## Abstract

Spin Seebeck effect (SSE) refers to the generation of an electric voltage transverse to a temperature gradient via a magnon current. SSE offers the potential for efficient thermoelectric devices because the transverse geometry of SSE enables to utilize waste heat from a large-area source by greatly simplifying the device structure. However, SSE suffers from a low thermoelectric conversion efficiency that must be improved for widespread application. Here we show that the SSE substantially enhances by oxidizing a ferromagnet in normal metal/ferromagnet/oxide structures. In W/CoFeB/AlO_{x} structures, voltage-induced interfacial oxidation of CoFeB modifies the SSE, resulting in the enhancement of thermoelectric signal by an order of magnitude. We describe a mechanism for the enhancement that results from a reduced exchange interaction of the oxidized region of ferromagnet, which in turn increases a temperature difference between magnons in the ferromagnet and electrons in the normal metal and/or a gradient of magnon chemical potential in the ferromagnet. Our result will invigorate research for thermoelectric conversion by suggesting a promising way of improving the SSE efficiency.

### Similar content being viewed by others

## Introduction

The thermoelectric effect that converts heat to electricity in solid-state devices is attracting much attention as a promising candidate for a carbon-free power generation from waste heat^{1}. Thermoelectric generation based on conventional Seebeck effect employs a longitudinal geometry^{2}, in which an electric voltage is generated along a temperature gradient \(\nabla T\) (Fig. 1a). The longitudinal geometry is not favored for applications because it requires a thermopile composed of multiple and alternatively connected thermoelectric materials of different types^{3}, which is complex to cover a large-area heat source. This limitation can be overcome by a thermoelectric device in transverse geometry using the spin Seebeck effect (SSE)^{4,5,6,7,8} that generates an electric voltage in the direction perpendicular to a temperature gradient^{9} (Fig. 1b). For practical applications, however, a thermoelectric conversion efficiency of SSE is insufficient and must be substantially enhanced.

In normal metal (NM)/ferromagnet (FM) heterostructures (Fig. 1b), a basic building block for SSE, the thermoelectric conversion via longitudinal SSE consists of three separate processes; First, a vertical temperature gradient generates a temperature difference \({T}_{m-e}\) between magnons in FM and electrons in NM (described by the magnon temperature model^{10,11,12}) and a magnon spin current associated with a magnon chemical potential gradient \(\nabla {\mu }_{m}\) in FM (described by the magnon drift-diffusion model^{13,14}). Second, a thermal spin pumping from FM to NM occurs. Third, a spin current generates a transverse voltage via inverse spin Hall effect (ISHE) of NM. These three processes can be independently controlled so that the enhancement of SSE in each process is multiplied. Previous studies have focused mainly on the improvement of the second process by increasing the spin-mixing conductance at the NM/FM interface^{15,16,17} and the third one by employing NM with large spin Hall angle^{18,19}. In addition, lowering the damping of FM^{20} for the first process or reducing the thermal conductivity of FM^{21} enhances the SSE efficiency by several factors.

In this work, we report an efficient way to enhance the SSE signal through the first process by reducing the exchange interaction \({J}_{{ex}}\) at the hotter region of FM. As described below, a reduction of \({J}_{{ex}}\) increases a magnon heat current, which in turn increases \({T}_{m-e}\) and thus the SSE signal. Moreover, as \(\nabla {\mu }_{m}\) contributes to a magnon spin current, the SSE can enhance by increasing \(\nabla {\mu }_{m}\) at a given temperature gradient. Following the Bloch’s \({T}^{3/2}\) law, the most important factor for the magnon chemical potential is \({J}_{{ex}}\) because the magnon density at a given temperature is determined by the Curie temperature. Therefore, a reduction of \({J}_{{ex}}\) at the hotter region of FM increases a magnon spin current, which also enhances the SSE signal.

