Microwave magnetoimpedance and ferromagnetic resonance in Pr0.6Sr0.4MnO3

We report the magnetic field dependence of electrical impedance (magnetoimpedance) of a ferromagnetic Pr0.6Sr0.4MnO3 sample carrying alternating current (ac) of frequency f = 1 MHz to 3 GHz measured using an impedance analyzer and broad band ferromagnetic resonance (f = 2 to 18 GHz) measured using a coplanar wave guide based spectrometer. Ac magnetoresistance is much larger than dc magnetoresistance and its sign at low magnetic fields changes from negative to positive with increasing frequency of the ac current. The field dependence of ac magnetoresistance shows a peak around Hdc = 0 for low frequencies but a double peak feature emerges at Hdc = ±Hp at higher frequencies and it shifts to higher magnetic field as the frequency of ac current increases. The field derivative of microwave power absorption measured by the broad band spectrometer shows features of ferromagnetic resonance and the resonance field increases with increasing frequency of microwave radiation following Kittel's equation for ferromagnetic resonance. A close correlation is found between the ferromagnetic resonance line shape and the positive peak in the ac magnetoresistance, which suggests the possibility of electrical detection of ferromagnetic resonance using high frequency current injected into a conducting magnetic sample.


Introduction
The Mn-based perovskites known as manganites (R 1Àx A x MnO 3 where R ¼ La 3+ , Pr 3+ , etc., and A ¼ Sr 2+ , Ca 2+ etc.) have been extensively studied over the last three decades because of the two most exciting physical phenomena exhibited by them: colossal negative magnetoresistance for lighter rare earth ions (R ¼ La, Pr, Nd) 1,2 and spin-driven ferroelectricity in parent RMnO 3 for heavy rare earth ions (R ¼ Tb, Tm, Y). 3 Parent compounds (RMnO 3 ) possessing only Mn 3+ ions are antiferromagnetic insulators whereas divalent cation substituted compounds containing mixed valent ions (Mn 3+ : t 3 2g e 1 g and Mn 4+ : t 3 2g e 0 g ) are ferromagnetic metals for x ¼ 0.2-0.45 and antiferromagnetic insulators for 0.5 # x # 1 for R ¼ La. The compositional range for ferromagnetism shrinks and ferromagnetic Curie temperature decreases as the ionic radius of R ion decreases. The inuence of magnetic eld on resistivity is greatest at the paramagnetic-ferromagnetic phase boundary. Majority of available studies focused on the magnetoresistance measured with a direct-current (dc) owing in samples. Magnetoresistance in response to an alternating current (ac) through the sample barely received attention despite some claims of remarkable enhancement in the magnitude of ac magnetoresistance in the radio frequency regime (f ¼ 1-15 MHz) compared to dc magnetoresistance in a eld of few hundreds of Oersted. [4][5][6][7][8] Such a large enhancement in the ac magnetoresistance with alternating currents has potential for practical applications compared to the dc magnetoresistance if the low-eld sensitivity can be further improved.
Since hopping of the e g electron between Mn 3+ (t 3 2g e 1 g ) and Mn 4+ (t 3 2g e 0 g ) via the intervening oxygen anion is responsible for electrical conduction in manganites, it is also of scientic curiosity to know how the resistivity and magnetoresistance are affected if the e g electron is forced to oscillate at MHz and GHz frequencies. M. Dominguez et al. 9 reported 70% magnetoresistance for 600 Oe near its Curie temperature (T C ) in Nd 0.7 Sr 0.3 -MnO 3 thin lm and V. Srinuvasu et al. 10 found 80% magnetoresistance for a eld of 600 Oe near T C in La 0.7 Ba 0.3 -MnO 3 powder when these samples placed inside a microwave resonant cavity were irradiated with electromagnetic elds in microwave frequency range (f ¼ 10 GHz). Microwave magnetoresistance was estimated from changes in microwave reectivity of the cavity in absence and in presence of a dc magnetic eld. In contrast to these reports, here, we report microwave magnetotransport in Pr 0.6 Sr 0.4 MnO 3 by passing alternating current (ac) of frequency f through the sample and measuring its electrical impedance in presence of an external dc magnetic eld.
