A scalable molecule-based magnetic thin film for spin-thermoelectric energy conversion

Spin thermoelectrics, an emerging thermoelectric technology, offers energy harvesting from waste heat with potential advantages of scalability and energy conversion efficiency, thanks to orthogonal paths for heat and charge flow. However, magnetic insulators previously used for spin thermoelectrics pose challenges for scale-up due to high temperature processing and difficulty in large-area deposition. Here, we introduce a molecule-based magnetic film for spin thermoelectric applications because it entails versatile synthetic routes in addition to weak spin-lattice interaction and low thermal conductivity. Thin films of CrII[CrIII(CN)6], Prussian blue analogue, electrochemically deposited on Cr electrodes at room temperature show effective spin thermoelectricity. Moreover, the ferromagnetic resonance studies exhibit an extremely low Gilbert damping constant ~(2.4 ± 0.67) × 10−4, indicating low loss of heat-generated magnons. The demonstrated STE applications of a new class of magnet will pave the way for versatile recycling of ubiquitous waste heat.

A scalable molecule-based magnetic thin film for spin-thermoelectric energy conversion Oh et al. roughness of the film surface was 6.78 nm and 14.3 nm for 1×1 m and 5×5 m area, respectively  1m by 1m R q = 6.78 nm 5m by 5m R q = 14.3 nm

Magnetic properties of Cr-PBA
The magnetic characteristics of the ECD deposited Cr-PBA film were studied by using SQUID-VSM (Quantum Design) immediately after the deposition. Magnetic hysteresis of the Cr-PBA film measured for in-plane applied magnetic field at 100 K exhibits a coercivity of about 2.5 mT (Fig.   1f). The gradual flip of the magnetization shows polycrystalline characteristic of the Cr-PBA film.
In order to examine the stability of sample, we measured magnetic hysteresis of Cr-PBA after keeping the sample for one month in an ambient air. We didn't observe any discernible change in magnetization. To determine the critical temperature of our Cr-PBA film by using Arrott plot method, we plotted M 2 vs B/M for various temperatures from 190 K to 250 K as shown in Fig. S3.
The plot should display a straight line passing through the origin at the transition temperature. The obtained transition temperature of our Cr-PBA film was about 230 K as shown in the inset of Fig.   S3. This value is close to Tc ~ 240 K of the crystalline powder samples 1 . This discrepancy is likely due to a slight change in the stoichiometric ratio between Cr 2+ (S = 2) and Cr 3+ (S = 2/3), as it changes net spin numbers, variations of crystal field, and the strength of superexchange coupling 2 . The temperature-dependent saturation magnetization curves exhibit typical behavior of temperature dependent magnon excitation. Fig. S4a magnetization as a function of T 3/2 displaying a good linearity over the wide range of temperature.
Measurement was done with applying magnetic field of B = 0.5 T. Fitting with M(T) = M0(1−aT 3/2 ) provides the value of slope ~ 2.6×10 -4 K -3/2 , which is much higher than those of inorganic magnets.
b Temperature dependent magnetization with applying various magnetic field from 0.001 T to 0.5 T.

Supplementary Note2. Temperature calibration and SSE characterization
Thermal conductivity of Cr-PBA To determine the thermal conductivity of the Cr-PBA film, we adopted the differential 3ω method 4,5 . The differential 3ω technique especially has been used to determine the anisotropic thermal conductivity of thin films because it allows measurement of the temperature drop across only the intended film with removing uncertainties in the thermal properties of the other layers 4,5 . As shown in Fig. S5a, we deposited a Cr-PBA film (4 m) on the half of the Cr (10 nm) /p-Si substrate. Then, the thin insulating layer of parylene C was coated by using a parylene coater (Alpha plus).
Thickness of the parylene layer was about 400 nm, guaranteeing electrical isolation of the gold heater to function as a thermometer. In this way, the sample (Parylene/Cr-PBA/Cr/p-Si) and the reference (Parylene/Cr/p-Si) were fabricated on the same substrate. Then, 100 m × 5 mm gold heater lines were patterned on top of both sides of the sample and reference sample parts.
Measurements of both the third harmonic voltage (V3ω) and the first harmonic voltage (V1ω) enable to determine the cross-sectional temperature drop (T) from the relation, where R is the resistance of a Au heater line. where df, wh, and lh are the thickness of the film, the width and length of the Au heater, respectively.
The thermal conductivity of the Cr-PBA film was estimated to be 2.18±0.01 W/mK, when the applied heating power was 88 mW. We repeated measurements with increasing the applied heater power as shown in Fig. S5c. The obtained average value of the thermal conductivity was 2.17±0.01 W/mK.  The difference of the temperature (Tfilm) is calculated to be 0.32 K. c Estimated the thermal conductivity as increasing the heater power. The error bars indicate the standard deviations of  estimated from the standard deviations of the measured Tfilm between the sample and reference.