In what follows, we discuss two different theoretical mechanisms to describe the SSE based on the magnon temperature model^{10,11,12} and the magnon drift-diffusion model^{13,14}. Both mechanisms may coexist^{14} but we consider these separately for simplicity. We first describe the magnon temperature model^{10,11,12} for an insulator/FM1/FM2/NM structure where \({J}_{{ex}}\) differs between FM1 and FM2 (Fig. 1c). From the thermal circuit model equivalent to the layered structure of Fig. 1c and ignoring magnon relaxation, the SSE voltage \({V}_{{{{{{\rm{SSE}}}}}}}\) is found to be proportional to (Supplementary Note 1):

where \({Q}_{i}^{{{{{{\rm{FM}}}}}}}\) is the magnon heat current of FM*i* (*i* = 1, 2), \({R}_{i}^{{{{{{\rm{FM}}}}}}}\) is the magnon heat resistance of FM*i*, and \({R}_{{{{{{\rm{F}}}}}}2{{{{{\rm{|F}}}}}}1}^{{{{{{\rm{int}}}}}}}\) (\({R}_{{{{{{\rm{F}}}}}}1{{{{{\rm{|N}}}}}}}^{{{{{{\rm{int}}}}}}}\)) is the interface magnon heat resistance at the FM2/FM1 (FM1/NM) interface. Assuming no loss of magnon heat current at the FM2|FM1 interface (i.e., \({R}_{{{{{{\rm{F}}}}}}2{{{{{\rm{|F}}}}}}1}^{{{{{{\rm{int}}}}}}}\to 0\)) and \({R}_{1}^{{{{{{\rm{FM}}}}}}}+{R}_{2}^{{{{{{\rm{FM}}}}}}}\,\gg \,{R}_{{{{{{\rm{F}}}}}}1{{{{{\rm{|N}}}}}}}^{{{{{{\rm{int}}}}}}}\), Eq. (1) is simplified as

Using \({Q}_{i}^{{{{{{\rm{FM}}}}}}}={\kappa }_{i}\nabla T\) and \({R}_{i}^{{{{{{\rm{FM}}}}}}}={d}_{{Fi}}/({\kappa }_{i}A)\) with the magnonic heat conductivity \(\kappa\), the temperature gradient \(\nabla T\), the FM thickness \({d}_{F}\), and the area \(A\) of the structure, \({V}_{{{{{{\rm{SSE}}}}}}}\) is found to be proportional to \({\kappa }_{1}{\kappa }_{2}\left({d}_{F1}+{d}_{F2}\right)/({\kappa }_{1}{d}_{F2}+{\kappa }_{2}{d}_{F1})\). Given \({\kappa }_{i}\propto {\left({J}_{{ex},i}\right)}^{-1/2}\) [14] (Supplementary Table 1), the ratio \({r}_{{{{{{\rm{SSE}}}}}}1}\) of \({V}_{{{{{{\rm{SSE}}}}}}}\) with \({J}_{{ex},1}\,\ne \,{J}_{{ex},2}\) to \({V}_{{{{{{\rm{SSE}}}}}}}\) with \({J}_{{ex},1}={J}_{{ex},2}\) for the magnon temperature model is given as

Equation (3) shows that \({r}_{{SSE}1}\) is larger than 1 for \({J}_{{ex},2}\, < \,{J}_{{ex},1}\) (Fig. 1d). It is because a reduced \({J}_{{ex}}\) at the hotter region of FM (i.e., FM2) decreases \({R}_{2}^{{{{{{\rm{FM}}}}}}}\), which in turn increases \({V}_{{{{{{\rm{SSE}}}}}}}\).

We next describe the magnon drift-diffusion model^{13,14} for the same structure of Fig. 1c. Ignoring \({T}_{m-e}\) and solving magnon diffusion equations in FMs coupled with spin diffusion equation in NM gives \({V}_{{{{{{\rm{SSE}}}}}}}\) as (Supplementary Note 1).

where \({\theta }_{{SH}}\) is the spin Hall angle of NM, \({l}_{N}\) is the spin diffusion length of NM, \({l}_{{Fi}}\) is the magnon diffusion length of FM*i*, \(\sigma\) is the charge conductivity of NM, \({\sigma }_{{Fi}}\) is the magnon spin conductivity of FM*i*, \({L}_{i}\) is the spin Seebeck coefficient of FM*i*, \({d}_{N}\) is the NM thickness, and \(d\) is the electrode distance to measure \({V}_{{{{{{\rm{SSE}}}}}}}\). We obtain Eq. (4) with assumptions of continuous magnon chemical potential at the FM2/FM1 interface and \({d}_{F1(2)}\,\ll \,{l}_{F1(2)}\) to simplify \({V}_{{{{{{\rm{SSE}}}}}}}\) (Supplementary Note 1). Given \({\sigma }_{F}\propto L\propto {J}_{{ex}}^{-1/2}\) and \({l}_{F}\propto {J}_{{ex}}^{1/2}\) [14] (Supplementary Table 1), we obtain the ratio \({r}_{{{{{{\rm{SSE}}}}}}2}\) of \({V}_{{{{{{\rm{SSE}}}}}}}\) with \({J}_{{ex},1}\,\ne \,{J}_{{ex},2}\) to \({V}_{{{{{{\rm{SSE}}}}}}}\) with \({J}_{{ex},1}=\,{J}_{{ex},2}\) for the magnon drift-diffusion model as

