Fabrication and characterization of Cr-PBA/Cr bilayers

Figure 1a shows the schematic illustration of an STE coating over a wide area and the electrical energy harvesting from the thermally excited magnons. Here, the vertical temperature gradient (∇T_z) generates vertical propagation of magnons in a magnetic insulator, which induces thermally pumped spin angular moments at the interface. Then, the transferred vertical spin flow will be converted into a longitudinal charge current via ISHE, J_LSSE ∝ J_s × σ (J_s and σ denote a thermally generated spin current vector and a spin polarization vector of electron, respectively). Figure 1b displays a schematic experimental set-up for ECD of the Cr-PBA film on a Cr metal. We employed a Cr thin film (10 nm) as a working electrode because it could provide relatively high spin–charge conversion, as evidenced in various literatures^24,25. Heavy metals, such as Pt and Pd, are not appropriate for the working electrode due to a catalytic effect during the deposition. The Cr-PBA films are deposited through the reaction between [Cr(CN)₆]³⁻ and labile Cr²⁺ in the aqueous solution of K₃Cr(CN)₆ and CrCl₃·H₂O. A cross-sectional transmission electron microscope image of the developed Cr-PBA/Cr heterojunction is shown in Fig. 1c displaying a sharp interface. Further details of material preparation and characterization are described in “Methods” and Supplementary Note 1. Cyclic voltammetry curves for the observation of reductive reaction are shown in Supplementary Fig. 1. Cr-PBA has a structure consisting of interpenetrating face-centered cubic sublattices with ferrimagnetic spin alignments between Cr²⁺ (S = 2) and Cr³⁺ (S = 3/2) (Fig. 1d). X-ray diffraction spectra of Cr-PBA films are displayed in Fig. 1e. Results confirm a face-centered cubic phase of Cr-PBA with main peaks 24.2° (220), 34.5° (400), 38.7° (420), and 52.8° (600)²⁶. The surface morphology of a Cr-PBA film probed by atomic force microscopy (AFM) is displayed in Supplementary Fig. 2. The magnetic hysteresis of the developed Cr-PBA film exhibits a coercivity of ~0.25 mT for in-plane applied magnetic field at 100 K (Fig. 1f). The Curie temperature of the developed Cr-PBA determined by Arrott plot method was T_c ~ 230 K (see Supplementary Fig. 3). Supplementary Fig. 4 displays a magnetization versus T^3/2 plot exhibiting a good linearity following the Bloch T^3/2 law. Fitting with M(T) = M₀(1 − aT^3/2) provides the value of slope a ~ 2.6 × 10⁻⁴ K^−3/2. This value of the slope is much higher than those observed in Ni (7.5 × 10⁻⁶ K^−3/2)²⁷ and YIG (5.8 × 10⁻⁵ K^−3/2)²⁸. Thus, the excitations of magnons with low wave vectors would be more effective in our Cr-PBA film.

STE characterization of Cr-PBA/Cr hybrid heterostructures

For the characterization of spin thermoelectricity of the developed heterojunction devices, a heat gradient was applied by Joule heating from an Au line on top of the device as shown in Fig. 2a. The on-chip Au line was also simultaneously used as a temperature sensor^11,23. An electrical insulation between the top Au heater and Cr-PBA/Cr bilayer was done by the insertion of Al₂O₃ (130 nm)/Parylene (400 nm) films. The bottom of a device substrate (Si) was in thermal contact with a heat reservoir. Figure 2b shows the measured LSSE signals (V_LSSE) as a function of zy angle of the applied magnetic field (1 T). V_LSSE exhibits a sinusoidal behavior with the maximum magnitude when B and ∇T_z are perpendicular to each other because it is proportional to |J_s × σ|. Figure 2c shows V_LSSE as a function of applied B_y measured for different I_heater. V_LSSE exhibits a small coercivity and nearly saturates at ~300 mT. With increasing I_heater, V_LSSE also increases. The obtained ΔV_LSSE (ΔV_LSSE = |V(0.5 T) − V(−0.5 T)| for I_heater = 20 mA was 47.3 μV.

