Generation of spin currents by surface plasmon resonance

Surface plasmons, free-electron collective oscillations in metallic nanostructures, provide abundant routes to manipulate light–electron interactions that can localize light energy and alter electromagnetic field distributions at subwavelength scales. The research field of plasmonics thus integrates nano-photonics with electronics. In contrast, electronics is also entering a new era of spintronics, where spin currents play a central role in driving devices. However, plasmonics and spin-current physics have so far been developed independently. Here we report the generation of spin currents by surface plasmon resonance. Using Au nanoparticles embedded in Pt/BiY2Fe5O12 bilayer films, we show that, when the Au nanoparticles fulfill the surface-plasmon-resonance conditions, spin currents are generated across the Pt/BiY2Fe5O12 interface. This spin-current generation cannot be explained by conventional heating effects, requiring us to introduce nonequilibrium magnons excited by surface-plasmon-induced evanescent electromagnetic fields in BiY2Fe5O12. This plasmonic spin pumping integrates surface plasmons with spin-current physics, opening the door to plasmonic spintronics.

sample without Au NPs (see gray triangle data points) and found that its λ dependence is similar to the result for the Pt(5 nm)/BiY2Fe5O12 sample without Au NP. Similar signals appear also in the Black-ink/Pt(15 nm)/BiY2Fe5O12 sample. These results confirm that the background spin-current signals in the Pt/BiY2Fe5O12 samples without Au NPs are attributed to the heating of the samples, or the longitudinal spin Seebeck effect (LSSE) (note that the enhancement of the heating signal in the Black-ink/Pt(15 nm)/BiY2Fe5O12 sample is due to the larger temperature rise caused by light absorption by the black ink). In the Pt(15 nm)/BiY2Fe5O12/Au-NP sample, we observed the voltage enhancement due to the plasmonic spin pumping under the SPR condition (see blue circle data points). The voltage enhancement observed here is weaker than that in the Pt(5 nm)/BiY2Fe5O12/Au-NP sample because the thicker Pt layer blocks the transmission of light and reduces the magnitude of the near fields in the BiY2Fe5O12 layer, a situation which changes the relative magnitude between the plasmonic-spin-pumping signal and the background LSSE signal.  According to the experimental results in the main text, the wavelength of the incident electromagnetic waves is fixed at λ = 690 nm (λ = 630 nm) for the Pt/BiY2Fe5O12/Au-NP model without (with) the void. c,d, Simulated distributions of |E| in the Pt/BiY2Fe5O12/Au-NP models without and with the void in the z-x plane across the centre of the Au spheroid. In the model without the void, the strong near fields are induced in BiY2Fe5O12 in the vicinity of the Au spheroid due to the SPR. In contrast, in the model with the void, most of the photon energy is confined in the void, indicating that the plasmon-induced near fields cannot interact with magnons in BiY2Fe5O12 with voids. These simulation results are consistent with our experiments, where the plasmonic spin pumping appears in the contacted Pt/BiY2Fe5O12/Au-NP sample while only heating effect appears in the voided sample. e,f, Simulated distributions of the power dissipation Q in the Pt/BiY2Fe5O12/Au-NP models without and with the void in the z-x plane across the centre of the Au spheroid. The maximum of Q is in the vicinity of the Au spheroid in both the models, indicating that the heating due to the SPR is induced near Au NPs irrespective of the presence of voids, allowing us to conclude that the temperature gradient induced by the SPR is of an opposite sign to that induced by the heating of the Pt layer in both the contacted and voided Pt/BiY2Fe5O12/Au-NP samples.
