SUPPLEMENTARY INFORMATIONDOI 101038NPHYS3738

NATURE PHYSICS | wwwnaturecomnaturephysics 11

Supplemental Materials for ldquoPhoto-Spin-Voltaic Effectrdquo

David Ellsworth1 Lei Lu1 Jin Lan23 Houchen Chang1 Peng Li1 Zhe Wang3 Jun Hu2 Bryan Johnson1 Yuqi Bian1 Jiang Xiao34 Ruqian Wu23 and Mingzhong Wu1

1Department of Physics Colorado State University Fort Collins CO 80523 USA 2Department of Physics and Astronomy University of California Irvine CA 92697 USA

3Department of Physics Fudan University Shanghai 200433 China 4Collaborative Innovation Center of Advanced Microstructures Fudan University Shanghai 200433

China

1 Materials and Experimental Methods

The substrates for yttrium iron garnet (Y3Fe5O12 YIG) and Ga-doped YIG film samples were single-crystal (111)-oriented gadolinium gallium garnet (Gd3Ga5O12 GGG) The 49-m-thick YIG films the 104-m-thick YIG films and the 78-m-thick Ga-doped YIG films were grown by liquid phase epitaxy techniques1 The doped YIG films contain 25 (atomic) of gallium The 21-nm-thick YIG films were grown by RF sputtering23 The 12-m-thick barium hexagonal ferrite (BaFe12O19 BaM) films were grown on single-crystal c-axis in-plane sapphire substrates by pulsed laser deposition techniques4 The Pt and Cu layers were grown by DC sputtering at room temperature The YIG doped YIG and BaM films were characterized by field-in-plane ferromagnetic resonance (FMR) measurements Fitting of the FMR frequency vs field responses with the Kittel equation yielded an effective saturation magnetization (4πMs) of 1920 G for the 49-microm-thick YIG films 950 G for the 78-microm-thick Ga-doped YIG films 1757 G for the 21-nm-thick YIG films and 3870 G for the 12-m-thick BaM films Static magnetic measurements indicated that the BaM films had an effective uniaxial anisotropy field of 165 kOe and a remnant magnetization of 3440 G both along the in-plane c axis

The optical spectra of different light sources were measured with an Ocean Optics IRRAD200 visible spectrometer (350-1000 nm) and an Ocean Optics NIRQuest512-25 near-infrared (NIR) spectrometer (950-2500 nm) The light was collected using an Ocean Optics QP600-2-VIS-NIR patch cord with a 600 microm fiber optic core and an Ocean Optics P450-1-FLUORIDE patch cord with a 450 μm core for visible and NIR measurements respectively The optical transmission properties of the samples and the optical filters were measured with the same spectrometers and patch cords by placing the sample or filter over the end of the patch cord between the fiber and the light source Note that the responses of the various short-pass and long-pass filters used in this experiment are not ideal The short-pass filters in particular function more like band-stop than edge filters See for example the blue curve in Fig 4e for the 800 nm short-pass filter However we were able to take advantage of the complicated response of these filters and were able to do more extensive comparisons to the theory detailed below

For the phot-spin-voltaic (PSV) measurements the magnetic field was provided by a pair of permanent magnets and was measured by a LakeShore model 450 gaussmeter The electrical voltages were measured by Cu wires attached to the sample with silver paste and connected to a Keithly 2182A nanovoltmeter The temperatures were measured by National Instruments USB-TC01 thermometers with Omega 5SC-TT-T-40-36 Type-T thermocouples For the measurements of the data shown in Figs 2 and 6 the sample was mounted horizontally on a stage beneath the light as shown in Fig 2a and a piece of

Photo-spin-voltaic effect

copy 2016 Macmillan Publishers Limited All rights reserved

2 NATURE PHYSICS | wwwnaturecomnaturephysics

SUPPLEMENTARY INFORMATION DOI 101038NPHYS3738

2

white grid paper was used to align the sample The reflection of light from the paper slightly enhanced the signal strength For the measurements of the data in Figs 4 and S4 the sample was mounted in the same way but instead of a piece of white paper used a piece of black tape to eliminate reflections For the measurements of the data presented in Fig 3 the sample was mounted vertically between two lights as shown by the small diagrams at the top of Fig 3A as viewed from above With this configuration there are no reflections from the sample holder In order to maximize the signal-to-noise ratio the experimental setup was placed on an optical table to minimize mechanical vibrations and was covered with an enclosure to minimize air flows To minimize the temperature gradients across the sample thickness and length an 8 cm fan was used to circulate air within the sample enclosure The primary light source was a 100 W 120 VAC halogen light bulb

FMR-driven spin pumping measurements were also carried out on the PtYIG(49 m)GGG samples The experimental configuration was similar to that shown in Fig 2a in the text Instead of a light bulb a 50-microm-wide microstrip line was placed on the top of the sample (on the Pt side and perpendicular to the sample length) and was fed with microwaves When the magnetic field (H=90) was fixed and the microwave frequency was swept one observed a negative ISHE voltage signal at the FMR frequency of the YIG film The voltage flipped its sign when the magnetic field direction was reversed As a result it can be concluded that the ISHE voltage signals for the FMR and PSV spin pumping processes showed opposite signs for the same samplefieldelectrode configuration

2 Multiplication Rule

The multiplication rule states that the degrading factor of the observed PSV signal due to the use of multiple filters is the product of the degrading factors due to each single filter If one defines the PSV signal with no filter with only filter A with only filter B and with both filters A and B as 1198811198810 119881119881A 119881119881B 119881119881AB respectively the multiplication rule can be expressed as

119881119881AB1198811198810

= 119881119881A1198811198810

times 119881119881B1198811198810

(S1)

The establishment of the multiplication rule observed in the experiment implies that the PSV must be generated by the light in a relatively narrow wavelength (120582120582) range as argued below

From experimental observations it is reasonable to write down the PSV signal as

119881119881 = int 119879119879(120582120582)119868119868(120582120582)119862119862(120582120582) d120582120582 (S2)

where 119879119879(120582120582) is the general transmission function of the light filter(s) 119868119868(120582120582) is the general incident total light intensity and 119862119862(120582120582) is the general conversion function between the incident light intensity and the PSV signal All of these three parameters are functions dependent on 120582120582 Then the multiplication rule implies that the following relation for two filters A and B is satisfied

int 119868119868(120582120582)119862119862(120582120582) d120582120582 times int 119879119879A(120582120582)119879119879B(120582120582)119868119868(120582120582)119862119862(120582120582) d120582120582 = int 119879119879A(120582120582)119868119868(120582120582)119862119862(120582120582) d120582120582 times int 119879119879B(120582120582)119868119868(120582120582)119862119862(120582120582) d120582120582 (S3)

