Hard magnetic ferrite with a gigantic coercivity and high frequency millimetre wave rotation.

Magnetic ferrites such as Fe(3)O(4) and Fe(2)O(3) are extensively used in a range of applications because they are inexpensive and chemically stable. Here we show that rhodium-substituted ε-Fe(2)O(3), ε-Rh(x)Fe(2-x)O(3) nanomagnets prepared by a nanoscale chemical synthesis using mesoporous silica as a template, exhibit a huge coercive field (H(c)) of 27 kOe at room temperature. Furthermore, a crystallographically oriented sample recorded an H(c) value of 31 kOe, which is the largest value among metal-oxide-based magnets and is comparable to those of rare-earth magnets. In addition, ε-Rh(x)Fe(2-x)O(3) shows high frequency millimetre wave absorption up to 209 GHz. ε-Rh(0.14)Fe(1.86)O(3) exhibits a rotation of the polarization plane of the propagated millimetre wave at 220 GHz, which is one of the promising carrier frequencies (the window of air) for millimetre wave wireless communications.

Magnetic ferrite, which is composed of iron oxide, was discovered in the seventh century B.C. Since then, magnetic ferrites have contributed to daily life12, for example, magnetic motors, magnetic recording media, magnetic fluids and electromagnetic wave filters. However, due to their low magnetocrystalline anisotropies345, the coercivity of magnetic ferrites is generally low. Hence, the development of magnetic ferrites with a large coercive field (Hc) is an important issue because this type of ferrite can be used as various advanced materials678.

Of the several polymorphs of Fe2O3 (refs 9,10), γ-Fe2O3 and α-Fe2O3 phases have been well studied. γ-Fe2O3, which is a representative soft magnet, is a ferrimagnet with a spinel structure. α-Fe2O3 has a corundum structure and shows weak ferromagnetism due to the Dzyaloshinsky−Moriya mechanism1112. In contrast, ε-Fe2O3 is a rare phase, and research on this phase had been running behind131415. It is only recently that ε-Fe2O3 was found to exhibit a huge coercive field of 20 kOe at room temperature16. Since then, its magnetic properties have received much attention1718192021.

In this Article we synthesized rhodium-substituted ε-iron oxide, ε-RhFe2−O3, nanomagnets and found that this series exhibits the highest Hc value of 31 kOe among metal oxides. This Hc value is comparable to those of rare-earth magnets2223. Furthermore, it displays electromagnetic wave absorption with the highest resonance frequency among whole magnetic materials. Herein, we report the synthesis, crystal structure, magnetic properties, first-principles calculations, high frequency millimetre wave absorption properties and magnetic rotation of the propagated millimetre wave.

Results

Synthesis and crystal structure of ε-RhFe2−O3 nanomagnets

A series of rhodium-substituted epsilon-iron oxide nanoparticles (ε-RhFe2−O3, x=0, 0.04, 0.07, 0.11 and 0.14) were prepared by impregnating a methanol and water solution containing iron nitrate and rhodium nitrate into mesoporous silica, subsequently heating at 1,200 °C in air, and removing the silica matrix using an aqueous sodium hydroxide solution (Fig. 1a) (see Methods). The transmission electron microscope image indicates that the obtained sample is composed of nanoparticles with an average particle size of ca. 35 nm (inset of Fig. 1a; Supplementary Fig. S1).

Figure 1

Synthesis, crystal structure and thermodynamic stability of ε-RhFe2−O3 nanomagnets.