To further discuss the heating effects, we measured the LSSE in the contacted Pt/BiY 2 Fe 5 O 12 /Au-NP and Pt/BiY 2 Fe 5 O 12 samples. As shown in Supplementary Fig. 4a  Following ref. 10, the Hamiltonian that gives rise to the scattering of light by a magnetic system is written where E 1(2) is the incident (scattered) electric field at position r i , j 1(2) represents a Cartesian component of the field vector, and Π j 1(2) (r i ), a term containing the spin operator S(r i ), describes the spin-dependent polarizability tensor at r i . For systems such as BiY 2 Fe 5 O 12 , equation (1) can be expressed in the form 11 to the lowest order in the spin operators, where S ± = S x ± iS y , E ± = E x ± iE y , and v 0 = V/N 0 is the effective block spin volume with the number of unit cells N 0 . In the above equation, Γ ± = G ± iM is the dimensionless magnon-photon coupling constant, where we assume that G and M are real numbers. Note that the magnon-photon coupling in equation (2) forms the basis for the Brillouin light scattering investigation of Y 3 Fe 5 O 12 (ref. 12). The incident electric field E 1 is an external c-number field with the representation where the coefficient satisfies E −K1,ζ1 (t) = E * K1,ζ1 (t) and is expressed as E K1,ζ1 (t) = ξ(K 1 , ζ 1 )E K1,ζ1 with the wavenumber K 1 , polarization ζ 1 , and amplitude E K1,ζ1 . The scattered electric field E 2 is, on the other hand, expressed in a quantized form 10 . It is custom to express this field by using the vector potential A 2 as where c is the velocity of light. The vector potential is represented as where with the photon frequency ν K = cK, the photon annihilation and creation operators a K2,ζ2 and a † −K2,ζ2 , and the polarization vector ξ(K 2 , ζ 2 ). Using the linear spin-wave approximation and (6) with the size of the localized spin S 0 , the magnon-photon interaction is represented as where H.c. means the Hermitian conjugate. In the present situation, the incident electric field E 1 comes from the near-field photons induced by the localized SPR in the Au NPs embedded in the BiY 2 Fe 5 O 12 film.
Therefore, we assume that its polarization direction as well as its propagating direction should be averaged out in the final step of our calculation.
Following the formalism developed in ref. 3, we now calculate the spin current J S generated by the plasmonic spin pumping. We consider a model shown in Supplementary Fig. 6 where s is the conduction-electrons' spin density in PM, S is the localized spin in FI, and J sd is the strength of the interface s-d exchange coupling. The spin current J S generated in PM can be calculated as a rate of change of the spin density in PM as J S = 2 ∑ ri∈PM ∂ t s(r i , t) , where · · · denotes the statistical average at a given time t. Assuming that the spin-orbit interaction is weak enough in the neighborhoods of the interface, the Heisenberg equation of motion for s yields where J k−q sd is the Fourier transform of J sd (r) = J sd ∑ r0∈interface a 3 S δ(r − r 0 ), N P(F) is the number of lattice sites in PM (FI), and we represent the effective block spin volume as v 0 = a 3 S by introducing a S . Here, C < k,q (ω) is the Fourier transform of the interface correlation C < k,q (t, t ) = −i b + q (t )s − k (t) between the magnons and the spin density The process relevant to the plasmonic spin pumping is shown in Supplementary Fig. 6; in the case of the plasmon-induced spin injection, the near-field photons concomitant with surface plasmons excite only magnons in the BiY 2 Fe 5 O 12 film since they are localized in the vicinity of the BiY 2 Fe 5 O 12 /Au-NP interface (see Fig. 3 in the main text and Supplementary Figs 1, 2, and 5). Due to the similarity between this diagram and that for the acoustic spin pumping (ASP) 1,2 (Fig. 10 of ref. 3), the present calculation for the plasmonic spin pumping is mostly the same as that for the ASP, with the replacement of external phonon lines by external photon lines. One big difference is that the intermediate state is given by scattered photons in the present situation whereas it is given by magnons for the ASP. This is because the energy of external photons (1.6-3.1 eV) is much larger than that of magnons (< 0.1 eV), and most of the external photon energy contributing to this process is transferred to scattered photons, leaving a small energy transfer to magnons.