Considering the complicated behaviors for 119868119868(120582120582) 119879119879A(120582120582) and 119879119879B(120582120582) generally Eq (S3) is not satisfied since the integration and multiplication operations do not commute To satisfy Eq (S3) the special condition 119862119862(120582120582) = 1198621198620δ(120582120582 minus 1205821205820 ) must be satisfied where δ(120582120582) is the Dirac delta function This condition signifies that the main contribution for the PSV signal must come from the light in a narrow wavelength centered at 1205821205820

3 Diffusion Processes

3

With the incident light intensity of 119868119868 the total optical spin excitation in the ferromagnetic Pt region can be estimated as 119904119904 = 1198601198601198681198681198891198890(120576120576

primeprime minus 120576120576primeprime) where 119860119860 denotes the coefficient between the light intensity 119868119868 and

the lightrsquos electric field 1198891198890 is the effective thickness of the ferromagnetic Pt region and 120576120576()primeprime is the

imaginary part of the dielectric function for up-spin (down-spin) Since the magnetization in the Pt atomic layers away from the Ptmagnetic insulator (MI) interface are unaffected by the MI film the optical excitation in these layers is spin un-polarized A spin current density 119869119869e (119869119869h) and a spin density 119904119904e(119904119904h) inside the Pt film then results from the outward diffusion of non-equilibrium spin-polarized hot electrons (holes) One may estimate 119869119869 and 119904119904 by solving a diffusion equation with boundary conditions at the PtMI (119911119911=0) and Ptvacuum (119911119911=119889119889) interfaces described by

119863119863eh

part2119904119904(119911119911)part1199111199112 minus 119904119904(119911119911)

120591120591eh+ 1198601198601198681198681198891198890(120576120576

primeprime minus 120576120576primeprime)δ(119911119911) = 0 (0 lt 119911119911 lt 119889119889)

part119904119904(119911119911)part119911119911 = 0 (119911119911 = 0 119889119889)

(S4)

where 119863119863eh is the spin diffusion coefficient for the electronsholes 120591120591eh is the spin relaxation time for the electronsholes and 119868119868 is the light intensity Since very few Pt atomic layers near the PtMI interface are spin polarized by the MI film one can use the delta function δ(119911119911) along with 1198601198601198681198681198891198890(120576120576

primeprime minus 120576120576primeprime) to describe

the source of spin polarization Accordingly the spin current distribution inside the Pt film is given as

119869119869eh(119911119911) = ∓119863119863ehpart119904119904eh

part119911119911 = ∓1198601198601198681198681198891198890(120576120576primeprime minus 120576120576

primeprime)sinh 119911119911minus119889119889

119871119871eh

sinh 119889119889119871119871eh

(S5)

where 119871119871eh = radic119863119863eh120591120591eh is the spin mean free path of the electronsholes and the sign ∓ is for the spin carried by the electronsholes Considering that the excited hot electrons carry much higher energy than the holes a reasonable spin mean free path relation is 119871119871e ≪ 119871119871h Specifically under the limit 119871119871e ≪ 119889119889 ≪119871119871h the total spin current contributed 119869119869eh

tot = int 119869119869eh(119911119911)d119911119911dz=0 is given by

119869119869etot 0 and 119869119869h

tot = minus 12 1198601198601198681198681198891198890119889119889(120576120576

primeprime minus 120576120576primeprime) (S6)

One can see that the optically excited holes dominate the contribution to overall spin current flowing across the Pt thickness which is ultimately transformed into the final voltage signal via the ISHE Meanwhile the optically excited electrons contribute almost no overall spin currents due to the extensive spin relaxation processes experienced

4 DFT Methods and Parameters

To mimic the magnetic proximity effect in the Pt atomic layers near the interface with an MI density functional theory (DFT) calculations were carried out A magnetic moment of 02 Batom was introduced in the bulk face-centered-cubic Pt with a lattice constant of 3924 Aring The 5d6s6p orbitals of the Pt atoms were treated as valence states while all the other inner orbitals were treated as core states The projector augmented wave (PAW) method was adopted for the description of the core-valence interaction56 The spin-polarized DFT calculations were performed using the Vienna ab initio simulation package (VASP)78 The electronic exchange correlation among the electrons at the level of a generalized-gradient approximation (GGA) was considered by the use of the PBE function proposed by Perdew Berke and Ernzerhof9 An energy cutoff of 400 eV was used for the plane wave basis expansion of the wave functions The spin-orbit coupling was invoked in the self-consistent loop using the non-collinear mode of the VASP As a result of the magnetization the band structure of the Pt shows a small spin splitting as presented in Fig 5b in the text and the two spin channels respond differently to the light as required for the PSV effect

copy 2016 Macmillan Publishers Limited All rights reserved

NATURE PHYSICS | wwwnaturecomnaturephysics 3

SUPPLEMENTARY INFORMATIONDOI 101038NPHYS3738

2

white grid paper was used to align the sample The reflection of light from the paper slightly enhanced the signal strength For the measurements of the data in Figs 4 and S4 the sample was mounted in the same way but instead of a piece of white paper used a piece of black tape to eliminate reflections For the measurements of the data presented in Fig 3 the sample was mounted vertically between two lights as shown by the small diagrams at the top of Fig 3A as viewed from above With this configuration there are no reflections from the sample holder In order to maximize the signal-to-noise ratio the experimental setup was placed on an optical table to minimize mechanical vibrations and was covered with an enclosure to minimize air flows To minimize the temperature gradients across the sample thickness and length an 8 cm fan was used to circulate air within the sample enclosure The primary light source was a 100 W 120 VAC halogen light bulb

FMR-driven spin pumping measurements were also carried out on the PtYIG(49 m)GGG samples The experimental configuration was similar to that shown in Fig 2a in the text Instead of a light bulb a 50-microm-wide microstrip line was placed on the top of the sample (on the Pt side and perpendicular to the sample length) and was fed with microwaves When the magnetic field (H=90) was fixed and the microwave frequency was swept one observed a negative ISHE voltage signal at the FMR frequency of the YIG film The voltage flipped its sign when the magnetic field direction was reversed As a result it can be concluded that the ISHE voltage signals for the FMR and PSV spin pumping processes showed opposite signs for the same samplefieldelectrode configuration