(a) Upper row illustrates the synthesis of ε-RhFe2−O3. In the first step, a mesoporous silica template is synthesized in a conical flask to give a white powder. In the second step, an aqueous solution of Fe(NO3)3 and Rh(NO3)3 with methanol is impregnated into the silica to yield a yellow powder. In the third step, the resulting product is calcinated in air, and in the fourth step, the final product is obtained after etching the silica matrix with an aqueous NaOH solution. Lower left transmission electron microscope (TEM) image shows the obtained mesoporous silica where the small white dots are the mesopores. Illustration in the dotted frame depicts the formation process of ε-phase during calcination; as the temperature increases, Fe(NO3)3 and Rh(NO3)3 in the mesopores turn into γ-phase (~800 °C). Around the melting temperature of glass (1,000 °C), the particles begin to aggregate. As shown in the centre TEM image, ε-phase is the main phase at 1,200 °C. Lower right TEM image is the final product after etching the silica matrix. The scale bars below the three TEM images indicate 30 nm. (b) (left) Crystal structure of γ-phase. Green and light green indicate octahedral and tetrahedral Fe sites, respectively. (centre) Crystal structure of ε-phase. Dark red, red, orange and yellow indicate the four nonequivalent Fe sites for FeA, FeB, FeC and FeD, respectively. (right) Crystal structure of α-phase. Fe site is shown as blue octahedrons. Grey lines indicate the unit cell. (c) Calculated G/Vm versus d curves for i-phases (i=γ, ε and α). Green, red and blue curves correspond to γ-phase, ε-phase and α-phase, respectively. The curves are calculated under the condition of μγ >με >μα, σγ <σε <σα and (σε−σγ)/(σα−σε) < (με−μγ)/(μα−με), where μ is the chemical potential of i-phase and σ is the surface energy of i-phase.

The X-ray diffraction patterns confirm that the crystal structure is orthorhombic with Pna21 space group (Fig. 1b). Rh substitutes for a specific iron site (FeC site) among the four nonequivalent iron sites (FeA–FeD sites) in the crystal structure of ε-RhFe2−O3. The unit cell volume refined by the Rietveld analysis gradually increases with Rh concentration. At higher Rh concentrations, α-RhFe2−O3 is formed as a byproduct (Supplementary Fig. S2 and Supplementary Table S1). The particle size distribution depends on the sintering temperature; the particle size increases as the sintering temperature increases, and the phase changes from γ-phase to ε-phase and then to α-phase (Fig. 1c). The threshold sizes for the transformation from γ- to ε-phase and from ε- to α-phase are evaluated to be 10 and 55 nm, respectively (Supplementary Fig. S3).

Magnetic properties

The magnetic properties were measured by a superconducting quantum interference device (SQUID) magnetometre. The temperature dependences of the magnetization of ε-RhFe2−O3 powder samples show that the Curie temperatures (TC) are 505 K (x=0), 495 K (x=0.04), 484 K (x=0.07), 474 K (x=0.11) and 469 K (x=0.14) (Supplementary Fig. S4a). The magnetization versus external magnetic field plots at 300 K demonstrate that the Hc value increases as the x value increases, that is, 22 kOe (x=0), 23 kOe (x=0.04), 24 kOe (x=0.07), 25 kOe (x=0.11) and 27 kOe (x=0.14) (Fig. 2a and Supplementary Fig. S4b).

Figure 2

Magnetic properties of ε-RhFe2−O3 nanomagnets.

(a) Magnetization versus external magnetic field plot of non-oriented ε-Rh0.14Fe1.86O3 nanoparticles at 300 K exhibiting a coercive field of 27 kOe. (b) Magnetization versus external magnetic field plot of crystallographically oriented ε-Rh0.14Fe1.86O3/resin at 300 K exhibiting a coercive field of 31 kOe.

Furthermore, crystallographically oriented ε-Rh0.14Fe1.86O3 nanoparticles dispersed in resin (see Methods) reveal a gigantic Hc value of 31 kOe (Fig. 2b), which is related to the magnetic anisotropy field (Ha) as Hc≈Ha/2 with a uniaxial magnetic anisotropy. The magnetic hysteresis loop indicates that the estimated Ha value of the sample for x=0.14 is 53 kOe, which is much larger than those of γ-Fe2O3 (0.2 kOe) and Fe3O4 (0.5 kOe).