Pr 0.6 Sr 0.4 MnO 3 is ferromagnetic at room temperature (T C ¼ 305 K) but its magnetization shows a step-like change around T S ¼ 89 K ((T C ), which is apparently triggered by orthorhombic (Pnma space group) to monoclinic (I/2a space group) structural transition. 11,12 Interestingly, this compound exhibits normal and inverse magnetocaloric effects at T C and T S , respectively. 13 A close correlation was also found between the magnetic entropy change, magnetothermopower and magnetization. While dc resistivity showed a very weak anomaly at T S in a single crystalline sample, 14 it was not detectable in the polycrystalline sample. However, ac resistance (1 MHz < f < 5 MHz) showed a pronounced anomaly at T S . It is of our interest to understand the behavior of magnetoresistance at frequencies higher than 5 MHz. Here, we extend the magnetotransport measurement in Pr 0.6 Sr 0.4 MnO 3 over a wide frequency range (f ¼ 1 MHz to 3 GHz) in response to radio frequency current owing through the sample. In addition, we also report microwave absorption for multiple frequencies (f ¼ 2 to 10 GHz) of microwave electromagnetic eld. Our results indicate that high frequency magnetoimpedance shows features of ferromagnetic resonance (FMR). Although FMR and electron spin resonance (ESR) in Kand Na-doped Pr 0.6 Sr 0.4 MnO 3 (ref. 15) as well as other manganites [16][17][18] have been studied using conventional MW cavity resonators, FMR excited by MW current owing through the sample has not been investigated. Here, we demonstrate a broadband detection of FMR in Pr 0.6 Sr 0.4 MnO 3 by electrical means using an impedance analyzer. The main advantage of our magnetoimpedance (MI) method is the broad operational frequency range unlike the conventional MW cavity resonator based technique which usually operates at a xed frequency (around 9.8 GHz) in X-band. Because the MI technique probes spin dynamics, it can be exploited to obtain Gilbert's damping parameter, which is not possible with a single frequency cavity resonator FMR technique.

Experimental details
Polycrystalline sample of Pr 0.6 Sr 0.4 MnO 3 was prepared by conventional solid state reaction method. It crystallizes in single phase with orthorhombic structure (space group Pnma) at room temperature. 19 Magnetization was measured using a vibrating sample magnetometer (VSM) and four probe electrical resistivity was measured in a Physical Property Measuring System (PPMS). The sample was cut into a rectangular plate of dimensions 5 mm Â 3 mm Â 2 mm for both dc resistivity and magnetoimpedance measurement. A radio frequency impedance analyzer (Agilent E4991A) was used to measure the resistive (R) and reactive (X) components of the complex impedance, Z(f) ¼ R(f) + iX(f) of the sample by employing the radio frequency (rf) current-voltage method. As shown in the Fig. 1(a), the sample placed on an Agilent test probe stage is attached to the signal line at one end and the other end of the sample is connected to the ground plate using silver paint. To avoid electrical contact between the sample surface and the ground plate, a layer of kapton tape was inserted between them. The rf current ows through the sample from the signal line to the ground plane. The test probe stage is placed at the center of an electromagnet. We dene the angle between the direction of rf current ow and that of the dc magnetic eld (H dc ) produced by the electromagnet by q. The R and X at selected frequencies were measured while sweeping H dc for q ¼ 0 , 30 , 60 and 90 . We dene dc magnetoresistance as MR dc ¼ [r(H) À r(H ¼ 0)]/r(H ¼ 0) Â 100%, where, r is the dc electrical resistivity of the sample. AC magnetoresistance is dened as for a frequency f of alternating current and the magnetoreactance is dened as We also dene magnetoimpedance as, The magnetic eld dependence of the eld derivative of microwave power absorption (dP/dH) was measured using a commercial broadband ferromagnetic resonance spectrometer (NanOsc Phase-FMR from Quantum Design Inc.) that makes use of coplanar waveguide method. The PPMS was used to provide an in-plane dc magnetic eld (H dc ) in such a way that the rf magnetic eld (H rf ) generated in the waveguide is perpendicular to H dc (see Fig. 4(a)). The dc magnetic eld was modulated using a pair of Helmholtz coils, which provided low amplitude (1 Oe) and low frequency (440 Hz) ac magnetic eld (H ac ). Because of the eld modulation and the lock-in technique used, microwave power absorption was recorded as the eld derivative (dP/dH) as like in conventional ESR spectrometers.