2 Multiplication Rule

The multiplication rule states that the degrading factor of the observed PSV signal due to the use of multiple filters is the product of the degrading factors due to each single filter If one defines the PSV signal with no filter with only filter A with only filter B and with both filters A and B as 1198811198810 119881119881A 119881119881B 119881119881AB respectively the multiplication rule can be expressed as

119881119881AB1198811198810

= 119881119881A1198811198810

times 119881119881B1198811198810

(S1)

The establishment of the multiplication rule observed in the experiment implies that the PSV must be generated by the light in a relatively narrow wavelength (120582120582) range as argued below

From experimental observations it is reasonable to write down the PSV signal as

119881119881 = int 119879119879(120582120582)119868119868(120582120582)119862119862(120582120582) d120582120582 (S2)

where 119879119879(120582120582) is the general transmission function of the light filter(s) 119868119868(120582120582) is the general incident total light intensity and 119862119862(120582120582) is the general conversion function between the incident light intensity and the PSV signal All of these three parameters are functions dependent on 120582120582 Then the multiplication rule implies that the following relation for two filters A and B is satisfied

int 119868119868(120582120582)119862119862(120582120582) d120582120582 times int 119879119879A(120582120582)119879119879B(120582120582)119868119868(120582120582)119862119862(120582120582) d120582120582 = int 119879119879A(120582120582)119868119868(120582120582)119862119862(120582120582) d120582120582 times int 119879119879B(120582120582)119868119868(120582120582)119862119862(120582120582) d120582120582 (S3)

Considering the complicated behaviors for 119868119868(120582120582) 119879119879A(120582120582) and 119879119879B(120582120582) generally Eq (S3) is not satisfied since the integration and multiplication operations do not commute To satisfy Eq (S3) the special condition 119862119862(120582120582) = 1198621198620δ(120582120582 minus 1205821205820 ) must be satisfied where δ(120582120582) is the Dirac delta function This condition signifies that the main contribution for the PSV signal must come from the light in a narrow wavelength centered at 1205821205820

3 Diffusion Processes

3

With the incident light intensity of 119868119868 the total optical spin excitation in the ferromagnetic Pt region can be estimated as 119904119904 = 1198601198601198681198681198891198890(120576120576

primeprime minus 120576120576primeprime) where 119860119860 denotes the coefficient between the light intensity 119868119868 and

the lightrsquos electric field 1198891198890 is the effective thickness of the ferromagnetic Pt region and 120576120576()primeprime is the

imaginary part of the dielectric function for up-spin (down-spin) Since the magnetization in the Pt atomic layers away from the Ptmagnetic insulator (MI) interface are unaffected by the MI film the optical excitation in these layers is spin un-polarized A spin current density 119869119869e (119869119869h) and a spin density 119904119904e(119904119904h) inside the Pt film then results from the outward diffusion of non-equilibrium spin-polarized hot electrons (holes) One may estimate 119869119869 and 119904119904 by solving a diffusion equation with boundary conditions at the PtMI (119911119911=0) and Ptvacuum (119911119911=119889119889) interfaces described by

119863119863eh

part2119904119904(119911119911)part1199111199112 minus 119904119904(119911119911)

120591120591eh+ 1198601198601198681198681198891198890(120576120576

primeprime minus 120576120576primeprime)δ(119911119911) = 0 (0 lt 119911119911 lt 119889119889)

part119904119904(119911119911)part119911119911 = 0 (119911119911 = 0 119889119889)

(S4)

where 119863119863eh is the spin diffusion coefficient for the electronsholes 120591120591eh is the spin relaxation time for the electronsholes and 119868119868 is the light intensity Since very few Pt atomic layers near the PtMI interface are spin polarized by the MI film one can use the delta function δ(119911119911) along with 1198601198601198681198681198891198890(120576120576

primeprime minus 120576120576primeprime) to describe

the source of spin polarization Accordingly the spin current distribution inside the Pt film is given as

119869119869eh(119911119911) = ∓119863119863ehpart119904119904eh

part119911119911 = ∓1198601198601198681198681198891198890(120576120576primeprime minus 120576120576

primeprime)sinh 119911119911minus119889119889

119871119871eh

sinh 119889119889119871119871eh

(S5)

where 119871119871eh = radic119863119863eh120591120591eh is the spin mean free path of the electronsholes and the sign ∓ is for the spin carried by the electronsholes Considering that the excited hot electrons carry much higher energy than the holes a reasonable spin mean free path relation is 119871119871e ≪ 119871119871h Specifically under the limit 119871119871e ≪ 119889119889 ≪119871119871h the total spin current contributed 119869119869eh

tot = int 119869119869eh(119911119911)d119911119911dz=0 is given by

119869119869etot 0 and 119869119869h

tot = minus 12 1198601198601198681198681198891198890119889119889(120576120576

primeprime minus 120576120576primeprime) (S6)

One can see that the optically excited holes dominate the contribution to overall spin current flowing across the Pt thickness which is ultimately transformed into the final voltage signal via the ISHE Meanwhile the optically excited electrons contribute almost no overall spin currents due to the extensive spin relaxation processes experienced

4 DFT Methods and Parameters

To mimic the magnetic proximity effect in the Pt atomic layers near the interface with an MI density functional theory (DFT) calculations were carried out A magnetic moment of 02 Batom was introduced in the bulk face-centered-cubic Pt with a lattice constant of 3924 Aring The 5d6s6p orbitals of the Pt atoms were treated as valence states while all the other inner orbitals were treated as core states The projector augmented wave (PAW) method was adopted for the description of the core-valence interaction56 The spin-polarized DFT calculations were performed using the Vienna ab initio simulation package (VASP)78 The electronic exchange correlation among the electrons at the level of a generalized-gradient approximation (GGA) was considered by the use of the PBE function proposed by Perdew Berke and Ernzerhof9 An energy cutoff of 400 eV was used for the plane wave basis expansion of the wave functions The spin-orbit coupling was invoked in the self-consistent loop using the non-collinear mode of the VASP As a result of the magnetization the band structure of the Pt shows a small spin splitting as presented in Fig 5b in the text and the two spin channels respond differently to the light as required for the PSV effect

copy 2016 Macmillan Publishers Limited All rights reserved

4 NATURE PHYSICS | wwwnaturecomnaturephysics

SUPPLEMENTARY INFORMATION DOI 101038NPHYS3738

4

Furthermore the strong intermixing between the valence states near the Fermi level in two spin channels (bands shown in green in Fig 5b) suggests the easiness of the spin flipping process in the Pt and hence a short spin mean free path for electrons or holes away from the interface region

To determine the optical response of the ldquoferromagneticrdquo Pt self-consistent electronic structures were first obtained Then the frequency dependent dielectric function was calculated according to the expression (in atomic units)10

