Broadband Electron Spin Resonance Study in a Sr2FeMoO6 Double Perovskite.

We report broadband magnetic resonance in polycrystalline Sr2FeMoO6 measured over the wide temperature (T = 10-370 K) and frequency (f = 2-18 GHz) ranges. Sr2FeMoO6 was synthesized by the sol-gel method and found to be ferromagnetic below T C = 325 K. A coplanar waveguide-based broadband spectrometer was used to record the broadband electron spin resonance (ESR) both in frequency sweep and field sweep modes. From the frequency sweep mode at fixed dc magnetic fields, we obtain the spectroscopic splitting factor g ∼ 2.02 for T ≥ T C K, which confirms the 3+ ionic state of Fe in the material. The effective g value was found to decrease monotonically with decreasing temperature in the ferromagnetic regime. Resonance frequency decreases and the line width of the spectra increases as the temperature decreases below T C. At room temperature (RT) and above, the line width (ΔH) of the ESR signal increases linearly with frequency, giving Gilbert damping constant α ∼0.032 ± 0.005 at RT. However, at lower temperatures, a minimum emerges in the ΔH vs frequency curve, and the minimum shifts to a higher frequency with decreasing temperature, confining the linear frequency regime to a narrow-frequency regime. Additional inhomogeneous broadening and low-field-loss terms are needed to describe the line width in the entire frequency range.

Introduction

Double perovskites with the general formula A2BB′O6 (A = divalent or trivalent cation; B and B′ = transition metals) are made up of perovskite blocks, where the transition metal ion sites are alternatively occupied by B and B′ ions. They show a number of interesting magnetic and electric properties arising from the band structure and a variety of magnetic interactions between B and B′ ions.[1−4] A2FeMoO6 shows ferromagnetic ordering near and above room temperature (TC = 420, 330, and 320 K for A = Sr, Ba, and Ca, respectively). The discovery of giant magnetoresistance due to tunneling between ferromagnetic grains at room temperature and prediction of half-metallic behavior in Sr2FeMoO6 made this series of double perovskites more popular in recent years.[5−7] Although the origin of ferromagnetism was attributed to the ferromagnetic superexchange interaction between Fe2+ (3d6, S = 2) ions, with Mo6+ (4d0) playing no role in magnetism in earlier studies, later studies favored an interpretation in terms of the ferromagnetic interaction between Fe3+ (3d5, S = 5/2) mediated by the itinerant down-spin t2g1 electron of Mo5+ (4d1, S = 1/2) that couples antiferromagnetically with the up-spin t2g3 electrons of Fe2+ ions.[8,9] Static (dc) magnetization alone does not distinguish between Fe2+–Mo6+ and Fe3+–Mo5+ combinations because both can give a saturation magnetization of 4 Bohr magneton/formula unit. Experiments such as electron spin resonance (ESR), Mossbauer spectroscopy, or X-ray magnetic circular dichroism (XMCD) can be used to probe valance states of the Fe ions.[10] Based on ESR investigations in the paramagnetic state over a wide temperature range (T = 125–560 K), Causa et al.[11] and Niebieskikwiat et al.[12] conclude that Fe exists in the trivalent state and Flores et al.[13] attributed the line width variation to the divalent state of Fe in Sr2FeMoO6. However, these ESR studies were done at a single frequency (f = 9.2 GHz) due to limitations of cavity resonance-based conventional ESR spectrometers.

Sr2FeMoO6, being ferrimagnetic at room temperature and highly spin-polarized, has potential for spintronic applications. Resonant absorption of microwaves at multiple frequencies is essential to extract damping parameters that determine the switching time of magnetization. Motivated by the absence of literature on the dynamic magnetic behavior of Sr2FeMoO6 and lack of ESR work below room temperature, we explore microwave absorption in this compound at different frequencies (f = 2–18 GHz) and over a wide temperature range (T = 390–10 K) using a coplanar waveguide-based spectrometer. This enables us to get an accurate estimation of the gyromagnetic ratio, γ, which is related to the spectroscopic g-factor. γ = (gμB/ℏ), where μB is the Bohr magneton, ℏ is the reduced Planck’s constant, and g is the spectroscopic splitting factor or Lande g-factor. An accurate determination of g is of paramount importance since it is an intrinsic property of the material related to the relative spin and orbital moments.[14] One can also obtain information about spin–orbit interactions,[15] relaxation mechanisms,[16] and damping mechanisms originating from intrinsic or extrinsic considerations.[17]

