Submicron Particles of Cr-Substituted Strontium Hexaferrite: Anomalous X-ray Diffraction Studies, Hard Magnetic Properties, and Millimeter-Wave Absorption

Problem

To date, only three compounds are considered hard magnetic insulators: cobalt ferrite ($\mathrm{CoFe}_2\mathrm{O}_4$), epsilon iron(III) oxide ($\epsilon\text{-}\mathrm{Fe}_2\mathrm{O}_3$), and M-type hexaferrites ($\mathrm{MFe}_{12}\mathrm{O}_{19}$, $\mathrm{M}^{2+} = \mathrm{Ba}^{2+}, \mathrm{Sr}^{2+}, \mathrm{Pb}^{2+}$). Due to their large magnetocrystalline anisotropy, they can provide rather high coercivity and natural ferromagnetic resonance (NFMR) in the millimeter range (30–300 GHz). These functional properties are in demand in many application areas, ranging from magnetic recording to spintronics.

The most effective way to increase their anisotropy field $H_a = 2K_1\rho^{-1}M_S^{-1}$ (where $K_1$ is the magnetocrystalline anisotropy constant, $\rho$ is the density, and $M_S$ is the mass saturation magnetization) is a reduction of the saturation magnetization $M_S$ by substituting $\mathrm{Fe}^{3+}$ ions with diamagnetic ones. The most outstanding results were achieved for partial substitution with $\mathrm{Al}^{3+}$, which led to a more than fivefold increase in coercive force and NFMR frequencies to 36 kOe and 250 GHz, respectively.

Chromium substitution has not been sufficiently studied due to difficulties in obtaining single-phase materials. To date, single-domain particles of Cr-substituted hexaferrites with a wide composition range have not been reported, and their magnetic properties and millimeter-wave absorption have not been systematically studied.

Methods/Ideas

For the first time, the authors obtained submicron particles of single-phase hexaferrites with the chemical composition of $\mathrm{SrFe}_{12-x}\mathrm{Cr}_x\mathrm{O}_{19}$ ($x = 0-8$) via an optimized citrate-nitrate auto-combustion method.

Synthesis:

• High-purity reagents: strontium carbonate, iron(III) nitrate nonahydrate, chromium(III) nitrate nonahydrate, citric acid
• Citrate method with molar ratio 1:3 between metal ions and citrate
• Solution neutralized with aqueous ammonia and dehydrated
• Product spontaneously combusted to form porous precursor
• Precursor annealed at 1200 °C for 2 h in air

Characterization:

• Anomalous X-ray diffraction (AXRD) at SLS synchrotron (X04SA-MS beamline) near Cr K-edge to determine Cr distribution over iron sites
• XRD (Rigaku D-Max 2500) for phase analysis and lattice parameters
• SEM for particle morphology and size distribution
• SQUID magnetometry (MPMS XL) for magnetic properties and Curie temperature
• Terahertz time-domain spectroscopy for NFMR spectra (300 K, zero magnetic field)
• Mössbauer spectroscopy for hyperfine field analysis

Results

Crystal Structure Analysis

Anomalous XRD Results:

• Cr$^{3+}$ ions predominantly occupy octahedral sites: 2a, 12k, and 4f2
• Trigonal bipyramidal 2b and tetrahedral 4f1 sites only weakly affected
• Unit cell volume decreases with Cr content (rate: -2.80 ų per Cr ion)
• Lattice parameters change linearly with x

Lattice Parameters:

Mössbauer Spectroscopy

• Mean hyperfine fields decrease with increasing chromium content
• Cr$^{3+}$ behaves as a diamagnetic dopant despite having unpaired electrons
• Complex superexchange interactions lead to weak positive $J_{\mathrm{FeCr}} \approx 1$ K
• Quadrupole shift decreases with x, indicating increased crystal field symmetry

Particle Morphology

SEM Analysis:

• All samples contain single-phase M-type hexaferrite
• Particles have plate-like morphology
• Mean particle diameter: 430–1400 nm depending on composition

• Cr introduction significantly increases critical domain size $D_{cr}$
• For $x \geq 1$, particles are in single-domain state

Magnetic Properties

Temperature-Dependent Magnetization:

• Curie temperature decreases linearly with Cr content
• From 740 K ($x = 0$) to 257 K ($x = 8$)
• Sample with $x = 7$ ($T_C = 314$ K) exhibits behavior close to superparamagnetism

Hysteresis Loop Characteristics (300 K):

Key observations:

• Coercivity increases from 4.4 kOe ($x = 0$) to maximum 13.9 kOe ($x = 5.5$)
• For $x > 6$, coercivity drops due to $T_C$ approaching measurement temperature
• $M_R/M_S \approx 0.5$ for single-domain samples (Stoner–Wohlfarth behavior)

Millimeter-Wave Absorption (NFMR)

FMR Frequencies and Parameters:

Key findings:

• NFMR frequency increases from 51 GHz ($x = 0$) to 129 GHz ($x = 5.5$)
• Damping factor $\Gamma$ decreases with x (unusual behavior)
• For $x \geq 7$, no clear resonance due to proximity to $T_C$

Anisotropy Field and Magnetocrystalline Anisotropy

Calculated Parameters:

Mechanism:

• $K_1$ decreases with Cr content
• $M_S$ decreases more rapidly than $K_1$
• Anisotropy field $H_a = 2K_1\rho^{-1}M_S^{-1}$ increases
• Maximum $H_a$ at $x = 5.5$ correlates with maximum $H_C$ and $f_r$

Comparative Analysis: Al vs. Ga vs. Cr Substitution

Comparison at optimal substitution levels:

Key differences:

• Al³⁺: Most effective due to small ionic radius and occupation of 2a and 12k sites (uncompensated spins)
• Cr³⁺: Occupies 2a, 12k, and 4f2; moderate enhancement but narrower FMR lines
• Ga³⁺: Predominantly occupies 4f1, 2a, 12k; least improvement

Advantages of Cr substitution:

• Smaller lattice distortion (Fe–Cr size difference only 5% vs. 17% for Fe–Al)
• Narrower FMR absorption lines (better for applications below 130 GHz)
• Easier to obtain single crystals and epitaxial films with high substitution
• Cr oxide does not enhance glass stability, facilitating incorporation during glass crystallization

DC Spin Current Estimation

• Hexaferrites can generate pure spin currents via NFMR
• $J_S^{DC}$ values up to two orders of magnitude higher than antiferromagnetic $\mathrm{MnF}_2$
• For Cr-series: significant $J_S^{DC}$ for $x \leq 6$ (frequencies 50–130 GHz)
• Promising for sub-THz spintronic devices

Conclusions

The study demonstrates the first systematic investigation of single-domain chromium-substituted hexaferrite particles:

1. Successful synthesis of single-phase $\mathrm{SrFe}_{12-x}\mathrm{Cr}_x\mathrm{O}_{19}$ ($x = 0-8$) submicron particles via citrate-nitrate auto-combustion

2. Anomalous XRD revealed Cr$^{3+}$ predominantly occupies octahedral 2a, 12k, and 4f2 sites

3. Enhanced hard magnetic properties:

   • Coercivity: 4.4 → 13.9 kOe (at $x = 5.5$)
   • NFMR frequency: 51 → 129 GHz (at $x = 5.5$)
   • Anisotropy field: 18.2 → 46.2 kOe (at $x = 5.5$)

4. Mechanism: Cr$^{3+}$ behaves as diamagnetic dopant; $M_S$ decreases faster than $K_1$, leading to increased $H_a$

5. Comparison with Al and Ga:

   • Al: highest $H_C$ and $f_r$ (36 kOe, 250 GHz)
   • Cr: moderate enhancement with narrower FMR lines
   • Ga: least improvement

6. Applications:

   • Rare-earth-free permanent magnets
   • Sub-terahertz spintronics
   • Next-generation wireless communication (6G)
   • Textured ceramics, single crystals, epitaxial films

7. Technological advantages of Cr:

   • Less lattice distortion
   • Easier single crystal growth
   • Better suited for glass crystallization method

Chromium-substituted hexaferrites offer an effective route to enhance hard magnetic properties and high-frequency performance, complementing Al and Ga substitutions for various technological applications.