Similar to \({r}_{{{{{{\rm{SSE}}}}}}1}\) [Eq. (3)], \({r}_{{{{{{\rm{SSE}}}}}}2}\) is larger than 1 for \({J}_{{ex}2}\, < \,{J}_{{ex}1}\) (Fig. 1d). It is because a reduced \({J}_{{ex}}\) at the hotter end of FM increases a gradient of magnon chemical potential \(\nabla {\mu }_{m}\), which in turn increases \({V}_{{{{{{\rm{SSE}}}}}}}\).

Since the above analytic theories are obtained with several crude approximations, we also carry out numerical simulations based on the stochastic Landau-Lifshitz-Gilbert equation for thermal spin pumping (Supplementary Note 2), following the procedure of Ref. ^{22}. Numerical results (symbols in Fig. 1d) show a qualitatively similar trend with the analytic theories. All these results support our argument that a reduced \({J}_{{ex}}\) at the hotter region of FM (= FM2) enhances \({V}_{{{{{{\rm{SSE}}}}}}}\).

To experimentally demonstrate the enhancement of \({V}_{{{{{{\rm{SSE}}}}}}}\) by reducing \({J}_{{ex}}\) at the hotter region, we employ a W (4 nm)/CoFeB (2 nm)/AlO_{x} (2 nm) wire device, in which a ZrO_{2} gate oxide and a Ru gate electrode are incorporated (Fig. 2a; see details in the Methods section). In this structure, we reduce \({J}_{{ex}}\) at the hotter region of CoFeB by utilizing gate voltage (*V*_{G})-induced oxygen migration, which is known to efficiently modulate magnetic properties of FM through redox reactions^{23,24}. *V*_{G}-induced oxygen migration allows us to control the oxidation state (i.e., magnetic properties) of FM in *single* sample and thus to avoid possible ambiguities caused by sample-to-sample variations.

To confirm that *V*_{G} modulates \({J}_{{ex}}\) of CoFeB, we measure temperature-dependent anomalous Hall resistance (*R*_{H}) of a W (4 nm)/CoFeB (1 nm)/AlO_{x} (2 nm) sample with *V*_{G} = ±13 V (equivalent to 3.25 MV/cm). Here *V*_{G} is applied for 5 min at 100 °C, and the measurement is carried out with the gate floating. This is possible due to the non-volatile nature of the gate effect in our sample, which persists even after *V*_{G} is turned off. As CoFeB (1 nm) has the in-plane magnetization, we apply an out-of-plane field of 9 T to measure *R*_{H}. This field is much larger than the demagnetization field (~ 1 T) so that *V*_{G}-induced change in the magnetic anisotropy does not affect *R*_{H} versus temperature. Figure 2b shows that the normalized *R*_{H} gradually decreases with temperature, and in particular the sample with *V*_{G} = −13 V has a stronger temperature dependence. Since the magnetic moment of the CoFeB does not change at the measurement temperature up to 380 K (Supplementary Note 3), this result shows that the Curie temperature and \({J}_{{ex}}\) of CoFeB decrease with a negative voltage. Note that in our sign convention, oxygen ions are drifted toward (away from) the CoFeB/AlO_{x} interface for a negative (positive) *V*_{G}. Therefore, the result of Fig. 2b indicates that the oxidation reduces \({J}_{{ex}}\) of CoFeB near the CoFeB/AlO_{x} interface.

We next measure a thermoelectric voltage (*V*_{TE}) at various *V*_{G}. In the sample, a vertical temperature gradient (\(\nabla {T}_{z}\)) is generated by irradiating a focused laser (laser power = 30 mW) with a wavelength of 660 nm, and then *V*_{TE} is measured while sweeping a magnetic field (*B*_{x}) in the direction transverse with the voltage probe or rotating a magnetic field of 100 mT in the *x*-*y* plane (azimuthal angle \({\varphi }_{B}\)). Figure 2c shows the results; for the case of without applying *V*_{G} (black symbols), *V*_{TE} is positive for a positive *B*_{x} (i.e., *M*//+*x* where *M* is the CoFeB magnetization), and changes its sign when *M* is reversed. Defining Δ*V*_{TE} = [*V*_{TE} (*M*//+*x*) – *V*_{TE} (*M*//−*x*)]/2, we find that Δ*V*_{TE} is 0.7 μV for the case without *V*_{G} but is largely modulated by applying *V*_{G}; Δ*V*_{TE} is 5.5 μV for *V*_{G} = +13 V, which is almost eight times greater than that without *V*_{G}. Furthermore, Δ*V*_{TE} even changes the sign by a negative *V*_{G}; Δ*V*_{TE} = −4.3 μV for *V*_{G} = −13 V.