First-principles calculations

First-principles calculations of ε-RhFe2−O3 were conducted to understand the electronic structure of this series (see Methods). The density of states (DOS) shows that ε-RhFe2−O3 is a charge-transfer type insulator with an O2p valence band and a Fe3d conduction band (Supplementary Fig. S5). Rh4d is distributed in the same energy region as the O2p band below the Fermi energy (EF) level, suggesting that Rh4d and O2p overlap greatly. In the occupied region, the 3d bands of the FeB and FeC sites are occupied by α spins, whereas those of the FeA and FeD sites are occupied by β spins, that is, (FeA, FeB, FeC, FeD)=(β, α, α, β) (Supplementary Fig. S6). Although we attempted several alternative spin configurations, their energies are higher than that of (β, α, α, β), suggesting that these other configurations are not suitable. This finding is consistent with the spin configuration reported for ε-Fe2O3, which is a collinear ferrimagnet composed of positive sublattice magnetizations at the FeB and FeC sites and negative sublattice magnetizations at the FeA and FeD sites2425. The charge density map shows strong hybridization between Fe3+ and O2−; the electron charge is partially transferred from O2− to Fe3+ through hybridization (Supplementary Fig. S7).

Millimetre wave absorption properties

The electromagnetic wave absorption properties were measured under a zero-magnetic field at room temperature in the millimetre wave range (30–300 GHz) using terahertz time domain spectroscopy (THz-TDS) (see Methods and Supplementary Fig. S8). As shown in Fig. 3a, resonance frequencies (fr) are observed at 182 GHz (x=0), 186 GHz (x=0.04), 190 GHz (x=0.07), 198 GHz (x=0.11) and 209 GHz (x=0.14). These fr values are the highest among all magnetic materials. The fr versus Hc plot shows that the fr value proportionally increases with increasing Hc (the inset of Fig. 3a). Before this work, ε-Fe2O3 exhibited the highest fr value of 182 GHz26. As for the quality of the absorption, the Q-factor of the absorption, which is expressed as Q=fr/Δf, where Δf is full width at half maximum, is evaluated to be 38 (x=0), 20 (x=0.04), 21 (x=0.07), 19 (x=0.11) and 17 (x=0.14).

Figure 3

Millimetre wave absorption and millimetre wave magnetic rotation of ε-RhFe2−O3 nanomagnets.

(a) Millimetre wave absorption spectra of ε-RhFe2−O3 under a zero-magnetic field at room temperature for x=0 (blue), x=0.04 (light blue), x=0.07 (green), x=0.11 (orange) and x=0.14 (red) measured by THz-TDS. Inset plots the resonance frequency (fr) versus coercive field (Hc). Colours of the dots are consistent with the x values of the absorption spectra. Black line is to guide the eye. (b) Millimetre wave magnetic rotation and ellipticity change of ε-Rh0.14Fe1.86O3. Rotation angle (red dotted line) and ellipticity (black dotted line) spectra measured by irradiating from the N-pole side (left) and S-pole side (right) of the sample using THz-TDS. Solid lines are to guide the eye. (c) Schematic illustration of the magnetic rotation and ellipticity change of the propagated millimetre wave due to the optically induced magnetic dipole transition. The green and ochre arrows indicate the magnetic field and electric field components of the impulsive terahertz wave pulse, respectively. Red and blue sides of the disc denote the N- and S-poles of the magnetized pellet sample.

Magnetic rotation of the propagated millimetre wave

The rotation angle and ellipticity were measured under a zero-magnetic field using a magnetized ε-Rh0.14Fe1. 86O3 pellet sample, which was obtained by a strong pulsed magnetic field (ca. 8T). Irradiating with a millimetre wave from the N-pole side of the sample causes the rotation angle to display a dispersive spectrum centred at fr=209 GHz where the minimum and maximum values are −10° and +10° at 196 and 220 GHz, respectively, whereas the ellipticity exhibits a peak at fr with a value of +0.3 (Fig. 3b, left). Upsetting the magnetic poles of the sample inverts the signs of the rotation angle and ellipticity (Fig. 3b, right). The observed phenomenon clearly originates from the remanent magnetization and its direction (Fig. 3c). The figure of merit (F), which is defined as F=(rotation angle (deg))/(absorption (dB)), has a high value of 20 deg dB−1 at 220 GHz.

