High-Coercivity Hexaferrite Ceramics Featuring Sub-Terahertz Ferromagnetic Resonance

Introduction

Hard-magnetic materials are essential for producing permanent magnets used in electric motors, power generators, robotics, information storage, and medicine. Today, rare-earth magnets dominate the market due to their strong magnetic fields, high coercivity, and record maximum energy product values. However, their application is limited by low availability of rare-earth metals, high processing costs, and poor chemical stability.

Magnetically hard ferrites offer an alternative for applications where production cost reduction matters and high magnetization is not essential. Modern ferrite materials such as epsilon iron oxide ($\epsilon$-Fe$_2$O$_3$) and Al-substituted hexaferrites (BaFe$_{12}$O$_{19}$ or SrFe$_{12}$O$_{19}$) demonstrate coercivities up to 40 kOe at room temperature and electromagnetic radiation absorption in the 1-250 GHz range due to ferromagnetic resonance (FMR).

The Challenge

Ferrites demonstrate their highest magnetic hardness in the form of single-domain particles, which are generally produced as highly dispersed powders. However, for many important applications, a magnet should be a compact bulk with a high volume fraction of magnetic material to improve magnetization and maximum energy product.

The key problem: hexaferrites are usually used as dense ceramics, but their coercivity substantially reduces during high-temperature sintering due to intensive grain growth. To date, the reported coercivity of BaFe$_{12}$O$_{19}$ and SrFe$_{12}$O$_{19}$ ceramics does not exceed 5 kOe, far below single-domain sample values (up to 7 kOe).

The $\epsilon$-Fe$_2$O$_3$ is even more challenging to handle, requiring complex production methods for single-phase material with controllable particle morphology. Moreover, it is a metastable phase that cannot be directly sintered without conversion to stable $\alpha$-Fe$_2$O$_3$.

The Solution: Single-Domain Al-Substituted Hexaferrite Ceramics

Researchers developed a technique to fabricate rare-earth-free dense ceramics with giant coercivity at room temperature. The approach is based on sintering single-domain hexaferrite particles with composition Sr$_{0.67}$Ca$_{0.33}$Fe$_8$Al$_4$O$_{19}$, which have a large critical diameter for single-domain state — key for maintaining high magnetic hardness after compaction.

Materials and Methods

Synthesis Process

The fine hexaferrite powder with composition Sr$_{0.67}$Ca$_{0.33}$Fe$_8$Al$_4$O$_{19}$ was prepared via citrate-nitrate auto-combustion method:

1. Metal carbonates (CaCO$_3$ and SrCO$_3$) and nitrates (Fe(NO$_3$)$_3$$\cdot$9H$_2$O and Al(NO$_3$)$_3$$\cdot$9H$_2$O) mixed with citric acid (metal ions to citrate ions molar ratio 1:3)
2. Solution neutralized by NH$_4$OH under rapid stirring
3. Dehydrated by heating and burned to form precursor powder
4. Powder heated to 1200 °C for 24 hours

Ceramic Fabrication

The obtained hexaferrite powder was:

1. Ground in agate mortar
2. Pressed under 6 atm into pellets (12 mm diameter, 3 mm thickness)
3. Pellets crushed and re-pressed
4. Heated on platinum substrate to 1200-1500 °C (20 °C/min)
5. Exposed for 30 min followed by air quenching

Key Findings

Record-High Coercivity in Dense Ceramics

The obtained ceramics show coercivities up to 22.5 kOe and natural ferromagnetic resonance frequencies (NFMR) in the sub-THz range of 160-282 GHz.

At maximum density of 95% (1400 °C), the sample displays coercivity of 18.2 kOe — the highest value among dense ferrite materials reported so far.

Unusual NFMR Frequency Blueshift

An unusual blueshift of the NFMR frequency from 160 to 200 GHz (25% rise) occurs during material sintering between 1300 °C and 1350 °C. At higher sintering temperatures up to 1450 °C, a slight monotonous growth of FMR frequency to 214 GHz takes place.

At 1475 °C, two resonance peaks at 224 and 282 GHz appear in the absorption spectrum. The 282 GHz line represents the highest natural ferromagnetic resonance frequency reported so far for a magnetic material.