Fig. 2

LSSE characterization for Cr-PBA/Cr heterojunction devices.

a A schematic illustration for the LSSE characterization of the Cr-PBA/Cr STE device. The temperature gradient was applied by Joule heating of a top Au line. The vertical flow of magnons pumps a pure spin current to the adjacent Cr layer. Then, the induced spin flow is converted into a longitudinal charge current producing electric field of E_ISHE. b V_LSSE as a function of zy angle of the applied magnetic field (1 T) measured with different heating currents I_heater = 10, 15, and 20 mA at 100 K. Measurements were done for the Cr-PBA (1.4 μm)/Cr (10 nm) STE device. c V_LSSE upon sweeping the applied magnetic field measured with different heating currents I_heater = 10, 15, and 20 mA at 100 K. d ΔV_LSSE as a function of the estimated ΔT in a Cr-PBA film displaying a linear behavior. The obtained value of the slope is ΔV_LSSE/ΔT ~ 64.9 ± 3.13 μV/K at 100 K.

The spin Seebeck coefficient (S_LSSE) of our STE devices is defined as S_LSSE = E_ISHE/∇T = (ΔV_LSSE /L)/(ΔT/d), where is L the distance between voltage probes and d is the thickness of the Cr-PBA film. The estimation of the applied temperature gradient (∇T) in each layer of our STE device was done by employing the Fourier’s law ($$ q_x=-\kappa \frac{\mathrm{d}T}{\mathrm{d}x}$$) of a heat conduction. Here, we ignored the interfacial temperature drop as the interfaces are atomically contacted. The estimation of the temperature gradient on Cr-PBA may include slight uncertainty as the relative thickness of Cr-PBA is very thin compared to the interval where we measured temperature²⁹. The unknown thermal conductivity (κ) of the Cr-PBA film was characterized by employing a differential 3ω method^30,31 (Supplementary Note 2 and Supplementary Fig. 5). The estimated κ of Cr-PBA is ~2.17 ± 0.01 W/mK at 100 K, which is much lower than those of inorganic magnets. Thus, the studied molecule-based magnetic film will be effective in keeping the applied temperature gradient. Details of temperature calibration are described in Supplementary Note 2, Supplementary Figs. 6 and 7, and Supplementary Table 1. The estimated ΔT on the Cr-PBA film and measured ΔV_LSSE are all directly proportional to Joule heating power ~I² (Supplementary Fig. 8). Thus, ΔV_LSSE as a function of ΔT in Cr-PBA exhibits excellent linear dependence (Fig. 2d). The obtained ΔV_LSSE/ΔT is ~64.9 ± 3.13 μV/K at 100 K. Then, the S_LSSE of our device was calculated to be 18.2 nV/K. Supplementary Fig. 9 shows the estimated S_LSSE for the devices with several different thicknesses of Cr-PBA. Results display a general tendency of the enhancement of S_LSSE with increasing thickness of Cr-PBA. In order to confirm the origin of the observed ΔV_LSSE, anomalous Hall effect was also measured. Results clearly exclude the possibility of a proximity-induced ferromagnetism in the Cr layer and its contribution to ΔV_LSSE (Supplementary Fig. 10).

Temperature and field dependence of STE characteristics

Figure 3a displays V_LSSE (B_y) measured at various temperatures. The ΔV_LSSE, defined as $$ \mid V_{LSSE}\left(+B_y\right)V_{LSSE}\left(-B_y\right)\mid $$ at B_y = 0.5 T, as a function of temperature is plotted in Fig. 3b. As temperature increases, the ΔV_LSSE initially increases gradually and then it starts to decrease after exhibiting a peak at around 60 K. In the LSSE configuration, the temperature dependence of ΔV_LSSE relies on the magnon excitation and its vertical propagation in a magnetic thin film^32,33. As temperature decreases, the number of excited magnons gradually decrease following Bloch T^3/2 law but the magnon characteristic length (ξ) significantly increases. Within the atomic spin model, only the magnons excited at distances smaller than ξ contribute to ΔV_LSSE³⁴. Thus, the increase of ξ with lowering T leads to the enhancement of ΔV_LSSE because more number of magnons involve in spin pumping at lower temperature. In our Cr-PBA film, ξ becomes comparable to the thickness of the film below 60 K. This size effect together with Block T^3/2 law lead to the decrease of ΔV_LSSE below 60 K. We note that the peak of temperature-dependent V_LSSE shifts to lower temperature with increasing the thickness of Cr-PBA (Supplementary Fig. 11a). This behavior is consistent with the size effect associated with magnon propagation length. We also measured temperature-dependent κ of Cr-PBA to observe possible impacts of phonon on V_LSSE(T). Results show that the κ (T) of Cr-PBA increases with increasing temperature within the measurement window (up to 300 K) (Supplementary Fig. 11b).