120576120576(119864119864) = 1 + 4120587120587120570120570 sum sum 119891119891119898119898(119844119844)minus119891119891119899119899(119844119844)

[119864119864119898119898119899119899(119844119844)]2 sdot |119901119901119898119898119899119899(119844119844)|2

119864119864minus119864119864119898119898119899119899(119844119844)+i120590120590119898119898119898119898119844119844 (S7)

where 119864119864 is the incident photon energy 120570120570 is the volume of the unit cell 119891119891119898119898(119844119844) is the Fermi occupancy factor of the 119898119898-th eigenstate with a wave vector 119844119844 119864119864119898119898119898119898(119844119844) is the energy difference between the 119898119898-th and 119899119899-th states 120590120590 is a broadening width (120590120590 = 01 eV in the present work) and 119901119901119898119898119898119898 is the matrix element of the momentum operator An adapted version of Eq (S7) is then used to calculate the spin-dependent dielectric function 120576120576 For the calculations using Eq (S7) a fine 272727 119844119844-point mesh in the full Brillouin zone and 26 conduction bands were adopted to ensure the numerical convergence

5 Comparison of Experimental and Theoretical Results

In addition to the qualitative agreements between the experimental observations and the theory discussed in the text there exist also quantitative agreements between the experimental and theoretical results Figure S1 shows the comparison of measured and calculated voltages when using filters The solid circles show the experimental voltages normalized to the voltage obtained without using any filters The empty circles give the voltages calculated by

(S8)

where is the experimentally measured light intensity of the halogen lamp (see Fig 4c) is the

I T dV

I d

I T

Figure S1 | Comparison of voltages measured and calculated when optical filters were used The measured voltages are normalized to the voltage obtained without using any filters The calculations were carried out with Eq (S8) ldquoS(L)rdquo denotes a -nm short-pass (long-pass) filter ldquo49-m YIGrdquo denotes the same sample as described in Fig 2 and Fig 3a ldquo104-m YIGrdquo denotes a 58-mm-long 18-mm-wide Pt(26 nm)YIG(104 m)GGG(04 mm) sample The measurements were performed with the same light and field configurations as for the data shown by the red curve in Fig 2b

455L

590L

695L

800L

850L

900L

950L

1000

S95

0S90

0S80

0S70

0S10

00S

+850

L10

00S

+590

L10

00S

+900

S59

0L+8

50L

590L

+900

S90

0S+8

50L

1000

S+5

90L+

850L

1000

S+5

90L+

900S

590L

+900

S+8

50L

1000

S+5

90L+

900S

+850

L0

20

40

60

80

100 49-m YIG 104-m YIG Calculation

Vol

tage

()

1000

S+59

0L+9

00S+

850L

5

experimentally measured filter transmission (see Figs 4d 4e and 4f) and is theoretically calculated using DFT (see Fig 5c) One can see that the measured voltages match very well with the calculated voltages for the majority of the 22 different filter configurations Whatrsquos more such matching is true for both of the two samples

One important point should be made about the above experimenttheory comparison - if one shifts the peak center of the profile | | from 07 eV to 13 eV the level of the agreement between the calculated and measured voltages decreases notably as shown in Fig S2 Specifically Figure S2 gives three sets of voltage values calculated using three different | | profiles (1) the actual DFT result as presented in Fig 5c in the text (2) a Gaussian profile that best fits the main peak of the DFT result which is centered at 07 eV and has a width of 05 eV and (3) a Gaussian profile that is the same as (2) but with its center shifted to 13 eV While the agreement between the experimentally measured voltages and the theoretically calculated voltage values are satisfactory for both cases (1) and (2) it is much worse for case (3) This result clearly indicates the importance of having the correct data of the absorption spectra This result together with that shown in Fig S1 indicates the strong dependence of the PSV effect on the band structure of the Pt or more explicitly the strength of spin-orbit coupling in the Pt

The results from Figs S1 and S2 also indicate the critical wavelength range for the PSV effect in the PtMI system which should be around 1800 nm (07 eV) This agrees with the experimental observation presented in Fig 4 namely that there exists a narrow wavelength range over 1600-2000 nm that is critical for the PSV effect This agreement together with the facts that the Pt layer-caused reduction in the transmission of the sample is almost constant over the entire range and the light-on-Pt configuration yields weaker PSV signals than the light-on-MI configuration provides an evidence that the PSV effect mainly stems from an optical effect not a thermal effect when illuminated by the halogen lamp In case

Figure S2 | Wavelength characteristics of the PSV effect a | | profiles which are the difference between the imaginary parts of dielectric functions for the spin-up and spin-down channels The green profile was obtained by DFT calculations and is the absolute value of the value shown in Fig 5c in the text The light-blue profile shows a Gaussian profile that fits the main peak of the green profile centered at 07 eV The light-red profile shows a Gaussian profile that is the same as the light-blue profile but with the peak center shifted to 13 eV b Comparison of voltages measured and calculated when optical filters were used The measured voltages are normalized to the voltage obtained without using any filters ldquoS(L)rdquo denotes a -nm short-pass (long-pass) filter The measurements were performed with the same light and field configurations as for the data shown by the red curve in Fig 2b in the text and the sample was a 58-mm-long 18-mm-wide Pt(26 nm)YIG(104 m)GGG(04 mm) structure The

calculations were carried out using Eq (S8) in the text and the three| | profiles given in a

0 1 2 300

02

04

06

08

10

Photon energy (eV)

DFT calculation

Assumed a peak at 07 eV

Assumed a peak at 13 eV

455L

590L

695L

800L

850L

900L

950L

1000

S95

0S90

0S80

0S70

0S10

00S

+850

L10

00S

+590

L10

00S

+900

S59

0L+8

50L

590L

+900

S90

0S+8

50L

1000

S+5

90L+

850L

1000

S+5

90L+

900S

590L

+900

S+8

50L

1000

S+5

90L+

900S

+850

L

0102030405060708090

100

Volta

ge (

)

DFT calculation Assumed a peak at 07 eV Assumed a peak at 13 eV Experimental data

|- |

a b

copy 2016 Macmillan Publishers Limited All rights reserved

NATURE PHYSICS | wwwnaturecomnaturephysics 5

SUPPLEMENTARY INFORMATIONDOI 101038NPHYS3738

4

Furthermore the strong intermixing between the valence states near the Fermi level in two spin channels (bands shown in green in Fig 5b) suggests the easiness of the spin flipping process in the Pt and hence a short spin mean free path for electrons or holes away from the interface region