The *V*_{G}-induced modulation of Δ*V*_{TE} is further confirmed by the angle-dependent *V*_{TE} measurement that exhibits \({{\cos }}{\varphi }_{B}\)–dependence (Fig. 2d). This angular dependence is consistent with the symmetry of spin thermoelectrics^{5} where *V*_{TE} maximizes when *M* is aligned in the *x*-direction perpendicular to both \(\nabla {T}_{z}\) and the voltage probes. We also measure Δ*V*_{TE} as a function of laser power to confirm that Δ*V*_{TE} originates from \(\nabla {T}_{z}\). Figure 2e shows that Δ*V*_{TE} increases linearly with the laser power at both *V*_{G} polarities, demonstrating that the *V*_{G}-induced Δ*V*_{TE} enhances by increasing \(\nabla {T}_{z}\) in the sample.

All the above results are consistent with spin thermoelectric voltages induced by \(\nabla {T}_{z}\), but *V*_{G}-induced sign change of Δ*V*_{TE} demands a further investigation. This sign change is caused by the fact that CoFeB is a metallic FM and thus not only SSE of W/CoFeB but also anomalous Nernst effect (ANE) of CoFeB itself contributes to Δ*V*_{TE}. For a W/CoFeB bilayer where W has a negative spin Hall angle^{25}, the ANE of CoFeB has the opposite sign to the SSE of W/CoFeB^{26}. Then, an important question is whether the ANE or the SSE changes with *V*_{G}. To address this question, we examine *V*_{G}-induced Δ*V*_{TE} in a Ti (3 nm)/CoFeB (2 nm)/AlO_{x} (2 nm) sample. It is expected that the SSE contribution to Δ*V*_{TE} is negligible in this sample because of a negligibly small spin Hall angle of Ti^{27}. Figure 2f shows that the angle-dependent *V*_{TE}’s of Ti/CoFeB sample at different *V*_{G}’s are almost identical regardless of *V*_{G}. Since *V*_{TE} of Ti/CoFeB sample is predominantly determined by the ANE of CoFeB, this result shows that the effect of *V*_{G} on ANE is negligible. Therefore, the *V*_{G}-induced Δ*V*_{TE} in the W/CoFeB sample is almost entirely governed by the *V*_{G}-induced modulation of SSE and a negative *V*_{G} increases the magnitude of the SSE since the sign of SSE is negative for the W/CoFeB sample. This *V*_{G}-induced sign change of Δ*V*_{TE} in the W/CoFeB sample evidences that the *V*_{G}-induced modulation of SSE signal is sufficiently large to exceed the ANE signal that is almost independent of *V*_{G}. We also investigate samples with other NM electrodes of Pt or Ta (Supplementary Note 4). Both samples show that the magnitude of the SSE increases at negative *V*_{G}, consistent with the results of the W/CoFeB sample. Furthermore, the *V*_{G} modulation efficiency is closely related to the magnitude and sign of the spin Hall angle of the NM layer.

The above results unambiguously show that the gate voltage modifies the SSE. We attribute the main mechanism of the gate effect to the oxygen ion migration and associated oxidation of CoFeB because it exhibits non-volatile nature and has a threshold voltage. Figure 3a shows that Δ*V*_{TE} does not change significantly for |*V*_{G}| < 5 V. This threshold behavior may be related to the energy barrier for oxygen migration^{23,24}. On the other hand, when *V*_{G} exceeds the threshold, Δ*V*_{TE} increases with *V*_{G}. This result demonstrates that Δ*V*_{TE} can be continuously controlled by *V*_{G} in a reversible manner.