Using the same procedure as in ref. 3, the spin current generated by the process shown in Supplementary   Fig. 6 is calculated to be where N int is the number of localized spins in FI at the interface. The quantity B k,q (ν K0 ) is defined by with the shorthand notation is the retarded component of the itinerant-spin-density propagator in PM with χ P , λ sf , and τ sf being respectively the paramagnetic susceptibility, spin diffusion length, and spin relaxation time. Also, X R q (ω) = (ω− ω q +iαω) −1 is the retarded component of the magnon propagator with ω q = γH 0 + ω q and α being respectively the magnon frequency and Gilbert damping constant, and D R is the retarded component of the photon propagator. Integrating over ω by picking up the magnon poles and using the fact that the dominant contribution comes from a region q whereK 0 = K 0 /K 0 andq = q/q. Therefore, the spin current pumped by light illumination is finally given by where 3 Υ is a factor measuring the strength of the magnetic coupling at the PM/FI interface (corresponding to the spin mixing conductance), a is the lattice constant of PM, and (1+x 2 ) 2 +(2S0Jexτ sf / ) 2 y 2 ≈ 0.142a S K 0 with the strength of the exchange coupling J ex in FI and the dimensionless variables x = λ sf k and y = ω q /(2J ex S 0 ). In equation (2) in the main text, for simplicity, we describe ν K0 and E K0 as ν and E, respectively. Equation (13) represents a physical process in which magnons in FI is excited by a small energy transfer from external photons, thereby having the same sign as that for the ASP 1,2, * 3 . This situation is consistent with the experimental results of the ASP in a Pt/Y 3 Fe 5 O 12 structure (e.g., Fig. 4d of ref. 1), where the sign of the background LSSE signal owing to the heating of Y 3 Fe 5 O 12 is opposite to that of the ASP signal owing to the vibration of Y 3 Fe 5 O 12 . Since the direction of the temperature gradient across the Pt/BiY 2 Fe 5 O 12 interface in the present experimental configuration is opposite to that in the ASP configuration, the voltage signal coming from the plasmonic spin pumping has the same sign as the background LSSE signal (see Fig. 4b in the main text). Note that, theoretically, there can be another plasmonic spin pumping process in which the plasmon-enhanced near fields first excite phonons through phonon Raman scattering and then the resultant phonons drive the spin * 3 Note that the definition of the voltage V in this paper is opposite in sign to that in our previous literature on the ASP. pumping via magnon-phonon interaction. This higher-order process can be taken into account with the replacement Γ + Γ − → Λ 2 Υ 2 and B k,q (ν K0 ) → B k,q (ν K0 ), where Λ is the phonon-photon Raman scattering vertex, Υ is the magnon-phonon coupling constant, and with D R p (ε) = [(ε − ε p + i0 + ) −1 − (ε + ε p + i0 + ) −1 ] being the retarded component of a phonon propagator. Both these two processes can in principle contribute to the plasmonic spin pumping.
As an endnote to Supplementary Note 2, we mention the effect of the anisotropy of magneto-optical coefficients in BiY 2 Fe 5 O 12 . According to Table 2 in Ref. 11, the magnitude of the anisotropy in magnetic linear birefringence is estimated to be at most 50 % in Y 3 Fe 5 O 12 , which could in principle modulate the plasmonic-spin-pumping signal as the pumped spin current is proportional to Γ + Γ − (see equation (13)).
However, such anisotropy effects are irrelevant to the observed voltage signals for the following reasons.
Firstly, the anisotropy effects do not explain the experimental fact that the observed voltage signal is an odd function of the external magnetic field (Fig. 4d in the main text); the possible modulation of the plasmonic spin pumping induced by the anisotropy of magneto-optical coefficients must be an even function of the magnetic field. Secondly, in the present system, the polarization of near-field photons is distributed randomly, and thus such anisotropy effects are smeared out in the net signal. These arguments justify our conclusion that the voltage signal in the Pt/BiY 2 Fe 5 O 12 /Au-NP sample is not affected by the anisotropy of magneto-optical coefficients in BiY 2 Fe 5 O 12 .