To determine the optical response of the ldquoferromagneticrdquo Pt self-consistent electronic structures were first obtained Then the frequency dependent dielectric function was calculated according to the expression (in atomic units)10

120576120576(119864119864) = 1 + 4120587120587120570120570 sum sum 119891119891119898119898(119844119844)minus119891119891119899119899(119844119844)

[119864119864119898119898119899119899(119844119844)]2 sdot |119901119901119898119898119899119899(119844119844)|2

119864119864minus119864119864119898119898119899119899(119844119844)+i120590120590119898119898119898119898119844119844 (S7)

where 119864119864 is the incident photon energy 120570120570 is the volume of the unit cell 119891119891119898119898(119844119844) is the Fermi occupancy factor of the 119898119898-th eigenstate with a wave vector 119844119844 119864119864119898119898119898119898(119844119844) is the energy difference between the 119898119898-th and 119899119899-th states 120590120590 is a broadening width (120590120590 = 01 eV in the present work) and 119901119901119898119898119898119898 is the matrix element of the momentum operator An adapted version of Eq (S7) is then used to calculate the spin-dependent dielectric function 120576120576 For the calculations using Eq (S7) a fine 272727 119844119844-point mesh in the full Brillouin zone and 26 conduction bands were adopted to ensure the numerical convergence

5 Comparison of Experimental and Theoretical Results

In addition to the qualitative agreements between the experimental observations and the theory discussed in the text there exist also quantitative agreements between the experimental and theoretical results Figure S1 shows the comparison of measured and calculated voltages when using filters The solid circles show the experimental voltages normalized to the voltage obtained without using any filters The empty circles give the voltages calculated by

(S8)

where is the experimentally measured light intensity of the halogen lamp (see Fig 4c) is the

I T dV

I d

I T

Figure S1 | Comparison of voltages measured and calculated when optical filters were used The measured voltages are normalized to the voltage obtained without using any filters The calculations were carried out with Eq (S8) ldquoS(L)rdquo denotes a -nm short-pass (long-pass) filter ldquo49-m YIGrdquo denotes the same sample as described in Fig 2 and Fig 3a ldquo104-m YIGrdquo denotes a 58-mm-long 18-mm-wide Pt(26 nm)YIG(104 m)GGG(04 mm) sample The measurements were performed with the same light and field configurations as for the data shown by the red curve in Fig 2b

455L

590L

695L

800L

850L

900L

950L

1000

S95

0S90

0S80

0S70

0S10

00S

+850

L10

00S

+590

L10

00S

+900

S59

0L+8

50L

590L

+900

S90

0S+8

50L

1000

S+5

90L+

850L

1000

S+5

90L+

900S

590L

+900

S+8

50L

1000

S+5

90L+

900S

+850

L0

20

40

60

80

100 49-m YIG 104-m YIG Calculation

Vol

tage

()

1000

S+59

0L+9

00S+

850L

5

experimentally measured filter transmission (see Figs 4d 4e and 4f) and is theoretically calculated using DFT (see Fig 5c) One can see that the measured voltages match very well with the calculated voltages for the majority of the 22 different filter configurations Whatrsquos more such matching is true for both of the two samples

One important point should be made about the above experimenttheory comparison - if one shifts the peak center of the profile | | from 07 eV to 13 eV the level of the agreement between the calculated and measured voltages decreases notably as shown in Fig S2 Specifically Figure S2 gives three sets of voltage values calculated using three different | | profiles (1) the actual DFT result as presented in Fig 5c in the text (2) a Gaussian profile that best fits the main peak of the DFT result which is centered at 07 eV and has a width of 05 eV and (3) a Gaussian profile that is the same as (2) but with its center shifted to 13 eV While the agreement between the experimentally measured voltages and the theoretically calculated voltage values are satisfactory for both cases (1) and (2) it is much worse for case (3) This result clearly indicates the importance of having the correct data of the absorption spectra This result together with that shown in Fig S1 indicates the strong dependence of the PSV effect on the band structure of the Pt or more explicitly the strength of spin-orbit coupling in the Pt

The results from Figs S1 and S2 also indicate the critical wavelength range for the PSV effect in the PtMI system which should be around 1800 nm (07 eV) This agrees with the experimental observation presented in Fig 4 namely that there exists a narrow wavelength range over 1600-2000 nm that is critical for the PSV effect This agreement together with the facts that the Pt layer-caused reduction in the transmission of the sample is almost constant over the entire range and the light-on-Pt configuration yields weaker PSV signals than the light-on-MI configuration provides an evidence that the PSV effect mainly stems from an optical effect not a thermal effect when illuminated by the halogen lamp In case

Figure S2 | Wavelength characteristics of the PSV effect a | | profiles which are the difference between the imaginary parts of dielectric functions for the spin-up and spin-down channels The green profile was obtained by DFT calculations and is the absolute value of the value shown in Fig 5c in the text The light-blue profile shows a Gaussian profile that fits the main peak of the green profile centered at 07 eV The light-red profile shows a Gaussian profile that is the same as the light-blue profile but with the peak center shifted to 13 eV b Comparison of voltages measured and calculated when optical filters were used The measured voltages are normalized to the voltage obtained without using any filters ldquoS(L)rdquo denotes a -nm short-pass (long-pass) filter The measurements were performed with the same light and field configurations as for the data shown by the red curve in Fig 2b in the text and the sample was a 58-mm-long 18-mm-wide Pt(26 nm)YIG(104 m)GGG(04 mm) structure The

calculations were carried out using Eq (S8) in the text and the three| | profiles given in a

0 1 2 300

02

04

06

08

10

Photon energy (eV)

DFT calculation

Assumed a peak at 07 eV

Assumed a peak at 13 eV

455L

590L

695L

800L

850L

900L

950L

1000

S95

0S90

0S80

0S70

0S10

00S

+850

L10

00S

+590

L10

00S

+900

S59

0L+8

50L

590L

+900

S90

0S+8

50L

1000

S+5

90L+

850L

1000

S+5

90L+

900S

590L

+900

S+8

50L

1000

S+5

90L+

900S

+850

L

0102030405060708090

100

Volta

ge (

)

DFT calculation Assumed a peak at 07 eV Assumed a peak at 13 eV Experimental data

|- |

a b

copy 2016 Macmillan Publishers Limited All rights reserved

6 NATURE PHYSICS | wwwnaturecomnaturephysics

SUPPLEMENTARY INFORMATION DOI 101038NPHYS3738

6

that light-induced Pt heating plays an important role one would expect that the Pt layer cause a larger reduction in the optical transmission at a relatively narrow range centered at about 1800 nm and the voltage signals for the light-on-Pt configuration should be stronger than those for the light-on-MI configuration

