Particle size effect on millimeter-wave absorption, rotation, and ellipticity of gallium-substituted epsilon iron oxide

Various applications employ millimeter waves. For example, the carrier frequencies of vehicle radar in advanced driver assistance systems are 76–81 GHz millimeter waves. Here, we investigate the particle size effect on millimeter-wave absorption of gallium-substituted epsilon iron oxide ε-GaxFe2−xO3 with x = 0.44 ± 0.01. Samples were composed of nanoparticles with sizes of 16.9(1) nm, 28.8(2) nm, and 41.4(1) nm. Millimeter wave absorption, Faraday rotation, and Faraday ellipticity were measured by terahertz time-domain spectroscopy. This series exhibits millimeter-wave absorption at 78.7, 78.2, and 77.7 GHz without an external magnetic field. The millimeter-wave absorption increases from 4.6 dB to 9.4 dB as the particle size increases. In the magnetized sample, the Faraday rotation angle increases from 9.1° to 18.4°, while the Faraday ellipticity increases from 0.27 to 0.52. The particle size effect can be explained by the change in the ratio of the surface and core of the nanoparticles. The present study should contribute to the realization of high-performance millimeter-wave absorbers.


Introduction
Advanced driver assistance systems (ADAS) for automobiles are becoming ubiquitous. 1,2 Millimeter-wave car radars (76.5 GHz,79 GHz, and 81 GHz) are equipped in ADAS for forward monitoring because they are less susceptible to weather conditions such as rain and fog. 3,4 Additionally, the demand for technologies to suppress noise and electromagnetic interference is increasing. 5,6 Consequently, the development of millimeterwave absorbers and circulators is an important issue. Magnetic materials can absorb electromagnetic waves, which are due to magnetic loss. [7][8][9][10][11][12][13][14][15] However, the absorption frequencies of magnetic materials such as ferrite and metal are generally low compared to the carrier frequency of millimeter-wave car radar. 16,17 Epsilon iron oxide 3-Fe 2 O 3 nanomagnets have attracted much attention. They exhibit large magnetic anisotropy and high-frequency millimeter-wave absorption.  Additionally, metal-substituted epsilon iron oxide, 3-M x Fe 2−x O 3 , 46-70 exhibits millimeter-wave absorption in the range of  GHz, in which the resonance frequency is controlled by a kind of substitution metal and substitution ratio. Recently, the resonance frequency shi due to change on the particle size of 3-Fe 2 O 3 nanomagnets has been also reported. 45 Gallium-substituted epsilon iron oxide 3-Ga x Fe 2−x O 3 is suitable for the resonance of the millimeter-wave car radar frequency and should serve as a millimeter-wave absorber. 52 To enhance the millimeter-wave absorption, we investigate the effect of particle size on the millimeter-wave absorption properties of 3-Ga x Fe 2−x O 3 nanoparticles. In the present work, 3-Ga x Fe 2−x O 3 with different nanoparticle sizes are prepared by changing the sintering temperature in the range of 1050-1150 C. Then the magnetic properties and millimeter-wave absorption are measured. In addition, Faraday rotation and Faraday ellipticity are also measured from the viewpoint of application for millimeter wave devices such as isolators and circulators. Finally, the particle size effect is discussed.

Results and discussion
Materials, crystal structure, and morphology The samples were prepared by the sol-gel method according to the literature. 52 Iron nitrate and gallium nitrate were dissolved in water with a ratio of Ga : Fe ¼ 0.46 : 1.54, and ammonia and tetraethyl orthosilicate were added successively to obtain precursors. The precursors were sintered in air for 4 hours. To etch the silica matrix, the sintered samples were heated with a sodium hydroxide aqueous solution at 60 C for 1 day. Three samples were prepared at different sintering temperatures: 1050 C (1), 1100 C (2), and 1150 C (3).
Elemental analyses with inductively coupled plasma mass spectroscopy indicates that the formulas of the obtained samples are 3-Ga x Fe 2−x O 3 , where x ¼ 0.43(1) for 1, 0.45(1) for 2, and 0.45(2) for 3. The powder X-ray diffraction (PXRD) patterns show that all samples have an isomorphic structure of 3-Fe 2 O 3 (orthorhombic structure, space group of Pna2 1 ) ( Fig. S1 and Table S1 †). The crystal structure has four non-equivalent metal sites (A-D sites) (Fig. 1a). The Ga ion tends to substitute the D site. The crystalline size evaluated from the PXRD patterns using the FP method (d FP ) increases as the sintering temperature increases: 16.9(1) nm for 1, 28.8(2) nm for 2, and 41.4(1) nm for 3. TEM images conrm that the obtained samples are composed of nanoparticles (Fig. S2 †). The particle size evaluated from the TEM images also becomes larger as the sintering temperature increases: 15 AE 6 nm (1), 23 AE 11 nm (2), and 33 AE 18 nm (3) (Fig. 1b).