Results
The main panel of Fig. 1  T ¼ 350 K. The ferromagnetic Curie temperature (T C ) determined from the minimum of dM/dT curve is 305 K. The inset of Fig. 1(b) shows the magnetic eld dependence of magnetization at T ¼ 300 K which conrms the so ferromagnetic nature of the sample. The temperature dependence of dc resistivity r(T) (see the main panel of Fig. 1(c)) measured in zero external magnetic eld shows a change from thermally activated behavior in the paramagnetic state to metallic behavior below T C with a peak occurring at T C . The dc magnetoresistance (MR dc ) at T ¼ 300 K (inset of Fig. 1(c)) shows a single peak at H dc ¼ 0 with a negative sign and increases in magnitude. The absolute value of MR dc is 6% at H dc ¼ AE10 kOe. Fig. 2(a) shows the magnetic eld dependence of the ac magnetoresistance (MR ac ) at room temperature for different frequencies of the alternating current (f ¼ 1 MHz to 3 GHz). The dc magnetic eld (H dc ) produced by the electromagnet is parallel to the direction of rf current (I rf ) passing through the sample (q ¼ 0 ). MR ac is negative at f ¼ 1 MHz with an absolute value of 2% at H dc ¼ 5 kOe and shows a single peak at H dc ¼ 0.
As the frequency of the alternating current increases, the absolute value of MR ac increases up to a certain frequency ($500 MHz) but decreases for still higher frequencies. Above f ¼ 500 MHz, the single peak at H dc ¼ 0 splits into two symmetrical peaks at H dc ¼ AEH p on either sides of the zero eld and both these peaks migrate towards higher magnetic elds as f increases further. The sample shows a positive ac MR in the eld range ÀH p # H dc # +H p for f > 500 MHz. Fig. 2(b) shows the magnetic eld dependence of the magnetoreactance (MX). MX also shows double peaks at H dc ¼ AEH q (H q > H p ) above 500 MHz which also move towards higher eld with increasing frequency. The double peaks in MX at AEH q , unlike in MR ac , fade above f ¼ 1 GHz. In addition to the double peaks, MX also shows a single peak centered at origin (H dc ¼ 0) above 2 GHz culminating in double dips between H dc ¼ 0 and AEH q . The eld dependence of magnetoimpedance (MZ) shown in Fig. 2(c) is almost identical to that of MX.
The main panel of Fig. 3(a) displays the frequency dependence of MR ac at the highest eld for q ¼ 0 . The absolute value of negative ac MR increases with increasing frequency and becomes maximum around 500 MHz ($22%) but decreases towards zero with further increasing frequency. On the other hand, the value of positive ac MR at H dc ¼ AEH p increases gradually with increasing frequency and reaches $23% (see the inset of Fig. 3(a)) for f ¼ 3 GHz. It is noteworthy that the value of MR dc at 5 kOe is only 3% which is almost 7 times lower than the value of MR ac at the same eld for f ¼ 500 MHz.
