France



Perovskite manganites R&lt;sub&gt;x&lt;/sub&gt;A&lt;sub&gt;1-x&lt;/sub&gt;MnO&lt;sub&gt;3&lt;/sub&gt; (R = Rare earth, A = alkaline earth: 0&amp;lt;x&amp;lt;1) are well-known for their correlated charge, spin and lattice degrees of freedom [1]. While studies on hole-doped manganites are almost complete, the physical properties of electron-doped manganites are still being understood. Recent studies on R&lt;sub&gt;0.15&lt;/sub&gt;Ca&lt;sub&gt;0.85&lt;/sub&gt;MnO&lt;sub&gt;3&lt;/sub&gt; (R = Y, Gd and Dy) revealed interesting metamagnetic transition in the antiferromagnetically ordered state across which the samples show insulator to metal-like change in the electrical resistivity and also switches from an inverse magnetocaloric effect (MCE) to normal MCE [2]. In this work, magnetic and magnetocaloric properties of electron-doped Pr&lt;sub&gt;0.15&lt;/sub&gt;Ca&lt;sub&gt;0.85&lt;/sub&gt;MnO&lt;sub&gt;3&lt;/sub&gt; are studied in order to understand the effect of light rare earth substitution at the Ca-site of antiferromagnetic CaMnO&lt;sub&gt;3&lt;/sub&gt;. Polycrystalline Pr&lt;sub&gt;0.15&lt;/sub&gt;Ca&lt;sub&gt;0.85&lt;/sub&gt;MnO&lt;sub&gt;3&lt;/sub&gt; has been prepared by solid state reaction. The X-ray diffraction (XRD) data were collected at several temperatures (T) from 300 K down to 25 K (Cu Ka, Rigaku). It is found that Pr&lt;sub&gt;0.15&lt;/sub&gt;Ca&lt;sub&gt;0.85&lt;/sub&gt;MnO&lt;sub&gt;3&lt;/sub&gt; crystallizes in orthorhombic structure (space group &lt;i&gt;Pnma&lt;/i&gt;, no. 62, &lt;i&gt;oP20&lt;/i&gt;) at 300 K and orders antiferromagnetically at 147 K (T&lt;sub&gt;N&lt;/sub&gt;). Paramagnetic susceptibility follows Curie-Weiss law. The effective paramagnetic moment (m&lt;sub&gt;eff&lt;/sub&gt;) and paramagnetic Curie temperature (q&lt;sub&gt;p&lt;/sub&gt;) values are 4.47 m&lt;sub&gt;B&lt;/sub&gt;/f.u and +118 K respectively. The positive q&lt;sub&gt;p&lt;/sub&gt; value indicates the presence of coexisting ferromagnetic interactions in the system. The field dependent magnetization measured at 5 K in fields up to 70 kOe is almost linear suggesting the presence of dominant antiferromagnetic interactions. The magnetization value at 5 K in 70 kOe field is about 0.11 m&lt;sub&gt;B&lt;/sub&gt;/f.u. only. From low temperature XRD, it is observed that the crystal structure changes to monoclinic (space group &lt;i&gt;P2&lt;sub&gt;1&lt;/sub&gt;/m&lt;/i&gt;, no.11-2, &lt;i&gt;mP20&lt;/i&gt;) across the magnetic transition. No metamagnetic transition is evidenced in Pr&lt;sub&gt;0.15&lt;/sub&gt;Ca&lt;sub&gt;0.85&lt;/sub&gt;MnO&lt;sub&gt;3&lt;/sub&gt; at 5 K in fields up to 70 kOe suggesting robust antiferromagnetic state. Magnetocaloric effect (MCE) has been estimated in terms of isothermal magnetic entropy change (ΔS&lt;sub&gt;m&lt;/sub&gt;) using magnetization vs field (M-H) isotherms measured around T&lt;sub&gt;N&lt;/sub&gt;. Positive MCE (i.e. inverse MCE) is observed below T&lt;sub&gt;N&lt;/sub&gt; [Fig. 1a]. The maximum ΔS&lt;sub&gt;m&lt;/sub&gt; value is about 6.4 Jkg&lt;sup&gt;-1&lt;/sup&gt;K&lt;sup&gt;-1&lt;/sup&gt; at 137.5 K for 70 kOe field change. The peak in inverse magnetocaloric effect coincides with the magnetostructural transition temperature. The maximum value of isothermal magnetic entropy change, ΔS&lt;sub&gt;m&lt;/sub&gt;&lt;sup&gt;max&lt;/sup&gt;, at 142.5 K is plotted as a function of magnetic field change (ΔH) and is fitted to a power law, i.e. ΔS&lt;sub&gt;m&lt;/sub&gt;&lt;sup&gt;max&lt;/sup&gt; µ (ΔH)&lt;sup&gt;n&lt;/sup&gt; [Fig. 1b] and the ‘n’ value is found to be 1.75. It is recalled that a value of n = 2 is expected for antiferromagnets [3] and the decrease in the ‘n’ value could be indicative of the coexistence of ferromagnetic interactions in the system. Though Pr&lt;sub&gt;0.15&lt;/sub&gt;Ca&lt;sub&gt;0.85&lt;/sub&gt;MnO&lt;sub&gt;3&lt;/sub&gt; shows a strong electrical resistivity value in the antiferromagnetically ordered state, the electrical resistivity value decreased by several order below T&lt;sub&gt;N&lt;/sub&gt;. Non adiabatic polaron hopping conduction is observed above T&lt;sub&gt;N&lt;/sub&gt; and polaron activation energy is found to be ~40 meV. Electron spin resonance studies were performed from 300 K to down to 7 K reveal Dysonian broadening as a result of the intrinsic electrical conductivity of the material. The g-value observed at 300 K is less than the free electron g-value and it increases with decreasing temperature down to T&lt;sub&gt;N&lt;/sub&gt;. Thermopower measurements showed strong temperature dependence near T&lt;sub&gt;N&lt;/sub&gt; and a large negative thermopower of ~40 mV/K was obtained around 100 K.

**References:**

1. Y. Tokura, Rep. Prog. Phys. 69 (2006) 797&lt;br/&gt;2. Lakshman Dhal, Eesha Andharia, N. Shukla, T. Geetha Kumary, A. K. Nigam, S. K. Malik, P. N. Santhosh and R. Nirmala, J. Magn. Magn. Mater. 474 (2019) 215&lt;br/&gt;3. A. Biswas, S. Chandra, T. Samanta, M. H. Phan, I. Das and H. Srikanth, J. Appl. Phys. 113 (2013) 17A902

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7c4e653992c0eeae931c3f9dc5f0db42.jpg)
Fig. 1 (a) Isothermal magnetic entropy change (ΔS&lt;sub&gt;m&lt;/sub&gt;) vs temperature for various field changes and (b) Maximum magnetic entropy change vs ΔH at T&lt;sub&gt;N&lt;/sub&gt; and the fit to power law, (ΔH)&lt;sup&gt;n&lt;/sup&gt;, with n = 1.75.