To independently confirm that the observed gate effect originates from the oxidation of CoFeB, we directly oxidize the CoFeB layer by plasma oxidation. We fabricate W (4 nm)/CoFeB (2 nm)/AlO_{x} (1.5 nm) samples where the oxidation state of CoFeB is modulated by varying the oxidation time (*t*_{ox}), which ranges from 0 to 150 s. Figure 3b shows that *V*_{TE} strongly depends on *t*_{ox}; Δ*V*_{TE} is positive for *t*_{ox} = 0 s, gradually decreases with *t*_{ox}, and becomes negative when *t*_{ox} exceeds 75 s. It indicates that the magnitude of SSE increases with *t*_{ox}, which is the same trend as applying a negative *V*_{G} (Fig. 2). This result can be understood by the fact that a negative *V*_{G} makes oxygen ions to migrate from oxide to CoFeB, leading to the oxidation of CoFeB. Note that the oxidation-induced modulation of Δ*V*_{TE} is also seen in samples with thicker CoFeB (Supplementary Note 5).

To prove that the gate effect is equivalent to the CoFeB oxidation, we also investigate the effect of gate voltage (*V*_{G} = ±12 V) on Δ*V*_{TE} in the samples with different *t*_{ox}’s (Fig. 3c). When applying *V*_{G} = −12 V (+12 V), Δ*V*_{TE} becomes more negative (positive), i.e., SSE increases (decreases) for all samples regardless of *t*_{ox}. These results show that the gate effect is equivalent to the CoFeB oxidation. We also check whether the CoFeB oxidation near the CoFeB/AlO_{x} interface (i.e., the hotter region) or the CoFeB/W interface (i.e., the colder region) is important for the SSE change. To check this, the interfaces are intentionally modified by introducing a Ti (1 nm) insertion layer. Figure 3d,e show that the *V*_{G} effect disappears when the Ti layer is inserted at the CoFeB/AlO_{x} interface whereas an apparent *V*_{G} effect is still present when the Ti layer is inserted at the W/CoFeB interface. This result confirms that the oxidation state of CoFeB at the CoFeB/AlO_{x} interface, i.e., the hotter region, is crucial for the SSE. Note that oxidation of the CoFeB layer can modulate the shunting effect and consequently alter the SSE and ANE effects. However, the change in shunting estimated from the resistance change by *V*_{G} is only 3.2% (Supplementary Note 6), which is not sufficient to account for the magnitude and even sign modulation of the *V*_{TE} shown in Fig. 2c.

In this work, we demonstrate that the SSE signal enhances by gate voltage that modulates the oxidation state of FM. Our theory describes the enhancement of SSE with a reduced exchange interaction at the hotter region of FM.

Possible consequences of the oxidation other than a reduced exchange may include an increased damping, a formation of an antiferromagnetic phase such as CoO and FeO_{x} at the interface^{28}, a reduced saturation magnetization, or a change of magnetic anisotropy. Therefore, we also check whether these changes can explain our experimental observation. Numerical simulations based on the stochastic LLG equation (Supplementary Note 2) show that the increased damping at the hotter region enhances the SSE signal by <50%, which is much weaker than the effect of reduced exchange. Simulations also show that a formation of an antiferromagnetic phase, a reduced saturation magnetization, or a change of magnetic anisotropy of oxidized FM lattices is unable to describe a largely enhanced SSE due to the oxidation. On the other hand, it should be noted that the reduced electronic and phononic heat conductivity in oxidized FM lattices can induce a larger thermal gradient compared to non-oxidized ferromagnet layers, since insulators typically have lower thermal conductivity than metals. Although the net SSE enhancement induced by oxidation can include a contribution from an increased thermal gradient in general, our analysis suggests that the exchange modulation is dominant for our experiment (Supplementary Note 7). Therefore, we conclude that the reduced exchange interaction at the hotter region is a main cause of the observed efficient *V*_{G}-induced enhancement of SSE.

Although the magnitude of thermoelectric voltages in our device is still far from practical applications for energy harvesters, our work demonstrating a proof-of-concept for enhancing the SSE through the oxygen manipulation in NM/FM/oxide multilayers could pave an efficient way for further development for the SSE-based thermoelectric devices. As we explained in the beginning of this letter, the thermoelectric conversion via SSE consists of three separate processes and the enhancement of SSE in each process can be multiplied. Therefore, our approach, a reduced exchange interaction at the hotter region, can be combined with FM/NM interface engineering and strong spin-orbit-coupled NM to further enhance the SSE signal. Moreover, our approach is far more general than we demonstrate here. The reduced exchange at the hotter region can be realized in magnetic insulators that are widely used for the SSE studies^{2,15,16,17,18,19,20,21,29,30}. It is not limited to single layer FM but is also applicable to multiple layers consisting of two or more FMs having different exchange interaction, yielding a wide variation of material combinations. Moreover, the enhanced SSE by the exchange engineering can be combined with thermoelectric effect induced by couplings among magnon, electron, and phonon systems to further improve the thermoelectric signal^{31,32,33,34,35,36}. Optimization of such multilayers based on the concept we report here paves a way to realize practical applications based on the SSE and broadens the scope of material engineering for the SSE-based thermoelectric devices.