Discussion

Usually, iron oxide (Fe2O3) transforms directly from γ-phase into α-phase as the sintering temperature increases in the typical calcination process. However, in the present synthetic method, ε-phase exists as a stable phase due to the nanosize effects on the phase transformation via the following mechanism. In a nanoparticle, the free energy of each i-phase (G, i=γ, ε, or α) is expressed as the sum of the chemical potential (μ) and surface energy (Aσ), where A and σ represent the molar surface area and the surface free energy of the particle, respectively27; G=μ+Aσ. Because A is equal to 6Vm,/d, where Vm, and d represent the molar volume and particle diameter, respectively, the free energy per molar volume (G/Vm,) is expressed as G/Vm,=μ/Vm,+6σ/d. This equation suggests that the surface energy contribution increases as the particle diameter decreases. When the parameters in the equation satisfy the relationships of μγ >με >μα , σγ <σε <σα and (σε−σγ)/(σα−σε) <(με−μγ)/(μα−με), then the curves for Gγ/Vm,γ, Gε/Vm,ε and Gα/Vm,α intersect, leading to the stable ε-phase at an intermediate d value (Fig. 1c). Such a nanosize effect has also been reported in Al2O3 (refs 28,29) and Ti3O5 (ref. 30).

Next, we considered the mechanism of the large Hc value in the present material. One origin of the gigantic Hc is that the particle size of ca. 35 nm in the present series should be sufficiently small to form a single magnetic domain331. In fact, the magnetic force microscopy image for x=0 shows that each particle has a single magnetic domain (see Methods). In a single magnetic domain, only the magnetization rotation process operates, leading to a large Hc value. Another origin of the gigantic Hc is the magnetic anisotropy of the ε-phase. Because shape anisotropy in the present series is negligible (below 0.3 kOe), the observed Ha value of 53 kOe is determined by the magnetocrystalline anisotropy.

The results of the first-principles calculations indicate that the following mechanism explains the large magnetocrystalline anisotropy of this series. The charge density map (Supplementary Fig. S7) shows strong hybridization between Fe3+ and O2−, that is, the electron charge is partially transferred from O2− to Fe3+, resulting in an electron configuration of d5+ where q is the transferred charge. Such a hybridization causes a non-zero orbital angular momentum ( ≠ 0) on Fe ion, which induces a large magnetocrystalline anisotropy. Furthermore, Rh–O–Fe hybridization is observed around the Rh-substituted site, which enhances the magnetocrystalline anisotropy through the contribution from the orbital angular momentum on Rh. Thus, the large Hc value of the present material is attributed to the nanoscale particle size, which is suitable to form a single magnetic domain, and the huge Ha value due to the magnetocrystalline anisotropy.

Finally, we discuss millimetre wave absorption, magnetic rotation and ellipticity change of the propagated millimetre wave. In a ferromagnetic material with a uniaxial magnetic anisotropy, an electromagnetic wave is absorbed at fr, known as zero-field ferromagnetic resonance (natural resonance). Because the magnitude of the Ha value determines the fr value, that is, fr=νHa/2π, where ν is the gyromagnetic constant, the observed high fr values are due to the large Ha values of ε-RhFe2–O3. In fact, the fr versus Hc plot shows that the fr value proportionally increases with increasing Hc (Fig. 3a). Furthermore, zero-field ferromagnetic resonance generates changes in the rotation angle and ellipticity of the propagated millimetre wave. When an impulsive terahertz wave pulse is irradiated into the sample, the magnetic field component of the terahertz wave tilts the spontaneous magnetization away from the magnetic easy-axis direction due to gyromagnetic effect, which causes the bulk magnetization to precess around the easy axis. This precession produces a magnetic rotation of the propagated millimetre wave at a particular frequency (Fig. 3c; Supplementary Movie 1). These observed millimetre wave absorption, magnetic rotation and ellipticity change are due to the optically induced magnetic dipole transition, which differs from the conventional magneto–optic effect (Faraday effect) in the visible or near-infrared region through an optically induced electric dipole transition32.