INTERMAG 2021

 Inverse Magnetocaloric Effect and the Magnetostructural Transition in Pr0.15Ca0.85MnO3 Manganite

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Perovskite manganites RxA1-xMnO3 (R = Rare earth, A = alkaline earth: 0&lt;x&lt;1) are well-known for their correlated charge, spin and lattice degrees of freedom [1]. While studies on hole-doped manganites are almost complete, the physical properties of electron-doped manganites are still being understood. Recent studies on R0.15Ca0.85MnO3 (R = Y, Gd and Dy) revealed interesting metamagnetic transition in the antiferromagnetically ordered state across which the samples show insulator to metal-like change in the electrical resistivity and also switches from an inverse magnetocaloric effect (MCE) to normal MCE [2]. In this work, magnetic and magnetocaloric properties of electron-doped Pr0.15Ca0.85MnO3 are studied in order to understand the effect of light rare earth substitution at the Ca-site of antiferromagnetic CaMnO3. Polycrystalline Pr0.15Ca0.85MnO3 has been prepared by solid state reaction. The X-ray diffraction (XRD) data were collected at several temperatures (T) from 300 K down to 25 K (Cu Ka, Rigaku). It is found that Pr0.15Ca0.85MnO3 crystallizes in orthorhombic structure (space group Pnma, no. 62, oP20) at 300 K and orders antiferromagnetically at 147 K (TN). Paramagnetic susceptibility follows Curie-Weiss law. The effective paramagnetic moment (meff) and paramagnetic Curie temperature (qp) values are 4.47 mB/f.u and +118 K respectively. The positive qp value indicates the presence of coexisting ferromagnetic interactions in the system. The field dependent magnetization measured at 5 K in fields up to 70 kOe is almost linear suggesting the presence of dominant antiferromagnetic interactions. The magnetization value at 5 K in 70 kOe field is about 0.11 mB/f.u. only. From low temperature XRD, it is observed that the crystal structure changes to monoclinic (space group P21/m, no.11-2, mP20) across the magnetic transition. No metamagnetic transition is evidenced in Pr0.15Ca0.85MnO3 at 5 K in fields up to 70 kOe suggesting robust antiferromagnetic state. Magnetocaloric effect (MCE) has been estimated in terms of isothermal magnetic entropy change (ΔSm) using magnetization vs field (M-H) isotherms measured around TN. Positive MCE (i.e. inverse MCE) is observed below TN [Fig. 1a]. The maximum ΔSm value is about 6.4 Jkg-1K-1 at 137.5 K for 70 kOe field change. The peak in inverse magnetocaloric effect coincides with the magnetostructural transition temperature. The maximum value of isothermal magnetic entropy change, ΔSmmax, at 142.5 K is plotted as a function of magnetic field change (ΔH) and is fitted to a power law, i.e. ΔSmmax µ (ΔH)n [Fig. 1b] and the ‘n’ value is found to be 1.75. It is recalled that a value of n = 2 is expected for antiferromagnets [3] and the decrease in the ‘n’ value could be indicative of the coexistence of ferromagnetic interactions in the system. Though Pr0.15Ca0.85MnO3 shows a strong electrical resistivity value in the antiferromagnetically ordered state, the electrical resistivity value decreased by several order below TN. Non adiabatic polaron hopping conduction is observed above TN and polaron activation energy is found to be ~40 meV. Electron spin resonance studies were performed from 300 K to down to 7 K reveal Dysonian broadening as a result of the intrinsic electrical conductivity of the material. The g-value observed at 300 K is less than the free electron g-value and it increases with decreasing temperature down to TN. Thermopower measurements showed strong temperature dependence near TN and a large negative thermopower of ~40 mV/K was obtained around 100 K.

**References:**

1. Y. Tokura, Rep. Prog. Phys. 69 (2006) 797 2. Lakshman Dhal, Eesha Andharia, N. Shukla, T. Geetha Kumary, A. K. Nigam, S. K. Malik, P. N. Santhosh and R. Nirmala, J. Magn. Magn. Mater. 474 (2019) 215 3. A. Biswas, S. Chandra, T. Samanta, M. H. Phan, I. Das and H. Srikanth, J. Appl. Phys. 113 (2013) 17A902

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7c4e653992c0eeae931c3f9dc5f0db42.jpg)
Fig. 1 (a) Isothermal magnetic entropy change (ΔSm) vs temperature for various field changes and (b) Maximum magnetic entropy change vs ΔH at TN and the fit to power law, (ΔH)n, with n = 1.75.

poster

Properties of two-dimensional spatially periodic nanostructures formed by a corrugated 2D structured as substrate which covered by gold and Ce:YIG films were studied by magneto-optical spectroscopy techniques. It was shown that the structures exhibit a considerable magneto optical response to longitudinal Kerr effect at wavelength of 450 nm and this enhancement seems to be related to excitation of localized surface plasmon-polaritons(LSPR) in the array of nanorods created in this structure. Recent achievements in photonics and optoelectronic require the advanced magneto-photonic microdevice with ability of control the magneto-optical response in micron and submicron scales. The Advanced magneto-optical devices tend to miniature the components, which requires strong magneto-optical effect in small scale. Combination of magnetic and plasmonic materials with different functionalities into a magneto-plasmonic structure is considered as a promising route to enhance the magneto-optical activity [1]. On the one hand, plasmonics allows for extreme electromagnetic field enhancement and subwavelength localization. On the other hand, MO materials bring optical non-reciprocity properties in the presence of magnetic field. Early studies on magneto-plasmonic structures addressed propagating surface plasmon-polariton (SPP) along the smooth surface of a metallic film [2]. In parallel to the studies on SPPs, the rapid developments in nanofabrication, enable extending studies of optics in nanoscale with nanostructures also supporting localized surface plasmon (LSPR) [3,4]. In the recent work, we investigate the magneto-optical response of a 2D magnetoplasmonic nanostructure which can support LSPR. A two-dimensional 2D magneto-plasmonic nanostructure was prepared by nanoimprint lithography method. For this purpose, a 2D charge coupled device (CCD) separated from a camera was used as stamp and the poly-dimethylsiloxane (PDMS) substrate was patterned as 2D substrate. First, the substrate was covered by gold layer of 30 nm thickness as plasmonic material by using a PVD coating device. Then it was coated by a Ce:YIG layer with an approximate thickness about 100 nm as magnetic material by using of pulsed laser deposition method. Actually this structure composed of 2D array of cubic holes with width and length of 3 µm and depth of 500 nm. these cubic holes were arranged in 2D with a distance about 170 nm. The Schematic of this structure is shown in Fig. 1a. Also, the periodicity of the sample and its surface has been examined by scanning electron microscopy (SEM) and shown in Fig. 1b. The nanometric distance between holes well creates nanorods which can support LSPR in the structure and this surface lattice resonance. Investigation of MO activity of the prepaid sample was carried out by a home-made longitudinal spectral Kerr effect set up with applying a DC magnetic field in the plan of sample and parallel to the incidence plane. The linear polarized light was incident on the sample at incidence angle of 30°. In our set up, the linear poliarized light was achieved by passing the unpolarized broadband light from a polaroid sheet which can linearly polarized the light in the wavelength range of 400-700 nm. Thereafter, the reflected spectra of the sample were recorded for positive and negative directions of magnetic field in rotational analyzer method. Finally, the recorded spectra were analyzed by a Labview program. The longitudinal Kerr effect spectrum showed a sharp peak at the wavelength of 450 nm which is related to Ce:YIG magneto-optical response.