Here, we have observed that g is not independent throughout the temperature range; it is ∼2.01 at T ≥ TC, and decreases slowly, reaching ∼1.2 at 10 K. Spin relaxation time or damping is found to be intrinsic Gilbert type at T ≥ 300 K and at lower temperatures, extrinsic contributions dominate.

Results and Discussion

Figure shows the powder X-ray diffraction (XRD) pattern of the synthesized Sr2FeMoO6. All peaks can be assigned to the tetragonal crystal structure (space group I4/mmm). The inset shows the low-intensity (101) reflection peak at ∼19.7°, which is an indication of superstructure formation due to Fe and Mo ordering in the alternative sites of Sr2FeMoO6. Rietveld analysis of the XRD data was carried out to find the crystal structure and get a quantitative idea about Fe and Mo occupation factors in the B and B′ sites, respectively. The extracted refined lattice constants of the unit cell (a = b = 5.5882 Å, c = 7.9154 Å, and α = β = γ = 90°) match well with the previous report.[19] Antisite defects or AS defects refer to the presence of B = Fe ions at B′ = Mo positions of the lattice structure and vice versa in the double-perovskite A2BB′O6 structure (A = Sr, Ba, etc.) AS defects are common in double perovskites and are more prominent with decreasing particle size.[19,20] In the present case, the cationic disorder in B and B′ sites is ∼5.6%, which is obtained by varying the occupation of Fe and Mo ions at both B and B′ sites.

Figure 1

Observed and refined room-temperature XRD patterns for the Sr2FeMoO6 sample. The inset shows order-related peak that appear at 2θ ∼19.5°.

The main panel of Figure a shows magnetization (M) measured at H = 1 kOe while cooling from 400 K. Sr2FeMoO6 is a room-temperature ferromagnet with a broad paramagnetic to ferromagnetic transition (TC) occurring at ∼325 K, as suggested by the minimum of the dM/dT curve. TC observed here is lower than the reported value for bulk Sr2FeMoO6; however, it is well comparable with the result reported in thin films deposited on SrTiO3 substrates.[21] Isothermal M–H sweeps at 10 K show a hysteresis loop with small coercivity (HC = 147.5 Oe) and absence of saturation of M even at the highest applied field of 70 kOe (inset of Figure a). It is reported that an antiferromagnetic coupling between the Fe3+ (S = 5/2) and Mo (S = 1/2) sublattices induces a ferrimagnetic half-metallic state with saturation magnetization (MS) of 4 μB.[22,23] Thus, a perfect alternating order of Fe and Mo ions is needed to reach the saturation. In the present sample, the nonsaturation of magnetization might be related to the AS defect (Mo at the Fe site and vice versa), which alters the local interactions and favors antiferromagnetic (AFM) superexchange antisite interactions (Fe–O–FeMo or Mo–O–MoFe).

Figure 2

Temperature dependence of (a) magnetization (M) in a magnetic field of H = 1 kOe and (b) resistivity (ρ) for H = 0 kOe. (c) Field dependence of ρ at T = 10 and 325 K. The inset of (a) shows the magnetic field dependence of M at 10 K and (b) ln(ρ) vs 1/T plot. The solid line shows the fitted curves.