Microstructure Analysis

According to SEM analysis:

• Average grain diameters in samples obtained at 1300-1400 °C are in the range of 1-2 μm
• Grains are considered to be in a single-domain state, anticipating coherent magnetization reversal as the predominant mechanism
• Coercivity begins to fall at higher sintering temperatures when the fraction of grains of several microns in size becomes significant

Phase Composition Evolution

X-ray diffraction reveals:

• Phase composition remains unchanged at sintering temperatures up to 1400 °C
• At 1425 °C, magnetite phase (Fe$_3$O$_4$) emerges, with content increasing with temperature
• At 1475-1500 °C, intensive hexaferrite melting and solidification result in separation of two hexaferrite phases with different aluminum content

Investigating the Frequency Blueshift Mechanism

The observed jump of NFMR frequency between sintering temperatures of 1300 and 1350 °C is quite unusual. Researchers analyzed several hypotheses:

Hypothesis 1: Demagnetizing Field Effect

The demagnetizing field between magnetic domains could affect FMR frequency. However, in this case, the saturation magnetization is lower and the demagnetizing field is merely 2% of the anisotropy field (0.9 kOe vs. 40 kOe), which can lead to a maximum frequency shift of 1 GHz — not the observed 40 GHz.

Hypothesis 2: Intergranular Interface Changes

TEM analysis of lamella cuts from ceramics obtained at 1300 and 1400 °C showed:

• Most grains in the 1300 °C sample are separated by pores
• The 1400 °C sample is more uniform
• No interlayer at the interface between hexaferrite grains that could affect exchange interaction
• Grains accrete in random directions without noticeable epitaxy

Hypothesis 3: Crystal Structure Changes

Rietveld refinement showed aluminum atoms within samples obtained at 1200-1400 °C are distributed identically, mostly occupying octahedral 2a and 12k sites. The distribution of aluminum and associated crystal lattice distortions are unlikely causes of the frequency blueshift.

Hypothesis 4: Fe$^{2+}$ Ion Formation

Mössbauer spectroscopy at 308 °C (above Curie point) revealed:

• Samples obtained at 1300 and 1400 °C contain only Fe$^{3+}$ ions
• Sample obtained at 1500 °C shows spinel phase formation (~19%) with Fe$^{3+}$ and Fe$^{2.5+}$

However, researchers observed an unusual hysteresis of FMR frequency with annealing treatment:

• NFMR frequency of 200 GHz decreases to 180 GHz after annealing at 1200 °C for 30 min
• Frequency recovers to 200 GHz after repeated annealing at 1400 °C

This phenomenon could be explained by Fe$^{3+}$ $\rightleftharpoons$ Fe$^{2+}$ transitions with annealing temperature changes, though further studies are required.

Comparison with Other Hard-Magnetic Materials

Applications

The unique combination of properties makes these materials promising for:

1. Rare-earth-free durable permanent magnets — for applications where high magnetization is unimportant or even undesirable
2. Sub-terahertz technologies — THz radiation absorption without external magnetic field
3. Next-generation wireless communication — 5G/6G technologies operating at sub-THz frequencies
4. Spintronics — where device size and mass are critical
5. Frequency-switching devices — the sharp FMR frequency change effect can be used for absorption frequency tuning

Advantages Over Competing Materials

Among all hard-magnetic ferrites, only M-type hexaferrites are suitable for creating monolithic material with high magnetic phase fraction and large coercivity:

• CoFe$_2$O$_4$ has a small critical diameter (about 40 nm)
• $\epsilon$-Fe$_2$O$_3$ has low thermal stability and lacks scalable synthesis methods

The proposed approach is:

• Facile — simple citrate-nitrate auto-combustion synthesis
• Inexpensive — no rare-earth elements required
• Scalable — easily integrated into modern ferrite manufacture

Conclusions

This work demonstrates several groundbreaking achievements:

1. First fabrication of rare-earth-free dense ceramics with giant room-temperature coercivity
2. Maximum coercivity of 22.5 kOe at 67% density (1300 °C sintering)
3. Record 18.2 kOe coercivity at 95% density (1400 °C) — highest among dense ferrite materials
4. Natural FMR frequency jump from 160 to 200 GHz during sintering
5. Record-high 282 GHz NFMR frequency observed in solid-state material

The compact materials obtained possess high magnetic properties similar to $\epsilon$-Fe$_2$O$_3$, while the facile synthesis and scalability make them attractive for industrial applications. The effect of sharp ferromagnetic resonance frequency change discovered in this work can be used to develop devices with switching or tuning of absorption frequency.

These materials are very promising for rare-earth-free durable permanent magnets, sub-terahertz technologies, and next-generation wireless communication systems.

This article is based on research published in Materials Horizons (2022): “High-coercivity hexaferrite ceramics featuring sub-terahertz ferromagnetic resonance” by Evgeny A. Gorbachev, Lev A. Trusov, Liudmila N. Alyabyeva, Ilya V. Roslyakov, Vasily A. Lebedev, Ekaterina S. Kozlyakova, Oxana V. Magdysyuk, Alexey V. Sobolev, Iana S. Glazkova, Sergey A. Beloshapkin, Boris P. Gorshunov, and Pavel E. Kazin.