**References:**

[1] Maccaferri, N., Zubritskaya, I., Razdolski, I., Chioar, I. A., Belotelov, V., Kapaklis, V., & Dmitriev, A. 2020. J. Appl. Phys,127, 8, 080903. [2] D. Martin-Becerra, J.B. Gonzalez-Díaz, V.V. Temnov, A. Cebollada, G. Armelles, T. Thomay, A. Garcia-Martín and M. Ujue Gonzalez, 2010, Appl. Phys. Lett. 97, 183114. [3] V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, Achanta Venu Gopal, D. R. Yakovlev, A. K. Zvezdin, M. Bayer (2011), Nature Nanotechnol, 6, 370. [4] B. Sepúlveda, J. B. Gonzalez-Díaz, A. Garcia-Martín, L. M. Lechuga, and G. Armelles, 2010, Phys. Rev. Lett. 104, 147401.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a2bf0ac2c504a3ad8ec1b3e56b5fa519.jpg)
Fig1. (a) schematic of 2D magneto-plasmonic structure composed of PDMS corrugated substrate covered by gold layer with thickness of 30 nm and Ce:YIG layer with approximate thickness of 100 nm. (b) SEM image of prepaid magneto-plasmonic structure.

![](https://assets.underline.io/uploads/markdown_image/1/image/63662f9edd1974d5d788347bf635aa74.jpg)
Fig.2: MO spectrum of the 2D grating sample composed of Gold and Ce:YIG layer measured at incident angle of 30° by home-made spectral longitudinal Kerr set up.

 Unexpected Longitudinal Kerr rotation in two dimensional magneto plasmonic structure

Amorphous glass-coated microwires are among the excellent material that can be used in sensor and spintronic devices. The magnetization process is realized due to the fast domain wall propagation. The studies on domain wall dynamics showed that additional perpendicular magnetic field changes domain wall velocity [1, 2]. Moreover, after the rotation of the microwire in the perpendicular magnetic field the difference in the domain wall velocity is even more significant [3]. However, the obtained results are contrary to the expectations based on previous knowledge. Due to the cylindrical shape of the wires, no change in domain wall velocity was expected for different rotations. The results are explained in terms of the gradient of the perpendicular magnetic anisotropy in the cross-section of the wire. The gradient is induced to the microwire during the fabrication process. The water stream causes additional induced stresses due to the cooling of the microwire from one side (Fig. 1a). The direct observation of such stresses in the cross-section of the wire is not possible due to the amorphous structure of the microwires. However, it is clearly visible when the sample is annealed above the crystallization temperature (Fig. 1b). In this work, we present the domain wall (DW) dynamics studies on the sample (Fe76Si9B10P5) as-cast and annealed below the crystallization temperature (at 450 °C) (Fig. 2). The DW velocity v is described by the following relation [4]: v = S(H - H0) (1) where S is DW mobility, and H0 critical magnetic field. The DW velocity of the as cast sample is linearly increasing for different angles of rotation θ (Fig.2a). For θ = 180°, DW velocity increases up to 350 A/m with mobility S = 1.44 m2s-1A-1. From 350 A/m, the DW mobility is S = 24.9 m2s-1A-1. However, after annealing, the DW motion is observed from Haxial = 550 A/m with the mobility S = 1.73 m2s-1A-1 up to 700 A/m (Fig.2b). DW mobility from Haxial = 700 A/m is incomparably smaller in comparison to the case before annealing, with the value S = 6.79 m2s-1A-1. When the sample is annealed, it leads to the release of the stresses induced in the cross-section of the microwire. Annealing causes the homogenization of the sample, and as a result, a significant decrease in DW mobility is observed. Thus, an effective mechanism for suppressing the angular dependence of DW mobility in a perpendicular magnetic field is annealing under suitable conditions. Acknowledgements: This work was supported by Slovak Grant Agency VEGA 1/0053/19, VEGA 1/0195/17; Slovak Grant Agency grant number APVV-16-0079, APVV-17-0184, APVV SK-FR-2017-024 and Pavol Jozef Šafárik University internal grant system VVGS-2016-320.

**References:**

[1] R. Varga et al., Physica Status Solidi A, Vol. 213, p. 356–362 (2016). [2] K. Richter et al., Applied Physics Letters, Vol. 96, 182507 (2010). [3] L. Fecova, K. Richter, and R. Varga, Acta Physica Polonica A, Vol. 137 (5), p. 849-851 (2020). [4] V. Zhukova et.al, Journal of Applied Physics, Vol. 111, 07E311-1 (2012).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/70d8ab1607609771a6973e4fac77b8eb.jpg)
Fig.1 Taylor-Ulitovski method of drawing the glass-coated microwire Fe76Si9B10P5, which is quenched by the water jet from one side in order to obtain the amorphous structure (a), and the stress distribution in the section of the amorphous wire annealed above crystallization temperature (b).

![](https://assets.underline.io/uploads/markdown_image/1/image/d4ca30e3a4acdb9987c890d60d17e064.png)
Fig.2 Domain wall velocity as a function of the axial magnetic field in the perpendicular magnetic field for the as-cast sample (a) and sample annealed below the crystallization temperature (b).

 The annealing effect on domain wall dynamics in wires with induced gradient of the perpendicular anisotropy

Introduction Modern magnetic material applications require homogeneous microstructures consisting of monodisperse magnetic entities. A facile route towards such microstructures is to exploit other materials as templates of model nanostructures via a “bottom-up”, low-cost approach. To that end, monodisperse nanosphere single-layers which tend to form 2D-hexagonal close packed patterns can be utilized either as templates for the deposition of “nanocaps” or as masks for the formation of triangular-like islands [1]. Although a lot of work has been devoted to the optimization these arrays [2,3] little progress has been made towards the use of self-assembly magnetic materials [4–7]. Here, we explore the effect of in-plane and perpendicular magnetic fields on the spatial arrangement of superparamagnetic nanoparticles. Thus, we add the long range magnetic dipolar interactions to the competing nanoparticle-surface (substrate hydrophobicity-hydrophilicity) and the nearest neighbor nanoparticle-nanoparticle interactions which control order and agglomeration. We present the optimization of the self-assembly of paramagnetic polystyrene nanospheres (0.25 nm - 1.43 nm) obtained by spin coating and drop casting, with respect to monolayer formation, substrate coverage, 2D hexagonal packing, and size of ordered areas. Arrays prepared under zero field by drop casting and spin coating were compared with those obtained under the effect of an in plane or perpendicular magnetic field. Experimental Methods - Results We utilize PS nanospheres with different sizes (0.270μm, 0.536μm and 1.43μm) which incorporate superparamagnetic Fe3O4 nanoparticles. Thermally oxidized silicon wafers, with approximately 500nm oxidation layer, are used as substrates. Prior to the deposition, the substrate’s hydrophilicity is improved using piranha solution. Contact angle measurements were performed to determine the hydrophilicity of the substrates, before and after the surface treatment. After the surface treatment, contact angle was measured as low as 9.3deg compared to 46deg of the untreated wafer. The different methods utilized are summarized in Table 1. In the drop casting experiments droplets of an aqueous suspension were mixed with tritonX – 100 and methanol (1:400) were deposited on the hydrophilic surface. A small electromagnet was used to generate the magnetic field. This method has two main geometrical control parameters, substrate inclination and angle of the applied magnetic field. In spin coating experiments under perpendicular field the surface-treated substrate is rotated on the platform of the spin coater which is placed in the middle of a coil. For in-plane field application, the sample is rotated until the solution expands on the surface; then it is removed from the spin coater and left to settle under the field on horizontal platform inside a coil. As surface wettability is an important parameter, two different surfactants have been employed and the results are compared. For the tritonX-100 treated samples rotation speeds up to 8000 rpm with a standard acceleration rate of 200rpm/s were used. For the SDS treated samples experiments, lower rotation speeds up to 800 rpm are optimal. For the observation of the macroscopic and microscopic surface morphologies of the samples, we used a Zeiss AxioImager A1 optical microscope fitted with a Canon 80D DSLR and a Scanning Electron Microscope (SEM, JEOL Ltd). During spin coating, competing forces like gravity, centrifugal, magnetic dipolar interactions and surface tension have a significant impact on the NPs self-assembly. Without magnetic fields the arrays can be optimized for monolayer formation, substrate coverage, 2D hexagonal packing, and size of ordered areas. The use of in-plane magnetic fields permits the organization of NPs in directional arrays along the direction of the field. Perpendicular fields tend to create 3D structures in competition to the hydrophilicity of the substrates. Acknowledgement: This research is co-financed by Greece and the European Union (European Social Fund- ESF) through the Operational Programme «Human Resources Development, Education and Lifelong Learning 2014-2020» in the context of the project “Dynamic Response of Magnetically organized nanoelements (DAMON) (MIS5047646).