We have also studied how the observed anomalous features vary if the angle between radio frequency (rf) current direction Fig. 2 Magnetic field dependence of (a) ac magnetoresistance (MR ac ) (b) magnetoreactance (MX) and (c) magnetoimpedance (MZ) as a percentage change at T ¼ 300 K for q ¼ 0 for different frequencies of the ac current between f ¼ 1 MHz and 3 GHz. and the direction of dc magnetic eld (q) is changed. MR ac and MX for q ¼ 0 , 30 , 60 and 90 are depicted in the Fig. 3(b) and (c), respectively for f ¼ 3 GHz. It is clear that the intensity of the double peaks at H dc ¼ AEH p in MR ac as well as the double dips at H dc ¼ AEH q in MX decreases with increasing q. Moreover, the double peak (dip) positions in MR ac (MX) also shi to lower elds as q increases and they disappear completely for q ¼ 90 . Fig. 4(b) shows the magnetic eld dependence of microwave power absorption recorded as the eld derivative (dP/dH) for different frequencies of the microwave magnetic eld between f ¼ 2-10 GHz at room temperature. The microwave absorption signal for each frequency exhibits a magnetic resonance feature a dip at a higher eld followed by a peak at a lower eld when the dc eld is reduced from a high value to zero. The signal for 2 GHz shows a peak around H dc ¼ 160 Oe. The peak in dP/dH shis towards higher H dc as the frequency of the microwave electromagnetic eld increases similar to the behavior of ac MR.
To understand a possible link between the anomalous behaviors of MR ac and MX, we plot the MR ac (le scale) and the MX (right scale) together in a single graph for f ¼ 3 GHz in Fig. 5(a). A careful look reveals that the peak in MR ac isotherm almost coincides with the point of inection in MX isotherm but MX is nearly independent of H dc above 2 kOe unlike that of the MR ac . It is clear from the Fig. 5(b) that the peak in MR ac (le y-axis) coincides with the peak in the eld derivative of MX   (right y-axis). In Fig. 5(c), we plot the eld derivative of the MR ac on the le y-axis and dP/dH on the right y-axis for f ¼ 3 GHz. It is evident that the peak positions of d(MR ac )/dH and dP/dH closely match with each other. However, the linewidth of d(MR ac )/dH is higher than that of dP/dH.

Discussion
We summarize important observations from the above results as follows: (1) Pr 0.6 Sr 0.4 MnO 3 is a room temperature ferromagnet with T C ¼ 305 K. (2) The ac magnetoresistance MR ac is negative and shows a peak at H dc ¼ 0 for f # 500 MHz but exhibits positive double peaks at H dc ¼ AEH p for higher frequencies.
(3) The absolute value of negative ac MR at H dc ¼ 5 kOe increases with frequency and becomes maximum ($22%) at f ¼ 500 MHz which is signicantly higher than the value of dc MR ($À3%) at the same eld. (4) The value of positive MR ac at H dc ¼ AEH p increases with frequency and becomes $+23% for f ¼ 3 GHz. (5) As q increases from resonant (0 ) to non-resonant (90 ) conguration, the double peak at H dc ¼ AEH p in the MR ac shis towards the origin as well as the value of MR ac at H dc ¼ AEH p decreases considerably. (6) The magnetic eld corresponding to the peak in MR ac isotherm coincides with the point of inection of MX isotherm. (7) The dP/dH shows a Lorentzian line shape and the maximum in dP/dH shis towards higher H dc with increasing frequency. (8) The peak positions in d(MR ac )/dH and dP/dH closely match with each other.
Let us rst shed some light on the origin of such anomalous behavior of the ac magnetotransport in this sample. The application of a dc electric eld to the sample forces the mobile e g electron to hop between Mn 3+ and Mn 4+ ions in the background of immobile t 3 2g core electrons. The hopping is dependent on the relative angle between t 2g spins of Mn ions. While dc or low frequency ac current ows uniformly throughout the volume of the sample, high frequency current tends to ow only in thin surface layer of thickness "d" due to skin effect. The "skin depth" d decreases with increasing angular frequency (u ¼ 2pf) of the ac current and dependent on dc resistivity (r) and transverse magnetic permeability (m t ) of the sample through the ; where, m 0 is the free space permeability. Instead of resistance for dc current, we consider impedance for alternating current. The electrical impedance of a rectangular slab with thickness 2t and innite width is given by, 20 where, k ¼ (1 + i)/d is the wave vector and R dc is the dc resistance of the sample. Using r ¼ 55 Â 10 À5 U m at 300 K and taking m t ¼ 1 corresponding to the non-magnetic limit, the value of d in our sample at f ¼ 3 GHz is 220 mm which is almost 10 times smaller than the sample thickness (2 mm). When the skin effect is very strong, i.e., d ( 2t, kt [ 1 and hence, coth (kt) / 1. In that case, the expression for surface impedance of the sample Z becomes, 20 Besides the skin effect, the ow of radio frequency (rf) current in the sample generates a transverse circular rf magnetic eld (H rf ) which interacts with the magnetization of the sample and hence, affects the transverse component of the magnetic permeability (m t ). The transverse permeability is a complex quantity and given by m t ¼ m 0 t À i m 00 t where, m 0 t is the in-phase component (magnetization is in-phase with the rf magnetic eld) and m 00 t is the out-of-phase component (magnetization is not in-phase with the rf magnetic eld).