Fig. 3

Temperature- and field dependence of V_LSSE.

a Temperature dependence of V_LSSE measured with a Joule heating current, I_heater = 20 mA (ΔT_Cr-PBA = 0.72 K). Measurements were done for the Cr-PBA (1.4 μm)/Cr (10 nm) STE device with a sweeping magnetic field (B_y) between –0.5 and 0.5 T. V_LSSE (B_y) curves are vertically shifted for clarity. b Temperature dependence of ΔV_LSSE = $$ \mid V_{LSSE}\left(+B_y\right)V_{LSSE}\left(-B_y\right)\mid $$ (B_y = 0.5 T), displaying a peak at around 60 K. c High magnetic field dependence of V_LSSE measured at 100 K with I_heater = 20 mA (ΔT_Cr-PBA = 0.72 K).

Figure 3c displays the magnetic field dependence of ΔV_LSSE with applying magnetic fields up to 7 T. We note that the Nernst effect in the Cr layer produces field-dependent voltage (V_x(B_y)) having the same symmetry of V_LSSE (see Supplementary Fig. S12a–c). Thus, we subtracted the Nernst effect from the measured V_x(B_y) assuming that the Nernst effect in the Cr layer is temperature independent. As the magnitude of the magnetic field increases from 0.5 to 7 T, the LSSE signal is monotonically suppressed. The ratio of ΔV_LSSE change at 7 T, [(V_LSSE (7 T) − V_LSSE (0.5 T))/V_LSSE (0.5 T)] × 100%, is calculated to be ~14%, which is similar to that observed in YIG^22,28,35. Previous studies with YIG attributed the high-field suppression of V_LSSE to the suppression of sub-thermal magnon^28,36 (Supplementary Fig. 12d). However, the high-field suppression of the estimated V_LSSE in our studies could be due to the variation in the Nernst effect because the applied ΔT could be altered at different temperature (Supplementary Note 2). The field-dependent V_LSSE was also measured at different temperatures as shown in Supplementary Fig. 13. Results display no consistent tendency of the field-dependent suppression as varying system temperature. We note that the changes of resistance in the Au heater line and the Cr layer in a high magnetic field are negligible and not associated with high-field suppression of V_LSSE (Supplementary Fig. 14).

Spin dynamics and pumping at the Cr-PBA/Cr heterostructures

The generation, propagation, and detection of magnons in the Cr-PBA/Cr heterostructure were further studied through FMR and FMR with ISHE (FMR-ISHE) experiments. Figure 4a shows FMR spectra of a Cr-PBA (1.4 μm)/Cr (10 nm) heterojunction measured at various microwave frequencies. The frequency dependence of a resonance field (B_R) shown in Fig. 4b well follows the Kittel equation, $$ \nu =\frac{\gamma }{2\pi }{\left[B_{\mathrm{R}}\left(B_{\mathrm{R}}+{\mu }_0{M}_{\mathrm{s}}\right)\right]}^{1/2}$$, where ν is microwave frequency, γ is the gyromagnetic ratio, and M_s is a saturation magnetization. The frequency dependence of full-width at half-maximum (FWHM) shown in Fig. 4c gives the estimation of the effective Gilbert damping constant (α_eff) following the relation, $$ \mathrm{\Delta }B=\mathrm{\Delta }{B}_0+\frac{4\pi {\alpha }_{\mathrm{eff}}\nu }{\sqrt{3}\gamma }$$. Here, ΔB₀ denotes an inhomogeneous broadening by structural imperfections. Since the Cr-PBA film is grown on the Cr metal layer which absorbs spin angular momentum at the interface, the effective Gilbert damping in Cr-PBA/Cr becomes larger than the intrinsic damping in Cr-PBA. The obtained α_eff is ~7.5 × 10⁻⁴ for the Cr-PBA (1.4 μm)/Cr (10 nm) heterojunction. The intrinsic damping constant (α₀) of the Cr-PBA film and the spin mixing conductance ($$ g_{\mathrm{eff}}^{\uparrow \downarrow }$$) of the heterojunction can be estimated from the relation³⁷, $$ {\alpha }_{\mathrm{eff}}={\alpha }_0+\mathrm{\Delta }\alpha ={\alpha }_0+\frac{\mathrm{g}{\mu }_{\mathrm{B}}}{4\pi M_{\mathrm{s}}d}{g}_{\mathrm{eff}}^{\uparrow \downarrow }$$, where Δα is the additional Gilbert damping caused by spin pumping at the interface and d is the thickness of Cr-PBA. The thickness dependence of α_eff is displayed in Supplementary Fig. 15. The obtained α₀ is (2.4 ± 0.67) × 10⁻⁴ and $$ g_{\mathrm{eff}}^{\uparrow \downarrow }$$ is (6.5 ± 0.52) × 10¹⁸ m⁻², which are comparable to those of the epitaxial YIG and YIG/Pt^10,37. The observed small damping indicates that the generated magnons in the Cr-PBA film will be effectively delivered to the interface with low loss, relevant for effective spin thermoelectricity as well as magnon spintronics.

