Rare earth doped M-type hexaferrites; ferromagnetic resonance and magnetization dynamics

The vast applications of Barium hexaferrite (BaM) cover almost all the branches of science. In chemical sensing,¹ biomedical applications² and microwave device designing (filters, circulators, and phase shifters etc)^3,4 they play an important role. The M-type hexaferrite has hexagonal symmetry with space group p63/mmc. In its pure form, BaM has a large uniaxial anisotropy, high saturation magnetization, and very large coercive field. These extreme properties present the scope of modulation in magnetic properties of BaM and thus make it a material of choice for a diverse range of microwave applications.

Ferromagnetic resonance (FMR) is an important technique for microwave device designing and material characterization. The broad FMR linewidth and high resonance frequency (more than 50 GHz⁵) of BaM make it undesirable for a sensitive narrow-band filter in the lower microwave spectrum. Substitution of the rare earth elements (Samarium and Neodymium) due to their typical relaxation mechanism can alter the electromagnetic response of hexaferrite material.⁶ Many studies on rare earth doped BaM are centered only on improving the magnetic properties and this was generally achieved by simultaneous substitution of multiple dopants. This makes the structure complex and difficult to synthesize. Most of the studies of rare earth doped BaM in high-frequency band devoted to its microwave absorption property.^7,8 Almost all these studies are lacking investigation in magnetization dynamics and relaxation mechanism. We have synthesized samarium (Sm) and neodymium (Nd) doped barium hexaferrite nanoparticles (NPs) with cobalt as a base dopant. Detailed analysis has been carried out on their relaxation mechanism and magnetization dynamics. The FMR linewidth variation with frequency was fitted with Landau–Lifshitz–Gilbert damping models to find the damping parameters. The damping parameters play an important role in designing magnetic devices and sensors.⁹ The operating frequency of the doped hexaferrites was lowered down from 51 GHz (pure BaM) to 18 GHz for rare earth doped ferrite at around 9 KOe bias magnetic fields.

The nitrate salts of Barium (Ba), Iron (Fe), Cobalt (Co), Samarium (Sm) and Neodymium (Nd) of Sigma Aldrich (99.9%) were used in the present study. Nitrates of barium and iron were dissolved (Ba:Fe=1:12) in 0.6M of 30ml HCl (hydrochloric acid) solution. The nitrate salts of dopants (Co, Sm, and Nd) were dissolved in another 0.6M 10ml solution of HCl. A solution containing dopant was added drop wise into BaM solution. The solution was precipitated using 150ml of 5M NaOH solution. The settled-down brown slurry was treated hydrothermally at 150⁰ C for 15 hours. Thereafter, the slurry was centrifuged using deionized water (DI) and ethanol until its pH reached ∼7. The wet slurry was dried on a hot plate and the dry powder was calcined at 1000⁰C for 4 hours to get pure phase NPs. Four different samples: S1(BaFe₁₂O₁₉), S2(BaCo_0.5Fe_11.5O₁₉), S3(BaCo_0.5Nd_0.3Fe_11.2O₁₉) and S4(BaCo_0.5Sm_0.3Fe_11.2O₁₉) were prepared using above mentioned method.

X-ray diffraction (XRD) of powder samples was performed at room temperature using Cu-K_α radiation (λ= 1.5418A) in Miniflex Rigaku instrument. The magnetic characterization was done at room temperature using vibrating sample magnetometry in Physical Property Measurement System (PPMS) from Cryogenic Ltd.

The FMR experiments were done using a broad-band FMR system in transmission mode with a frequency range from 16 to 30 GHz and magnetic field from 0 to 15 kOe. To do this, we have coated the nanoparticles of prepared samples (S2, S3 and S4) by electrophoretic deposition (EPD) method directly on top of the coplanar waveguide.¹⁰ The scattering parameter (S₂₁) were recorded from the vector network analyzer (PNA-N5224A) for each field-sweep at a fixed frequency to derive resonance field (H_r) and resonance linewidth (ΔH) from the absorption data.

The XRD patterns of doped BaM are shown in Fig. 1(a). All the peaks are indexed using data from pure BaM (JCPDS file no. 84-0757). The pattern shows that the rare-earth dopants arranged themselves in the crystal lattice without disturbing the hexagonal structure of barium hexaferrite.

The room temperature magnetic hysteresis (M-H) curves for rare-earth doped Barium hexaferrite (BaM) are shown in Fig. 1(b). In the present investigation, values of both saturation magnetization (M_s) and coercivity (H_c) of hexaferrites decrease with the substitution of rare earth dopants. This is in agreement with earlier reported studies.^11,12 The substitution of only cobalt atom leads to the decrease in M_s from 74.5 emu/g to 53.6 emu/g. M_s further reduced to 47.62 emu/g with the doping of Nd ions with cobalt. But the addition of samarium (Sm) along with cobalt enhances both M_s and H_c to 66 emu/g and 2.37 kOe, respectively. A slight kink in the M-H loop of Sm doped BaM could be due to the presence of some impurity phases. Values of M_s and H_c of all the four samples obtained from VSM data are shown in the bar graph of Fig. 1(c). The bar graph is a visual representation of sample-wise derived M_s and H_c data from Fig. 1(b).