Hence, the complex surface impedance is given by, 21 where, p À m 00 t . Hence, the real (R) and imaginary (X) parts of the complex , respectively. Since m t is affected by external dc magnetic eld, it inuences the eld dependence of both R and X. So, unlike dc magnetoresistance, ac magnetoresistance in the high frequency regime is dominated mostly by magnetization dynamics of the sample rather than changes in scattering rate of the conducting electrons. When the applied dc magnetic eld (H dc ) is smaller than the saturation eld, m t of the sample depends on the relative alignment of the magnetic easy axis and the direction of H dc . If H dc is parallel to the easy axis, m t decreases monotonically from its maximum value in zero eld to nonmagnetic limit (m t ¼ 1) with increasing strength of the dc magnetic eld. However, if H dc is perpendicular to the magnetic easy axis, magnetization of the sample rotates but does not switch towards H dc unless H dc exceeds the anisotropy eld H k . The transverse permeability is expected to diverge at H ¼ H k for an ideal system but usually shows a peak at H k in non-ideal case, [20][21][22] Since, , the ac resistance or surface resistance increases with H dc and shows a peak at H dc ¼ AEH p , where H p is close to H k , which explains the appearance of double peaks in MR ac of our sample in the frequency range f ¼ 500-1000 MHz for the orthogonal conguration of H dc and H rf (q ¼ 0 ). The disappearance of double peak behaviour in MR ac for q ¼ 90 is expected because m t will decrease monotonically with H dc for the parallel conguration of H dc and H rf . The shi of R-peak at H dc ¼ AEH p with frequency is small in the frequency regime f ¼ 500-1000 MHz which could be due to dispersion in the anisotropy eld (only few tens of Oe). 23 However, gyromagnetic effect, i.e., precession of magnetization about the direction of dc magnetic eld dominates at frequencies higher than 500 MHz. When the frequency of magnetization precession matches with that of the rf magnetic eld, steady state precession of magnetization, i.e., ferromagnetic resonance (FMR) occurs in the sample. The FMR frequency f res for a thin plate like sample increases with the frequency following the Kittel's expression when H dc is perpendicular to H rf , 24 where, H k is the transverse anisotropy eld, M eff is the effective magnetization whose value is close to saturation magnetization (M S ) and g is the gyromagnetic ratio, g ¼ gm B /ħ, where "g" is the "Lande' g-factor". Britel et al., showed that a close link exists between the magnetoimpedance measured by electrical method and the FMR recorded using a microwave electron spin resonance (ESR) spectrometer. 25 In an ESR spectrometer, a sample placed inside a microwave (MW) resonant cavity is irradiated with electromagnetic eld in microwave range, usually 9-10 GHz. The magnetic component of electromagnetic eld impinging on the sample inside MW cavity is transverse to the dc magnetic eld produced externally by an electromagnet. Similarly, the rf/MW magnetic eld generated by rf/MW current in the sample is also transverse to the dc magnetic eld in our magnetoimpedance measurement when q ¼ 0 . The sample absorbs maximum power from the MW electromagnetic eld during FMR. The power absorption (P) in the sample per unit volume is related to the out-of-phase component of transverse permeability through the expression where, h rf is the amplitude of the alternating magnetic eld (H rf (t) ¼ H 0 + h rf cos ut), c 00 t ð¼ m 00 t Þ is the out-of-phase component of transverse susceptibility. m 00 t goes through a maximum at the resonance eld (H res ) and hence, P(H dc ) also shows maximum at ; the appearance of peak in MR ac at H dc ¼ AEH p can be considered as a consequence of the maximum power