High-frequency magnetotransport in La_1-xSr_xMnO₃ (x = 0.12-0.20)

Among Mn perovskites exhibiting colossal magnetoresistance, La_1-xSr_xMnO₃ series has been thoroughly investigated and its structural and magnetic phase diagrams have been established.^1–5 The insulating antiferromagnetic LaMnO₃ transforms into a metallic ferromagnetic for 20 to 50% of Sr²⁺ substitution at the La³⁺ sites. The substitution of divalent strontium for trivalent lanthanum cation converts equivalent fraction of Mn³⁺(d⁴) ions into Mn⁴⁺(d³) ions and dopes holes in the conduction band. Doped holes mediate ferromagnetic interaction between neighboring Mn³⁺ and Mn⁴⁺ ions. The ferromagnetic Curie temperature initially increases with Sr content, reaches a maximum value (∼378 K) for x = 0.33 and then declines. Simultaneous occurrence of ferromagnetism and metallic conductivity in these manganites are explained by Zener’s double exchange interaction: A large intra-atomic Hund’s exchange coupling aligns e_g electron spin (S =1/2) of Mn³⁺: (t_2g³e_g¹) ion parallel to the localized t_2g spin (S = 3/2) of the same ion.⁶ Since electrical conduction in these compounds is due to spin-polarized motion of e_g-hole along the Mn⁴⁺: (t_2g³e_g⁰)-O^2--Mn³⁺: (t_2g³e_g¹) network in the background localized t_2g³ spins, it is fundamental interest to explore and understand how high frequency electric current affect the electrical resistivity and magnetoresistance. While extensive studies are available on dc electrical resistivity of these compounds, not many studies are available on the electrical properties in MHz and GHz range. Lofland et al.⁷ studied electron spin resonance in single crystals La_1-xSr_xMnO₃ (x= 0.1, 0.2, and 0.3) above the ferromagnetic transition using a cavity resonance spectrometer operating at a fixed microwave frequency (f = 9.8 GHz). Belozorov et al.⁸ reported double negative refraction (left-handed property) in polycrystalline La_1-xSr_xMnO₃ (x = 0.15-0.6) in the frequency range f = 20-40 GHz using microwave transmission technique. Atsarkin et al. reported induction of a dc voltage in La_0.7Sr_0.3MnO₃ thin film during ferromagnetic resonance (f = 9.8 GHz) when the thin film sample was microwave irradiated inside a resonant cavity.⁹ Instead of using a resonant cavity, we studied magnetoresistance in La_1-xSr_xMnO₃ samples (x = 0.20, 0.18, 0.12) by passing alternating current of frequencies from f =30 MHz to 3000 MHz directly through the samples and measured their magnetoresistance using a radio-frequency impedance analyzer.

Bulk polycrystalline samples of La_1-xSr_xMnO₃ (x = 0.12, 0.18, and 0.20) were prepared by standard solid state reaction route. The samples were characterized by X-ray diffraction at room temperature and found to be single phase possessing orthorhombic structure. Four probe dc electrical resistivity and magnetization were measured using a physical property measuring system (PPMS) and a vibrating sample magnetometer probe attached to the PPMS. High-frequency resistance of these samples in the frequency range f = 30 MHz to 3 GHz was measured at room temperature using a single port Agilent E4991A rf impedance analyzer. The sample was attached to the probe stage (16454A) using thermally conductive grease (GE-varnish^TM) and a kapton tape electrically insulated the sample from ground. One end of the sample was connected to the signal line of the probe through which rf current was injected into the sample while the other end was connected to the ground plane using silver paint. A computer-controlled electromagnet was used to apply a dc magnetic field along the direction of rf current flow in the sample. Further experimental details can be found in Ref 15. In the configuration we have used, a rf magnetic field created by the rf current in the sample is perpendicular to the applied magnetic field. We define magnetoresistance (MR) as MR = [R(H, f)-R(H= 0, f)]/R(H= 0, f), where R is the measured ac resistance at a frequency (f) in the presence of magnetic field (H). dc MR represents magnetoresistance for f = 0 and ac MR stands for MR at a frequency f.