## Methods

### Sample preparation

Samples of W(or Ti)/CoFeB/AlO_{x} structure were grown on thermally oxidized Si substrates by magnetron sputtering with a base pressure of 4.0 × 10^{−6} Pa. The metallic layers were deposited at a working Ar pressure of 0.4 Pa and a power of 30 W, and the AlO_{x} layer was formed by plasma oxidation of an Al layer with an O_{2} pressure of 4 Pa and a power of 30 W. A bar-shaped device of 15 μm × 1000 μm was patterned by using photolithography and ion milling process. A gate oxide of ZrO_{2} (40 nm) was grown at 125 °C by plasma-enhanced atomic layer deposition using a TEMAZ [Tetrakis (ethylmethylamido) zirconium] precursor and O_{2}. The gate electrode (15 μm × 20 μm) of Ru (20 nm) was defined at the centre of the bar-shaped device.

### Thermoelectric measurement

Thermoelectric voltage was measured by illuminating a focused laser with a spot size of 5 μm and a wavelength of 660 nm that generated a vertical temperature gradient. During the measurement, the laser spot was positioned at the centre of the devices by monitoring the reflectance of the laser using a photodiode sensor. Prior to the measurement, a gate voltage was applied to the Ru gate electrode for 5 min at 100 °C with a ground connected to the W/CoFeB electrode. Thermoelectric measurements were carried out with the gate floating at room temperature, and each measurement was repeated more than 3 times.

### Numerical simulation

We perform atomistic model simulations with stochastic Landau-Lifshitz-Gilbert (LLG) equation for one-dimensional system consisting of ten layers along the *z*-axis. The system is allowed to have inhomogeneous exchange (including antiferromagnetic exchange) and damping. The stochastic LLG equation for the unit magnetization \({\hat{{{{{{\bf{m}}}}}}}}_{i}\) of the *i*th layer is \(\frac{d{\hat{{{{{{\bf{m}}}}}}}}_{i}}{{dt}}=-\gamma {\hat{{{{{{\bf{m}}}}}}}}_{i}\times \left({{{{{{\bf{H}}}}}}}_{{{{{{\rm{eff}}}}}},i}{{{{{\boldsymbol{+}}}}}}{{{{{{\bf{H}}}}}}}_{{{{{{\rm{th}}}}}},i}\right)+{\alpha }_{i}{\hat{{{{{{\bf{m}}}}}}}}_{i}\times \frac{d{\hat{{{{{{\bf{m}}}}}}}}_{i}}{{dt}}\), where \(\gamma\) is the gyromagnetic ratio and \({\alpha }_{i}\) is the damping parameter of the *i*th layer. The effective field \({{{{{{\bf{H}}}}}}}_{{{{{{\rm{eff}}}}}},i}\left({{{{{\boldsymbol{=}}}}}}\frac{2{A}_{{ex},i}}{{M}_{s}}\frac{{\partial }^{2}{\hat{{{{{{\bf{m}}}}}}}}_{i}}{\partial {z}^{2}}{{{{{\boldsymbol{-}}}}}}\frac{2{K}_{h}}{{M}_{s}}{m}_{z}\hat{{{{{{\bf{z}}}}}}}{{{{{\boldsymbol{+}}}}}}{H}_{{{{{{\rm{ext}}}}}}}\hat{{{{{{\bf{x}}}}}}}\right)\) consists of the exchange field, easy-plane anisotropy field, and external magnetic field \({H}_{{{{{{\rm{ext}}}}}}}\), where \({A}_{{ex},i}\) is the exchange stiffness of the *i*th layer, \({M}_{s}\) is the saturation magnetization, \({K}_{h}\) is the easy-plane anisotropy energy. The thermal fluctuation field \({{{{{{\bf{H}}}}}}}_{{{{{{\rm{th}}}}}},i}\) obeys \(\langle {{{{{{\bf{H}}}}}}}_{{{{{{\rm{th}}}}}},i}(t)\rangle=0\) and \(\langle {{{{{{\bf{H}}}}}}}_{{{{{{\rm{th}}}}}},i}(t){{{{{{\bf{H}}}}}}}_{{{{{{\rm{th}}}}}},j}({t{{\hbox{'}}}})\rangle=\frac{2{k}_{B}{T}_{i}{\alpha }_{i}}{\gamma V{M}_{s}}{\delta }_{{ij}}\delta \left(t-{t}^{{\prime} }\right)\), where \({k}_{B}\) is the Boltzmann constant, \({T}_{i}\) is temperature of the *i*th layer and \(V\) is the volume.

