France



Thermoelectric conversion elements using the spin Seebeck effect (SSE) have attracted much attention owing to their unique physical properties as well as the industrial applications in a relatively simple structure [1-3]. Many studies using Y&lt;sub&gt;3&lt;/sub&gt;Fe&lt;sub&gt;5&lt;/sub&gt;O&lt;sub&gt;12&lt;/sub&gt; (YIG) have been reported as a magnetic insulator for SSE measurements. Since YIG is an insulator with high Curie temperature that allows magnons to propagate over a long distance, it is suitable for SSE observation. SSE measurements are often carried out using YIG prepared in a sintered bulk or a film grown by a physical vapor deposition method, SSE has also been studied using YIG films prepared by metal–organic decomposition (MOD) which is a simple process used for surface coating [3]. We have previously observed SSE in YIG films prepared on a Si substrate by co-precipitation, which consist of densely packed YIG nanoparticles [4]. In order to enhance the SSE voltage, the YIG films are required to have a flat film surface made by a different chemical process, which enables magnons to coherently propagate. In this paper, we report on the longitudinal SSE (LSSE) voltage in YIG films prepared on a Si or gadolinium gallium garnet (GGG) substrate by sol-gel spin-coating to investigate the annealing-temperature dependence of LSSE voltage in the samples.&lt;br/&gt;YIG film samples were synthesized by sol-gel and subsequent spin-coating processes, followed by annealing at &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;a&lt;/sub&gt; = 1073-1273 K for 0.5 hour in air. From the XRD spectra of the YIG films, diffraction peaks associated with the garnet phase are readily observed in the spectra of all the annealed samples, proving that they are polycrystalline YIG. Figure 1 shows a surface morphological SEM image from a YIG film made on a Si substrate annealed at 1173 K. The average surface roughness measured by SPM is ~10 nm or less, which is 30% smaller than that of YIG films prepared by co-precipitation. The areal fraction of voids estimated in the film surface by SEM imaging is ~10%, which is 75% smaller than those of YIG films prepared by co-precipitation. The obtained results indicate that the YIG films with a flatter surface can be made by the sol-gel method.&lt;br/&gt;To conduct SSE voltage measurements, a 5 nm Pt metal was sputtered on the YIG films. A temperature gradient △&lt;i&gt;T&lt;/i&gt; was applied between the top of each sample (Pt side) and the bottom of the substrate to measure the voltage induced by LSSE. Figure 2 shows the variation of the SSE constant &lt;i&gt;S&lt;/i&gt; with the annealing temperature &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;a&lt;/sub&gt;. The values of &lt;i&gt;S&lt;/i&gt; in each sample are calculated from the △&lt;i&gt;T &lt;/i&gt;dependence of the saturation SSE voltage &lt;i&gt;V&lt;/i&gt;&lt;sub&gt;SSE&lt;/sub&gt;&lt;sup&gt;Sat&lt;/sup&gt;. The value of &lt;i&gt;S&lt;/i&gt; for YIG/Pt films made on a Si substrate decreases with increasing &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;a&lt;/sub&gt;, showing the same trend as those observed for co-precipitated YIG films, which is attributable to the microstructural evolution of the nanocrystalline YIG films upon annealing. Besides, the magnitude of &lt;i&gt;S&lt;/i&gt; is at least 30% smaller than that of co-precipitated YIG films. It is speculated that the observed decrease in the magnitude of &lt;i&gt;S&lt;/i&gt; is owing to the increase in the interfacial area between densely packed nanoparticles as the increase in the coercive force of YIG films prepared by sol-gel is observed according to their magnetic measurements by VSM. The values of &lt;i&gt;S&lt;/i&gt; in the YIG/Pt films synthesized on a GGG substrate annealed at 1173 K are larger than those made on a Si substrate presumably because a single crystal YIG film is formed on the GGG substrate which yields a high efficiency of magnon excitation.

**References:**

[1] K. Uchida et al, Nature, Vol. 455, p. 778 (2008)&lt;br/&gt;[2] K. Uchida et al, Nat. Mater. Vol. 9, p. 894 (2010)&lt;br/&gt;[3] A. Kirihara et al, Nat. Mater. Vol. 11, p. 686 (2012)&lt;br/&gt;[4] K. Yamada et al, IEEE Trans. Magn. Vol. 55, p. 4500104 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/140878e2be751346f3eeaa41cb7e47b2.jpg)
SEM surface image of a YIG film annealed at 1173 K.

![](https://assets.underline.io/uploads/markdown_image/1/image/fba6a1da143f2ae7c0b37407d6894e1b.jpg)
SSE constants &lt;i&gt;S&lt;/i&gt; of Pt(5 nm)/YIG films on a Si or GGG substrate plotted as a function of &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;a&lt;/sub&gt;.

INTERMAG 2021

 Annealing temperature dependence of longitudinal spin Seebeck voltage in YIG films prepared by sol-gel spin coating method

INTERMAG 2021 Welcome Video



	
<figure class="video_container">
 <iframe src="https://screencast-o-matic.com/player/crflqFVnUpZ?v=6&ff=1&title=0&controls=1" width=640 height=360 frameborder="0" allowfullscreen="true"> </iframe>
</figure>

Want to buy a ticket? 

Register for INTERMAG 2021 here

[![](https://assets.underline.io/uploads/markdown_image/1/image/17ce76e7960db633258024eef8d6da7f.png)](https://intermag.org/register)

Got your ticket, but still can’t access the event?

Contact us and our team will look into it.