In conclusion, we prepared a series of ε-RhFe2−O3 nanomagnets via a nanoscale synthetic method using mesoporous silica as a template. ε-Rh0.14Fe1.86O3 displays the largest Hc value of 31 kOe among metal-oxide magnets. The gigantic Hc value has potential in future high-density magnetic recording media because the large Hc value enables the particle size to be greatly reduced while maintaining coercivity. In addition, ε-RhFe2−O3 exhibits a zero-field ferromagnetic resonance up to 209 GHz, and the magnetic rotation and ellipticity change of the propagated millimetre wave occur due to an optically induced magnetic dipole transition at 220 GHz. The present material should be useful for high frequency millimetre wave absorbers and rotators (isolators or circulators) as it should restrict electromagnetic interference problems33 because the frequency of the magnetic rotation corresponds to the highest window of air (220 GHz band), which is the anticipated carrier frequency for next-generation millimetre wave wireless communications such as high-definition television communications and intra-board integrated circuit (IC) chip wireless communications343536.

Methods

Materials

An impregnation method using mesoporous silica nanoparticles was used to prepare a series of ε-RhFe2−O3 (x=0, 0.04, 0.07, 0.11 and 0.14) nanoparticles. Mesoporous silica nanoparticles were synthesized by modifying reported methods3738. Tetraethyl orthosilicate (62 mmol) was added to a solution of distilled water (4 mol), ethanol (0.18 mol), cetyltrimethylammonium chloride (16 mmol) and triethanolamine (62 mmol) at 60 °C, yielding mesoporous silica nanoparticles after centrifuging and heating at 600 °C in air. To obtain the target materials, a methanol and water solution containing iron nitrate and rhodium nitrate was immersed into mesoporous silica and sintered at 1,200 °C for 4 h in air. Silica matrices were etched by an aqueous sodium hydroxide solution at 70 °C.

Physical property measurements

Elemental analyses of the prepared samples were conducted with inductively coupled plasma mass spectroscopy (Agilent Technologies, HP 4500). Transmission electron microscope images were acquired with JEM 2000EX. The 2θ–θ scan X-ray diffraction measurements were performed using Rigaku Ultima IV and Rigaku RINT2100 with Cu Kα radiation (λ=1.5418 Å) at 293 K. Rietveld analyses were performed using the RIETAN-FP program39. The magnetic properties were measured using a SQUID magnetometer (Quantum Design, MPMS 7).

Preparation of an oriented sample

An oriented ε-Rh0.14Fe1. 86O3/resin was prepared. The ε-Rh0.14Fe1.86O3 nanoparticles were oriented by placing ε-Rh0.14Fe1.86O3 nanoparticles dispersed ultraviolet curing resin (SD-2200, DIC Corporation) in an applied magnetic field of 12.7 kOe. The sample was then irradiated with ultraviolet light (EX250, Hoya Candeo Optronics Corporation) to harden the curing resin and to pin the oriented nanoparticles.

Single magnetic domain of the nanoparticle

With respect to the magnetic domain, we previously performed magnetic force microscopy measurements on ε-Fe2O3, which was prepared by a combination of reverse-micelle and sol–gel methods. The magnetic force microscopy image showed that ε-Fe2O3 particles form a single magnetic domain. Therefore, ε-RhFe2−O3 is considered to be composed of a single magnetic domain. Additionally, the magnetic domain sizes of common metal-oxide–based magnets are much larger than the size of our nanoparticles. For example, the magnetic domain size of barium ferrite is about 1 μm40.