Room temperature fixed frequency FMR Measurements were performed in field sweep mode. Fig. 2(a) shows the FMR spectra in field sweep mode for sample S3(BaCo_0.5Nd_0.3Fe_11.2O₁₉). The resonance field (H_r) and corresponding linewidth (ΔH) at each operating frequency are derived from the calibrated S₂₁ experimental data. For all the doped samples (S2, S3 and S4), the resonance field increases with the increase in operating frequency. Fig. 2(b) shows the ensemble of the resonance fields (H_r) from Fig. 2(a) as a function of frequency. Fig. 2(b) also shows that at a particular frequency, the resonance field is highest for the Sm-doped hexaferrite (S4) and lowest for cobalt doped hexaferrite (S2) without rare-earth substitution. For a nanoparticle, the effective magnetic field (H_eff) is given by;

H_eff consist of H_D (demagnetizing field), H_a (Anisotropy field) and H_int (interaction field). The experimental data points are fitted with FMR resonance relation for spherical nanoparticles by using the following relation;¹⁰ 

where ω (=2πf) denotes the Larmor precession frequency, γ is the gyromagnetic ratio. In equation (2), the internal field $Hint=2mr3,$ where m (magnetic moments) and r (inter-particle distance). As seen in Fig. 2(b) sample S2(BaCo_0.5Fe_11.5O₁₉) has the lowest H_r. This could be attributed to the smaller interparticle distance of S2 in comparison to S3 (S3 has lower Ms than S2) which causes H_int to increase for S2. Hence resonance field for S2 become smaller than S3.

Fig. 3 shows the FMR linewidths of samples S2, S3 and S4. The observed FMR linewidths are broad, which is a normal feature of hexaferrites. But with the substitution of cobalt as well as rare-earth ions, linewidth reduces. The observed linewidth is a combination of intrinsic as well as extrinsic contributions to linewidths. Such linewidth responses are often interpreted in terms of a combined inhomogeneous broadening and Landau-Lifshitz-Gilbert (LLG) damping model. The experimental value of Gilbert damping parameter α can be deduced from the FMR linewidth ΔH as;¹⁰ 

where ΔH₀ is the linewidth at zero frequency - a measure of the inhomogeneous broadening (extrinsic contribution to linewidth). α is the parameter (slope of eq. (3)) which determines how the linewidth changes with frequency. The fitting of experimental data to the phenomenological LLG-expression is shown as dotted lines in the graphs of Fig. 3.

The fitting to eq. (3) produce a linear dependence of linewidth to frequency. A careful observation of experimental ΔH values indicated that there is a downward curvature in the high frequency values. To understand the down-ward curvature in high frequency region, we have employed model II (nonlinear) to fit the data points. As proposed by Bastrukov et al.,¹³ “The origin of the damping torque responsible for spin relaxation in multilayered metallic films is attributed to the coupling between the uniformly precessing magnetization-vector and the stress-tensors of intrinsic and extrinsic magnetic anisotropy.”

Bastrukov et al.¹³ discussed a model referred as modified-LLG model that considers both intrinsic and extrinsic damping torques. The intrinsic contribution refers to the fundamental physics of the material system whereas extrinsic damping occurs due to additional contributions such as defects and inhomogeneities in the physical system. Hence, the modified-LLG model is given as:

where α′ is the intrinsic damping parameter and β′ contributes to the extrinsic damping parameter. Both are used as empirical fitting parameters in eq. (4). The inhomogeneities and defects cause the actual FMR linewidth increase which is reflected from the values of β′. γ′ is the gyromagnetic ratio. Solid curves in Fig. 3 show the linewidth data fitting with equation (4). All the parameters obtained from VSM and FMR are shown in Table I.

We have determined numerical relaxation parameters using the above two fitting models. Model-I: The zero-frequency offset (extrinsic part) ΔH₀ is measured to be highest for S4. The value of Gilbert damping (α) increased from 3.48×10^-2 for S2 to 7.61×10^-2 for sample S4. From Fig. 3 it is shown that the inclination of the line S4 is much steeper than S2. This is because the slope of eq. (3) $αγ$ is 0.026 for S4, whereas it is half (0.012) for S2. The value of γ is almost independent on doping. Model-II: Similarly, fitting of experimental linewidth data to eq. (4) we have derived another set of relaxation parameters; ′, β′, γ′ for the samples S2, S3 and S4. The intrinsic (α′) Gilbert damping found to increase from 1.76×10^-2 for S2 to 6.14×10^-2 for S4. The extrinsic (β′) Gilbert damping is highest for S3 (6.11 × 10⁻²) and lowest for S2 (2.58 × 10⁻²). We have computed γ (gyromagnetic ratio) using both models 1 and model 2. We have used γ and γ′ as a fitting parameters while using eq. 3 and eq. 4. There is a slight variation (within ±5% error limit) in these two values obtained from both models. This can be treated as within experimental error limits. As observed above, rare-earth ions substitution in BaM induced an increased Gilbert damping.

The rare earth (Nd and Sm) doped M-type hexaferrite were successfully synthesized using the hydrothermal method. XRD and VSM results show the crystallization of the ferrite without any deviation from the hexagonal phase after substitution of the dopants ions. The saturation magnetization (M_s) decreased from 73.2 emu/g for (S1) pure BaM to 45.4 emu/g for S3(BaCo_0.5Nd_0.3Fe_11.2O₁₉). The doped samples (S2, S3 and S4) show resonance behavior from 16GHz to 30GHz, which is much lower than pure phase BaM. The resonance field (H_r) and linewidth (ΔH) data were fitted using two different analytical models. The fitting yields various intrinsic and extrinsic damping parameters. These parameters provide an insight of the damping mechanism in the material that is important in designing microwave devices.

The grant support of MHRD – IMPRINT India (Proposal Number: 7519), DST India through DST-Nano-mission and Purse-grant and UPOE-II are highly acknowledged.