6 Light-Induced Heating

It is known that the efficiency of the light-induced heating somewhat depends on the product of and E (photon energy) This product was calculated from the band structure of Pt as given in Fig S3b One can see a broadband response in the 05-3 eV range (or 410-2500 nm in wavelength) The broadband behavior of E is in contrast to the peak behavior of the spectrum shown in Fig S3a Two

important points should be made about the results shown in Fig S3b First the results indicate that the maximal heating efficiency should occur at the photon energy of about 098 eV (1270 nm) but the experimental data clearly indicate that the critical wavelength is not there Second the results also indicate that the heating efficiency at 206 eV (600 nm) should be large but the experimental data show that the measurements using a white LED source (600 nm) yielded very weak PSV signals These two facts provide additional support to the conclusion that heating effect is weaker than the PSV effect in the experiments in this work

7 Photo-Spin-Voltaic Effect vs Spin Seebeck Effect

There had been previous experiments on using light to create a temperature gradient and thereby realize the SSE4111213 Those experiments also used PtMI structures the same as in this work It is possible that the SSE and the PSV effect occur simultaneously in a PtMI structure upon exposure to light When the temperature difference across the sample thickness (Tt) is very small one can expect that the PSV effect overwhelms the SSE and the measured voltage signals resulted mainly from the PSV effect This is exactly the case in this work where the experimental setup was constructed to minimize Tt When Tt is relatively large the SSE is dominant which is the case studied in Refs [411-13] Note that in the experiments reported in Refs [111213] the SSE might be the only effect because the wavelength of the

Figure S3 | Calculated E profiles a profile b E profile and are the imaginary

parts of dielectric functions for the spin-up and spin-down channels respectively and E is the photon energy The and data were obtained through density function theory calculations and are the same as those used to

calculate presented in Fig S2a

0 1 2 3-1

0

1

2

3

4

5

0 1 2 31

0

-1

-2

-3

-4

-5

-

(

+

)E (a

u)

Photon energy E (eV) Photon energy E (eV)

a b

7

laser used for heating is far shorter than the critical wavelength range identified in this work and the PSV effect might be completely absent In a regime where Tt is neither very small nor very large the two effects coexist This situation is shown in Fig S4 On can see from the data in Fig S4 that different from the PSV effect the SSE voltage signal flips its sign when the light illumination direction is reversed and the SSE voltage varies with time in the same manner as Tt These results evidently confirm that the PSV effect is essentially different from the SSE Note that it has been studied previously that the SSE voltage vs time responses should follow the Tt vs time response413

It is possible that upon the exposure of a PtMI sample to light the light absorption raises the temperature of the electrons in the Pt and thereby quickly triggers imbalance among electron phonon and magnon systems at the interface potentially leading to an interface-related SSE It is believed that such an interface SSE should be weak in the experiments in this work because it is a thermal effect and should not depend on the wavelength of light while the observed voltage signals exhibit strong wavelength dependence as shown in Figs 4 5 and S1 The interface SSE is expected to be weak because the exchange of angular momentum between hot electrons (and holes) and quasiparticles (magnons and phonons) is low due to their large energy mismatch The hot electrons have an energy of a few tenth eV while the magnons and phonons have an energy of a few meV only Whatrsquos more even though the hot electrons may interact with the magnons this interaction would have weak spin dependence due to the high energy of the hot electrons Besides the current SSE theory is based on the quasi-equilibrium of magnon phonon and electron systems and in the theory both the temperatures and their gradients are well defined14 This is not applicable to the PSV effect for which the electrons in the Pt are far from their

Figure S4 | Comparison between PSV- and SSE-produced voltage signals a and b present the voltage and temperature Tt signals measured without and with the use of a heat sink respectively where Tt is the temperature difference measured across the sample thickness The sample and measurement configurations were almost identical to those described for the data in Fig 2c in the text and for all the measurements the light was turned on at t=50 s and then off at t=100 s The situation in a corresponds to a regime where Tt is very small and the PSV effect overwhelms the SSE The situation in b corresponds to a regime where Tt is relatively large due to the use of a heat sink and the PSV effect and the SSE take place simultaneously and both contribute to the voltage signals c presents the SSE voltage signals which were obtained by subtracting the PSV voltage signals in a from the voltage signals b The temperature signals in c are the same as presented in b

PtMI

PtMISink

PtMISink

SinkPtMI

SinkPtMI

PtMI

a PSV only b PSV amp SSE c SSE only

0 50 100 150

-02

00

02

04

Time (s)

Vol

tage

(V

)

-4

-2

0

2

4

6

Tt (degC

)

0 50 100 150

-02

00

02

04

Time (s)

Vol

tage

(V

)

-4

-2

0

2

4

6

Tt (degC

)

0 50 100 150

-02

00

02

04

Time (s)

Vol

tage

(V

)

-4

-2

0

2

4

6

Tt (degC

)

0 50 100 150

-02

00

02

04

Time (s)

Vol

tage

(V

)

-4

-2

0

2

4

6

Tt (degC

)

0 50 100 150

-02

00

02

04

Time (s)

Vol

tage

(V

)

-4

-2

0

2

4

6

Tt (degC

)

0 50 100 150

-02

00

02

04

Time (s)

Vol

tage

(V

)

-4

-2

0

2

4

6

Tt (degC

)

copy 2016 Macmillan Publishers Limited All rights reserved

NATURE PHYSICS | wwwnaturecomnaturephysics 7

SUPPLEMENTARY INFORMATIONDOI 101038NPHYS3738

6

that light-induced Pt heating plays an important role one would expect that the Pt layer cause a larger reduction in the optical transmission at a relatively narrow range centered at about 1800 nm and the voltage signals for the light-on-Pt configuration should be stronger than those for the light-on-MI configuration

6 Light-Induced Heating

It is known that the efficiency of the light-induced heating somewhat depends on the product of and E (photon energy) This product was calculated from the band structure of Pt as given in Fig S3b One can see a broadband response in the 05-3 eV range (or 410-2500 nm in wavelength) The broadband behavior of E is in contrast to the peak behavior of the spectrum shown in Fig S3a Two

important points should be made about the results shown in Fig S3b First the results indicate that the maximal heating efficiency should occur at the photon energy of about 098 eV (1270 nm) but the experimental data clearly indicate that the critical wavelength is not there Second the results also indicate that the heating efficiency at 206 eV (600 nm) should be large but the experimental data show that the measurements using a white LED source (600 nm) yielded very weak PSV signals These two facts provide additional support to the conclusion that heating effect is weaker than the PSV effect in the experiments in this work

