Enhancement of the spin Seebeck effect owing to bismuth substitution in thermoelectric generators fabricated from LPE Bi-substituted YIG films

A spin-thermoelectric (STE) generator is composed of a thin paramagnetic metal (PM) layer, a ferrimagnetic insulator (FMI) and a PM/FMI bilayer interface. Various studies have focused on improving the characteristics of each part of this structure in order to raise the spin-thermoelectric voltage V_STE.^1–11 

It has been reported that bismuth-substituted iron garnet (Bi:YIG) films grown by liquid phase epitaxy (LPE) on gadolinium gallium garnet (GGG) substrates exhibit a large growth-induced anisotropy perpendicular to the film surface.¹² This anisotropy increases the magnetic damping. The damping process occurs through energy dissipation by spin-orbit coupling (SOC). Although, as a modern concept in STE generation, the effect of spin-orbit interactions (SOI) on free s-electron spins in the PM layer is used to explain the inverse spin Hall effect (ISHE), here we consider the SOC of local d-electron spins that is known as Russell-Saunders coupling, and study its effects on spin-thermoelectric phenomena.

The melt composition for Bi:YIG films grown by LPE was based on a PbO-B₂O₃ flux with the addition of varying amounts of Bi₂O₃ and stepwise alteration of the cation (Y, Bi, Pb, B and Fe) ratios. Bi:YIG films grown on (111) GGG substrates with dimensions of 10 mm (L) × 10 mm (W) × 0.5 mm (T) were cut into rectangles with dimensions of 7 mm (L) × 3 mm (W) for STE measurements.⁵ The film thickness and composition were measured from cross-sections observed by scanning electron microscopy (SEM) and electron probe micro-analysis (EPMA), respectively. The crystallinity of the Bi:YIG films was confirmed by X-ray diffraction (XRD), checking the intensity and full width at half maximum FWHM of diffraction peaks, and a metal organic decomposition (MOD) Bi:NdIG (Nd₂Bi₁Fe₅O₁₂) film¹³ was observed for comparison. The crystal quality of the MOD Bi:NdIG film was lower than that of the LPE Bi:YIG films, whereas the crystallinity of the Bi:YIG films was as high as that of the GGG single crystal used as the LPE substrate.

Bi is characterized by strong polarizability. Thus, mixing of the 6p orbitals of Bi³⁺ with the O^2- 2p orbitals may be assumed, which increases the effective SOC responsible for level splitting of the iron ions.¹⁴ This means that the ligand fields for the 3d electrons of Fe are changed due to Bi-6p and O-2p orbital mixing, and that an orbital angular momentum L_3d-orbit is produced. Although the 3d-orbit degeneracy is removed by the ligand field and L_3d-orbit is normally zero, ligand field distortion produces an additional orbital component of angular momentum $Δ$L_3d-orbit with a non-zero value. This leads to LS coupling (Russell-Saunders coupling). As described in Sec. III, LPE Bi:YIG films grown on GGG substrates exhibit both a large growth-induced magnetic anisotropy, K_u^G, and a stress-induced anisotropy, K_u^λ, owing to the lattice misfit, $Δ$a, between the film and substrate. It is assumed that K_u^G and K_u^λ, which are enhanced by Bi substitution, increase the ligand field distortion.

LPE growth in the direction perpendicular to the film plane occurs without any restrictive force. However, LPE Bi:YIG films are distorted in the growth plane due to the $Δ$a between the film and the substrate. A large uniaxial magnetic anisotropy perpendicular to the film surface is observed for LPE Bi-substituted iron garnet films grown on (111) oriented GGG substrates. The uniaxial anisotropy constant K_u is composed of K_u^λ and K_u^G as follows:¹² 

and

Δa^⊥/a_Bi:YIG, E and μ₁₁₁ are the relative perpendicular lattice mismatch, the Young’s modulus and the Poisson constant, respectively. Δa^⊥ is given by the relation $Δa⊥=|aGGG−aBi:YIG⊥|$⁠. It has also been predicted that K_u^G is determined by iron ions at octahedral and tetrahedral sites which are affected by the ordering of Bi³⁺ ions.¹² The dependence of the magnetostriction constant λ₁₁₁ in the <111> direction on the Bi content x is given by the experimental relation λ₁₁₁ = (−2.73 × 10⁻⁶) × (1 + 0.23x).^12,E and μ₁₁₁ are 2.06 × 10¹¹ J/m³ and 0.30, respectively.¹⁵ With these values and those measured for Δa^⊥/a, K_u^λ given by Eq. (2) can be calculated to be 3.5 × 10³ J/m³ for a Bi content of x = 0.92. In experiments where the grown films were lattice-matched to the substrates, K_u^G was estimated to be 5.0 × 10³ J/m³ for x = 0.76 (lattice misfit: Δa < 2 × 10⁻³Å)¹⁵ or 0.5 − 1.5 × 10⁴ J/m³ for x = 0.90.¹²,Figure 1 shows the magnetization curves (M-H curves) for LPE Bi:YIG films observed under in-plane fields parallel to the film surface. The change in the shape of the curves with increasing x originates from the increase in uniaxial magnetic anisotropy perpendicular to the film surface. These uniaxial anisotropies can be evaluated from the relation K_u = M_SH_a/2. The values of K_u estimated for x = 0.65 and x = 1.27 are 3.0 × 10³ J/m³ and 4.4 × 10³ J/m³, respectively. Both K_u^λ and K_u^G are considered to play a role in the anisotropy of Bi:YIG films grown on (111) GGG substrates, since a large lattice misfit exists for those films as well. Growth-induced anisotropy was not observed in Bi-substituted neodymium iron garnet (Nd_3-xBi_xFe₅O₁₂, Bi:NdIG) films prepared on (001)- and (111)-oriented GGG substrates using the MOD method (see Fig. 4 in Ref. 16).