Several experimental and theoretical studies demonstrated the possible relation between the magnetic parameters (TC and MS) and the structural off-stoichiometry (i.e., Fe, Mo, and O vacancies and AS disorder) in double perovskites.[18,21,24−26] Alonso et al. elaborated that with an increase in the antisite defect density (y), MS decreases at a rate of (4.0–7.7y)μB, where y is the antisite concentration, but TC tends to increase due to the direct AFM interaction between neighboring Fe ions. Similarly, oxygen nonstoichiometry influences the magnetic parameters M and TC differently; an increase of oxygen vacancies in Sr2FeMoO6 lowers the magnetization value but increases the later.[21,27,28] Hoffmann et al. found that TC increased at a rate of +15 K per atom % of oxygen vacancies.[28]

Since magnetization is not saturated at 70 kOe, we can obtain an approximate value of MS from the law of approach to saturation (LOAS) given by the equationwhere the parameters a and b are related to the microstress and the first-order magnetocrystalline anisotropy coefficient (K1), respectively, and χH represents forced magnetization in the system. The anisotropy field (Hk) can also be estimated from the fitted parameter b using the equations and. The estimated values of MS and Hk are 2.6μB/f.u. and 1.09 kOe, respectively. Although the MS value observed here is significantly lower than the expected MS of the bulk material, it is comparable with the value reported for Sr2FeMoO6 prepared by the same technique[19] and the obtained TC is still favorable for the application purpose.

The temperature dependence of the resistivity (ρ) of Sr2FeMoO6 shows a semiconducting nature (Figure b). ρ(T) increases monotonically with decreasing temperature and a rapid increase occurs below 20 K. The estimated activation energy, obtained from the fitting of the ρ(T) curve with the Arrhenius equation (ρ = ρ(0) exp (−Ea/kBT)) in the temperature range T = 290–390 K, is Ea ∼ 85.67 meV (inset of Figure b). Magnetoresistance (MR) is obtained from the standard definition −MR% = [{(ρ(H) – ρ(0)) × 100}/ρ(0)], where ρ(H) and ρ(0) are the resistivities at H and the 0 kOe magnetic field, respectively. At 10 K, Sr2FeMoO6 shows negative MR with an absolute value of 10.3% in a magnetic field of 70 kOe, whereas MR is negligibly small (∼0.7% at 70 kOe) at TC (325 K) as shown in Figure c. The MR at low fields (<1 kOe) is due to tunneling between ferrimagnetic grains and linear MR at higher fields is most likely due to scattering by disordered spins at the grain boundaries.[1,2]

Figure a shows the magnetic field-dependent resonance spectra, plotted as the field derivative of power absorption (dP/dH) measured at a fixed frequency f = 9 GHz for different temperatures. At 370 K, the spectra are a single Lorentzian type. As the temperature decreases, the intensity of the dP/dH spectra reaches a maximum at 325 K, which indicates the change in the magnetization states. The intensity of the signal again decreases below TC and dP/dH is dominated by noise below 50 K.

Figure 3

(a) Magnetic field dependence of the resonance spectra plotted as the derivative of the absorbed power (dP/dH) at different temperatures, (b) Lorentzian fit of the dP/dH line shape taken at T = 300 and 350 K, and (c) variation of line width (ΔH) and resonance field (Hres) with temperature.

The spectra were fitted to a linear combination of symmetric and an antisymmetric Lorentzian function (Figure b) given bywhere Hres, ΔH, and C are the magnetic resonance field, peak-to-peak line width, and offset, respectively. An example of the fit is shown for 300 and 350 K in Figure b. The above equation is equivalent to the Dysonian equation, frequently used to fit the ESR data for conducting samples.[29] The extracted Hres and ΔH are summarized in Figure c. Two observations are evident. First, Hres is nearly temperature independent in the paramagnetic state but shifts to a lower field as the temperature decreases below TC. The decrease of Hres is due to the continuous increase in the effective internal fields, such as the anisotropy and saturation magnetization. Second, the variation of the line width ΔH (T) value closely follows M(T). Above TC, ΔH shows an increasing trend, whereas Hres remains almost constant. A similar trend in ΔH(T) was also observed in Ba2FeMoO6,[30] where the temperature variation of the line width also does not show any peak below TC as the temperature decreases to 50 K. The presence of a maximum in ΔH(T) would indicate an electronic conduction process between the multivalence Fe3+–Fe2+ ions. Fe2+ ions with a nonzero orbital momentum open up an additional slow-relaxation process in the crystal structure and give rise to a characteristic maximum in the ΔH(T) curve due to direct phonon modulation or indirect magnon modulation.[16] The absence of maximum in ΔH(T) confirms the absence of Fe2+ ions in our sample.

