Interference Induced Enhancement of Magneto-Optical Effect in Pt / TbCo Hetero-Structured Films

Magnetic films with a heavy metal layer show strong interfacial interaction of spin-orbit. Spin-orbit interaction is one of the key technologies for spintronics. In this paper, we measured magneto-optical Kerr spectra of Pt/TbCo hetero-structure films on a thermally oxidized silicon substrate (0.3 mm); A: Pt (3 nm)/TbCo (6 nm)/Pt (3 nm), B: Si3N4 (10 nm)/TbCo (6 nm)/Pt (3 nm), and C: Pt (3 nm)/TbCo (6 nm)/Si3N4 (10 nm). Magneto-optical Kerr spectra of each sample were measured with a wavelength range of 300–700 nm, and were compared to the simulated spectra using the effective refractive index method. In the sample A, which has a symmetric structure, the simulated spectra are consistent with the measured ones. On the other hand, in the samples B and C, with an asymmetric structure, there are some differences between the simulated spectra and the measured ones in a lower photon energy region. This may be caused by interfacial effects of the spin-orbit interaction.


Introduction
Magnetic films with a heavy metal layer show strong interfacial interaction of spin-orbit, such as the spin Hall effect (SHE) [1][2][3][4][5], the Dzyaloshinskii-Moriya interaction (DMI), and the interfacial Rasba effect [6][7][8].These effects change the formation of a magnetic moment at the interface and introduce a spin-state to the interface.Spin-orbit interaction (SOI) is interaction between electron spin and electron orbital angular momentum and related to magneto-optical properties [9][10][11][12].In current-induced domain wall motion (CIDM), these interactions promote a high domain wall (DW) velocity at a lower current density [13][14][15][16].SOI is one of the key technologies for spintronics and its applications.It is important to reveal the SOI in hetero-structure films.
It is known that magneto-optical Kerr effect is a useful method for detecting interfacial information, especially using an optical interference.We reported that large magneto-optical Kerr signals were obtained using ultrathin magnetic films deposited on Si substrates coated with silicon oxide (SiO 2 ), even for films with magnetic layer of ~1 nm thickness [17].Multiple reflections in the interface enhanced the magneto-optical effect.And they include interfacial information such as spin-orbit torques, chiral magnetism, and related effects [18][19][20][21][22][23][24].There are many reports about the magneto-optical Kerr effect in a rare earth transition metal (RE-TM) film, with a noble metal layer such as Pt, Pd, etc. [25,26].However, there are few reports with discussion of the SOI.
In this paper, we measured magneto-optical Kerr spectra of ultrathin Pt/TbCo hetero-structure films with symmetric and asymmetric structures.The measured spectra were compared with the simulated ones using the bulk value of optical constants.Furthermore, the contribution of the SOI to magneto-optical Kerr effect is discussed.

Materials and Methods
We prepared three samples on a thermally oxidized silicon (SiO 2, ) substrate (0.3 mm); A: Pt (3 nm)/TbCo (6 nm)/Pt(3 nm), B: Si 3 N 4 (10 nm)/TbCo (6 nm)/Pt (3 nm), and C: Pt (3 nm)/TbCo (6 nm)/Si 3 N 4 (10 nm) Si substrates were sourced from Nakayama Hutech Corporation, Kyoto, Japan.Figure 1 shows structures of these films.The SiO 2 underlayer with thickness of 100 nm was utilized to enhance the Kerr effect thanks to interference [17].A Si 3 N 4 layer was used as a non-heavy metal layer, as well as a protective layer for the TbCo layer.TbCo was deposited by DC magnetron co-sputtering, using Tb and Co targets.TbCo composition was estimated from the deposition rate of each target.Si 3 N 4 and Pt were deposited by RF magnetron sputtering using Si 3 N 4 and Pt, respectively.Pt, Tb, Co and Si 3 N 4 targets were sourced from Chemiston Corporation, Saitama, Japan.All processes were deposited continuously with an Ar pressure of 2 mTorr.Composition of TbCo is Tb 40 Co 60 at% with a rare earth-rich feature.Magneto-optical Kerr spectra were measured with a wavelength range of 300-700 nm, using a Xenon light source and a PEM (photo-elastic modulator, model PEM90, HINDS Instruments Inc., Portland, OR, USA).Details are described in ref [27].Optical indexes were measured by an ellipsometer of JASCO (model M-150, JASCO Corporation, Tokyo, Japan).

Results
Figure 2 shows polar Kerr hysteresis loops of the samples measured with a wavelength of 500 nm.Each sample shows a perpendicular magnetic anisotropy with a different coercivity.Kerr rotation angles were −0.03 degrees for sample A and around 0.11degrees for samples B and C. The polarity of the Kerr rotation angle was opposite between A and B, C, although these samples consisted of a TbCo layer with the same composition.Figure 3 shows the Kerr spectra of Kerr rotation (θ K ) and ellipticity (η K ) for samples A, B, and C. θ K and η K were significantly changed with a wavelength.The θ K of each sample showed maximum value at a wavelength of around 400 to 500 nm and a sign of each sample changed roughly coinciding with the maximum value of η K .A peak position of θ K in the symmetric structure of sample A slightly shifted to shorter wavelengths compared to that in the asymmetric structure of samples B and C. Each η K in the asymmetric structure samples B and C showed a large angle with longer wavelengths.In order to simulate the Kerr spectra, we used the effective refractive index method [28].Optical constants of the TbCo layer for a right and a left hand circular polarization light were calculated from the measured values of θ K , η K , and optical index (n, k) for a 100 nm thick TbCo film in the same method as in Ref. [17]. Figure 4