Thermoelectric conversion elements using the spin Seebeck effect (SSE) have attracted much attention owing to their unique physical properties as well as the industrial applications in a relatively simple structure [1-3]. Many studies using Y3Fe5O12 (YIG) have been reported as a magnetic insulator for SSE measurements. Since YIG is an insulator with high Curie temperature that allows magnons to propagate over a long distance, it is suitable for SSE observation. SSE measurements are often carried out using YIG prepared in a sintered bulk or a film grown by a physical vapor deposition method, SSE has also been studied using YIG films prepared by metal–organic decomposition (MOD) which is a simple process used for surface coating [3]. We have previously observed SSE in YIG films prepared on a Si substrate by co-precipitation, which consist of densely packed YIG nanoparticles [4]. In order to enhance the SSE voltage, the YIG films are required to have a flat film surface made by a different chemical process, which enables magnons to coherently propagate. In this paper, we report on the longitudinal SSE (LSSE) voltage in YIG films prepared on a Si or gadolinium gallium garnet (GGG) substrate by sol-gel spin-coating to investigate the annealing-temperature dependence of LSSE voltage in the samples. YIG film samples were synthesized by sol-gel and subsequent spin-coating processes, followed by annealing at Ta = 1073-1273 K for 0.5 hour in air. From the XRD spectra of the YIG films, diffraction peaks associated with the garnet phase are readily observed in the spectra of all the annealed samples, proving that they are polycrystalline YIG. Figure 1 shows a surface morphological SEM image from a YIG film made on a Si substrate annealed at 1173 K. The average surface roughness measured by SPM is ~10 nm or less, which is 30% smaller than that of YIG films prepared by co-precipitation. The areal fraction of voids estimated in the film surface by SEM imaging is ~10%, which is 75% smaller than those of YIG films prepared by co-precipitation. The obtained results indicate that the YIG films with a flatter surface can be made by the sol-gel method. To conduct SSE voltage measurements, a 5 nm Pt metal was sputtered on the YIG films. A temperature gradient △T was applied between the top of each sample (Pt side) and the bottom of the substrate to measure the voltage induced by LSSE. Figure 2 shows the variation of the SSE constant S with the annealing temperature Ta. The values of S in each sample are calculated from the △T dependence of the saturation SSE voltage VSSESat. The value of S for YIG/Pt films made on a Si substrate decreases with increasing Ta, showing the same trend as those observed for co-precipitated YIG films, which is attributable to the microstructural evolution of the nanocrystalline YIG films upon annealing. Besides, the magnitude of S is at least 30% smaller than that of co-precipitated YIG films. It is speculated that the observed decrease in the magnitude of S is owing to the increase in the interfacial area between densely packed nanoparticles as the increase in the coercive force of YIG films prepared by sol-gel is observed according to their magnetic measurements by VSM. The values of S in the YIG/Pt films synthesized on a GGG substrate annealed at 1173 K are larger than those made on a Si substrate presumably because a single crystal YIG film is formed on the GGG substrate which yields a high efficiency of magnon excitation.

**References:**

[1] K. Uchida et al, Nature, Vol. 455, p. 778 (2008) [2] K. Uchida et al, Nat. Mater. Vol. 9, p. 894 (2010) [3] A. Kirihara et al, Nat. Mater. Vol. 11, p. 686 (2012) [4] K. Yamada et al, IEEE Trans. Magn. Vol. 55, p. 4500104 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/140878e2be751346f3eeaa41cb7e47b2.jpg)
SEM surface image of a YIG film annealed at 1173 K.

![](https://assets.underline.io/uploads/markdown_image/1/image/fba6a1da143f2ae7c0b37407d6894e1b.jpg)
SSE constants S of Pt(5 nm)/YIG films on a Si or GGG substrate plotted as a function of Ta.

poster

The topological insulator (TI) and superconductor (SC) condensed matter states are different at the fundamental level. Superconductors spontaneously break gauge symmetry, while topological insulators are defined by a topological invariant of their band structure. Theoretical work by Fu and Kane in 2008 proposed a novel way to engineer an exotic superconducting system using the proximity effect, to combine the electronic properties of these two distinct systems [1]. They showed that the resulting system was a spinless superconductor, which does not break the time reversal symmetry. A proximity coupled topological insulator / superconductor (TI/SC) bilayer system is suitable to realize topological superconductivity [2]. Bi2Te3/Nb thin films constitute a simple proximity system of a topological insulator and an s-wave superconductor to study magnetotransport phenomena in topological superconductors, working toward coupling superconductivity and other spin states. In the present work we report studies on the structural and magnetotransport properties of Bi2Te3/Nb bilayer and Bi2Te3/Nb/Bi2Te3 trilayer samples, as well as reference single layer samples of Bi2Te3 and Nb. Samples were fabricated through DC magnetron sputtering process with base pressure 10-8 Torr, without breaking the vacuum to ascertain a perfect interface between Bi2Te3 and Nb for optimum proximity coupling. The Ar deposition pressure was fixed at 3 mTorr and the substrate’s temperature was held constant at 300 oC. Both systems, the Si(111)/Bi2Te3(100nm)/Nb(100nm) bilayer and the trilayer Si(111)/Bi2Te3(100nm)/Nb(100nm)/Bi2Te3(100nm) trilayer exhibited large pyramid-like structures of Bi2Te3 as observed with Field-Emission Scanning-Electron-Microscopy (FESEM) and Atomic Force Microscopy (AFM). The crystal structure of the topological insulator layer is consistent with the rhombohedral space group for Bi2Te3, and reveals a predominant texture with planes oriented along the (00l) direction as can be inferred from (006) and (00-15) peaks. The coherence diffraction domain size, estimated using Scherrer’s formula and considered as average crystallite size is 23 nm for the Bi2Te3 layer. The average crystallite size for the superconductor layer of Nb, which is cubic, was extracted from the (101) peak and is equal to 21 nm. For the magnetotransport measurements Hall bar shaped samples were prepared using a Hall stencil mask with current channel length 2.5 mm and width 0.4 mm, aligned in a 7x7 mm2 Si(111) substrate. A second mask was then aligned to make pads of Cr/Au and eventually the ohmic contacts were made using a wire bonder. The magnetotransport measurements were performed in a 9 T QD-PPMS and for temperatures varying from 2.5 K to 300 K. The temperature dependence of longitudinal resistance, Rxx, confirmed that the 100 nm Nb films present a superconducting transition at 8.7 K which decreases with decreasing film thickness, due mostly to dimensionality and increasing disorder. The magnetoconductivity, Δσxx(B), curves of the 100 nm thick Bi2Te3 reference sample, which are shown in Figure 1 in the low field region (B &lt; 0.2 T), were calculated from the magnetotransport data. Observation of a logarithmic variation of magnetoconductance at fields close to zero is an indication of weak antilocalization (WAL) effects that have been widely described in materials with strong spin–orbit coupling, such as topological insulators [3]. The parameters from fitting magnetoconductivity data to Hikami-Larkin-Nagaoka equation at low temperatures have been extracted. The phase coherence length, lφ, is approximately 300 nm and decreases as temperature is raised. The value of coefficient α that indicates the number of independent conducting channels in the system and the type of localization, is equal to 1 at 2.5 K (WAL in a perfect system with two surface conducting channels, each contributing to the pre-factor with a value of 0.5) and decreases to 0.5 at 15 K. Figure 2 presents low temperature magneto-transport measurements probing the nature of the SC in bilayers of Bi2Te3-Nb. The onset of superconductivity of Nb layer adjacent to the topological insulator destroys the WAL phenomena and topological properties of Bi2Te3 that at the single layer Bi2Te3 reference sample dominate in the low field regime at temperatures up to 20 K. At T=3 K the switching between the normal and superconducting state is found to occur at magnetic field value |B|=1.5 T, with an excitation current I = 2 mA. Magnetoconductance and differential magnetoresistance data are examined to show evidence of proximity effect and topological superconductivity.