Broadband ferromagnetic resonance (FMR) spectra for multiple frequencies (f = 2–18 GHz) at selected dc magnetic fields were measured to calculate the gyromagnetic ratio (γ). Since γ = gμB/ℏ, we can obtain the spectroscopic splitting factor or “Lande g-factor” of the material. Figure a shows the frequency derivative of the power absorption (dP/df) at room temperature as a function of the frequency of the microwave signal. The zero-crossing point of the spectrum can be identified as the resonance frequency (fres). We can see that fres increases with increasing strength of the static magnetic field. The recorded power absorption vs frequency pattern was fitted with the same Lorentzian equation (eq ) to accurately determine fres for all Hdc at temperatures down to 10 K (fitting is shown by the solid lines in the same figure).

Figure 4

(a) Room-temperature spectra recorded as a function of the frequency of microwave excitation under different static magnetic fields (Hdc = 1–5 kOe) and (b) Kittel fit to the fres vs Hdc parameters obtained from the dP/df line shape analysis; the inset shows the temperature dependence of the effective g factor (geff) of Sr2FeMoO6.

Once the resonance frequencies are extracted for different fields and temperatures, fres vs Hdc is plotted in Figure b. fres(Hdc) is linear above TC; however, as we cool down the sample, fres(Hdc) shows a continuous change in the slope. Nonlinearity increases as temperatures is lowered much below TC. These curves were fitted with Kittel’s expression for in-plane FMRwhere Meff is the effective magnetization. At T ≥ TC K, the extracted value of γ/2π (∼2.83 MHz/Oe) corresponds to a g factor of 2.02, which suggests the presence of paramagnetic Fe3+ ions.[12] It also confirms that no Fe2+ ions were probed in the FMR measurement as the g value expected from the band calculation of the localized Fe2+ (3d6) ion is much higher (g ≈ 3.4).[9] Tovar et al.[9] suggested that the itinerant electrons of both Fe and Mo as well as the localized core spins of Fe3+ contribute to the effective g-factor in Sr2FeMoO6. In the paramagnetic region, they found g = 2 for the localized and delocalized spins for Fe3+ and they are temperature independent. However, we find that the extracted value of effective g factor (geff) is not temperature independent in the magnetically ordered state; geff decreases slowly below TC as shown in the inset of Figure b. This change in geff possibly arises from spin–orbit or crystal fields affecting the localized electrons, as geff = g (1 ± κ/Δ), where Δ is the crystal-field splitting and κ is the spin–orbit coupling constant.[31]

We have also collected dP/dH spectra as a function of the dc magnetic field for selected frequencies in paramagnetic and ferromagnetic regions. The resonance conditions obtained here match nicely with the frequency sweeps described earlier. We employ the same method of Lorentzian function fitting to identify the parameters, Hres and ΔH. Figure a shows the acquired data points and the corresponding fitting for T = 300 K. Hres decreases monotonically with decreasing frequency of the microwave field from 15 to 3 GHz. The evolution of ΔH with frequency for temperatures 10–100 and 150–350 K is shown in Figure b,c, respectively. The line width linearly varies with frequency from 350 to 200 K; however, the line width for a particular frequency increases with a decrease in temperature.

Figure 5

(a) Dependence of the ESR signal at room temperature as a function of the dc magnetic field for different frequencies of spin excitation (f = 3–15 GHz). Scattered data points in (b) and (c) show the variation of ΔH with frequency at temperatures between T = 10–100 and 150–350 K, respectively. Solid lines represent the fitted curves (details provided in the text).