**References:**

[1] T.C. Ulbrich, D. Assmann, M. Albrecht, Magnetic properties of Co/Pt multilayers on self-assembled particle arrays, J. Appl. Phys. 104 (2008) 084311. https://doi.org/10.1063/1.3003064. [2] A. Chandramohan, N. V. Sibirev, V.G. Dubrovskii, M.C. Petty, A.J. Gallant, D.A. Zeze, Model for large-Area monolayer coverage of polystyrene nanospheres by spin coating, Sci. Rep. 7 (2017) 9–11. https://doi.org/10.1038/srep40888. [3] B. Park, S.Y. Na, I.-G. Bae, Uniform two-dimensional crystals of polystyrene nanospheres fabricated by a surfactant-assisted spin-coating method with polyoxyethylene tridecyl ether, Sci. Rep. 9 (2019) 11453. https://doi.org/10.1038/s41598-019-47990-z. [4] J.D. Feldmann, G.J. Kalman, P. Hartmann, M. Rosenberg, Ground state of magnetic dipoles on a two-dimensional lattice: Structural phases in complex plasmas, Phys. Rev. Lett. 100 (2008) 085001. https://doi.org/10.1103/PhysRevLett.100.085001. [5] V. Håkonsen, G. Singh, P.S. Normile, J.A. De Toro, E. Wahlström, J. He, Z. Zhang, Magnetically Enhanced Mechanical Stability and Super -Size Effects in Self-Assembled Superstructures of Nanocubes, Adv. Funct. Mater. 29 (2019) 1904825. https://doi.org/10.1002/adfm.201904825. [6] C. Jiang, Synthesis , Assembly , and Integration of Magnetic Nanoparticles for Nanoparticle-Based Spintronic Devices, Tesis. (2018). https://doi.org/10.13140/RG.2.2.17523.22563. [7] M. Hu, H.-J. Butt, K. Landfester, M.B. Bannwarth, S. Wooh, H. Thérien-Aubin, Shaping the Assembly of Superparamagnetic Nanoparticles, ACS Nano. 13 (2019) 3015–3022. https://doi.org/10.1021/acsnano.8b07783

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b380468d75bdd830a6c866b7024bdd5a.jpg)
Figure 1 - Optical microscopy image of 1,43μm superparamagnetic PS spheres deposited on a tritonX-100 treated surface, under an in-plane magnetic field.

![](https://assets.underline.io/uploads/markdown_image/1/image/79f88e3ce121f13fbf4151fb1a01c33f.jpg)
Table 1 - Methods utilized for drop casting and spin coating experiments

 Superparamagnetic nanosphere arrays: Self-assembly and the effect of applied magnetic fields.

Superparamagnetic Iron Oxide Nanoparticles (SPION) are nanosize beads of iron oxides. Their peculiar magnetic behaviour makes them particularly suited for a variety of biomedical applications, ranging from cellular imaging to cancer treatment by hyperthermia. The usual theory used to describe their magnetic behaviour is that developed by Paul Langevin [1], which only applies to idealized (isotropic, monodisperse in size and non-interacting) nanoparticles at high temperatures. Reality however usually deviates from that theoretical framework. First, real samples are polydisperse in size, which impacts the particles' magnetic moments and therefore their behaviour. Second, particles usually have at least one easy magnetization axis, which adds a term to their Hamiltonian. Finally, particulary in biological media, they tend to aggregate, leading to locally high particle volumic fractions and therefore dipolar interaction between their magnetic moments [2]. Moreover, as demonstrated by Néel and Brown [3], at low temperatures the particles’ magnetic moments and anisotropy axises appear effectively blocked at their initial directions. Under the Néel blocking temperature, the particles are unable to reorganize their internal moments to change the resulting moment's direction, and under the Brown blocking temperature they are unable to rotate so as to align their easy axis with their moment and/or the external field. All those phenomena impact the magnetization of particle ensembles in a non-trivial way and are impossible to study simultaneously theoretically. In this work, these deviations from the Langevin law are studied numerically, at thermodynamic equilibrium, using a Metropolis algorithm, and compared with experimental data obtained on a Vibrating Sample Magnetometer. The Metropolis algorithm is adapted to take into account the Néel and Brown blocking of the particles, as those time-dependant effects are not explained by free energy minimization. Its Hamiltonian is also chosen to take into account the particles' magnetic anisotropy and the dipolar interactions between the particles as well as the interaction of their moments with the magnetic field. Thorough tests were led on the simulation program to ensure correct convergence of the algorithm. Notably, the temperature step used in the ZFC curve does not impact the simulation results, as expected from a robust computation. Convergence was tested with respect to all of the simulation parameters, and the impact of the magnetic anisotropy on the MH curves was validated by comparing to previous theoretical results obtained by M. Respaud et al [4]. Various other validation tests were conducted. The interest of using numerical simulation is that it allows to discriminate the effects of each tweak to the theory, leading to a better understanding of their various impacts. Curves studying the effect of varying each parameter were obtained, as can be seen in figure 1, where the effect of the magnetic anisotropy on the MH curve is compared in different situations. The ultimate goal being to replicate by numerical simulation the experimental results, it is important to understand how each effect impacts the shape of the curves, to have a clear sense of which experimental parameters impact the results and which don't. In terms of experimental data, two types of magnetization curves in particular are obtained: so called MH curves, where the magnetization is plotted versus the external magnetic field that is applied, and magnetization vs temperature curves. These can be obtained following different protocols, leading to different types of curves, the most common being the zero field cooled (ZFC) curve and the field cooled (FC) curve. Their shape is, naturally, impacted by the different effects at play, and by the precise experimental protocol, as can be seen in figure 2, where a ZFC curve is compared with two FC curves: one obtained after freezing the sample under no magnetic field and one after freezing it under a 5 mT magnetic field. FC/ZFC curves and MH curves (at various temperatures) of three different particle samples were obtained and compared. In particular, PolyMAG particles, which are commercialized for transfection protocols, were studied, and revealed a very unusual ZFC curve, showing no peak nor the usual bell shape of those graphs. One of the future goals of the numerical simulation will be to explain, at least qualitatively, this peculiar behaviour.

