Giant Coercivity and Sub-Terahertz Ferromagnetic Resonance in Hard Ferrite Magnetic Insulators

Introduction

Hard magnetic ferrites are essential materials for modern technology, finding applications in permanent magnets, magnetic recording media, and antiradar systems. However, their magnetic properties are often overly sensitive to temperature changes, limiting their practical applications. Recently, researchers have discovered a new class of magnetically hard insulators based on aluminum-substituted strontium hexaferrites that exhibit extraordinary magnetic properties across a wide temperature range.

The Challenge

The operating temperature range of hard magnetic insulators is determined by magnetic transitions and the ratio of magnetic anisotropy energy to thermal energy ($k_B T$). Existing materials face significant limitations:

• 4d/5d element-based materials (La$_2$Ni$_{1.19}$Os$_{0.81}$O$_6$, Lu$_2$NiIrO$_6$) exhibit hard-magnetic properties only at temperatures well below 300 K and contain expensive elements
• 3d elements with nonzero orbital moment (CoFe$_2$O$_4$) are not magnetically hard at room temperature due to low spin-orbital interaction
• $\epsilon$-Fe$_2$O$_3$ requires complex synthesis and expensive rhodium doping to improve properties, and its coercivity drops drastically at low temperatures due to magnetic reorientation transitions

The Solution: Al-Substituted Strontium Hexaferrites

Researchers investigated single-domain particles of Ca-Al substituted strontium hexaferrite with the formula Sr$_{1-x/12}$Ca$_{x/12}$Fe$_{12-x}$Al$_x$O$_{19}$ (x = 1.5-5.5). The particles were synthesized using citrate-auto-combustion method and have plate-like shapes with mean diameters of 300-600 nm, which is below the single-domain limit for each compound.

Key Findings

Temperature-Stable Magnetic Hardness

All samples maintain their ultra-high magnetic hardness throughout the temperature range of 5-300 K. The magnetic hysteresis loops show typical behavior for randomly oriented Stoner-Wohlfarth particles with $M_r/M_s \approx 0.5$ at all temperatures.

Record-Breaking Coercivity

The coercivity ($H_C$) shows remarkable temperature dependence:

• For x = 1.5, $H_C$ decreases monotonously with temperature
• For x = 3-5.5, $H_C$ passes through maxima at specific temperatures
• With increasing aluminum concentration, the maximum shifts to lower temperatures

The highest coercivity of 42 kOe was observed for x = 5.5 at 180 K — the highest value among non-textured ferrite materials.

Sub-Terahertz Natural Ferromagnetic Resonance

The natural ferromagnetic resonance (NFMR) frequencies follow similar behavior to coercivity, as both are proportional to the anisotropy field ($H_a$):

The maximum NFMR frequency of 297 GHz was achieved for x = 5.5 at 180 K — the highest reported NFMR frequency among all materials.

Pure Spin Current Generation

One of the most promising features is the ability to generate pure spin current via the spin pumping effect. Calculations show:

• Spin current amplitude decreases with aluminum concentration but increases with cooling
• Even the x = 5.5 sample produces an order of magnitude higher spin current than the antiferromagnetic insulator MnF$_2$ at the same conditions (T ≈ 4 K, $f_r$ ≈ 260 GHz)
• At room temperature, the x = 5.5 sample still generates approximately three times higher spin current than MnF$_2$ at 4 K

Unique Advantages Over Competing Materials

Unlike $\epsilon$-Fe$_2$O$_3$, which requires complex synthesis and expensive rhodium doping, the hexaferrites offer:

• Simple and cost-effective synthesis
• Stable magnetic properties across 5-300 K
• No magnetic reorientation transitions
• Pure spin current generation without external magnetic field
• Response to unpolarized radiation (no chiral magnon mode requirements)

Physical Origin

The maxima in temperature dependencies of coercivity and NFMR frequencies relate to the behavior of the magnetocrystalline anisotropy constant $K_1$ and saturation magnetization $M_S$. Both $H_C$ and $f_r$ are proportional to the anisotropy field:

The extremum appears when $K_1$ begins to decline faster than $M_S$ at a specific temperature ($T_{max}$), which occurs at approximately 50% of the Curie temperature ($T_C$). Aluminum substitution decreases $T_C$, consequently shifting $T_{max}$ to lower temperatures.

Applications in Sub-THz Spintronics

These materials are exceptionally promising for:

• Electromagnetic radiation absorption and conversion at sub-terahertz frequencies
• Fast spin transport devices
• Sub-THz signal detection via spin pumping effect
• High-reliability magnetic storage maintaining magnetic moment position
• Next-generation wireless technologies (6G and beyond)

Conclusion

This work demonstrates the first example of magnetically hard insulators possessing extremely high coercivity and sub-terahertz electromagnetic wave absorption across a wide temperature range of 5-300 K. The tunable coercivity and NFMR frequency, combined with low temperature deviation, high processibility, and industrial integration potential, make Al-substituted hexaferrites highly promising for modern electronics applications.

The record-breaking 297 GHz NFMR frequency and 42 kOe coercivity, along with superior spin current generation capabilities, position these materials as the only known real candidates for generating powerful spin currents and detecting terahertz radiation in a broad temperature range — opening new possibilities for practical spintronic devices operating in the terahertz band.

This article is based on the research published in Materials Horizons (2023): “Hard ferrite magnetic insulators revealing giant coercivity and sub-terahertz natural ferromagnetic resonance at 5–300 K” by Evgeny A. Gorbachev, Ekaterina S. Kozlyakova, Liudmila N. Alyabyeva, Asmaa Ahmed, and Lev A. Trusov.