Microwave and millimeter wave dielectric permittivity and magnetic permeability of Epsilon-Gallium-iron-oxide nano-powders

The hexagonal ferrite materials such as Ba- and Sr-Fe₁₂O₁₉ show strong ferromagnetic absorption in the 40-60 GHz range . However, in the higher millimeter wave frequency range beyond 60 GHz, the natural ferromagnetic ferrite materials with high performance are lacking due to the limitation of material science and synthetic complexity . The synthesis of single phase of ε-iron oxide (ε-Fe₂O₃) enables the development of magnetic materials which have natural ferromagnetic resonance from 50 to 200 GHz . Among the four polymorphs of α-, ß-, γ-, ε-Fe₂O₃, the ß- and ε-Fe₂O₃ are rare and must be synthesized in the laboratory . The pure ε-Fe₂O₃ shows the largest coercive field value (Hc) of 20 kOe among metal oxide-based magnets at room temperature . Multiple factors contribute to the gigantic Hc in ε-Fe₂O₃ . One is the small ε-Fe₂O₃ crystal size . A large H_c value is expected when the particle size is sufficiently small to form a single magnetic domain . A particle size of ca . 100 nm in the material is suitable to realize a single magnetic domain . Another is the intrinsic magnetic property of the ε-Fe₂O₃ phase . The Hc value depends on the magnetocrystalline anisotropy constant (K) and saturated magnetization (Ms), i .e ., H_c K/M_s . Anaysis of the initial magnetization process estimates the K value in the present material as 2-4 x 10⁶ erg cm^-3, which greatly exceeds the K values of γ-Fe₂O₃ (ca . 10⁴ erg cm^-3) and α-Fe₂O₃ (ca . 10⁵ erg cm^-3) . In addition, the observed Ms value is small, 15 emu g^-1 (15 A m² kg^-1) at 7- .0 T . Therefore, it is concluded that the large Hc value of 20 kOe is due to (1) the suitable nanoscale size of particles that form a single magnetic domain and (2) the large K and small Ms values of ε-Fe₂O₃ . Such high Hc is very attractive in millimeter applications . By employing metal substitution method, the metal-substituted ε-iron oxide can exhibit an adjustable ferromagnetic resonant frequency at 35-182 GHz depending on the degree of metal substitution . These nano-sized materials can be further made into composite material and applied in millimeter wave devices such as phase shifter, isolator and circulator . The gallium substituted ε-iron oxide (ε-Ga_xFe_2-xO₃) in this paper with x=0 .22 and 0 .29 are characterized by the vector network analyzer from 6 to 40 GHz and by free space quasi optical method (30-120 GHz) . The tunability of the ferromagnetic resonance frequency depends on the x-parameter constituents . The ferromagnetic absorption peak moves to higher frequencies with decreasing x-parameter value . These absorptions are due to the natural resonance achieved by the large magnetic anisotropies in this series with change in x-parameter . The materials have ferromagnetic resonant frequencies in the frequency range from 30 GHz to 150 GHz relies on the concentration of gallium ions [1] . The ε-Ga_xFe_2-xO₃ is synthesized by sol-gel techniques [2] . The particle sizes are observed to be smaller than 100 nanometer . The nano-powders are characterized by vector network analyzer employing transmission and refection method [3] . The complex permittivity and permeability spectra over the X-band frequency range are shown in Figure 1 . The measurement was made in powder state . However the density value was recorded . The data seem to be mostly flat in this frequency range . Figure 2 shows the imaginary permeability in the millimeter wav