The magnetization dynamics of a ferromagnet influenced by the exchange interaction between moments has been described by defining the exchange interaction constant J_ex.^17,18 The exchange spin current that is produced under the magnetic exchange interaction can be expressed as J_S = AM × ∇M.¹⁸ M is the magnetization vector, and A, the exchange stiffness, is given by 2J_exa²/γ², where a is the spacing of local spins, and γ is the gyromagnetic ratio. The steady spin-wave spin currents flow by excitation of the magnetization dynamics. The exchange spin currents due to the spin-exchange interaction exhibit the dispersion relation ω_k = γH_eff + Dk² for an angular frequency ω_k and wavenumber k. By incorporating J_S into the Landau-Lifshitz-Gilbert equation,^19,20 low-lying magnetic excitations are described as follows:¹⁸ 

where D (=AγM_S) is the exchange stiffness and α is the Gilbert damping constant. Although the thermal fluctuation of magnetic moments is not considered in Eq. (3), a method that takes the random Langevin field h_l into consideration is known.²¹ The steady exchange spin currents represented by the second term on the right-hand side of Eq. (3) flow out by means of the magnetization dynamics magnetically or thermally excited inside a closed surface defined by Gauss’ divergence theorem. In the case of a spin current thermally generated by the temperature gradient, it has also been indicated that the spin current in the FMI is carried by the spin waves with wave vector k.²² The third term including the damping constant α represents the Gilbert damping torque $M×Ṁ$ by which M is relaxed in the direction of the effective field H_eff, and this term is based on the dissipation of energy transferred from the spin system to the phonon system through SOC²³ and inhomogeneous magnon scattering due to crystal imperfections.^24,25 The damping of the magnetization precession occurs through dissipating the spin precession energy, and the damping can be evaluated by measuring the FMR linewidth $Δ$H. By considering the type of spin-wave propagation, the inhomogeneity of a spin-wave medium (FMI) and the magnetic properties of the FMI, $Δ$H (∝ α) can be described by the expression

where γ₀ is the reduced gyromagnetic ratio γ/2π. The first term on the right-hand side represents $Δ$H_int due to intrinsic damping described by α_int. The second term $Δ$H_TMS is due to two-magnon scattering.^26,27 The third term $Δ$H_ILB is the inhomogeneous line-broadening term due to inhomogeneous scattering including the effect of the growth-induced magnetic anisotropy in FMI. By adding the energy dissipation term $Δ$H_pump (= (2/γ₀)α′f_r)^17,28 to the pumping of spin-wave spin currents at the PM/FMI interface, Eq. (4) expands as follows:

Here, α′(= α_pump) is an additional damping constant that represents the pumping of spin currents from the FMI to the PM layer. In this case, we do not consider the damping constant α_ec²⁷ for eddy currents.

Figure 2 shows the results for the FMR linewidth $Δ$H measured in the x range from 0 to 1.27. The $Δ$H_Pt/Bi:YIG measured for films having a Pt layer was almost the same as the $Δ$H_Bi:YIG for films with no Pt layer. While no significant difference in $Δ$H was observed between films having a 4-nm-thick Pt layer and those with no Pt layer, $Δ$H increased with increasing x. The $Δ$H for x = 1.27 (Y_1.73 Bi_1.27Fe₅O₁₂) was 2.17 times larger than that for x = 0 (Y₃Fe₅O₁₂) owing to growth-induced anisotropy appearing in LPE Bi:YIG films. On the other hand, the $Δ$H (= $Δ$H_Pt/Bi:NdIG) measured in the MOD Nd₂Bi₁Fe₅O₁₂ film increased by 35% as a result of a 4-nm-thick Pt layer. ΔH_pump ≈ 0 (ΔH_Pt/Bi:YIG ≈ ΔH_Bi:YIG) in the LPE Bi:YIG films that exhibit strong growth-induced magnetic anisotropy perpendicular to the film surface, while in the MOD Bi:NdIG films that do not exhibit growth-induced anisotropy, $Δ$H increases to a certain extent owing to the Pt coating (ΔH_Pt/Bi:NdIG > ΔH_Bi:NdIG). The thickness of the LPE Bi:YIG films is 5 – 10 μm, and that of the MOD Bi:NdIG films is 100 – 200 nm.¹³ The volume ratio V_LPE/V_MOD is 50. While the PM/FMI interface related to $Δ$H_pump is a two-dimensional plane, $Δ$H_ILB including the effect of K_u has a volume dependence on magnetic damping. Namely, the thickness of the LPE and MOD films is a significant factor influencing the value of $Δ$H_ILB. In addition to that, the damping constant α_ILB of LPE Bi:YIG films is initially large because of the growth-induced anisotropy. We presume that another reason why the $Δ$H_pump observed in LPE Bi:YIG films appeared to be very small or almost zero has to do with the difference in thickness between the LPE and MOD films. We believe the relation $Δ$H_ILB>$Δ$H_pump is enhanced in LPE Bi:YIG films.