Fig. 1(a) shows the temperature dependence of magnetization (M) of La_1-xSr_xMnO₃ for x = 0.12, 0.18, and 0.20 samples while cooling from 400 K under a magnetic field of H = 1 kOe. The paramagnetic to ferromagnetic transition is characterized by a rapid increase of M(T) at the ferromagnetic Curie temperature (T_C), which is extracted from the inflection point of dM/dT curve in each sample. We obtained T_C = 306, 292 and 239 K for x = 0.20, 0.18 and 0.12, respectively. The inset shows M vs H curves for all three samples at 300 K. The M(H) curve of x = 0.20 reflects its soft ferromagnetic nature, while M increases linearly with H in the entire field range for x = 0.12 due to its paramagnetic nature. On the other hand, M(H) of x = 0.18 shows nonlinear field dependence in low magnetic fields and a linear field dependence at higher fields. Neither hysteresis nor remenance was found while cycling the field direction for x = 0.18 and 0.12. The low-field non-linear behavior seen in x = 0.18 may indicate the presence of short-range correlations among Mn-spins above T_C

The magnetic field dependence of dc MR for all the three samples in the field range -20 kOe ≤ H ≤ 20 kOe are shown in Fig. 1(b). All three samples exhibit negative magnetoresistance, i.e., dc resistance decreases upon application of a magnetic field. The dc MR for x = 0.12 varies as ∼-H² in the measured field range. However, the field dependence of dc MR of x = 0.18 and 0.20 look alike and differ from x = 0.12. The magnitude of dc MR at 20 kOe increases from ∼4.9% for x = 0.12 to ∼17.5% for x = 0.2. Fig. 1(c) shows the field dependence of the ac MR at f = 30 MHz in a field regime (-3 kOe ≤ H ≤ 3 kOe) smaller than in Fig. 1(b). We can notice that magnitude of the ac MR is greatly enhanced in all three samples (∼21% for x = 0.20 and ∼10% for x = 0.18 at 3 kOe). Also, the ac MR shows a rapid increase in low-fields (-0.5 kOe ≤ H ≤ 0.5 kOe) in both x = 0.18 and 0.20, and the change is larger in x = 0.2.

We compare the field dependence of the ac MR for all the three samples in Fig. 2 at four selected frequencies: (a) f = 500, (b) 1000, (c) 2000 and (d) 3000 MHz for magnetic fields up to H= ±3 kOe at room temperature. We have shown the data as the field is swept from +3 kOe to -3 kOe. We did not find hysteresis while cycling the field in forward and reverse directions. The ac MR at f = 500 MHz is negative in all the three samples and the absolute value at 3 kOe is the highest (∼40%) for x = 0.2. While the ac MR curve in each sample shows a single peak at H = 0 at f = 500 MHz, a peak develops away from the origin on either side of the origin at H = ±H_r for f = 1000 MHz, leading to a double peak structure. As the frequency is increased further to 2000 MHz and 3000 MHz, the field H = ±H_r corresponding to this double peak also increases. Also, the sign of the ac MR at 3 kOe changes depending on the frequency and composition. For example, the ac MR is positive in all the samples at 3 kOe for f = 3000 MHz. While the ac MR for x = 0.2 at 3000 Hz is positive in the entire field range, it is negative as the field is increased from zero to a certain value (∼860-890 Oe) in lower compositions and becomes positive as the field is increased further. When f = 2000 MHz, the ac MR in x = 0.2 changes from positive for H < 1.8 kOe to negative at higher fields. As we will see at the discussion part, H_r is identified as the resonance field for electron spin resonance of Mn ions. A double peak feature was also found by us earlier in La_0.6Ca_0.4MnO₃ and Ca doped La_0.7Sr_0.3MnO₃ and it appears to be intrinsic behavior though its magnitude and the field position on the hole-content or magnetization yet to be fully understood.¹⁰ 