**References:**

[1] P. Langevin, J. Phys. Theor. Appl., Vol. 4 (1), p. 678, (1905) [2] M. Lévy, C. Wilhelm, et al., Nanoscale, Vol. 3, p. 4402 (2011) [3] W.F. Brown, Jr, Physical Review, Vol. 130(5), p. 1677 (1963) [4] M. Respaud, J. App. Phy., Vol. 86, p. 556 (1999)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/debde9c1e8e3d098529f51c4e4fed9ce.jpg)
Simulated MH curve of the system in different cases : without considering magnetic anisotropy, and considering magnetic anisotropy with various dispositions of the particles' anisotropy axises ; aligned with the external field (θ = 0), perpendicular to it (θ = 90°) or randomly oriented ("distributed" case).

![](https://assets.underline.io/uploads/markdown_image/1/image/a3934a84a7017a45325a9cf929652605.jpg)
Experimental ZFC and FC curves of a 6nm sample under different freezing protocols: freezing the sample under 0T to 2K (ZFC), freezing it under 5mT to 2K, and freezing it under 5mT to 175K and then under 0T to 2K.

 Monte Carlo and Experimental Study of the Magnetic Relaxation of Superparamagnetic Nanoparticle Ensembles

The magnetic anisotropy and the coercive field (HC) are key properties of the magnetic nanoparticles (NPs) considering their applications in biomedicine, for drug delivery and magnetic hyperthermia, and for the development of free-rare-earth magnets. Cobalt ferrite (CoxFe3-xO4) nanoparticles exhibit the largest coercive field between all the Fe oxides nanoparticles with spinel structure. The large coercive property is correlated to the Co2+ contain, that gives rise to the single ion- anisotropy, but the role of other parameters like: cationic occupancy, structural quality, magnetic order, structure, particle size and morphology and surface properties, have been considered very important [1-4]. In general, to optimize and tailoring the magnetic properties of NPs annealing treatments are employed fruiting the thermal induced structural magnetic properties of Cobalt ferrite nanoparticles that is induced by an alternative solvent mediated annealing process in mild temperatures. Co0.4Fe2.6O4 nanoparticles of average size of 32 (8) nm were synthesized by thermal decomposition technique and further solvent mediated annealing at temperatures between 150-320° C. We obtain an important change of the coercive field but not of the remanence ratio neither the specific magnetization as function of the treatment temperature. The NPs annealed at 210 °C exhibit maximum HC of 0.19 T with high specific magnetization (79 Am2/kg) being the HC almost 50% larger than the value of the as-prepared NPs (HC=0.12T). A wide structural (XRD), morphological (HRTEM), chemical (Mossbauer) and magnetic characterization was performed to determine the main mechanism that gives rise to the coercive improvement. These characterizations exclude the role of the particle size, the particle morphology or the inversion degree in the magnetic changes. The analysis of the temperature dependence of the hysteresis and the remanence measurements do not evidence changes in the reversal process. Herein we demonstrate that a solvent mediated annealing treatment in mild conditions permits the reduction of the concomitant internal stresses generated during the nanocrystal growth. Therefore, the increase in the coercive field observed in the post treatment process in a solvent media increase substantially the performances of this type of material for the development of novel rare-earth free permanent magnets. This research was supported by EU- H2020 AMPHIBIAN Project (H2020-NMBP-2016-720853).

**References:**

[1] C. Moya et al. J. Mater. Chem. C 3, 4522 (2015) [2] A. López-Ortega et al., Chem. Mater. 27, 4048 (2016). [3] E. Lottini et al., Chem. Mater. 28, 4214 (2016). [4] A. López-Ortega, E. Lottini, G. Bertoni, C. de Julián Fernández, C. Sangregorio, Chem. Mater. 29, 1279 (2017).

**Images:**

 Magnetic Hardening of Cobalt Ferrite Nanoparticles by a controlled solvent-mediated annealing

The magnetic nanoparticles can develop superparamagnetic properties in certain conditions1 and this feature attracted the researchers that began to study this class of materials in order to exploit their magnetic properties for applications. The main magnetic peculiarities which make these samples so interesting are the high magnetization and near zero coercive field that allow to use the magnetic nanoparticles for biomedical purposes2,3. Among all the magnetic nanoparticles, the Fe3O4 (magnetite) ones are very attractive due to their biocompatibility and because they show a low toxicity suggesting their possible use in different scopes4,5. Unfortunately, the magnetite nanoparticles are very sensitive to the action of oxygen, thus some of them might undergo oxidation to ferric hydroxide (Fe(OH)3) or to maghemite (γ-Fe2O3) phases. To limit this undesired effect and also the aggregation of primary nanoparticles of low dimension (10-30 nm), specific surface treatments and techniques of encapsulation are currently used to allow their utilization6. In this work, two samples of Fe3O4 magnetic nanoparticles coated with oleic acid (Fe3O4-OA) and citric acid (FeO4-CA) have been studied by means of DC magnetization measurements as a function of temperature (T) in Zero Field Cooling (ZFC) and Field Cooling (FC) conditions at different magnetic fields. The measurements have been performed by means of a Quantum Design PPMS equipped with a VSM option. The M(T) measurements have shown a superparamagnetic behavior in both the samples although with different characteristics which have been highlighted studying the field dependence of the blocking and irreversibility temperature. These two temperatures give important information on the nanoparticles distribution and their dispersion together with information on the diameter of the nanoparticles. In particular, the blocking temperature TB can be identified by taking the maximum of the ZFC curve which, in the case of superparamagnetic samples, has a dome shape behavior. The maximum M value of the ZFC curve can be considered as the blocking temperature of the entire sample, which, of course, differs from the blocking temperatures of the various nanoparticles of different sizes present in the sample. It can be considered as a sort of average blocking temperature of the sample useful when these materials are considered in view of applications. On the other hand, to estimate the TB distribution of the sample it is possible to use the procedure reported in our previous paper7. In this work, the attention has been focused only on the TB obtained from the maximum of ZFC curves. In Fig. 1, an example of M(T) measurement at H = 700 Oe has been reported. The panel(a) and (b) show the M(T) behavior of Fe3O4-OA and Fe3O4-CA, respectively. It can be noted in the insets that both the ZFC curves show a dome shape behavior with the presence of the maximum which identifies the TB of the samples. For the sample Fe3O4-OA, TB ≈ 160 K while for the sample Fe3O4-CA TB ≈ 145 K. In this framework, it is worth to underline that, for H = 700 Oe, the samples are in a superparamagnetic state at room temperature since Troom &gt; TB in both the cases. The temperature value where the ZFC and FC curves separate identifies the irreversibility temperature Tirr. In an ideal case where the nanoparticles are of the same dimensions, the TB and the Tirr are equal. Usually, this is quite uncommon and, in the real case, the Tirr represents the temperature at which all the nanoparticles are certainly unblocked, as the reversible phase occurs after it. Specifically, Tirr represents the unblocking moment of the particles with larger dimensions, which, given the bigger volume than the particles with lower dimensions, unblock at higher temperatures. It is evident that in our case TB ≠ Tirr for both the samples which indicates that the nanoparticles have different diameters. In particular, the temperature difference ΔT between Tirr and TB for Fe3O4-OA is lower respect to the Fe3O4-CA one. In fact, Fe3O4-OA has Tirr ≈ 197 K while Fe3O4-CA has Tirr ≈ 282 K, so giving ΔT(Fe3O4-OA) = 37 K and ΔT(Fe3O4-CA) = 137 K indicating a bigger diameters difference among the nanoparticles of the Fe3O4-CA than the Fe3O4-OA. Finally, performing M(T) measurements at several magnetic fields, the magnetic field dependence of TB and Tirr has been determined and fitted with power and exponential equations extracting interesting samples peculiarities.