To measure V_STE, a 4-nm-thick Pt layer was deposited by ultra-high-vacuum magnetron sputtering on the FMI surface. The length and width of the Pt layer were 7 mm and 1 mm, respectively. In the V_STE measurements, the probe distance l_d and temperature difference $Δ$T were set to 5 mm and 10 K, respectively.

Figure 3 shows the dependence of the spin Seebeck coefficient S_SSE on x. Figure 3 includes plots of S_SSE data measured for STE generators incorporating MOD films: curves (b)¹⁶ and (c).² The S_SSE for spin generators incorporating MOD films increases with increasing x. That increase is particularly clear for spin generators incorporating LPE films. The S_SSE value for x = 1.3 is about 1.5 times that for x = 0 in our measurements. As described in Sec. II, it has been suggested that mixing of the 6p orbitals of Bi ions with the O-2p orbitals increases the effective SOC for Fe³⁺ ions.¹² SOC is thought to expedite the energy transfer between the spin and phonon systems. We presume that this physical phenomenon might increase α_Bi:YIG and, during STE generation, the enhanced energy transfer mechanism due to SOC for the heat excitation of magnetization precession will contribute to the generation of larger spin currents in Bi:YIG films.

As shown in Fig. 3, there is a large difference in the S_SSE values for STE generators incorporating LPE and MOD films. Whereas growth-induced anisotropy was not observed in the MOD Bi-substituted films, a difference in Pt layer thickness t_Pt exists between the LPE and MOD film as seen in Fig. 3. Here, the t_Pt of the LPE films is 4 nm, and that of the MOD films is 10 nm. S_SSE values observed in STE generators with thicker Pt layers are typically smaller than those observed in generators with thinner Pt layers.^4,5 However, we presume that this difference might be due to thickness differences between the LPE and MOD films. The MOD films tested are as thin as 100 – 200 nm, whereas the LPE films have a thickness of 5 – 10 $μ$m. The dependence of S_SSE on film thickness has been presented in Fig. 3 of Ref. 2, Fig. 2(a) of Ref. 29 and Fig. 3 of Ref. 22, which indicate the strong dependence of S_SSE on film thickness.

We expected based on previous theoretical^17,30–32 and experimental³³ studies that the damping constant α_Pt/Bi:YIG would become much larger when a Pt layer is sputtered on the Bi:YIG film surface. However, the α_Pt/Bi:YIG observed by FMR measurements was almost the same as α_Bi:YIG. This indicates that gyromagnetic energy dissipation at the Pt/Bi:YIG interface is very small or almost zero. On the other hand, large uniaxial magnetic anisotropy was induced in the LPE Bi-substituted YIG films, and very large α_Bi:YIG values were observed. The strong damping due to the large magnetic anisotropy induced in the Bi:YIG films leads to the dissipation of a large amount of spin precession energy through the SOC produced in local d-electrons. A comparison of the α and S_SSE characteristics of MOD Bi- and Yb-substituted YIG (Yb:YIG) films revealed that MOD Bi:YIG films exhibit good characteristics for spin pumping while Yb:YIG films show good characteristics for spin current generation.² α_PM/FMI ≈ α_FMI and enhanced S_SSE characteristics have been observed for MOD Yb:YIG films, as confirmed by Figs. 4(a) and 4(b) in Ref. 2. The damping characteristics observed in the case of our LPE Bi:YIG films and the S_SSE characteristics of STE generators incorporating LPE Bi:YIG films are very similar to those of the MOD Yb:YIG films reported in the literature, though the S_SSE value observed for the LPE films (1.17 $μ$V/K for Y_1.97Bi_1.03Fe₅O₁₂) is much larger than the value observed for the MOD films (0.08 μV/K for Y_2.2Yb_0.8Fe₅O₁₂). We conclude that larger spin currents were generated in the LPE Bi-substituted YIG films, which exhibit large growth-induced magnetic anisotropy, and thus, increased values of V_STE were observed in STE generators incorporating LPE Bi:YIG films.

We would like to express our gratitude to Y. Kono of Denso Corp. for useful discussions, and Y. Fukuma of Kyushu Institute of Technology for his assistance in the FMR measurements.

The data that support the findings of this study are available within the article.