The observed features in the ac MR are most likely due to consequence of magnetization dynamics in the sample. The flow of an rf current generates an oscillating magnetic field transverse to the direction of current flow in the sample which makes localized t_2g spins to oscillate. Since the applied dc magnetic field is orthogonal to the rf magnetic field, resonance can be induced when the energy of rf magnetic field matches with Zeeman splitting. Hence, rf power is absorbed by the sample from the rf field causing the ac resistance to increase. Hence, the field dependence of ac resistance may show a peak value at the resonant field and decreases as H exceeds the resonance field. In a ferromagnetic or paramagnetic insulator, the rf power absorption (⁠$P∝ωHrf2μ″$⁠) is proportional to the imaginary part of the high frequency permeability (μ″), angular frequency of the rf field (ω), and square of the amplitude of the rf magnetic field (⁠$Hrf2$⁠). The samples discussed here are not insulators but have resistivity of the order of a few mΩ cm at room temperature. Hence, the skin effect is non-negligible as the frequency increases. The cross sectional area for the rf current flow and the penetration of rf magnetic field within the sample diminishes with increasing frequency of the current. In the strong skin depth regime, the surface impedance of a metallic conductor can be written as $Z=iωρμ∝ωρμR+iμX$ where μ_R and μ_X are “resistive” and “reactive” relative permeabilities and they are given by $μR=μt+μt′′$ and $μX=μt−μt′′$⁠, where μ_t′ and $μt′′$ describes the in-phase and the out-of phase components of transverse permeability and $μt=μt′2+μt″2$⁠.^11,12 Thus, the high-frequency resistance or magnetoresistance is influenced by the frequency and field dependence of μ_R⋅

Hence, we attempt to fit the resistance ratio R(H)/R(0) to Eq. 1 which contains both a symmetric Lorentzian term and a dispersive asymmetric term for x=0.12 and 0.18.

where A_sym and A_asym are the frequency dependent magnitudes of the symmetric and asymmetric dispersive components of the signals and B is a constant offset. The data and the fits for x = 0.12 and 0.18 are shown in Fig. 3(a) at room temperature and f = 3000 GHz. From these fits, linewidth (∆H) and resonance field (H_r) were extracted. Since x = 0.20 showed a very broad linewidth, the data could not be fitted satisfactorily with Eq. 1 and hence we do not show the fit. In Fig. 3(b), we plot H_r for x = 0.12 and 0.18 obtained from the fits as a function of frequency f. We can see that resonance field increases linearly with increasing frequency for x = 0.12 and 0.18 for f above 0.9 GHz. It is known that H_r for electron spin resonance is expected to vary linearly with the frequency of rf magnetic field as:

where γ is the gyromagnetic ratio (γ = gμ_B/ℏ, g is the Landé g-factor, μ_B is the Bohr magneton and ℏ is the reduced plank’s constant). From the slope of the line, we obtain γ/2π = 2.428 MHz/Oe and 2.690 MHz/Oe for x = 0.18 and 0.12 respectively. The extracted γ/2π value for x = 0.18 sample, in comparison to x = 0.12, is significantly smaller than 2.8 MHz/Oe for free electron with spin only contribution. This could be due to the presence of superparamagnetic clusters as suggested by M vs H curve in the inset of Fig. 1. Since our attempt to fit the line shape of x = 0.2 with Eq. 1 was not successful, we do not show H_r versus f data for this sample.

In summary, the high-frequency magnetoresistance spectra in La_1-xSr_xMnO₃ series in GHz range resemble that of electron paramagnetic resonance in x = 0.12 and 0.18. Future work should address the limitations and viability of this technique for other materials.

R. M. thanks the Ministry of Education, Singapore for supporting this work (Grant numbers R144-000-381-112 and R144-000-422-114).