**References:**

[1] Liang Fu and C.L. Kane, Superconducting proximity effect and Majorana Fermions at the Surface of a Topological Insulator, Phys. Rev. Lett. 100 096407 (2008) [2] Gad Koren, Proximity effects at the interface of a superconductor and a topological insulator in NbN-Bi2Se3 thin film bilayers, Supercond. Sci. Technol. 28 025003 (2015) [3] J.J. Cha et al. Weak antilocalization in Bi2(SexTe1−x)3 nanoribbons and nanoplates, Nano Lett. 12 1107–1111 (2012)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9c9692e192e0e5d18676604dad6ebc60.jpg)
Figure 1: Magnetoconductivity data for the Bi2Te3 reference sample, with magnetic field perpendicular to film plane.

![](https://assets.underline.io/uploads/markdown_image/1/image/cfc1b757135aba7e1f863dfdfe3a19f5.jpg)
Figure 2: Longitudinal resistance data for the Bi2Te3/Nb bilayer film, with the magnetic field perpendicular to film plane.

 Magnetotransport Phenomena in Topological Insulator / Superconductor Bi2Te3/Nb Bilayer and Trilayer Thin Films

The generation, detection, and manipulation of pure spin currents have attracted considerable attention in the field of spintronics owing to their rich physical phenomena and potential applications [1-2]. The most convenient method for generating and detecting the pure spin currents is to utilize the spin Hall magnetoresistance (SMR) [3-4]. In this letter, a novel structure consisting of two heavy metals that delivers competing spin currents of opposite spin indices is presented. We studied spin Hall effect in Ta-Pt alloys with various Ta composition for Ta/Pt/Ni80Fe20/ MgO (001) heterostructures by means of SMR. To determine the relative contributions of Pt and Ta, we measured a series of samples of Ta（tTa=0-3nm）/Pt（3nm）/Ni80Fe20/MgO (001) with a constant Pt (3) layer and various thicknesses of the Ta layer. Low resistivity, flat, and highly (111)-textured Pt-Ta alloy films are synthesized. It is found the SMR ratio is enhanced with a Ta capping layer at an optimum composition of x between 0.5nm to 1nm. The spin accumulation enhancement at the Pt/Ni80Fe20 interface after capping with a Ta layer, which functions as a spin sink at small thickness, is responsible for the SMR ratio enhancement, even though Ta and Pt have opposite spin Hall angels. Our results not only demonstrate a viable scheme for multiple spin currents, but also expand a new avenue for switching a perpendicular ferromagnetic layer by competing spin currents.

**References:**

[1] Q. L. Ma, Y. F. Li, D. B. Gopman, Y. P. Kabanov, Phys. Rev. Lett., 120, 117703 (2018). [2] Z. Z. Luan, L. F. Zhou, P. Wang, Phys. Rev. B, 99, 174406 (2019). [3] Y. J. Xu, Y. M. Yang, H. Xie, Appl. Phys. Lett., 115, 182406 (2019). [4] P. Yang, Q. M. Shao, G. Q. Yu, Appl. Phys. Lett., 117, 082409 (2020).

**Images:**

 Enhancement of the Spin Hall Magnetoresistance in Ta/Pt/Ni80Fe20/MgO(100) Heterostructures by Competing Spin Currents

Surface acoustic waves (SAWs) in the GHz frequency range passing through a ferromagnetic layer can excite magnon–phonon dynamics, i.e., a precessional magnetization motion mediated by the magnetoelastic effect [1-3]. This process is known as acoustic ferromagnetic resonance (A-FMR) [4-7]. The A-FMR driven by SAWs can generate spin currents diffusing into adjacent non-magnetic metal layers via the spin pumping effect [8]. This coupled magnon–phonon dynamics can thus be used as a spin current generation method [9] named as acoustic spin pumping (ASP) [10,11]. The generated spin currents can be detected by the inverse spin Hall effect (ISHE) [9,12], or the inverse Edelstein effect (IEE) [6,13]. In SAW driven A-FMR devices, interdigital transducers (IDT) are used for the generation and detection of SAWs [2–7,9,14]. Since the SAWs propagate on both sides of the IDT, at least half of the phonon energy is lost. To reduce the loss and enhance the spin current generation via ASP, we employ acoustic cavity structures. An acoustic cavity (resonator) consists of a pair of acoustic wave reflector gratings, analogous to the distributed Bragg reflector for light [15]. In this presentation, we demonstrate the enhancement of A-FMR and ASP in the presence of acoustic cavities. By applying an external magnetic field, SAWs passing a Ni film induce A-FMR. When the A-FMR occurs, SAW power is attenuated due to the energy conservation, thus the SAW power absorption PSAW is proportional to the induced A-FMR intensity. The measured SAW power absorption in Fig.1 shows the A-FMR signal fitted with a Lorentzian curve. We confirmed an enhancement of 2.04 ± 0.02 times A-FMR on the sample with acoustic cavity. The A-FMR in the Ni layer generates spin current into the Cu layer by the ASP. The generated spin current is converted to a charge current at the interface between Cu and Bi2O3 via IEE. We detect the generated electric voltage via IEE at the maximum A-FMR field angles φ = 45° and 225°, as shown in Fig.2. We define ΔVASP as the amplitude of the symmetric Lorentzian fitting of DV. The detected electric voltage from the ASP is caused by the charge current, derived from an electric field E induced by the IEE, which is proportional to the flow direction of the spin current density Js and its spin polarization σ; E ∝ Js×σ [16]. The converted charge current density Jc is described as Jc = λIEEJs, where λIEE is the IEE length [17]. Since the Ni/Cu/Bi2O3 trilayers of all samples are fabricated at the same time and the applied external magnetic field angle is the same, thus, ΔVASP ∝ Js. The enhancement factor of ΔVASP is 2.96 ± 0.02 at the low-power range, and 1.6 ± 0.7 at the high-power range. However, the power dependence of ΔVASP has non-linear behavior in the range from 25 mW to 126 mW. This non-linearity in the power dependence is not fully understood. Since this behavior is similar to the case of FMR experiments at the high input radio-frequency (rf) power [21,22] we assume it is from the saturation of magnetic precessional cone angle [23] or multi-magnon scattering [24,25]. We observe a more significant enhancement factor of ASP in the low-power range than the enhancement of A-FMR. In contrast, we find a similar enhancement factor of ASP in the high-power range with that enhancement of A-FMR. The enhancement factor in the high-power range is well described by the multi-magnon scattering in Ref. [26]. However, as far as the author knowledge goes the origin of the higher enhancement factor in the low-power range has not been observed and further understanding is required. In summary, we have demonstrated the enhancement of A-FMR and the spin current generation by using acoustic cavities. Enhancement of 2.04 ± 0.02 times of A-FMR and enhancements of spin current generation from 1.6 ± 0.7 (at a high input rf power) to 2.96 ± 0.02 (at a low input rf power) times were achieved. All the measurements in the present study were carried out at room temperature. At lower temperatures, the SAW confinement can be strengthened by minimizing the interaction with thermal phonons. Minimization of phonon energy losses by further engineering of the acoustic cavities, as well as minimization of magnon energy losses by appropriate selection of materials may lead to magnon–phonon studies in the strong coupling regime.