According to the Landau–Lifshitz–Gilbert (LLG) model of spin relaxation, the intrinsic line width is proportional to the frequency and is given bywhere α is the unitless Gilbert damping parameter that contains both the intrinsic and extrinsic contributions and ΔH0 is a frequency-independent extrinsic factor attributed to inhomogeneous line width broadening. At 350 K, ΔH follows the LLG model and gives an intrinsic value of α ∼ 0.115 (±0.003). The slope of the linear ΔH vs f curve is higher at 350 K than at 325 and 300 K. We estimate α ∼ 0.032 ± 0.005 at room temperature and it is three orders of magnitude higher than the damping factor obtained from the angular dependence study of a Sr2FeMoO6 thin film.[6] As shown in the figure, ΔH shows Gilbert-like damping at temperatures below but close to TC. Interestingly, far below the room temperature, the damping parameter could not be extracted using eq as ΔH(f) shows a minimum and linearity is confined to a narrow-frequency range above the minimum. The frequency at which the line width shows a minimum increases with decreasing temperature. While the minimum occurs at 6 GHz when T = 200 K, it occurs at 15 GHz when T = 10 K. It has been reported that the FMR line width is enhanced at low frequencies due to a nonuniform magnetization distribution or spatial inhomogeneities in the magnetic property apart from field fluctuations and magnetic noise.[32,33] Hence, an additional power-law term of the excitation frequency is added to eq to ΔH fittingThe last term in eq is usually neglected in FMR studies since line width is reported mostly for the applied field greater than the anisotropy field. We obtain β = 1 at 200 K and its value increases to 4 for 10 K. This indicates the growing contribution of low-field losses in Sr2FeMoO6. As observed in the magnetization results (M(H) at 10 K), the saturation is not achieved even at 5 T field at low temperature due to the presence of AS defects in the lattice.

Conclusions

We have investigated the magnetic resonance over a frequency range of 2–18 GHz in polycrystalline Sr2FeMoO6. Our results indicate that the Lande g-factor is ∼2.02 in the paramagnetic state corresponding to the presence of an Fe3+ ion and it decreases with decreasing temperature in the ferromagnetic state. The resonance field smoothly decreases, and the line width increases with decreasing temperature in the ferromagnetic regime. ΔH obtained from the dc magnetic field swept shows linear growth with frequency at T ≥ 300 K in agreement with Gilbert damping, whereas below that temperature, the nonlinear behavior of ΔH vs f indicates the existence of multiple damping factors in the composition. These findings highlight a major difference in the information that can be obtained from a cavity resonance technique reported before and a broadband technique employed here.

Experimental Details

Sr2FeMoO6 was synthesized by the sol–gel reaction method using high-purity Sr(NO3)2, Fe(NO3)3·9H2O, and MoO2 powders. Stoichiometric amounts of the salts were well mixed in an aqueous solution of 1 M citric acid at 60 °C to prepare the sol. At 80–90 °C, the sol changed to a thick gel, which was dried at 200 °C for a day. Later, the precursors were kept at 500 °C for 4 h in air to decompose. A finely ground powder was further annealed at 800 °C for 10 h in air. Finally, the pelletized sample was annealed at 1200 °C for 6 h in a slightly reducing atmosphere (5% H2 + 95% Ar), which is necessary to avoid molybdenum evaporation and limit the concentration of the antisite defects in Sr2FeMoO6.[18][18] Crystalline structure analysis of the double perovskite was performed using a Philip’s X’PERT MPD powder X-ray diffractometer with a Cu Kα (1.542 Å) radiation source. Magnetization measurements were performed using a physical property measuring system (PPMS), equipped with a vibrating sample magnetometer. The frequency and magnetic field dependence of the derivative of microwave power absorption of a 4 × 4 × 1 mm3 pellet were measured using a broadband ferromagnetic resonance spectrometer (NanOsc Phase-FMR from Quantum Design Inc.) that makes use of the coplanar waveguide method. The flow of microwave (MW) current in the coplanar waveguide creates a magnetic field (HMW) perpendicular to the direction of the MW current and the dc magnetic field provided by the superconducting coils in the PPMS. Thus, the dc and MW magnetic field configurations are similar to those in a conventional microwave cavity-based electron spin resonance spectrometer. The field and frequency swept resonance spectra at room temperature were also repeated for the sample in the powder form, and the resonance fields and line widths were found to be identical for both bulk and powder samples, which suggests that the microwave penetrates through the bulk of the sample.