Following Ref. ^{22}, we calculate the SSE signal from \({j}_{{Tgrad}}^{s}-{j}_{{Tconst}}^{s}\) where \({j}_{{Tgrad}}^{s}\) is the spin pumping current proportional to the time average \(\langle {[{\hat{{{{{{\bf{m}}}}}}}}_{N}\times d{\hat{{{{{{\bf{m}}}}}}}}_{N}{{{{{\boldsymbol{/}}}}}}{dt}]}_{x}\rangle\) with \(N=10\) (i.e., the coldest layer) in the presence of temperature gradient whereas \({j}_{{Tconst}}^{s}\) is the spin pumping current at a constant temperature.

## Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## References

Elsheikh, M. H. et al. A review on thermoelectric renewable energy: Principle parameters that affect their performance.

*Renew. Sust. Energ. Rev.***30**, 337–355 (2014).Disalvo, F. J. Thermoelectric cooling and power generation.

*Science***285**, 703–706 (1999).Bell, L. E. Cooling, heating, generating power, and recovering waste heat with thermoelectric systems.

*Science***321**, 1457 (2008).Uchida, K. et al. Observation of the spin Seebeck effect.

*Nature***455**, 778–781 (2008).Uchida, K. et al. Spin Seebeck insulator.

*Nat. Mater.***9**, 894–897 (2010).Jaworski, C. M. et al. Observation of the spin-Seebeck effect in a ferromagnetic semiconductor.

*Nat. Mater.***9**, 898–903 (2010).Jaworski, C., Myers, R., Johnston-Halperin, E. & Heremans, J. Giant spin Seebeck effect in a non-magnetic material.

*Nature***487**, 210–213 (2012).Bauer, G. E. W., Saitoh, E. & van Wees, B. J. Spin caloritronics.

*Nat. Mater.***11**, 391–399 (2012).Kirihara, A. et al. Spin-current-driven thermoelectric coating.

*Nat. Mater.***11**, 686–689 (2012).Xiao, J., Bauer, G. E. W., Uchida, K., Saitoh, E. & Maekawa, S. Theory of magnon-driven spin Seebeck effect.

*Phys. Rev. B***81**, 214418 (2010).Adachi, H., Ohe, J., Takahashi, S. & Maekawa, S. Linear-response theory of spin Seebeck effect in ferromagnetic insulators.

*Phys. Rev. B***83**, 094410 (2011).Schreier, M. et al. Magnon, phonon, and electron temperature profiles and the spin Seebeck effect in magnetic insulator/normal metal hybrid structures.

*Phys. Rev. B***88**, 094410 (2013).Rezende, S. M. et al. Magnon spin-current theory for the longitudinal spin-Seebeck effect.

*Phys. Rev. B***89**, 014416 (2014).Cornelissen, L. J., Peters, K. J. H., Bauer, G. E. W., Duine, R. A. & van Wees, B. J. Magnon spin transport driven by the magnon chemical potential in a magnetic insulator.

*Phys. Rev. B***94**, 014412 (2016).Yuasa, H., Tamae, K. & Onizuka, N. Spin mixing conductance enhancement by increasing magnetic density.

*AIP Adv.***7**, 055928 (2017).Kikuchi, D. et al. Enhancement of spin-Seebeck effect by inserting ultra-thin Fe

_{70}Cu_{30}interlayer.*Appl. Phys. Lett.***106**, 082401 (2015).Kalappattil, V. et al. Giant spin Seebeck effect through an interface organic semiconductor.

*Mater. Horiz.***7**, 1413 (2020).Yuasa, H., Nakata, F., Nakamura, R. & Kurokawa, Y. Spin Seebeck coefficient enhancement by using Ta

_{50}W_{50}alloy and YIG/Ru interface.*J. Phys. D: Appl. Phys.***51**, 134002 (2018).Tian, K. & Tiwari, A. CuPt alloy thin films for application in spin thermoelectrics.

*Sci. Rep.***9**, 3133 (2019).Chang, H. et al. Role of damping in spin Seebeck effect in yttrium iron garnet thin films.