**References:**

[1] A. K. Ganguly, K. L. Davis, D. C. Webb, and C. Vittoria, J. Appl. Phys. 47, 2696 (1976). [2] I. A. Feng, M. Tachiki, C. Krischer, and M. Levy, J. Appl. Phys. 53, 177 (1982). [3] R. F. Wiegert and M. Levy, J. Appl. Phys. 61, 4270 (1987). [4] M. Weiler, L. Dreher, C. Heeg, H. Huebl, R. Gross, M. S. Brandt, and S. T. B. Goennenwein, Phys. Rev. Lett. 106, 117601 (2011). [5] 8L. Dreher, M. Weiler, M. Pernpeintner, H. Huebl, R. Gross, M. S. Brandt, and S. T. B. Goennenwein, Phys. Rev. B 86, 134415 (2012). [6] M. Xu, J. Puebla, F. Auvray, B. Rana, K. Kondou, and Y. Otani, Phys. Rev. B 97, 180301(R) (2018). [7] J. Puebla, M. Xu, B. Rana, K. Yamamoto, S. Maekawa, and Y. Otani, J. Phys. D 53, 264002 (2020). [8] Y. Tserkovnyak, A. Brataas, and G. E. W. Bauer, Phys.Rev.B 66, 224403 (2002). [9] M. Weiler, H. Huebl, F. Goerg, F. Czeschka, R. Gross, and S. T. B. Goennenwein, Phys. Rev. Lett. 108, 176601 (2012). [10] K. Uchida, H. Adachi, T. An, T. Ota, M. Toda, B. Hillebrands, S. Maekawa, and E. Saitoh, Nat. Mater. 10, 737 (2011). [11] K. Uchida, H. Adachi, T. An, H. Nakayama, M. Toda, B. Hillebrands, S. Maekawa, and E. Saitoh, J. Appl. Phys. 111, 053903 (2012). [12] E. Saitoh,M.Ueda, H. Miyajima,and G. Tatara, Appl. Phys. Lett. 88, 182509 (2006). [13] J. C. Rojas Sanchez, L. Vila, G. Desfonds, S. Gambarelli, J. Attane, J. M. De Teresa, C. Magen, and A. Fert, Nat. Commun. 4, 2944 (2013). [14] I. S. Camara, J. Y. Duquesne, A. Lemaitre, C. Gourdon, and L. Thevenard, Phys. Rev. Appl. 11, 014045 (2019). [15] D. T. Bell and R. C. M. Li, Proc. IEEE 64(5), 711 (1976). [16] S. Karube, K. Kondou, and Y. Otani, Appl. Phys. Express 9, 033001 (2016). [17] H. Tsai, S. Karube, K. Kondou, N. Yamaguchi, F. Ishii, and Y. Otani, Sci. Rep. 8, 5564 (2018). [18] R. Manenti, A. F. Kockum, A. Patterson, T. Behrle, J. Rahamim, G. Tancredi, F. Nori, and P. J. Leek, Nat. Commun. 8, 975 (2017). [19] A. Azevedo, L. Vilela-Leao, R. Rodriguez-Suarez, A. Lacerda Santos, and S. Rezende, Phys. Rev. B 83, 144402 (2011). [20] W. Zhang, B. Peng, F. Han, Q. Wang, W. Soh, C. Ong, and W. Zhang, Appl. Phys. Lett. 108, 102405 (2016). [21] V. Castel, N. Vlietstra, B. J. Van Wees, and J. B. Youssef, Phys. Rev. B 86, 134419 (2012). [22] M. B. Jungfleisch,A.V.Chumak, A. Kehlberger,V.Lauer,D.H. Kim,M.C. Onbasli, C. A. Ross, M. Kl€aui, and B. Hillebrands, Phys.Rev.B 91, 134407 (2015). [23] B. Rana, Y. Fukuma, K. Miura, H. Takahashi, and Y. Otani, Sci. Rep. 7, 2318 (2017). [24] M. B. Jungfleisch, A. V. Chumak, V. I. Vasyuchka, A. A. Serga, B. Obry, H. Schultheiss, P. A. Beck, A. D. Karenowska, E. Saitoh, and B. Hillebrands, Appl. Phys. Lett. 99, 182512 (2011). [25] A. V. Chumak, A. A. Serga, M. B. Jungfleisch, R. Neb, D. A. Bozhko, V. S. Tiberkevich, and B. Hillebrands, Appl. Phys. Lett. 100, 082405 (2012). [26] T. Tashiro, S. Matsuura, A. Nomura, S. Watanabe, K. Kang, H. Sirringhaus, and K. Ando, Sci. Rep. 5, 15158 (2015).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e961acf5358be357a602fd0cc3d3b76e.jpg)
Power absorption PSAW at the in-plane magnetic field φ = 45° at the SAW resonance peak of samples with (blue circles) and without (red squares) acoustic cavity. 10 mW of input rf power is used. Solid curves exhibit Lorentzian fitting curves from the experimental data.

