-GaAs. Because the spin current induced by spin pumping is proportional to the damping term in the LLG equation, V_ISHE is expected to be proportional to the time averaged z′ projection of the damping term^11,40, V_ISHE(αω/M_z)[Im(m_x)Re(m_y)−Re(m_x)Im(m_y)]sinθ_M, where θ_M is the angle between M and [001] orientation (the overscore denotes the time average). When the sample size is finite, electric field ε of microwave along z′ direction (Fig. 1a) may generate the PHE and AHE signals (V_PHE and V_AHE) in (Ga,Mn)As. We obtain V_PHEεM_zRe(m_x)sinθ_M and V_AHEεM_zRe(m_y)sinθ_M, where x||x′. Figure 5 shows the calculated lineshapes and θ_H dependences of ISHE, PHE and AHE, which indicates that V_ISHE and V_PHE have symmetric lineshape, whereas V_AHE has anti-symmetric lineshape, and that the three signals have the same linewidth. Although it is hard to distinguish the ISHE from the PHE in each spectrum due to the same symmetry and linewidth, the difference in θ_H dependence (Fig. 5d) allows us to separate the components of the ISHE and PHE from V_sym.

Figure 5: Calculated lineshapes and magnetic field angle dependence of d.c. voltages.

In calculation, experimentally obtained parameters are utilized (Supplementary Note 1). (a–c) Lineshapes of d.c. voltages induced by the ISHE (V_ISHE), PHE (V_PHE) and AHE (V_AHE) under in-plane magnetic field. (d–f) Out-of-plane field angle θ_H dependences of V_ISHE, V_AHE and V_PHE, which are normalized by microwave absorption coefficient I. arb. units, arbitrary units.

In Fig. 6a, we show the θ_H dependence of normalized V_sym/I as well as the fit, which is sum of calculated V_ISHE/I and V_PHE/I curves, and the ratio of the two signals is adopted as a fitting parameter. The fitting reproduces the θ_H dependence of V_sym/I well, and shows that the contributions to V_sym from the ISHE and PHE are 11.8% and 88.2%, respectively. Figure 6b shows the θ_H dependence of normalized V_a-sym/I and the calculated AHE curve, which shows that the θ_H dependence of V_a-sym can be described well by V_AHE. Moreover, non-monotonic T dependence of V_a-sym in Fig. 4c supports that the origin of V_a-sym is the AHE, because similar non-monotonic T dependence of the anomalous Hall resistance is observed in d.c. transport measurements using a Hall bar. The observed comparable magnitudes of V_sym and V_a-sym in d.c. voltages (Figs 3c and 4b) agree with what we expect from the amplitudes of planar Hall and anomalous Hall resistances determined by d.c. transport measurements (Supplementary Note 4).

Figure 6: Angle dependence of d.c. voltage.

Open circles denote the d.c. voltage obtained at 45 K. Magnetic field angle θ_H dependence of (a) symmetric component V_sym and (b) anti-symmetric component V_a-sym of d.c. voltage, normalized by microwave absorption coefficient I. Dotted and dashed lines in panel a show the θ_H dependence of d.c. voltages induced by the inverse spin Hall effect V_ISHE/I and planar Hall effect V_PHE/I, where the ratio of the magnitudes of V_ISHE and V_PHE is adjusted to reproduce the experimental result. Solid line represents total contributions, V_ISHE/I+V_PHE/I. Solid line in b shows the θ_H dependence of d.c. voltage induced by the AHE V_AHE normalized by I. arb. units, arbitrary units.

From V_sym=15 μV at T=45 K and P=20 mW, V_ISHE is calculated to be 1.77 V. By using this value, the spin Hall angle of p-GaAs is obtained to be 0.006 (Supplementary Note 6). If the entire symmetric component (V_sym=15.0 μV) were treated as the ISHE signal, the spin Hall angle would have been θ_SHE=0.05, which is comparable with heavy metals (Liu et al.⁴¹ and references therein).

We also measure d.c. voltage of a 10-nm-thick permalloy (Py) film deposited on thermally oxidized Si substrate, which shows that Py also generates symmetric and anti-symmetric voltages induced by galvanomagnetic effects (not shown), although the magnitudes of them are sensitive to Ni-Fe composition (Py has large PHE and small AHE)⁴². As Py-based structures is one of the most investigated systems for spin pumping and ISHE^{14,16,17,18,20,21,22,23}, our approach used here is useful for systems other than the (Ga,Mn)As-based one.

In summary, we have demonstrated spin injection from (Ga,Mn)As into p-GaAs by means of spin pumping and its detection by the inverse spin Hall effect. While the PHE produces the same symmetric spectral lineshape as that of the inverse spin Hall effect, we have shown that the two can be separated by measuring the angle dependence of the signal. This allows us to determine the spin Hall angle of p-GaAs (p=9.5 × 10¹⁸ cm⁻³) as 0.006. The present study shows that one needs to take sufficient care to convert d.c. voltages to the inverse spin Hall effect and thus to the spin Hall angle of the non-magnetic layer, indicating the critical importance of separating the inverse spin Hall effect from galvanomagnetic effects.

Methods

Sample preparation

(Ga,Mn)As (20 nm, Mn composition x=0.065)/GaAs:Be (20 nm, hole concentration p=9.5 × 10¹⁸ cm⁻³) bilayer structure is grown on semi-insulating GaAs (001) substrate by molecular beam epitaxy through a GaAs (100 nm) buffer layer. The growth temperature is 560 ^oC for GaAs buffer and GaAs:Be and 250 °C for (Ga,Mn)As. During growth, V/III beam equivalent pressure ratio is kept at 8. The carrier concentration of GaAs:Be is calibrated by room-temperature Hall measurements on separately prepared 1-μm-thick GaAs:Be layers. The thickness of GaAs:Be (20 nm) is a few times thicker than a surface-depletion layer of p-GaAs with p~;10¹⁹ cm⁻³. The wafer is cleaved into a piece with lateral dimension of 1 × 3 mm² and then the two edge regions of top (Ga,Mn)As are removed by wet etching to pattern 1 × 2 mm² rectangular (Ga,Mn)As mesa. The etching depth is ~;25 nm, which is confirmed by atomic force microscopy. The samples is annealed at 250 ^°C for 30 min in air, to form two In ohmic contacts on exposed surface of GaAs:Be. A reference sample without GaAs:Be layer is also prepared by virtually identical growth and annealing conditions.