Raising the thermoelectric voltage in spin thermoelectric generators is an important subject. We investigated the substitution of bismuth for yttrium to increase spin pumping at the paramagnetic metal and ferrimagnetic insulator (PM/FMI) interface, and tested bismuth-substituted iron garnet films grown by liquid phase epitaxy. Epitaxial Bi-substituted iron garnet films exhibit large growth-induced magnetic anisotropy perpendicular to the film surface. This anisotropy increases the magnetic damping α in the FMI; α also increases with increasing Bi content. We report the rise in voltage observed in a spin thermoelectric generator incorporating Bi-substituted YIG films grown by liquid phase epitaxy, and explain the origin of the voltage rise based on the results of FMR measurements.
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 VSTE.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.
II. CRYSTALLINITY AND SOC OF LPE Bi:YIG FILMS
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 O2- 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 L3d-orbit is produced. Although the 3d-orbit degeneracy is removed by the ligand field and L3d-orbit is normally zero, ligand field distortion produces an additional orbital component of angular momentum L3d-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, KuG, and a stress-induced anisotropy, Kuλ, owing to the lattice misfit, a, between the film and substrate. It is assumed that KuG and Kuλ, which are enhanced by Bi substitution, increase the ligand field distortion.
III. GROWTH-INDUCED MAGNETIC ANISOTROPY OF LPE Bi:YIG FILMS
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 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 Ku is composed of Kuλ and KuG as follows:12
Δa⊥/aBi: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 . It has also been predicted that KuG 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, Kuλ 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, KuG 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 Ku = MSHa/2. The values of Ku estimated for x = 0.65 and x = 1.27 are 3.0 × 103 J/m3 and 4.4 × 103 J/m3, respectively. Both Kuλ and KuG 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 (Nd3-xBixFe5O12, Bi:NdIG) films prepared on (001)- and (111)-oriented GGG substrates using the MOD method (see Fig. 4 in Ref. 16).
IV. FMR CHARACTERISTICS OF LPE Bi:YIG FILMS
The magnetization dynamics of a ferromagnet influenced by the exchange interaction between moments has been described by defining the exchange interaction constant Jex.17,18 The exchange spin current that is produced under the magnetic exchange interaction can be expressed as JS = AM × ∇M.18 M is the magnetization vector, and A, the exchange stiffness, is given by 2Jexa2/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 ωk = γHeff + Dk2 for an angular frequency ωk and wavenumber k. By incorporating JS into the Landau-Lifshitz-Gilbert equation,19,20 low-lying magnetic excitations are described as follows:18
where D (=AγMS) 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 hl 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 by which M is relaxed in the direction of the effective field Heff, 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 H. By considering the type of spin-wave propagation, the inhomogeneity of a spin-wave medium (FMI) and the magnetic properties of the FMI, 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 Hint due to intrinsic damping described by αint. The second term HTMS is due to two-magnon scattering.26,27 The third term HILB 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 Hpump (= (2/γ0)α′fr)17,28 to the pumping of spin-wave spin currents at the PM/FMI interface, Eq. (4) expands as follows:
Here, α′(= αpump) 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 αec27 for eddy currents.
Figure 2 shows the results for the FMR linewidth H measured in the x range from 0 to 1.27. The HPt/Bi:YIG measured for films having a Pt layer was almost the same as the HBi:YIG for films with no Pt layer. While no significant difference in H was observed between films having a 4-nm-thick Pt layer and those with no Pt layer, H increased with increasing x. The H for x = 1.27 (Y1.73 Bi1.27Fe5O12) 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 H (= HPt/Bi:NdIG) measured in the MOD Nd2Bi1Fe5O12 film increased by 35% as a result of a 4-nm-thick Pt layer. ΔHpump ≈ 0 (ΔHPt/Bi:YIG ≈ ΔHBi: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, H increases to a certain extent owing to the Pt coating (ΔHPt/Bi:NdIG > ΔHBi: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 VLPE/VMOD is 50. While the PM/FMI interface related to Hpump is a two-dimensional plane, HILB including the effect of Ku has a volume dependence on magnetic damping. Namely, the thickness of the LPE and MOD films is a significant factor influencing the value of HILB. In addition to that, the damping constant αILB of LPE Bi:YIG films is initially large because of the growth-induced anisotropy. We presume that another reason why the Hpump 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 HILB>Hpump is enhanced in LPE Bi:YIG films.
V. SPIN THERMOELECTRIC VOLTAGE
To measure VSTE, 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 VSTE measurements, the probe distance ld and temperature difference T were set to 5 mm and 10 K, respectively.
Figure 3 shows the dependence of the spin Seebeck coefficient SSSE on x. Figure 3 includes plots of SSSE data measured for STE generators incorporating MOD films: curves (b)16 and (c).2 The SSSE for spin generators incorporating MOD films increases with increasing x. That increase is particularly clear for spin generators incorporating LPE films. The SSSE 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 αBi: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 SSSE 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 tPt exists between the LPE and MOD film as seen in Fig. 3. Here, the tPt of the LPE films is 4 nm, and that of the MOD films is 10 nm. SSSE 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 m. The dependence of SSSE 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 SSSE on film thickness.
We expected based on previous theoretical17,30–32 and experimental33 studies that the damping constant αPt/Bi:YIG would become much larger when a Pt layer is sputtered on the Bi:YIG film surface. However, the αPt/Bi:YIG observed by FMR measurements was almost the same as αBi: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 αBi: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 SSSE 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 αPM/FMI ≈ αFMI and enhanced SSSE 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 SSSE 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 SSSE value observed for the LPE films (1.17 V/K for Y1.97Bi1.03Fe5O12) is much larger than the value observed for the MOD films (0.08 μV/K for Y2.2Yb0.8Fe5O12). 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 VSTE 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.