![](https://assets.underline.io/uploads/markdown_image/1/image/154fd492b133d6498154f25b785f92bc.jpg)
Detected electric voltage when a 10 mW of rf power is applied to an IDT and an external in-plane magnetic field φ = 45° and 225° is applied. Data are taken from samples with acoustic cavity (blue circles) and without (red squares) acoustic cavity. The detected voltage is normalized with the voltage value at μ0H =100 mT (ΔV =V −V100mT).

 Enhancement of Acoustic Spin Pumping by Acoustic Distributed Bragg Reflector Cavity

Spin-torque ferromagnetic resonance (ST-FMR) has been widely used to determine the spin-orbit torque (SOT) efficiency in ferromagnet/heavy-metal bilayer systems [1]. When a radio frequency (rf) current flows within the HM, the spin Hall effect (SHE) induced SOT and Oersted field act on the FM layer. When the frequency of the rf current and the applied external magnetic field satisfies the ferromagnetic resonance (FMR) condition, the magnetization of the FM layer oscillates with relatively large amplitude around the equilibrium state. This results in a non-negligible resistance oscillation due to the anisotropic magnetoresistance (AMR) of the FM layer. Consequently, a rectified dc voltage is generated as a result of the interplay of the oscillating current and resistance. Importantly, the lineshape of voltage curve due to the damping-like torque is Lorentzian symmetric, while that from the field-like torque (both SHE and Oersted field origin) is anti-symmetric. Thus, one can obtain the SOT efficiency from lineshape analysis of ST-FMR voltage curve. However, the precession of FM moments also acts as the source for an angular momentum flow, which pumps a pure spin current into its neighboring HM [2]. Wherein, an additional contribution to the dc voltage arises from the inverse spin Hall effect (ISHE) [3] which has Lorentzian symmetric lineshape. In this work, we develop a new method to quantitatively separate the SP-ISHE signal from the ST-FMR signal without tedious symmetry analysis. With the precession angles obtained in both setups via the microwave photoresistance measurements [4], we directly obtain the SP-ISHE contribution in the ST-FMR. Our method does not rely on many unknown parameters such as the spin diffusion length, spin Hall angle of HM, and the effective spin-mixing conductance of FM-HM interface etc. Interestingly, we find that the SP-ISHE is in the opposite sign to the symmetric component of ST-FMR for Py(Ni80Fe20)/Pt bilayer layer. Through the Py thickness dependent measurements, we further estimate both the SHE-induced damping-like-torque efficiency and field-like-torque efficiency for Py/Pt bilayer system.

**References:**

[1] L. Liu, T. Moriyama, D. C. Ralph, and R. A. Buhrman, Phys. Rev. Lett. Vol. 106, p. 036601 (2011). [2] Y. Tserkovnyak, A. Brataas, and G. E. W. Bauer, Phys. Rev. B Vol. 66, p. 224403 (2002). [3] O. Mosendz, V. Vlaminck, J. E. Pearson, et al. Phys. Rev. B Vol. 82, p. 214403 (2010). [4] N. Mecking, Y. S. Gui, and C. M. Hu, Phys. Rev. B Vol. 76, p. 224430 (2007).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4bdc274a6b4d2fc20d3aef42834ddb4b.jpg)
FIG. 1. (a), (b), (c) are the measurements with SP-ISHE configuration at φ=-90° , f=9 GHz and (d), (e), (f) are the measurements with ST-FMR configuration at φ=-10° , f=9 GHz. (a) and (d) are the magnetic field-dependent voltages of the Py(6 nm)/Pt(6 nm) sample with dc current +I0 (+1 mA, black curve) and −I0 (−1 mA, orange curve) . (b) and (e) are the magnetic field-dependent microwave photoresistance. (c) and (f) are the relationship between the measured corresponding amplitudes and the product of the in-plane and out-of-plane precession angles.

![](https://assets.underline.io/uploads/markdown_image/1/image/287c76f13bb9f8ca37b462064d7374bc.jpg)
FIG. 2. (a) tPy dependent saturation magnetic moment MS of Py. (b) Corrected (red) and uncorrected (black) 1/ξFMR versus 1/(μ0MStPy), the lines are fittings with Eq. (4).

 Influence of the spin pumping induced inverse spin Hall effect on spin-torque ferromagnetic resonance measurements

In order to unambiguously demonstrate the transverse M-independent spin current generated by the SHE in FM and eliminate interference from AHE. In this work, we employed spin-torque ferromagnetic resonance (ST-FMR) technique to study the SHE in the ferrimagnetic insulator/ ferromagnetic metals (FMI/FM) systems with FMI being Y3Fe5O12 and FM being NiFe and CoFeB. The key of this experiment relies on different FMR frequencies of the YIG and the FM film at the same field. Thus at the FMR mode of the YIG driven by spin torque due to SHE, a dc rectification voltage can be detected due to spin Hall magnetoresistance (SMR) while (1) spin current induced by AHE cannot contribute to the dc voltage due to the vanishing mYIG×mNiFe (2) the anisotropic magnetoresistance (AMR) of FM has no contribution to the measured Vdc signal because FM is not in its the precession state. We have indeed obtained large SHE in FM without contamination from AHE. The measured spin torque efficiency ξ of NiFe was 0.009, 25% as large as that of Pt. These results indicate that the spin Hall effect of FM should also be taken into account when investigating the FM/HM heterostructures and furthermore this effect can also benefit the development of spin-orbit torque devices.