**References:**

1C.P. Bean and J.D. Livingston, J. Appl. Phys. 30, S120 (1959). 2O. Veiseh, J.W. Gunn, and M. Zhang, Adv. Drug Deliv. Rev. 62, 284 (2010). 3R. Hergt, S. Dutz, R. Müller, and M. Zeisberger, J. Phys. Condens. Matter 18, S2919 (2006). 4H. wang Zhang, Y. Liu, and S. heng Sun, Front. Phys. China 5, 347 (2010). 5J. Huang, L. Bu, J. Xie et al, ACS Nano 4, 7151 (2010). 6A. Ali, H. Zafar, M. Zia et al, Nanotechnol. Sci. Appl. 9, 49 (2016). 7M. Polichetti, M. Modestino, A. Galluzzi et al, Mater. Today Proc. 20, 21 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5cc8cd2f476b6ca2d52b8abd6a717159.jpg)
Fig. 1 M(T) ZFC-FC curves for Fe3O4-OA (a) and Fe3O4-CA (b) at H = 700 Oe. The insets show an enlargement of the region near the maximum of ZFC curves and the arrows indicate the blocking temperatures of the samples.

 Field dependence of blocking and irreversibility temperature in Fe3O4 magnetic nanoparticles coated by oleic and citric acid

Recently, studies of structured systems based on magnetic fluids have become popular. These media include magnetic emulsions, magnetorheological suspensions, magnetic elastomers, ferrogels [1]. Due to significant changes in magnetic, mechanical, rheological, optical, and other properties under the action of a field, such systems are referred to as Smart Materials. One of the most typical representatives of such systems are magnetic emulsions - dispersed systems in the form of droplets of a magnetic fluid of micron and submicron size, suspended in other immiscible and non-magnetic fluid media [2,3]. In this work, we present the results of studying the possibilities of using magnetic emulsions with low interfacial tension as magneto-optical media. Low interfacial tension magnetic emulsions were produced as follows. Magnetic fluid based on kerosene with magnetite nanoparticles was mixed with AMG-10 hydraulic oil. The volume concentration of magnetite in the initial magnetic fluid was 5%. The size range of magnetite nanoparticles is 8–20 nm. Depending on the preparation conditions, the size of microdroplets in the magnetic emulsion could vary from 1000 to 10000 nm. To study the optical effects in magnetic emulsions, we used an optical setup consisting of a helium-neon laser with a radiation wavelength of 633 nm. The sample under study was placed in two types of cuvettes: in the form of a cylinder and in the form of a thin flat layer. Transmission spectra of the magnetic emulsion were studied using an ELLIPS-1891 spectral ellipsometer in the spectrophotometer mode in the wavelength range of 400-1050 nm. Exposure to a magnetic field leads to a rapid (within 0.1-0.3 s) drawing of microdroplets of the magnetic emulsion into long needle-like structures. This effect leads to a significant change in the transparency of the magnetic emulsion (Fig. 1), which opens up prospects for the use of such systems as magnetically controlled optical filters. The most pronounced effect is achieved in the longitudinal field (the relative change in transparency reaches 25-30%). In this case, the magnitude of the change in transparency can be controlled not only by the magnitude of the field strength but also by its orientation relative to the light beam. The effect of changing transparency has a pronounced saturation at a magnetic field strength of over 5 kA/m. For light with a wavelength of less than 550 nm, the magnetic emulsion is practically opaque and therefore has a characteristic yellow-brown color. The mechanism for changing the transparency of magnetic emulsions under the action of a field seems to be quite simple. The transparency of the system T is determined by the concentration of particles and the cross-section of light scattering by an individual particle. When the emulsion droplets are stretched along the direction of the field (and the light beam in this case), the attenuation cross-section significantly decreases at a practically unchanged concentration of particles, which leads to a pronounced effect of changing the transparency. When exposed to a magnetic field perpendicular to the direction of propagation of light, a pronounced effect of small-angle anisotropic scattering of light on elongated needle-shaped microdroplets appears in magnetic emulsions (Fig. 2). A qualitative interpretation of the effect of diffraction scattering in polydisperse magnetic emulsions can be based on the representation of the system in a magnetic field as an irregular diffraction grating, which is formed from microdroplets of a magnetic emulsion elongated in a magnetic field. In the absence of a field, the microdroplets have a spherical shape and the intensity of light diffracted by polydisperse drops smoothly decreases from the center to the periphery of the diffraction pattern without pronounced minima. The action of the field in the direction perpendicular to the light beam leads to a strong elongation of the emulsion droplets and the appearance of pronounced anisotropy of small-angle light scattering (light is scattered mainly in the plane perpendicular to the direction of droplet extension). In a magnetic field, the optical properties of magnetic emulsions change significantly. Deformation of drops of a magnetic emulsion in a magnetic field creates an oriented structure in the emulsion, in which pronounced effects of anisotropic attenuation and diffraction scattering of light are observed. A magnetic field directed along the light beam increases the transparency of the emulsion without changing the transmission spectrum. This allows magnetic emulsions with low interfacial tension to be used as neutralizing filters with fine-tuning of light transmission by the magnetic field. The effect of diffraction by needle-shaped microdroplets can be used in magneto-optical sensors to determine the orientation and strength of the magnetic field. The use of magnetic emulsions can significantly expand the range of applications of liquid magnetic nanostructures [4-6]. This work was financially supported by the Ministry of Science and Higher Education of Russia (project no. 0795-2020-007).

**References:**

S. Odenbach, Arch. Appl. Mech., Vol. 86, p. 269 (2016). A.R. Zakinyan and Y.I. Dikansky, J. Magn. Magn. Mater., Vol. 431, p. 103 (2017). I.M. Subbotin and A.O. Ivanov, Magnetohydrodynamics, Vol. 52, No. 1, p. 269 (2016). J. Philip and J.M. Laskar, J. Nanofluids., Vol. 1, p. 3 (2012). V. Mahendran and J. Philip, Appl. Phys. Lett., Vol. 100, 073104 (2012). P. Das, M. Colombo, and D. Prosperi, Colloids and Surfaces B: Biointerfaces.. Vol. 174. p. 42 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7d7554bc0e8f618c6e7a7879009bc8a0.jpg)
The transmission spectrum of a magnetic emulsion under the action of a magnetic field

![](https://assets.underline.io/uploads/markdown_image/1/image/d74cdba524b23f06f55a3d6a7bbd89e3.jpg)
Diffraction light scattering in a magnetic emulsion