Magnetic properties
The magnetic hysteresis was measured at 300 K using a superconducting quantum interference device (SQUID) magnetometer. The coercive elds are 4.1 (1), 7.1 (2), and 7.5 kOe (3) (Fig. 1c). The magnetization values at 5 tesla are 21.5 (1), 25.3 (2), and 26.7 emu g −1 (3). The magnetism of 3-Ga x Fe 2−x O 3 is classied as a ferrimagnet, where the sublattice magnetizations at the B and C sites are positive, while the sublattice magnetizations at the A and D sites are negative. [71][72][73][74][75][76] The D site has a smaller sublattice magnetization than those at the other sites, resulting in the appearance of ferrimagnetism.

Faraday rotation and ellipticity in the millimeter-wave region
To measure the Faraday rotation and ellipticity in the millimeter-wave region, wire grid polarizers were introduced in the THz-TDS system. 47,53,57 Polarizers were placed aer the emitter and before the detector to precisely dene the polarization of the THz pulse as horizontal. The vertical and horizontal components of the transmitted THz pulses were obtained as the difference or the sum of the transmitted THz pulses with the polarizers set as 45 and −45 . The rotation  angle and ellipticity of the transmitted light were obtained from the vertical and horizontal components. Prior to the measurements, the pellet samples were magnetized by placing the pellet under a magnetic eld of 8 tesla. Fig. 3a shows the rotation angle and ellipticity in the millimeter-wave region, where the incident THz pulse was irradiated from the S-pole of the magnetized pellet sample. The rotation angle spectrum shows the dispersive shape centered at the peak frequency of ellipticity. The rotation angle increases as the particle size becomes larger: 9.1 (1), 14.1 (2), and 18.4 (3).
The Faraday ellipticity shows the peak at the same frequency as the absorption peak frequency. The ellipticity increases with increasing the particle size: 0.27 (1), 0.39 (2), and 0.52 (3). Irradiating the incident THz pulse from the opposite pole, Npole, the signs of rotation angle and ellipticity change (Fig. 3b and c).

Mechanism of particle size effect
Here, we consider the particle size effect on millimeter-wave absorption. The plot of the absorption versus the particle size shows that the absorption decreases as the particle size decreases (Fig. 4). We assume that this decrease is due to the loss of ferromagnetism of the iron atoms near the surface. The TEM images show that the present materials are composed of nanoparticles. The volume of the core and the total volume of the particle are expressed as 4p(d/2 − d s ) 3 /3 and 4p(d/2) 3 /3, respectively, where d s shows the thickness from the surface.
Therefore, the ratio of the core volume to the total particle volume is {4p(d/2 − d s ) 3 /3}/{4p(d/2) 3 /3}. Assuming that the core contributes to absorption, the absorption area (A) is described by where A N is the absorption area without the surface effects. The particle size dependence of the absorption is well tted by eqn (1), indicating that the ferromagnetism near the surface layer is lost. Hence, millimeter-waves cannot be absorbed at the surface. The tted value of d s ¼ 1.6 nm almost corresponds to one unit cell of the crystal structure. The value of A N ¼ 73 dB GHz is the intrinsic absorption of the present series with a lling ratio of 60 vol%, which corresponds to 120 dB GHz mm −1 . Therefore, a larger particle size may realize a larger absorption as a millimeter-wave absorber and a larger Faraday rotation and ellipticity effect in the millimeter-wave region.

Conclusions
Herein the millimeter-wave absorption, rotation, and ellipticity of 3-Ga x Fe 2−x O 3 with various particle sizes were investigated. Increasing the particle size improves the millimeter-wave absorption and rotation properties of 3-Ga x Fe 2−x O 3 . Analysis of the particle size dependence indicates that ferromagnetism near the surface layer is lost, inhibiting the absorption of millimeter-waves. The thickness of 1.6 nm almost corresponds to one unit cell of the crystal structure. Therefore, a larger particle size may achieve a larger absorption for an absorber as well as a larger Faraday rotation and ellipticity effect in the millimeter-wave region.

Conflicts of interest
There are no conicts to declare.