**References:**

[1] V. P. Amin, J. Li, M. D. Stiles, and P. M. Haney, Phys. Rev. B 99, 2019, 220405. [2] D. Tian, Y. Li, D. Qu, S. Y. Huang, X. Jin, and C. L. Chien, Phys. Rev. B 94, 2016, 020403. [3] K. S. Das, W. Y. Schoemaker, B. J. van Wees, and I. J. Vera-Marun, Phys. Rev. B 96, 2017, 220408. [4] W. Wang, T. Wang, V. P. Amin, Y. Wang, A. Radhakr-ishnan, X. Fan et al, Nature Nanotech. 14, 2019, 819. [5] H. Wu, S. A. Razavi, Q. Shao, X. Li, K. L. Wong, Y. Liu, G. Yin, and K. L. Wang, Phys. Rev. B 99, 2019, 184403.

**Images:**
![](https://assets.underline.io/uploads/markdown_image/1/image/a0bfe564b13086f4fc76de03562d5a22.jpg)

 Determination of Spin Torque Efficiency in Ferromagnetic Metals via Spin-Torque Ferromagnetic Resonance

Spin pumping is a technique widely used to generate pure spin current and characterize the spin-charge conversion efficiency of heavy metals，which utilizes a microwave to excite the precession of the magnetic moments. However, the microwave irradiation may also bring possible thermoelectric artifacts. Both the eddy currents in conductors and magnon–phonon scattering in ferromagnet could heat the samples [1]. Typically, for devices with a thin film deposited on a thick substrate, the temperature increase might establish a perpendicular temperature gradient, which gives rise to thermoelectric signals such as the longitudinal spin Seebeck effect (LSSE) [2] and the anomalous Nernst effect (ANE) [3]. Therefore, the spin pumping signals are potentially contaminated with thermoelectric contributions [4]. The separation of the LSSE and ANE contributions from the spin pumping signal is not straightforward. Under an out-of-plane (perpendicular) temperature gradient, the LSSE and ANE produce thermoelectric signal with Eth∝▽ZT×M, where M represents the magnetization direction of ferromagnet. One can readily find that the spin pumping, LSSE, and ANE voltages all share the same symmetry with the same angular dependence, hence inseparable and additive. Furthermore, if the thermoelectric contributions are dominating, the measured signal in the ferromagnet/heavy metal structure may even fail to denote the spin Hall angle sign of the heavy metal [5]. Therefore, it is important to develop a quantitative method to separate thermoelectric contributions in the spin pumping experiments. In this work, we present a universal and quantitative method to obtain the thermoelectric contributions in spin pumping voltage via the assistance of the microwave-photoresistance measurements. We apply this method on two typical systems, i.e., Py(Ni80Fe20)/Pt and YIG(Y3Fe5O12)/Pt bilayers, and find that the microwave radiation indeed can raise the sample temperatures and create a perpendicular temperature gradient. This vertical temperature gradient induces a sizable thermal voltage due to the LSSE and the ANE near zero magnetic field, which acts as a background for spin pumping signals at higher fields. However, the additional heat dissipation due to magnon-phonon scattering at the ferromagnetic resonance condition is negligibly small, in consistent with previous findings [6]. This conclusion is further supported by the field-dependent microwave absorption measurement using a vector network analyzer. Therefore, we conclude that the thermoelectric contributions are little, if any, as compared with the spin pumping signal in our measurement geometry.

**References:**

[1] N. Yoshikawa and T. Kato, J. Phys. D: Appl. Phys. Vol. 43, p. 425403 (2010). [2] K. Uchida, H. Adachi and E. Saitoh, Appl. Phys. Lett. Vol. 97, p. 172505 (2010). [3] T. Miyasato, N. Abe and Y. Tokura, Phys. Rev. Lett. Vol. 99, p. 086602 (2007). [4] Y. Huo, F. L. Zeng and Y. Z. Wu, Phys. Rev. Appl. Vol. 8, p. 014022 (2017). [5] W. W. Lin and C. L. Chien, arXiv :1804.01392(2018). [6] P. Noel, M. Cosset-Cheneau and J. P. Attane, J. Appl. Phys. Vol. 127, p. 163907 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a7adaa058098cf7f0ce5f5806dbff6a6.jpg)
Fig. 1 (a) Schematic illustration of the experimental setup for spin pumping measurements of Py/Pt bilayer. (b) Field-dependent voltage for a Py(6 nm)/Pt(3 nm) bilayer stripe with 8.5 GHz microwave irradiation, where the magnetic field is applied along the y-direction. The black symbols represent the experimental data, and the red lines are the Lorentz line fittings. The inset presents the zoomed-in feature near zero magnetic field. 2△V0 denotes the difference of the voltage background for the positive and negative fields. (c) Microwave frequency f dependent resonance field Hr. Black circles are the experimental data, and the red line is the fitting with Kittel equation. (d) Microwave input power dependent Vr (black hexagon, left scale) and △V0 (red triangle, right scale). The lines are linear fittings.

![](https://assets.underline.io/uploads/markdown_image/1/image/ddf6716071faa41eb5e55e19f5e780c7.jpg)
Fig. 2 (a) R-T curve of a Py(6 nm)/Pt(3 nm) bilayer near room temperature, with a slope of 7.12(±0.02) Ω/K. R300K = 8.86 kΩ. (b) Magnetic field-dependent voltages with dc current +I0 (+0.9 mA, red curve) and −I0 (−0.9 mA, black curve) for the Py/Pt sample, respectively. (c) The resistance difference △R of the Py/Pt bilayer between microwave on and off states. (d) Linear relation between the thermoelectric ground △V0 and the resistance difference background △Rb. (e) Magnetic field dependent △R for different α. The curves are shifted for clarity. (f) Magnetic field-dependent S21 parameter data for a “7 mm×7 mm” Py(6 nm)/Pt(3 nm) film.