*Sci. Adv.***3**, e1601614 (2017).Kim, M. Y., Park, S. J., Kim, G.-Y., Choi, S.-Y. & Jin, H. Designing efficient spin Seebeck-based thermoelectric devices via simultaneous optimization of bulk and interface properties.

*Energy Environ. Sci.***14**, 3480–3491 (2021).Ohe, J.-i, Adachi, H., Takahashi, S. & Maekawa, S. Numerical study on the spin Seebeck effect.

*Phys. Rev. B***83**, 115118 (2011).Bauer, U. et al. Magneto–ionic control of interfacial magnetism.

*Nat. Mater.***14**, 174–181 (2015).Baek, S. C. et al. Complementary logic operation based on electric-field controlled spin–orbit torques.

*Nat. Electron.***1**, 398 (2018).Pai, C.-F. et al. Spin transfer torque devices utilizing the giant spin Hall effect of tungsten.

*Appl. Phys. Lett.***101**, 122404 (2012).Gamino, M. et al. Longitudinal spin Seebeck effect and anomalous Nernst effect in CoFeB/non-magnetic metal bilayers.

*J. Magn. Magn. Mater.***527**, 167778 (2021).Du, C., Wang, H., Yang, F. & Hammel, P. C. Systematic variation of spin-orbit coupling with d-orbital filling: Large inverse spin Hall effect in 3d transition metals.

*Phys. Rev. B***90**, 140407(R) (2014).Lee, D. J. et al. Effects of interfacial oxidization on magnetic damping and spin–orbit torques.

*ACS Appl. Mater. Interfac.***13**, 19414 (2021).Fayaz, M. U. et al. Simultaneous detection of the spin Hall magnetoresistance and Joule heating-induced spin Seebeck effect in Gd

_{3}Fe_{5}O_{12}/Pt bilayers.*J. Appl. Phys.***126**, 183901 (2019).Kurokawa, Y. et al. Scalable spin Seebeck thermoelectric generation using Fe-oxide nanoparticle assembled film on flexible substrate.

*Sci. Rep.***12**, 16605 (2022).Zhou, W. et al. Seebeck-driven transverse thermoelectric generation.

*Nat. Mater.***20**, 463–467 (2021).Pan, Y. et al. Giant anomalous Nernst signal in the antiferromagnet YbMnBi

_{2}.*Nat. Mater.***21**, 203–209 (2022).Yang, Z. et al. Scalable Nernst thermoelectric power using a coiled galfenol wire.

*AIP Adv.***7**, 095017 (2017).Watzman, S. J. et al. Magnon-drag thermopower and Nernst coefficient in Fe, Co, and Ni.

*Phys. Rev. B***94**, 144407 (2016).Jaworski, C. M. et al. Spin-Seebeck Effect: A Phonon Driven Spin Distribution.

*Phys. Rev. Lett.***106**, 186601 (2011).Uchida, K. et al. Long-range spin Seebeck effect and acoustic spin pumping.

*Nat. Mater.***10**, 737–741 (2011).

## Acknowledgements

This work was supported by support from Samsung Research Funding Center of Samsung Electronics under Project Number SRFC-MA1802-01 and the National Research Foundation of Korea (NRF) (NRF-2022R1A4A1031349). K.-J.L. was supported by the NRF (NRF-2020R1A2C3013302). K.-J.K and B.-G.P were supported by KAIST-funded Global Singularity Research Program for 2021. K.-W.K. was supported by the KIST institutional program.

## Author information

### Authors and Affiliations

### Contributions

B.-G.P. and K.-J.L. planned and supervised the study. J.-M.K. and M.-G.K. fabricated devices and performed thermoelectric measurements with the help of J.-G.C., S.L., J.P., C.V.P., K.-J. K., and J.-R.J. S.-J.K., K.-W.K. and K.-J.L. performed theoretical and numerical studies. K.-J.L., B.-G.P., J.-M.K., S.-J.K., and M.-G.K. wrote the paper.

### Corresponding authors

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

*Nature Communications* thanks Ken-ichi Uchida and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

## Additional information

**Publisher’s note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Supplementary information

## Rights and permissions

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

## About this article

### Cite this article

Kim, JM., Kim, SJ., Kang, MG. *et al.* Enhanced spin Seebeck effect via oxygen manipulation.
*Nat Commun* **14**, 3365 (2023). https://doi.org/10.1038/s41467-023-39116-x

Received:

Accepted:

Published:

DOI: https://doi.org/10.1038/s41467-023-39116-x

## Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.