Discussion
The Kerr hysteresis loops in Figure 2 and the Kerr spectra in Figure 3 include optical interference in the SiO 2 underlayer and an interfacial effect in the heavy metal of Pt layers.To clarify these contributions, we simulated Kerr spectra using the effective refractive index method as in Refs.[17,28].In this method, we calculated the refractive index of each layer and effective refractive index from the substrate to i layer, where i is layer number.Repeating this procedure until the top layer, we could obtain an effective refractive index for the whole film.We took optical constants for the TbCo layer in Figure 3, for Pt, Si, SiO 2 , and Si 3 N 4 in ref [29], which were widely used in the literature.
Figure 5 shows a simulated magneto-optical Kerr spectrum of the sample A deposited on the SiO 2 under layer with thicknesses of 0, 100, 200 nm.The Kerr spectrum θ K , η K were enhanced with the SiO 2 underlayer, and were strongly dependent on wavelengths for the films with the SiO 2 underlayer thicknesses of 100 nm and 200 nm.Maximum values of θ K and η K in these films were larger than those in a 100 nm thick TbCo film.An optical interference induced significant enhancement of the magneto-optical effect.Moreover, polarity of θ K in the films with the SiO 2 underlayer with thicknesses of 100 nm and 200 nm changed with wavelengths.At these wavelengths, the η K showed the maximum value.These results show that the θ K and η K have a Kramers-Kronig relation.We could also confirm the relation in Figure 2. At a wavelength of 500 nm, θ K for the film with a 100 nm thick SiO 2 underlayer shows a small and negative θ K .One of reasons for the small θ K and the opposite polarity of the Kerr hysteresis loop in Figure 2 of sample A would be mainly owing to optical interference in the SiO 2 layer.Figure 6 shows the simulated magneto-optical Kerr spectra and the measured ones as a function of photon energy for (a) Pt (3 nm)/TbCo (6 nm)/Pt (3 nm), (b) Si 3 N 4 (10 nm)/TbCo (6 nm)/Pt (3 nm), and (c) Pt (3 nm)/TbCo (6 nm)/Si 3 N 4 (10 nm).Lines and dots represent the simulated and measured results, respectively.In sample A with a symmetric structure, the simulated spectra were consistent with the measured ones.On the other hand, in the samples B and C with an asymmetric structure, there were some differences between the simulated and measured results.In a higher energy region, the simulated θ K and η K were consistent with the measured ones.In a lower energy region around 2 eV, the simulated θ K and η K were smaller than measured ones, especially the η K .We cannot explain these results by optical interference effects.Reflection lights from the sample include optical and/or magnetooptical properties in each layer.The inverse stack of samples B and C with the asymmetric structures showed almost the same dependencies in the Kerr spectrum.This could have been caused by an enhancement of not optical, but magneto-optical properties.On the other hand, sample A with a symmetric structure showed no enhancement of magneto-optical properties.These results suggest that the spin-orbit interaction at the interface could have been enhanced in the hetero-structure and lead to larger Kerr signals in a lower photon energy region.

Conclusions
We demonstrated the magneto-optical spectra of Pt/TbCo hetero-structure films.By using a Si substrate with the 100nm of SiO 2 underlayer, we could enhance the magneto-optical Kerr effect to a suitable magnitude.The spectra may include a Kerr effect of the TbCo layer and also an enhanced Kerr effect of Pt/TbCo or TbCo/Pt interface.To clarify these contributions, we simulated Kerr spectra based on the effective refractive index method.In the film with a symmetric structure of Pt/TbCo/Pt, the simulated spectrum was consistent with the measured one.On the other hand, in the films with the asymmetric structures of Pt/TbCo and TbCo/Pt, the simulated spectra were different from the measured ones.In a lower energy region, the measured θ K and η K in these films were larger than the simulated ones, especially the η K .The reason for an enhanced magneto-optical effect may be due to interfacial effects of the spin-orbit interaction.
These results show that Kerr spectra of ultrathin films using an optical interference effect can be utilized to study interface states, including the spin-orbit interaction.
shows measured and calculated results for a 100 nm thick TbCo film (a) measured Kerr spectrum of θ K and η K, (b) measured optical constants (n, k), and (c) calculated optical constants for a right + and a left hand circular − polarization, where real part: N± and imaginary part: K±.The θ K and η K of the film monotonously decreased with increasing wavelengths.Optical constants for a right and a left hand circular polarization almost overlapped.

Figure 4 .
Figure 4. Light wavelength dependence of (a) measured Kerr rotation angel (θ K ) and ellipticity (η K ), (b) measured optical constants (n, k), and (c) optical constants of real part N±, imaginary part K± for a right and a left hand circular polarization calculated from (a) and (b) for a 100 nm thick TbCo film.

Figure 5 .
Figure 5. Simulated magneto-optical Kerr spectra of the sample A deposited on the SiO 2 under layer with thicknesses of 0, 100 and 200 nm.Black, blue, and dark blue lines show Kerr rotation θ K and purple, orange and red lines show ellipticity η K .