Fig. 4

FMR and FMR-driven ISHE results for Cr-PBA/Cr heterojunctions.

a First derivative FMR spectra of the Cr-PBA (1.4 μm)/Cr (10 nm) heterojunction at various microwave frequencies measured at 100 K. The recorded data are fitted by using the derivative of the Lorentzian function. b Frequency dependence of resonance field B_R. Fitting with the Kittel equation produces M_s = 12.676 kA/m and g-factor = 1.96. c FWHM as increasing the frequency of r.f. field. The slope of a linear fit produces a low effective Gilbert damping constant, α_eff ~ 7.5 × 10⁻⁴. d A schematic illustration of the spin pumping from microwave driven magnon propagation in the Cr-PBA film and its conversion into an electrical current in the Cr layer via ISHE. e V_ISHE(B) measured for the Cr-PBA (1.4 μm)/Cr (10 nm) bilayer upon applying 9 GHz of microwave. f V_ISHE(B) of Cr-PBA/Cr heterojunctions with various Cr-PBA thicknesses.

In order to investigate the conversion of spin angular momentums into an electric current at the Cr-PBA/Cr interface further, we measured FMR-driven ISHE as illustrated in Fig. 4d. The transferred spin angular momentums at the interface induce a spin current in the adjacent Cr layer. Then, the conversion from spin to charge flow via the ISHE allows electrical detection of microwave pumped magnons. Because E_ISHE ∝ J_s × σ, a maximum magnitude of V_ISHE can be obtained when magnetic field B is normal to the direction of voltage probes. Figure 4e displays measured V_ISHE by applying continuous microwave f = 9 GHz to the Cr-PBA (1.4 μm)/Cr (10 nm) heterojunction. The FWHM and B_R of V_ISHE are consistent with those of FMR spectra shown in Fig. 4a. V_ISHE reverses polarity when reversing the field direction (Fig. 4e). These behaviors clearly suggest that the observed V_ISHE originates from the FMR-generated magnon flow in the Cr-PBA film. As increasing d, the FMR-driven V_ISHE substantially increases as shown in Fig. 4f. Using the obtained $$ g_{\mathrm{eff}}^{\uparrow \downarrow }$$, we can estimate the transferred spin current density $$ j_{\mathrm{s}}^0$$ at the interface (Supplementary Note 3). Then, the spin Hall angle ($$ {\theta }_{\mathrm{SHE}}^{\mathrm{Cr}}$$) of the Cr layer can be obtained from the relation, $$ V_{\mathrm{ISHE}}=\frac{2e}{ħ}\frac{{\theta }_{\mathrm{SHE}}^{\mathrm{Cr}}{\lambda }_{\mathrm{s}}^{\mathrm{Cr}}\omega J_{\mathrm{s}}^0}{{\sigma }^{\mathrm{Cr}}{d}^{\mathrm{Cr}}}\tanh \left(\frac{2d^{\mathrm{Cr}}}{{\lambda }_{\mathrm{s}}^{\mathrm{Cr}}}\right)$$, where $$ {\lambda }_{\mathrm{s}}^{\mathrm{Cr}}$$ and σ^cr are the spin diffusion length and conductivity of the Cr layer, respectively. Taking $$ {\lambda }_{\mathrm{s}}^{\mathrm{Cr}}$$ = 2.1 nm from the literature²⁵, we obtain the spin Hall angle ($$ {\theta }_{\mathrm{SHE}}^{\mathrm{Cr}}$$) ~ −0.014. This value is within the range of $$ {\theta }_{\mathrm{SHE}}^{\mathrm{Cr}}$$ values in the literatures^24,25. Here, improving spin–charge conversion with other compatible electrodes, such as transition metals^38,39, alloy metals^40,41, and topological insulators⁴², would significantly enhance the spin Seebeck coefficient of Cr-PBA. In short, our FMR-ISHE studies confirm an effective generation of a magnonic spin flow in Cr-PBA and spin-pumping process at the Cr-PBA/Cr interface.