7 Photo-Spin-Voltaic Effect vs Spin Seebeck Effect

There had been previous experiments on using light to create a temperature gradient and thereby realize the SSE4111213 Those experiments also used PtMI structures the same as in this work It is possible that the SSE and the PSV effect occur simultaneously in a PtMI structure upon exposure to light When the temperature difference across the sample thickness (Tt) is very small one can expect that the PSV effect overwhelms the SSE and the measured voltage signals resulted mainly from the PSV effect This is exactly the case in this work where the experimental setup was constructed to minimize Tt When Tt is relatively large the SSE is dominant which is the case studied in Refs [411-13] Note that in the experiments reported in Refs [111213] the SSE might be the only effect because the wavelength of the

Figure S3 | Calculated E profiles a profile b E profile and are the imaginary

parts of dielectric functions for the spin-up and spin-down channels respectively and E is the photon energy The and data were obtained through density function theory calculations and are the same as those used to

calculate presented in Fig S2a

0 1 2 3-1

0

1

2

3

4

5

0 1 2 31

0

-1

-2

-3

-4

-5

-

(

+

)E (a

u)

Photon energy E (eV) Photon energy E (eV)

a b

7

laser used for heating is far shorter than the critical wavelength range identified in this work and the PSV effect might be completely absent In a regime where Tt is neither very small nor very large the two effects coexist This situation is shown in Fig S4 On can see from the data in Fig S4 that different from the PSV effect the SSE voltage signal flips its sign when the light illumination direction is reversed and the SSE voltage varies with time in the same manner as Tt These results evidently confirm that the PSV effect is essentially different from the SSE Note that it has been studied previously that the SSE voltage vs time responses should follow the Tt vs time response413

It is possible that upon the exposure of a PtMI sample to light the light absorption raises the temperature of the electrons in the Pt and thereby quickly triggers imbalance among electron phonon and magnon systems at the interface potentially leading to an interface-related SSE It is believed that such an interface SSE should be weak in the experiments in this work because it is a thermal effect and should not depend on the wavelength of light while the observed voltage signals exhibit strong wavelength dependence as shown in Figs 4 5 and S1 The interface SSE is expected to be weak because the exchange of angular momentum between hot electrons (and holes) and quasiparticles (magnons and phonons) is low due to their large energy mismatch The hot electrons have an energy of a few tenth eV while the magnons and phonons have an energy of a few meV only Whatrsquos more even though the hot electrons may interact with the magnons this interaction would have weak spin dependence due to the high energy of the hot electrons Besides the current SSE theory is based on the quasi-equilibrium of magnon phonon and electron systems and in the theory both the temperatures and their gradients are well defined14 This is not applicable to the PSV effect for which the electrons in the Pt are far from their

Figure S4 | Comparison between PSV- and SSE-produced voltage signals a and b present the voltage and temperature Tt signals measured without and with the use of a heat sink respectively where Tt is the temperature difference measured across the sample thickness The sample and measurement configurations were almost identical to those described for the data in Fig 2c in the text and for all the measurements the light was turned on at t=50 s and then off at t=100 s The situation in a corresponds to a regime where Tt is very small and the PSV effect overwhelms the SSE The situation in b corresponds to a regime where Tt is relatively large due to the use of a heat sink and the PSV effect and the SSE take place simultaneously and both contribute to the voltage signals c presents the SSE voltage signals which were obtained by subtracting the PSV voltage signals in a from the voltage signals b The temperature signals in c are the same as presented in b

PtMI

PtMISink

PtMISink

SinkPtMI

SinkPtMI

PtMI

a PSV only b PSV amp SSE c SSE only

0 50 100 150

-02

00

02

04

Time (s)

Vol

tage

(V

)

-4

-2

0

2

4

6

Tt (degC

)

0 50 100 150

-02

00

02

04

Time (s)

Vol

tage

(V

)

-4

-2

0

2

4

6

Tt (degC

)

0 50 100 150

-02

00

02

04

Time (s)

Vol

tage

(V

)

-4

-2

0

2

4

6

Tt (degC

)

0 50 100 150

-02

00

02

04

Time (s)

Vol

tage

(V

)

-4

-2

0

2

4

6

Tt (degC

)

0 50 100 150

-02

00

02

04

Time (s)

Vol

tage

(V

)

-4

-2

0

2

4

6

Tt (degC

)

0 50 100 150

-02

00

02

04

Time (s)

Vol

tage

(V

)

-4

-2

0

2

4

6

Tt (degC

)

copy 2016 Macmillan Publishers Limited All rights reserved

8 NATURE PHYSICS | wwwnaturecomnaturephysics

SUPPLEMENTARY INFORMATION DOI 101038NPHYS3738

8

equilibrium state and the temperature of electrons is not defined Of course the spin-selective reflection of hot electrons from the PtMI interface may also contribute to spin currents in the Pt

There are three additional notes that should be made First the wavelength characteristics of the PSV effect results from the energy dependence of the light-induced hot electron excitation The spin-orbit coupling in the Pt that converts spin currents to charge currents is energy independent just as in the SSE Second for the SSE voltage signal presented in Fig S4 the physical process involves lattice-heated Pt electrons not the hot electrons directly excited by light Those heated electrons have lower energy than the hot electrons Finally there might exist a charge current across the thickness of the Pt layer at the onset of illumination due to the different diffusion properties of the excited hot electrons and holes However this current if present should be transient because there is no complete circuit for it to flow in For this reason the PSV-produced spin current is not a spin-polarized electron current but a pure spin flow and there is neither the ordinary Hall effect nor the anomalous Hall effect in the structure

References

1 R C Linares ldquoEpitaxial growth of narrow linewidth yttrium iron garnet filmsrdquo J Cryst Growth 3 443-446 (1968)

2 T Liu H Chang V Vlaminck Y Sun M Kabatek A Hoffmann L Deng and M Wu ldquoFerromagnetic resonance of sputtered yttrium iron garnet nanometer filmsrdquo J Appl Phys 115 17A501 (2014)

3 H Chang P Li W Zhang T Liu A Hoffmann L Deng and M Wu ldquoNanometer-Thick Yttrium Iron Garnet Films With Extremely Low Dampingrdquo IEEE Magn Lett 5 6700104 (2014)