 Quantitative Estimation of Thermoelectric Contributions in Spin Pumping Signals through microwave photoresistance measurements

Dynamical spin injection based on ferromagnetic resonance (FMR) has been intensively investigated owing to its simple structure with variable applications [1]. When the FMR is excited in ferromagnetic-metal (FM)/nonmagnetic-metal (NM) bilayer thin films, the spin current flows from the FM layer into the NM layer. Although the mechanism of the dynamical spin injection is mainly explained by spin pumping, FMR-heating could be a possible reason for the dynamical spin injection [2]. To investigate the dominant contribution for the dynamical spin injection, we measured the temperature dependence of the inverse spin Hall signal in a CoFeB/Pt/CoFeB trilayer structure. Fig.1 shows the schematic illustration of the measurement system. Here, the bottom Cu layer acts as the coplanar wave guide for genrating a high frequency magnetic field, resulting in the efficient excitation of the FMR of the trilayer structure. In addition, since the Cu layer with sufficiently low electrical resistivity is directly connected to the trilayer, we are able to purely observe inverse spin Hall signal in the Pt due to the dynamical spin injection with eliminate the spurious signals such as the rectified anisotropic magnetoresistance and anomalous Nernst effects.[3] The observed inverse spin Hall signals at room temperature (297K) and low temperature(77K) are shown in Fig.2. It should be emphasized that the sign of the inverse spin Hall signal at 77 K is opposite from that at 297 K. This can be explained by the change of the thermal gradient in CoFeB/Pt/CoFeB/Cu/Sub, indicating that the FMR heating is a dominant mechanism for the dynamical spin injection.

**References:**

 [1] Ryo Iguchi and Eiji Saitoh JPSJ 86. 011003(2017) [2] Kazuto Yamanoi et al, APL107, 182410(2017) [3] Sora Obinata et al. MMM Conference November2-6, 2020; virtual

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d79919ae5885ad82e01d6c9b34e9c1d9.jpg)
Fig.1 Schematic illustration of measurement setup

![](https://assets.underline.io/uploads/markdown_image/1/image/ca05fe135bfea30d69485af5de5a3b04.jpg)
Fig.2 ISHE signals measured at 297K and 77K

 Qualitative evaluation of the temperature dependence of dynamical spin injection in CoFeB/Pt/CoFeB trilayer thin films

Spin-orbit coupling (SOC) is one of the most important parts of spintronics. The momentum and spin of electrons are coupled by spin-orbit interaction. Two of the representative phenomena that originated from SOC are Rashba-Edelstein effect (REE) [1] and spin Hall effect (SHE) [2, 3]. There are numerous studies on REE and SHE, but direct observation of those effects has been elusive. Concerning the spin Hall effect, a current-induced spin accumulation has been directly observed using the magneto-optic Kerr effect (MOKE). [4, 5] However, there has been no direct observation of spin accumulation induced by the Rashba-Edelstein effect. In this study, we investigated the current-induced spin accumulation in InAs two-dimensional electron gas (2DEG) channel directly by using the MOKE. As a result, the in-plane spin accumulation throughout the channel by REE and the out-of-plane spin accumulation at the edges of the 2DEG channel by SHE were directly observed. Our result is of importance because it exhibits both spin accumulation components originating from REE and SHE in the same structure and they are unambiguously separated. Moreover, we determined the current-induced magneto-optic constant of InAs 2DEG, which is essential for further optical studies on this structure.

**References:**

[1] V. M. Edelstein, Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems. Solid State Communications 73, 233-235. (1990) [2] M. I. D’yakonov, and V. I. Perel, Current-induced spin orientation of electrons in semiconductors. Phys. Lett. 35A, 459 (1971) [3] M. I. D’yakonov, and V. I. Perel, Possibility of Orienting Electron Spins with Current. Sov. Phys. JETP Lett. 13, 467 (1971) [4] Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Observation of the spin Hall effect in semiconductors. Science 306, 1910-1913. (2004) [5] C. Stamm, C. Murer, M. Berritta, J. Feng, M. Gabureac, P. M. Oppeneer, and P. Gambardella, Magneto-Optical Detection of the Spin Hall Effect in Pt and W Thin Films. Phys. Rev. Lett 119, 087203. (2017)

**Images:**

 Direct magneto-optical observation of current-induced spin accumulation in InAs two-dimensional electron gas (2DEG) structure

The generation and detection of spin currents are key a role in investigating basic physics phenomena and for applications in the field of spintronics. One method of generating spin current is the spin Seebeck effect (SSE) via applying a heat current along with the magnetic materials. The spin current can be converted to an electrical voltage in large spin-orbit coupling materials due to the inverse spin Hall effect (ISHE). Recently, many reports have been shown that paramagnetic, ferrimagnetic, and antiferromagnetic materials reveal large spin-to-charge current conversion [1-4]. In this work, we investigate the SSE in thin-film the antiferromagnetic PtMn on top of sputtered YIG films. We prepared the following film stacks using rf and dc magnetron sputtering: substrate/buffer/Y3Fe5O12 (100 nm)/800 C/Pt0.35Mn0.65 (10 nm)/MgO (2 nm)/Ta (1 nm)/375 C, where the temperatures are the post-annealing temperatures, and the films are grown at the room temperature. We used four substrate/buffer combinations: Gd3Ga5O12 (GGG) sub., Si/SiO2 sub., Si/SiO2/Ta (5 nm), and Si/SiO2/Ta (5 nm)/Pt (5 nm). We optimized the YIG’s sputtering growth condition for stoichiometry, high saturation magnetization, low ferromagnetic resonance damping constant, and low surface roughness. The PtMn is made with rich Mn composition having an fcc phase. Subsequently, we measured the SSE. We applied a thermal gradient across the thickness direction of the substrate, and measured the conversion of generated spin current to electric voltage by means of ISHE in PtMn. Figure 1(a-b) shows our measurement result in the Si/SiO2/YIG /PtMn and GGG/YIG/PtMn samples as a function of applied magnetic field Hx at ΔT = 4 K. We observed that SSE voltage VSSE is revealed in both samples. Moreover, the magnitude of VSSE is proportional to ΔT as shown in Fig. 1(c-d). Even though our films are antiferromagnetic and have a Mn-rich composition, the magnitude of VSSE in our samples is comparable to what is found in YIG/Pt systems [4]. Further data and discussion will be presented. This work was supported by the Center for Science and Innovation in Spintronics (CSIS), Center for Spintronics Research Network (CSRN), Tohoku University, and by JSPS KAKENHI Grant Number JP19K15429. JP20H02185

**References:**

[1] Nakata et al., "Spin Seebeck voltage enhancement by Mn system metals insertion at the interface between YIG and nonmagnetic layer." Japanese Journal of Applied Physics 58, no. SB (2019): SBBI04. [2] Seki et al., "Observation of inverse spin Hall effect in ferromagnetic FePt alloys using spin Seebeck effect." Applied Physics Letters 107, no. 9 (2015): 092401. [3] Kikkawa et al. "Longitudinal spin Seebeck effect free from the proximity Nernst effect." Physical review letters 110, no. 6 (2013): 067207. [4] Mendes et al., "Large inverse spin Hall effect in the antiferromagnetic metal Ir 20 Mn 80." Physical Review B 89, no. 14 (2014): 140406

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ae6968b7c2263f52936059e4033429d1.jpg)
(a-b) Field dependence of SSE voltage in the PtMn at ΔT=4 K, (c-d) ΔV as a function of ΔT .