absorption by the sample due to FMR. Similar behavior was reported in magnetic eld dependence of impedance (Z) for Fe-Co-Si-B amorphous ribbons 26 where the eld corresponding to the peak in real component of Z shis rapidly to higher elds with increasing frequency. D. de Cos et al., 27 also found a close correlation between dR ac /dH obtained from magnetoimpedance and dP/dH obtained from microwave power absorption in cavity resonator. The magnetic eld dependence of power absorption, P(H dc ) usually shows a Lorentzian line shape described by the expression, 28 where, P max is the absorbed power at the resonance eld (H dc ¼ H res ) and DH is the full line width at half the peak power (FWHM). Since the magnetic eld dependence of R reects the behavior of P(H dc ), the eld dependence of the high frequency MR ac can also be described by the Lorentzian function. We have tted the MR ac line shapes with the following equation, 29 where, R sym and R asym are the coefficients of symmetric and antisymmetric Lorentzian functions, H res and DH are the resonance eld and linewidth, respectively for the MR ac line shape and R 0 is a constant offset parameter. Eqn (7) is composed of a symmetric and an antisymmetric Lorentzian function which is generally used for the electrical detection of FMR. 29,30 The symmetry of FMR line shape depends on the relative phase between microwave electric and magnetic eld components. 29 The symmetric line shape accounts for the contribution of rf current which is in-phase with the rf magnetization and the antisymmetric line shape accounts for the out-of-phase contribution. 31 Thus, the resultant line shape is a linear combination of symmetric and antisymmetric contributions which leads to the asymmetric nature of the FMR line shape. 29 Fig. 6(a) displays the tting of the MR ac line shape with the eqn (7) for a few selected frequencies between f ¼ 1 and 3 GHz. The main panel of Fig. 6(b) shows H dc corresponding to the peak in MR ac on x-scale and the corresponding frequency on yscale which clearly indicates the evolution of double peaks and their rapid upshiing in H dc with increasing frequency of ac current. The plot f vs. resonance eld (H res ) above 1 GHz obtained from the tting of the MR ac line shape are shown in the le inset of Fig. 6(b). Fitting of the f vs. H res curve with the Kittel's equation for FMR described by eqn (4) yields g/2p ¼ 2.75 MHz Oe À1 and hence, g ¼ 1.9657 which is slightly lower than the theoretically expected value of g ¼ 2 for ferromagnetic manganites. 32 Belmeguenai et al. 33 obtained g ¼ 1.95 in La 0.7 -Sr 0.3 MnO 3 thin lms using the microstrip FMR (MS-FMR) technique. In order to obtain an accurate value of g factor, measurements need to be extended to several tens of GHz. As shown in the right inset of Fig. 6(b), DH increases non-linearly with frequency in the low frequency region but linearly in the high frequency regime. We have also extracted the values of 4pM S and H k from the tting which are 1900 AE 70 Oe and 190 AE 20 Oe, respectively.
In order to conrm whether the observed anomalous behaviour of the MR ac corresponds to FMR, we have tted the eld derivative of the power absorption (dP/dH) by a combined function containing derivatives of symmetric and antisymmetric Lorentzian functions as 34 where, P sym and P asym are the coefficients of symmetric and antisymmetric Lorentzian derivatives, H res and DH are the resonance eld and linewidth (FWHM), respectively for the dP/ dH line shape and P 0 is the constant offset parameter. Fig. 7(a) displays the tting of dP/dH line shape with the eqn (8) for selected frequencies between f ¼ 2 and 10 GHz. The plot of frequency (f) vs. resonance eld (H res ) obtained from the tting of dP/dH line shapes are shown in main panel of Fig. 7(b).