4 P Li D Ellsworth H Chang P Janantha D Richardson F Shah P Phillips T Vijayasarathy and M Wu ldquoGeneration of pure spin currents via spin Seebeck effect in self-biased hexagonal ferrite thin filmsrdquo Appl Phys Lett 105 242412 (2014)

5 P E Bloumlchl ldquoProjector augmented-wave methodrdquo Phys Rev B 50 17953-17979 (1994) 6 G Kresse and D Joubert ldquoFrom ultrasoft pseudopotentials to the projector augmented-wave methodrdquo

Phys Rev B 59 1758-1775 (1999) 7 G Kresse and J Furthmuumlller ldquoEfficiency of ab-initio total energy calculations for metals and

semiconductors using a plane-wave basis setrdquo Comput Mater Sci 6 15-50 (1996) 8 G Kresse and J Furthmuumlller ldquoEfficient iterative schemes for ab initio total-energy calculations using a

plane-wave basis setrdquo Phys Rev B 54 11169-11186 (1996) 9 J P Perdew K Burke and M Ernzerhof ldquoGeneralized Gradient Approximation Made Simplerdquo Phys Rev

Lett 77 3865-3868 (1996) 10 J L P Hughes and J E Sipe ldquoCalculation of second-order optical response in semiconductorsrdquo Phys

Rev B 53 10751-10763 (1996) 11 M Weiler M Althammer F D Czeschka H Huebl M S Wagner M Opel I-M Imort G Reiss A

Thomas R Gross S T B Goennenwein ldquoLocal Charge and Spin Currents in Magnetothermal Landscapesrdquo Phys Rev Lett 108 106602 (2012)

12 M Agrawal V I Vasyuchka A A Serga A Kirihara P Pirro T Langner M B Jungfleisch A V Chumak E Th Papaioannou B Hillebrands ldquoRole of bulk-magnon transport in the temporal evolution of the longitudinal spin-Seebeck effectrdquo Phys Rev B 89 224414 (2014)

9

13 N Roschewsky M Schreier A Kamra F Schade K Ganzhorn S Meyer H Huebl S Gepraumlgs R Gross

S Goennenwein ldquoTime resolved spin Seebeck effect experimentsrdquo Appl Phys Lett 104 202410 (2014) 14 J Xiao G E W Bauer K Uchida E Saitoh and S Maekawa ldquoTheory of magnon-driven spin Seebeck

effectrdquo Phys Rev B 81 214418 (2010)

copy 2016 Macmillan Publishers Limited All rights reserved

NATURE PHYSICS | wwwnaturecomnaturephysics 9

SUPPLEMENTARY INFORMATIONDOI 101038NPHYS3738

8

equilibrium state and the temperature of electrons is not defined Of course the spin-selective reflection of hot electrons from the PtMI interface may also contribute to spin currents in the Pt

There are three additional notes that should be made First the wavelength characteristics of the PSV effect results from the energy dependence of the light-induced hot electron excitation The spin-orbit coupling in the Pt that converts spin currents to charge currents is energy independent just as in the SSE Second for the SSE voltage signal presented in Fig S4 the physical process involves lattice-heated Pt electrons not the hot electrons directly excited by light Those heated electrons have lower energy than the hot electrons Finally there might exist a charge current across the thickness of the Pt layer at the onset of illumination due to the different diffusion properties of the excited hot electrons and holes However this current if present should be transient because there is no complete circuit for it to flow in For this reason the PSV-produced spin current is not a spin-polarized electron current but a pure spin flow and there is neither the ordinary Hall effect nor the anomalous Hall effect in the structure

References

1 R C Linares ldquoEpitaxial growth of narrow linewidth yttrium iron garnet filmsrdquo J Cryst Growth 3 443-446 (1968)

2 T Liu H Chang V Vlaminck Y Sun M Kabatek A Hoffmann L Deng and M Wu ldquoFerromagnetic resonance of sputtered yttrium iron garnet nanometer filmsrdquo J Appl Phys 115 17A501 (2014)

3 H Chang P Li W Zhang T Liu A Hoffmann L Deng and M Wu ldquoNanometer-Thick Yttrium Iron Garnet Films With Extremely Low Dampingrdquo IEEE Magn Lett 5 6700104 (2014)

4 P Li D Ellsworth H Chang P Janantha D Richardson F Shah P Phillips T Vijayasarathy and M Wu ldquoGeneration of pure spin currents via spin Seebeck effect in self-biased hexagonal ferrite thin filmsrdquo Appl Phys Lett 105 242412 (2014)

5 P E Bloumlchl ldquoProjector augmented-wave methodrdquo Phys Rev B 50 17953-17979 (1994) 6 G Kresse and D Joubert ldquoFrom ultrasoft pseudopotentials to the projector augmented-wave methodrdquo

Phys Rev B 59 1758-1775 (1999) 7 G Kresse and J Furthmuumlller ldquoEfficiency of ab-initio total energy calculations for metals and

semiconductors using a plane-wave basis setrdquo Comput Mater Sci 6 15-50 (1996) 8 G Kresse and J Furthmuumlller ldquoEfficient iterative schemes for ab initio total-energy calculations using a

plane-wave basis setrdquo Phys Rev B 54 11169-11186 (1996) 9 J P Perdew K Burke and M Ernzerhof ldquoGeneralized Gradient Approximation Made Simplerdquo Phys Rev

Lett 77 3865-3868 (1996) 10 J L P Hughes and J E Sipe ldquoCalculation of second-order optical response in semiconductorsrdquo Phys

Rev B 53 10751-10763 (1996) 11 M Weiler M Althammer F D Czeschka H Huebl M S Wagner M Opel I-M Imort G Reiss A

Thomas R Gross S T B Goennenwein ldquoLocal Charge and Spin Currents in Magnetothermal Landscapesrdquo Phys Rev Lett 108 106602 (2012)

12 M Agrawal V I Vasyuchka A A Serga A Kirihara P Pirro T Langner M B Jungfleisch A V Chumak E Th Papaioannou B Hillebrands ldquoRole of bulk-magnon transport in the temporal evolution of the longitudinal spin-Seebeck effectrdquo Phys Rev B 89 224414 (2014)

9

13 N Roschewsky M Schreier A Kamra F Schade K Ganzhorn S Meyer H Huebl S Gepraumlgs R Gross

S Goennenwein ldquoTime resolved spin Seebeck effect experimentsrdquo Appl Phys Lett 104 202410 (2014) 14 J Xiao G E W Bauer K Uchida E Saitoh and S Maekawa ldquoTheory of magnon-driven spin Seebeck

effectrdquo Phys Rev B 81 214418 (2010)

copy 2016 Macmillan Publishers Limited All rights reserved