 Spin Seebeck Effect in Antiferromagnetic PtMn/YIG(Yttrium Iron Garnet) Thin Films

Introduction: Biomagnetic measurement systems, such as a magnetoencephalography (MEG), are commonly composed of multi-channel magnetic sensor array more than 100. It is very important to know the positions, orientations, and sensitivities of the magnetic sensors precisely to accurately estimate the neuronal activity. So far, a calibration technique is employed to measure the sensor geometry and sensitivity after assembling or cooling the sensor arrays [1]. This calibration technique is performed by estimating the geometry and sensitivity of the sensors from the measured magnetic field distribution generated by a multi-coil array. However, there is no discussion about the accuracy of the estimation because the coil array itself has not been calibrated and its accuracy has not been evaluated. Therefore, we propose the calibration technique for the coil array based on the three-dimensional (3D) measurement using an X-ray computed tomography (CT). In this paper, we present a calibration result of the coil array and a comparison of the accuracy of the MEG source localization between using the designed and calibrated coil array geometries to measure positions, orientations, and sensitivities of MEG sensors. We fabricated a 18-channel coil array. This coil array was composed of 6 coil modules that have concentric 3 coils orthogonal to each other. The diameter and the distance between each coil were designed 30 mm and about 70 mm, respectively. (1) 3D measurement using X-ray CT The 3D measurement was performed using an X-ray CT machine (inspeXio SMX-225CT FPR HR, Shimazu Corporation). The center position, the orientation of the normal vector, and the radius of each coil were obtained by fitting a circle equation to the 3D data. We call this process “calibration of the coil array”. (2) Measurement of the MEG sensor geometries In this study, we used a whole-head MEG system, which was installed at the Kanazawa Institute of Technology [2]. This MEG system consisted of 160 arrayed SQUID (superconducting quantum interference device) sensors, which had the first-order axial gradiometers. The coil array was placed at the center of the helmet of the MEG cryostat, and the magnetic signals were generated by applying sinusoidal current waveform (80 Hz) to each coil. After measuring the magnetic signals, we estimated the sensor array layout (position, orientation, and sensitivity of each sensor). The sensor array layouts were obtained by solving the inverse problem using (A) designed and (B) 3D measured coil array geometry. (3) MEG source localization In order to confirm that the performance of the MEG system can be improved by employing the 3D-measured coil array geometry, we compared the source localization accuracy using the sensor layouts between (A) and (B). An MEG phantom, which emulates the neuronal activity in human brain as equivalent current dipoles (ECDs) [3], was used to provide the signal sources. The magnetic signals from the ECDs were measured by the MEG sensors, then the sources were localized using the sensor layouts (A) and (B). Results and Discussions: (1) 3D measurement using X-ray CT Figure 1 shows the results of the 3D measurement of the coil array using the X-ray CT. Figure 1 (a) is the entire polygon data converted from the X-ray CT image, and Fig.1 (b) shows the designed geometries of the coils in the module 1 (blue) and the obtained circles based on the X-ray CT measurement (red). The differences between designed and the 3D-measured coil geometries were 0.6±0.3 mm, 0.7±0.4 degrees, and 0.3±0.1 mm (mean±standard deviation of 18 coils) in the center position, the orientation of the normal vector, and the radius, respectively. (2) Measurement of the MEG sensor geometries The sensor array layouts were estimated using the designed and the 3D-measured coil array geometries. The differences of the estimated layouts were 1.2±0.9 mm, 1.0±0.6 degrees, and 0.7±1.9 % (mean±standard deviation of 160 sensors) in position, orientation, and sensitivity, respectively. (3) MEG source localization Figure 2 shows the differences between true value and localized values of the sources in position and orientation, respectively. Both displacements in position and orientation decreased by using the 3D-measured coil array geometry. It was demonstrated that the source localization accuracy was improved by defining the sensor layout using the calibrated coil array geometry. Conclusion: We demonstrated the calibration method of the coil array based on the 3D measurement using the X-ray CT machine. Although the coil array was fabricated preciously, the calibration of the coil array is necessary to bring the best out of the MEG system.

**References:**

[1] T. Yoshida, et al., “Calibration system for multichannel SQUID magnetometer,” in Proc. 16th Annu. Int. Conf. IEEE Eng. Adv. New Opportunities Biomed. Eng., pp.171-172 (1994). [2] H. Kado, et al., “Magnetoencephalogram systems developed at KIT,” IEEE Trans. Appl. Supercond., vol. 9 (2), pp. 4057-4062 (1999). [3] D. Oyama, et al., “Dry phantom for magnetoencephalography － Configuration, calibration, and contribution,” J. Neurosci. Methods, vol. 251, pp. 24-36 (2015).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2321ed5ac6ba860c99e1487530a02181.jpg)
Fig. 1 Results of X-ray CT measurements of the coil array. (a) entire polygon data, (b) designed and 3D-measued geometries of the coils on the module 1.

![](https://assets.underline.io/uploads/markdown_image/1/image/bf4370f47df771b814ee17abdf75c1a6.jpg)
Fig. 2 Results of the source localization experiment. This graph shows the differences between the true value and the localized values of the signal sources in position and orientation. The lengths of the squares and the error bars indicate the mean and the standard deviation of 49 signal sources).

Next from INTERMAG 2021

Magnetotransport Phenomena in Topological Insulator / Superconductor Bi2Te3/Nb Bilayer and Trilayer Thin Films

Similar lecture

Theoretical Study on Four-fold Symmetric Anisotropic Magnetoresistance Effect in Cubic Single-crystal Ferromagnetic Model