Fitting of the f vs. H res curve with eqn (4) yields g/2p ¼ 2.78 MHz Oe À1 and hence, g ¼ 1.987 which is close to the value of g-factor extracted from the tting of ac MR line shape. The extracted the values of 4pM S and H k from the tting of dP/dH line shape are 2200 AE 100 Oe and 190 AE 30 Oe, respectively. It is to be noted that the value of H k obtained from both magnetoimpedance and microwave absorption measurements are close to H k ¼ 200 AE 10 Oe estimated from the tting of M(H) isotherm with the law of approach to saturation model which is expressed as, 35 where, the coefficient a is related to micro-stress and the coef-cient b is connected to the rst order magnetocrystalline anisotropy coefficient K through the expression, b ¼ 8 105 The anisotropy eld H k can be estimated from the relation: H k ¼ 2K/m 0 M S . The frequency dependence of DH extracted from the tting of dP/dH curve is shown in the inset of Fig. 7(b) which clearly shows a nonlinear dependence below 6 GHz but a linear dependence for higher frequencies.
Nonlinear f-dependence of DH was found in various magnetic nanostructures which was attributed to the presence of two relaxation processes: the intrinsic Gilbert's damping and the two-magnon scattering. 36 The two-magnon scattering is an extrinsic damping mechanism which causes inhomogeneous broadening of DH and responsible for damping enhancement.
We have tted the f dependence of DH above 6 GHz with the following equation, 37 where, DH 0 accounts for the extrinsic damping contributions and a is the Gilbert's damping parameter. The value of a extracted from the tting is 13.6 Â 10 À3 AE 0.8 Â 10 À3 and it is higher than the value found in La 0.7 Sr 0.3 MnO 3 /NGO thin lm (a ¼ 7.8 Â 10 À4 ) 38 and Pt capped La 0.7 Sr 0.3 MnO 3 /STO thin lm (a ¼ 5.93 Â 10 À3 ). 39 A possible reason for the large value of a observed could be due to polycrystalline nature of our sample. We need to investigate spin dynamics in epitaxial thin lms by this magnetoimpedance technique in future.
In recent years, electrical detection of FMR using microstrip (MS) or co-planar waveguide (CPW) is gaining popularity to investigate spin dynamics in magnetic nanostructures. 33,40 Fig. 7 (a) Fitting of dP/dH line shapes at T ¼ 300 K for different frequencies, (b) main panel shows the Kittel-fit to the plot of frequency (f) vs. resonance field (H res ) extracted from dP/dH data and the inset shows frequency dependence of DH with a linear fit for f > 6 GHz.
These techniques make use of a vector network analyzer (VNA) or a combination of MW signal generator, microwave diode and lock-in amplier. The sample to be investigated is placed on the signal line of CPW or MS and the microwave magnetic eld arising from the ow of MW current in the signal line induces spin precession in the sample. On the contrary, RF/WW current is directly injected into the sample in our method and our technique requires only an impedance analyzer to source MW current and record the impedance of the sample. Unlike a network analyzer, the rf impedance analyzer does not need a 50 ohm impedance matching. Even though the maximum attainable frequency is limited to 3 GHz, there are ample opportunities to exploit this technique to other ferromagnetic systems.

Summary
In summary, we have studied the magnetic eld dependence of electrical impedance in the room temperature ferromagnet Pr 0.6 Sr 0.4 MnO 3 using an impedance analyzer by passing alternating current in the frequency range 1 MHz to 3 GHz directly through the sample. Our magnetoimpedance studies show signature of ferromagnetic resonance which was also conrmed by microwave absorption measurements for multiple frequencies (f ¼ 2 to 10 GHz) of microwave electromagnetic eld using a commercial broadband ferromagnetic resonance spectrometer. Our line shape analysis indicates a large Gilbert's damping in this sample (a ¼ 13.6 Â 10 À3 ). Our results show that highfrequency magnetoimpedance can be used as a materials characterization tool. Ferromagnetic resonance do nd applications in catalysis. 41 Application of this magnetoimpedance technique to other conducting magnetic oxides may open up a new area of research direction in physical chemistry.

Conflicts of interest
There are no conicts to declare.