Film deposition and characterization

For the fabrication of Cr-PBA/Cr heterojunctions, a Cr metal thin film (10 nm) for a working electrode was first deposited on a SiO₂ (300 nm)/p-Si (500 μm) substrate by e-beam evaporation under the base pressure of ~7 × 10⁻⁷ Torr. The electrochemical processes were carried out using a potentiostat with a reference electrode (Ag/AgCl) and a Pt counter electrode. For a Cr-PBA deposition, the aqueous solution of 7.5 mM CrCl₃·H₂O and 5 mM K₃[Cr(CN)₆] was used. The coating of a Cr-PBA film was obtained by electrochemical reduction (at a fixed potential E = –0.88 V vs. Ag/AgCl reference electrode) of Cr³⁺ in an aqueous solution containing [Cr(CN)₆]³⁻ anions. The Cr²⁺ species formed at the surface of the Cr metal electrode react with the [Cr(CN) ₆]³⁻ developing an insoluble PBA coating. The deposition rate of the PBA film in our processing was typically ~140 nm/min. For the study of STE characterizations, the electrodepositions of PBA films were done for 10 minutes producing a thickness of 1.4 μm. The surface roughness of the Cr-PBA film was measured using atomic force microscopy (DI-3100, Veeco) and the cross-sectional image of the bilayer was investigated by normal-TEM (ZEM-2100). The crystallization of the film was probed by using a X-ray diffraction (D8 ADVANCE, Bruker AXS). The magnetic properties of the Cr-PBA film were measured by using a superconducting quantum interference device-vibrating sample magnetometer (SQUID-VSM, Quantum Design).

Spin-TE device fabrication with an on-chip heater

We used a heterojunction of Au (20 nm)/Al₂O₃ (130 nm)/Parylene (400 nm)/Cr-PBA (1.4 μm)/Cr (10 nm) for the characterization of LSSE in the Cr-PBA/Cr STE device. After the deposition of Cr-PBA on the Cr film, 400 nm of parylene was deposited to protect the entire sample by using a standard parylene coater (Alpha plus). For the fabrication of the studied device, the reactive ion etching was done with O₂ and Cl₂ gas by using a thick photoresist (AZ9660) as a protective buffer patterned for a dimension of 5 mm length and 100 μm width. After removing the buffer photoresist by acetone, the additional insulating layer of Al₂O₃ (130 nm) and the top Au heater (20 nm) patterned into the same dimension of Cr-PBA (5 mm length and 100 μm width) were successively deposited by e-beam evaporation.

STE characterization with temperature calibration

The current source for the Joule heating was applied by using a Keithley 2636 sourcemeter. The temperature of the Au layer was estimated based on the temperature dependence of the electrical resistivity of the Au layer (Supplementary Fig. 6a). Temperature stabilization of the top Au layer depends on the heating current and usually takes less than a few minutes (Supplementary Fig. 6b). LSSE measurements were performed after the temperature of the top Au layer was sufficiently stabilized. For the measurement of the thermal conductivity of the Cr-PBA film, we used the differential 3ω method by using Keithley 6221 ac sourcemeter and SR830 Lock-in amplifier to measure harmonic ac voltage. Measurements of the thermal conductivity are further described in Supplementary Note 2. Details of temperature calibration and SSE characterization are also explained in Supplementary Note 2. Under the applied temperature gradient, the induced voltage from SSE and ISHE was measured by using a Keithley 2182 nanovoltmeter. All measurements for LSSE were performed in a Physical Property Measurement System (PPMS) (Quantum Design) with varying temperature and magnetic field.

FMR and FMR-ISHE measurements

For the FMR measurements, we used the broadband FMR of the PPMS option with a coplanar waveguide and a NanOsc Phase FMR spectrometer operated in the frequency range 2–19 GHz. For the FMR-driven ISHE measurements, we used coplanar waveguide FMR with contact pads for the detection of ISHE (KBSI and RNDWARE Co. Ltd). Devices used for FMR-ISHE studies have a channel size of 1 mm width and 2 mm length with gold contact pads at both sides. Voltages generated by FMR-ISHE were detected by using Keithley 2182 nanovoltmeter. All FMR and FMR-ISHE measurements were performed in the PPMS chamber.