 Magnetic Emulsions as Prospective Magneto-Optical Media

A magnetic field pulser works by feeding a pulsed signal to a switching device which drives current through an inductor to generate magnetic field. These pulsers can be designed to output different levels of magnetic field intensity depending on its application. At the same time, a short switching time, on both the rise and fall end, is preferred to keep the outputted magnetic field clean and in synced with the initial pulsed signal. This is especially important in some use cases. In application of the magnetic field pulser is in an all-optical communication system. The pulser generates a magnetic field which causes a polarization rotation in the light signal as per the theory of Faraday rotation [1]. In this situation, the ideal magnetic field intensity is relatively high to ensure sufficient polarization rotation for the end sensors to detect and a short switching time to prevent signal deterioration or contamination. Another application of the magnetic field pulser is to perform transcranial magnetic stimulation, a medical treatment for certain mental disorders [2]. Small, controlled pulses of magnetic field are targeted at parts of the brain to stimulate it without the need to perform open surgery. The noninvasive nature of this treatment is safer and more accessible for the patients. For this application, the pulser generates a magnetic field with much lower intensity and a shorter pulse width. These are some of the many fields where a variant of magnetic field pulser is found. The mechanics behind a magnetic field pulser can be perceived as simple on paper. The pulser design can be broken into four parts: 1. Switching device 2. Inductor coil 3. Dissipation loop 4. Capacitor banks These are by no means complicated systems. However, applications such as the all-optical communication system requires a magnetic field pulser with high magnetic field intensity and fast switching. That factor coupled with the restrictions in physical dimensions mean the pulser is using a relatively large inductor coil. This introduces a fair amount of reactance into the circuit hence affecting the switching time. Hence, a balance between the magnetic field intensity and switching time is needed. The larger reactance and parasitic effects also affect the natural response of the circuit. This investigation will look to tackle several of these factors to bring improvements to an aging design. Firstly, this investigation will examine the switching device of the magnetic field pulser. In most cases, a silicon-based transistor is used as the switching device. Recent developments in transistor technologies have enabled production of transistors with higher drain current, superfast switching, and smaller on-resistance. Compared to transistors from yesteryears, these new products are better replacements to achieve the balance as mentioned above. A quick comparison between several pre-selected transistors can be seen in Figure 1 attached below. These are based on the same magnetic field pulser design by Pritchard, Weber, and Mina (2013) albeit with different transistors [3]. Alternately, the technology behind gallium nitride-based (GaN) transistors has make it another potential candidate as the switching device. Compared to silicon-based (Si) transistors, GaN transistors show higher electron mobility. This means a similarly sized GaN transistor (compared to a Si transistor) will have higher drain current, faster switching time, and smaller on-resistance [4]. By comparing the different parameters in the transistor technologies, this investigation looks to present a better pulser design that can output a higher magnetic field intensity with faster switching time compared to prior published designs. Next, this investigation also analyzes the natural response of the magnetic field pulser. As previously mentioned, the natural response of the circuit is affected by the presence of the relatively big inductor coil. As a result, it is common to see either underdamped or overdamped response on either or both rise and fall ends. This investigation will consider ideal compensation components to mitigate these effects. For better understanding, the investigation looks at the rise and fall end as separate RLC circuits. As a result, the new pulser design can produce a magnetic field pulse that is clean on the rise, fall, and steady-state sides as shown in Figure 2 attached below. In the case of the all-optical communication system, the cleaner magnetic field output prevents cross signal contaminations which results in bad light signal to the end sensors. On the other hand, in the case of the transcranial magnetic stimulation, the cleaner magnetic field output ensures no accidental over or under-stimulation of the patient’s brain. In conclusion, this investigation seeks to improve upon the magnetic field pulser design that has been around for a while. The authors will present a design that shows a significant improvement over previously published designs and a paper that shows the procedure of achieving it. The authors are confident the paper can be of tremendous help to readers who are looking into creating their own magnetic field pulser to fit into their individual requirements.

**References:**

1. J. W. Tioh, M. Mina, and R. J. Weber, “All-optical integrated switch utilizing Faraday rotation,” IEEE Trans. Magn., vol. 46, no. 6, pp. 2474–2477, Jun. 2010. 2. J. Selvaraj, P. Rastogi, N. P. Gaunkar, R. L. Hadimani, and M. Mina, “Transcranial magnetic stimulation: Design of a stimulator and a focused coil for the application of small animals,” IEEE Transactions on Magnetics, no. 99, pp. 1–5, 2018. 3. J.W. Pritchard, M. Mina, and R.J. Weber, “Magnetic Field Generator Design for Magneto-Optic Switching Applications,” IEEE Transactions on Magnetics, Vol. 49, No. 7, pp. 4242-4244, 2013. 4. L. F. Eastman and U. K. Mishra, "The toughest transistor yet [GaN transistors]," IEEE Spectrum, vol. 39, no. 5, pp. 28-33, May 2002, doi: 10.1109/6.999791.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d576a83153d4d12099210e0d49982323.jpg)
Comparing magnetic field pulsers using three different transistors including one from previously published paper

![](https://assets.underline.io/uploads/markdown_image/1/image/25b4de1ed386a824751fab013e51892f.jpg)
Comparing magnetic field pulser before and after adding compensation components

 Design improvements for a magnetic field pulser: A look into switching device and circuit effects

Among a variety of magneto-optical effects we focus on the inverse Faraday effect (IFE) that plays a crusial role for optical magnetic switching. The IFE is the emergence of magnetization in a transparent medium illuminated by a circularly polarized high-frequency electromagnetic wave [1]. It provides a new way for efficient control of magnetization at GHz and THz rates. Quantitatively the IFE magnetic field is determined by the distribution of the electric field inside the magnetic layer [2]: HIFE∼[E×E*]. Recently it has been demonstrated that optical confinement of light in the magnetophotonic crystals (MPC) or in magnetophotonic microcavity leads to the significant increase of the IFE [2-4]. It happens due to the photonic crystal (PC) defect mode existing in such magnetophotonic crystals or microcavities. These states are spectrally located inside the band gaps and reveal themselves as a sharp peaks in transmittance spectra of a nanostructure. These defect modes also provide strong localization of light inside the magnetic layer that leads to the significant enhancement of the IFE. In this work we propose the novel design of the MPC nanostructures with gradual variation of the magnetic layer thickness. So, the spectral position of the defect mode of the MPC nanostructure depends on the spatial position of input light spot on the sample surface. Therefore, the resonant enhancement of the IFE associated with the peak in transmittance band gap also changes with the input light spot position. Besides that, the design of the MPC nanostructure with perforated magnetic layer provide a spatially localized emergence of the IFE in the spots of several microns that seems very promising for practical applications. The principle scheme of the PC nanostructure with smooth magnetic layer consist of the magnetic layer sandwiched between two non-magnetic Bragg mirrors (Fig. 1). Iron-garnet films doped with bismuth (or BIG films) provide a large Faraday effect and have a relatively low optical absorption in the long-wavelengths visible spectral range [2]. Illuminating this nanostructure by the circularly polarized light at the normal incidence one can observe a defect mode, when the resonance peak appears in the bandgap of the transmittance spectrum. The spectral position and amplitude of this peak depend on the thickness of the magnetic layer h. The spectral position of the defect mode changes from 0.6 μm for 120nm-thick magnetic layer to 0.675 μm for 180nm-thick one. So, the gradual tuning of the resonance spectral position can be realized in sample with the gradient change of the BIG layer thickness. The IFE is determined by the electromagnetic field intensity localized in magnetic layer. In Fig. 2 the spectral dependence of the total energy in the BIG layer normalized by the layer thickness is presented for several values of h. Therefore, the magnitude of the inverse Faraday effect can also be detuned by moving the input beam along the gradient direction of the sample. Besides the smooth gradient magnetic layer, the PC nanostructure with the magnetic layer with etched discs is proposed. In the BIG magnetic layer with the constant thickness the discs with diameter of dozen microns are etched. The etching depth is different for various discs. As a result, the thickness of the magnetic layer is smaller in the area of these discs. Therefore, the enhanced IFE occurs at the different frequencies for each disc. This approach allows us to achieve spatial localization of the IFE limited just by the disc diameter. To sum up, we propose two designs of the MPC nanostructures with gradient of the magnetic layer thickness for tunable inverse Faraday effect. The spectral position and amplitude of the transmittance peak and resonant IFE depend on the thickness of the magnetic layer. The first design of the MPC nanostructure has smooth magnetic layer with thickness gradient that allows to tune the spectral position of peak in transmittance spectra and the IFE gradually. The second design has perforated magnetic layer and provide spatially localized emergence of the IFE in the spots of several microns. The sample fabrication and the experimental verification of the reported results is expected. This study was supported by Russian Science Foundation (project No. 19-72-10139).