First-principles calculations were performed using Vienna ab initio Simulation Package, which is a plane–wave projector augmented wave method program4142. The exchange-correlation functional was approximated with generalized gradient approximation (GGA) parameterized by Perdew–Burke–Ernzerhof (PBE) in the spin-restricted condition. To describe the Fe3d and Rh4d orbitals, the Hubbard U term (GGA+U) was considered. Referring to the reported calculations for α-Fe2O3 and γ-Fe2O3, the difference between the Coulomb interaction energy (Ucoul) and exchange interaction energy (Jex), Ucoul−Jex, was set to 4.0 eV. The basis set size was regulated by a cutoff energy of 520 eV. Gaussian methods (smearing width: 0.2 eV) were used to integrate the Brillouin zone with a 3×3×3 k-mesh and to calculate the DOS with a 5×3×3 k-mesh. Among the 16 Fe atoms in the unit cell, a Rh atom substituted for one Fe atom at the FeC site. Supplementary Figures S5–S7 show the calculated DOS and charge density map.

Millimetre wave absorption measurements

A pump-probe measurement system was used for the THz-TDS measurements. Supplementary Figure S8 schematically diagrams the THz-TDS system. A mode-locked Ti:sapphire pulse laser delivered 20-fs long ultrashort light pulses with a central photon energy of 1.55 eV at a pulse repetition rate of 76 MHz. A beam splitter divided the output of the mode-locked Ti:sapphire femtosecond pulse laser into pump and probe beams. Dipole type and bowtie type low-temperature-grown GaAs photoconductive antennas were used as the THz wave emitter and detector, respectively. The emitted THz wave was collimated and irradiated into the sample, which was mounted on a sample holder and placed between a set of paraboloidal mirrors. The transmitted THz electric field was detected with the bowtie type low-temperature-grown GaAs photoconductive antenna, which was triggered by optical probe pulses with variable time delays between the pump and probe pulses; consequently, the electric field of the transmitted THz pulse wave was formed in the time domain. The absorption spectra of the THz waves were calculated as (Absorption)=−10 log |t(ω)|2 [dB], where t(ω) is the complex amplitude transmittance. Samples were held in paper containers with filling factors of ca. 30%.

Millimetre wave magnetic rotation measurements

To obtain the millimetre wave magnetic rotation spectra, we employed three polarizers (P1–P3) to measure the horizontal and vertical polarization components (Supplementary Fig. S8). The measurement system operated only the horizontal polarization component of the electric field because the antenna determined the directions of the THz wave emitter and detector. To precisely define the polarization of the THz wave as horizontal (0°), P1 was placed after the emitter while P3 was placed before the detector. The components of +45° and −45° were measured by rotating P2 behind the sample. The vertical and horizontal polarization components were obtained as their difference and sum, respectively. The rotation angle and ellipticity were obtained from the horizontal and vertical components (E(t), E(t)) of the transmitted electric fields, which are expressed as

The rotation angle φ(ω) and ellipticity η(ω) spectra are expressed as

where δ(ω)=δ1(ω)−δ2(ω) is the phase difference. a(ω) and η(ω) can be directly determined as the Fourier-transformed amplitude and phase of the temporal waveforms.

Author contributions

S.O. and A.N. designed and coordinated this study, contributed to all the syntheses, measurements, and calculations, and wrote the paper. M.Y. performed the THz-TDS measurements and first-principles band calculations. K.Y. prepared the oriented sample and measured its magnetic properties. S.S. carried out the syntheses and characterization. T.G., T.Y. and T.M. contributed to the syntheses. M.N. and T.S. conducted the measurements using THz-TDS. H.T. performed magnetic property and XRD measurements of the oriented sample and prepared the figures. All authors commented on the manuscript.

Additional information

How to cite this article: Namai, A., et al. Hard magnetic ferrite with a gigantic coercivity and high frequency millimeter wave rotation. Nat. Commun. 3:1035 doi: 10.1038/ncomms2038 (2012).

Supplementary Figures and Supplementary Table

Supplementary Figures S1-S8 and Supplementary Table S1.

Supplementary Movie 1

Animation of magnetic rotation of the propagated millimetre wave polarization place caused by optical transition of the magnetic dipole.