Temperature calibration
To estimate the spin Seebeck coefficient (SLSSE) of our STE devices, a temperature gradient applied on the Cr-PBA film need to be obtained. We employed the top Au heating layer as an in-situ temperature sensor 6,7 . Thus, heat loss at the interface between a STE device and a temperature sensor can be ignored allowing a precise calibration of temperature. The measurements were We then calculated the temperature gradient applied in each layer by using the Fourier's Law, where qx, , A are the heat flux (W), thermal conductivity (W/mK), and surface area, respectively.
Thus, the temperature difference applied on each layer will be proportional to d/ , where d is the thickness of each layer. Here, we ignored the interfacial temperature drop as the interfaces are atomically contacted. The estimation of 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 temperature 8 . The reference values of are used for the thermal conductivity of each layer except the Cr-PBA layer. The unknown thermal conductivity of Cr-PBA was obtained basedon the differential 3 method. The calculated temperature difference on each layer for various heating currents is summarized in Table 1.
been observed in previous works with YIG film 9 . To investigate contribution of phonon on the spin Seebeck effect, we measured the temperature dependence of the thermal conductivity of Cr-PBA. Results show that the thermal conductivity of the Cr-PBA film increases with increasing temperature within the measurement window (up to room temperature) as shown in Fig. 11b. Thus, we can confirm that the observed peak of VLSSE(T) is a size effect associated with magnon propagation length. Fig. S12a-c shows magnetic field dependent Vx(By) measured at T = 100 K and 300 K, while applying vertical temperature gradient (∇ ). The linear suppression of the measured voltage was also observed even above the Curie temperature of Cr-PBA, which can be attributed to the ordinary Nernst effect in Cr layer because it has the same symmetry of VLSSE. Assuming the Nernst effect is nearly temperature independent for metal, we subtracted the linear slop of Nernst effect measured at 300 K for each sample to the measured Vx(By) in order to obtain the fielddependent LSSE signal separately. Fig. S12d displays the extracted VLSSE as a function of applied magnetic field for different thickness of Cr-PBA. Results display high-field suppression ratio of the LSSE signal tends to increase with increasing thickness of Cr-PBA film, as observed in previous works 10,11 . However, precise subtraction of the Nernst effect in our devices is unattainable task because the applied T in the thin Cr layer will be largely temperature dependent. We estimated T in each layer by using the Fourier's law. But, thermal conductivities in every layer are generally temperature dependent as in Cr-PBA, whose  value at 300 K is nearly twice of the value at 100 K (Fig. S11b). Thus, the applied T in the thin Cr layer is temperature dependent, so does the size of Nernst voltage. Therefore, actual high-field suppression in VLSSE could be considerably different from the estimated VLSSE(By) shown in Fig. S12d. Fig. S13 shows field dependent LSSE signal measured at various temperatures for the device with 1.4 m thick Cr-PBA, after subtracting the linear fit to ordinary Nernst effect measured at 300 K. Results exhibit no consistent tendency of the field-dependent suppression ratio as varying system temperature. We also tested magneto-resistance (MR) of the Au and Cr layer to confirm parasite effect that may contribute to the observed VLSSE, especially in high magnetic field (Fig. S14). For the measurement of MR in the Cr layer, we applied from 1 A to 100 A to exclude Joule heating and applied the external magnetic field up to 7 T. The observed resistance change at high magnetic field was less than 0.043 %. For the Au heater line, we measured MR by applying 10 mA to examine heating variation as increasing magnetic field. The change of resistance was less than 0.037 %, which does not contribute to the relatively larger variation in VLSSE at high magnetic field.

Supplementary Note3. FMR and FMR-ISHE measurements
We studied the generation, propagation, and detection of magnons in the Cr-PBA/Cr heterojunction further through ferromagnetic resonance (FMR) and FMR with inverse spin Hall effect (FMR-ISHE) experiments. Both FMR and FMR-ISHE measurements were done with coplanar waveguide. The FMR spectra were recorded with sweeping the external magnetic field at microwave frequencies in the range of 3-19 GHz (Fig. 4a). The resonance field (BR) and linewidth (ΔB) of FMR spectra were extracted from the first derivative of Lorentzian, as follows [4( − R ) 2 +(∆ ) 2 ] + slope + offset eq(4) The dependence of the resonance field (BR) on the microwave frequency can be well described The conversion of spin angular momentum into an electric current in the Cr-PBA/Cr heterojunction was studied further through FMR-driven ISHE as illustrated in the Fig. 4d. Fig. 4e displays measured VISHE at continuous microwave f = 9 GHz in the Cr-PBA/Cr heterojunction.
Both B and BR of VISHE are in consistent with those of FMR spectra shown in Fig. 4a. This clearly suggests that the measured VISHE originates from FMR-generated magnon flow in the Cr-PBA film.
The transferred spin current density s 0 at the interface can be determined from the relation,