**References:**

A. Kirilyuk, A.V. Kimel, and T. Raising, Rev. Mod. Phys. Vol. 82, pp. 2731 (2010). M.A. Kozhaev, A.I. Chernov et al., Sci. Rep. Vol. 8, p. 11435 (2018). T. Goto, A.V. Baryshev, M. Inoue et al., Phys. Rev. B, Vol. 79, p. 125103 (2009). M. Inoue, et al., J. Phys. D. Appl. Phys. Vol. 39, p. R151 (2006).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3d88bf2c81e92be02ad6b0e66654c6dd.jpg)
Fig. 1. The principle scheme of the photonic crystal nanostructure with smooth magnetic layer (the gradient of the magnetic layer thickness isn’t shown).

![](https://assets.underline.io/uploads/markdown_image/1/image/3327d1b959c15f1285f79297fab57267.jpg)
Fig. 2. Spectra of the total energy localized in the magnetic layer of the MPC for various values of h.

 Photonic Crystal Nanostructures with the Magnetic Layer of Gradient Thickness for Optical Magnetic Switching

Introduction We have been trying to develop magneto-optical spatial light modulators (MO-SLMs) driven by current-induced domain wall motion (CIDWM) because MO-SLMs offer a high-frame rate and high-resolution adequate for holographic display applications [1-3]. Each pixel consists of a magnetic nanowire that modulates the beam by MO Kerr effect (MOKE) and two hard magnets (HMs) embedded at both ends of the nanowire. When a pulse current is injected into the nanowire, a magnetic domain of the nanowire expands and shrinks according to the direction of electron flow. We fabricated a single light modulator with a dimension of 1 μm × 2 μm and successfully demonstrated magnetization reversal by pulse current injection [2]. Using the fact that the reversal magnetic field of the nanowires changes depending on the presence or absence of HMs, we fabricated an array device that displays a magnetic grating pattern with different magnetization directions for each pixel row by applying an external magnetic field and succeeded in measuring diffraction characteristics [3]. The SLM should have high diffraction efficiency because the diffracted beam’s intensity provides the brightness of reproduced images. The intensity of the diffracted beam by the magnetic grating is proportional to the MO figure of merit (FOM), which is the product of the reflectivity and the square of the complex Kerr rotation angle of the nanowire. In this study, we optimized the device structure and the incident angle and polarization direction of the incident beam to amplify the FOM and enhance the diffracted beam’s intensity. Experimental method Figure 1(a) shows the structure of the array device. The nanowire material was Gd24Fe76, which was expected to provide large MOKE and magnetization reversal at low current density. The HMs material was a Co/Pd multilayer with perpendicular magnetic anisotropy. The HMs’ magnetization directions were fixed anti-parallel using the different coercivity. The red dotted line indicates a single pixel. The light modulators were arranged at a pitch of 1 μm × 2 μm. HM1 and the nanowires were partially shared with adjacent pixels to expand the aperture ratio. The width and length of the nanowires was 0.5 μm and 3.8 μm, respectively. The widths of HM1 and HM2 were 0.1 μm, and the lengths were 600 and 0.8 μm, respectively. The coercivity of HM1 and HM2 was controlled by fabricating them at different lengths [2]. When the external magnetic field is applied to the array device, only the magnetization direction of the nanowire with HM2 is reversed. Figure 1(b) shows a two-dimensional magnetic grating pattern displayed on the array. Figure 1(c) shows a cross-sectional illustration of the nanowire. Inside the nanowire, the beam is reflected complexly at each interface. We calculated the dependence of the FOM on the thickness of the Si–N cap layer and the incident beam angle using an optical analysis simulator for multilayers (Multilayer from MM Research, Inc. [4]). The thickness of the cap layer was set at 5 nm steps from 5 to 30 nm, and the incident angle was set at 1° steps from 0° to 89° in the vertical direction of the film surface. Figure 1(d) shows the optical setup for measuring the diffracted beam. A linearly polarized laser beam with a wavelength of 532 nm was incident at a tilt in the x-axis direction. The first-order diffracted beam’s intensity was measured using a laser power meter. The magnetic grating pattern was turned on and off by applying an external magnetic field from an electromagnet placed at the back of the array device. The incident angle was set to be between 0° and 15° since the first-order diffraction angle of the array device is 15.4°. The polarization direction of the incident beam was set to p-polarization and s-polarization, and the diffracted beam’s intensity was measured, respectively. Results and discussions Figure 2(a) shows the FOM calculated by the simulator. The FOM is larger when the thickness of the cap layer is thinner, and it has a maximum at an incident angle of around 50 degrees in this device. It is worth noting that the FOM does not depend on the polarization direction. Figures 2(b) and (c) show the diffraction efficiency of the array device when p- and s-polarized beams were incident, respectively. The diffraction efficiency behaved differently depending on the polarization direction of the incident beam. This is attributed to the pixel shape, which is 1 μm × 2 μm and not square. For s-polarized beam, the diffraction efficiency showed the same behavior as that of the FOM, i.e., it was maximum when the thickness of the cap layer was thin, and the incident angle was large. When the thickness of the cap layer was 5 nm, the diffraction efficiency increased by a factor of 5.9 by optimizing the incident angle and polarization direction. These results showed that the diffracted beam’s intensity can be enhanced by amplifying the FOM of Gd–Fe film, including cap and under layers in MO-SLMs. Also, it showed that the maximum intensity of the diffracted beam can be obtained by considering the polarization direction in MO-SLMs with non-square pixel shapes.

**References:**

[1] K. Aoshima et al., Jpn. J. Appl. Phys., Vol.57, p.09TC03 (2018) [2] R. Higashida et al., Jpn. J. Appl. Phys., Vol.59, p.053001 (2020) [3] R. Higashida et al., Opt. Eng., vol. 59(6), p.064104 (2020) [4] M. Mansuripur, J. Appl. Phys., vol. 67, p.6466 (1990)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/44044a584f48cf1201e7cd6c4532bb82.jpg)
Fig. 1 (a) Domain wall motion type light modulator array (b) illustration of the two-dimensional magnetic grating (c) cross-sectional illustration of the nanowire (d) optical setup for measuring the diffracted beam

![](https://assets.underline.io/uploads/markdown_image/1/image/b8f86f6a8b7ad01b4e8abfb026097c9d.jpg)
Fig. 2 (a) Calculated FOM of the Gd–Fe film including cap and under layers, (b) diffraction efficiency of the fabricated array device in the p-polarized incident beam, and (c) s-polarized incident beam

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