Gilbert damping constant of FePd alloy thin films estimated by broadband ferromagnetic resonance

Magnetic relaxation of FePd alloy epitaxial thin films with very flat surfaces prepared on MgO(001) substrate are measured by in-plane broadband ferromagnetic resonance (FMR). Magnetic relaxation is investigated as for FMR absorption peak by frequency sweep measurements. is calculated by using the measured . Gilbert damping constant, , is estimated by employing a straight line fitting of the resonant frequency dependence of . The value for an FePd film deposited at 200  ̊C, which shows disordered A1 structure, is 0.010 and 0, which is frequency independent part of , is 10 Oe. The value for a film annealed at 400  ̊C, which shows partially L10 ordered structure (S=0.32), is 0.013, which is slightly larger than that for the disorder A1 structure film. However, 0 for the annealed film is 85 Oe, which is much larger than that for the film with disordered structure. The results show that the magnetic relaxation of the 400  ̊C annealed film is mainly dominated by 0, which is related with magnetic in-homogeneity caused by the appearance of perpendicular anisotropy of partially ordered phase.


Introduction
Spin-transfer switching is an attractive technique to deduce the electronic current for switching the magnetization direction of a magnetic element in devices like perpendicularly magnetized magnetoresistance random access memory (PMRAM) [1,2].For PMRAM devices, perpendicularly magnetized magnetic thin films with small Gilbert damping constant, , are required [1].An L1 0 ordered FePd alloy epitaxial thin film is one of candidate materials.Ferromagnetic resonance (FMR) is a powerful method in studying Gilbert damping constant, of magnetic thin film .There are a few FMR studies of epitaxial FePd thin films with perpendicular magnetic anisotropy [3,4].It is reported that the line width of the uniform mode is found to be independent of frequency and hence departs from the linear frequency variation predicted by the Landau-Lifshitz-Gilbert (LLG) relaxation type [3].However, it is well known that the magnetic relaxation in magnetic metal obeys mostly on the LLG type [5].Therefore, it is interesting to investigate how the magnetic relaxation varies depending on the crystallographic ordering from disordered A1 to the ordered L1 0 state in FePd thin film.
In this study, Gilbert damping constant is estimated for Fe 50 Pd 50 (at.%) alloy epitaxial thin films with very flat surfaces, which are obtained on MgO(001) singlecrystal substrates by employing a two-step process; low-temperature deposition at 200 ºC followed by hightemperature annealing at 400 ºC [6].Very flat surface is required in FMR measurements to evaluate intrinsic magnetic relaxation in order to avoid extrinsic effect by surface roughness [7].Broadband FMR measurements using a VNA are carried out for 40nm thick films under static magnetic fields up to 1 kOe in the film plane to measure magnetic relaxation.A difference in the magnetic relaxation between FePd films with a disordered A1 structure and with a partially ordered L1 0 structure is discussed.

Experimental procedures
FePd alloy thin films were prepared on polished MgO(001) single-crystal substrates by using a radiofrequency (RF) magnetron sputtering system equipped with a reflection high-energy electron diffraction (RHEED) facility.The base pressures were lower than 4 × 10 -7 Pa.The detail of sample preparation is reported in our previous paper [6].FePd films of 40 nm thickness were deposited on MgO(001) substrates at 200 ºC.Then, the films were annealed at 300 and 400 ºC for 1 h.The The magnetization curves were measured by using a vibrating sample magnetometer.A VNA was used to measure dynamic magnetic property covering up to 10 GHz, where RF magnetic field was applied orthogonally to the static magnetic field using a shorted micro-strip line [7,8].The resonant frequency was determined as a frequency when an experimental complex permeability, , showed a maximum value.Gilbert damping constant, , was estimated by using measured half line width between 1/2-power points for frequency sweep, as explained in the next section.

Estimation method of Gilbert damping constant, , and perpendicular magnetic anisotropy
The magnetic relaxation of magnetic thin films are usually discussed by using H, which is full line width between 1/2-power points for magnetic field sweep FMR measurements, and is expressed in the following formula [9].
where H 0 , which is magnetic relaxation caused by inhomogeneity, is frequency independent part of H is Gilbert damping constant, f r is resonant frequency, and is gyromagnetic constant.
However, our FMR measurements are carried out not by magnetic field sweep but by frequency sweep.Then the measured value is not H but .Therefore, we need to calculate H by using the measured employing the following conversion formula [9].
where r =2 f r , m = M s / 0 , M s is saturation magnetization, and 0 is permeability of vacuum. is calculated from the straight line fitting of the formula (1) with the measured f r dependence of H. H 0 is defined as the intercept from the straight fitting.On the other hand, damping constant, , is also evaluated by fitting the calculated to each absorption peak of experimental with best fitting parameters [7].The line width of each absorption peak includes magnetic relaxation resulting from various factors.Therefore, the damping constant evaluated by this method is denoted as app .
Perpendicular magnetic anisotropy field is determined using the following the Kittel resonant formula.
where H ex is applied static magnetic field, H in is in-plane magnetic anisotropy field, and H out is perpendicular magnetic anisotropy field.H out is determined by fitting the formula (3) with the measured H ex dependence of f r .

Results and discussion
Very flat surfaces are realized for the FePd films prepared by employing the two-step process.The properties of the films employed in the present study are listed in Table 1 [6].Thin film samples with very flat surface with R a less than 0.3 nm are obtained.L1 0 order parameter, S, changes from 0 for an as-deposited film to 0.32 for a film annealed at 400 ºC.The magnetic easy axis is in-plane for all the films.In-plane magnetization curves are shown in Fig. 1.The easy magnetization axis is along <100> for all three films.The anisotropy fields of as-deposited and 300 ºC annealed films are almost similar at 30 Oe, whereas that of 400 ºC annealed film is 70 Oe which is larger than the other two films.In-plane magnetic anisotropy seems to have varied with increasing partial ordering of L1 0 structure.The coercivity is also changed from 10 Oe for the as-deposited film to 24 Oe for the 400 ºC annealed film which suggests that domain wall motions are suppressed in the 400 ºC annealed film.As shown in Table 1, small partial order (S=0.21) is developed even in the 300 ºC annealed film, but such small partial order shows no effect on static in-plane magnetic property.The examples of measured complex permeability for three FePd films are shown in Fig. 2, where applied static magnetic filed is 174 Oe along <100>.Clear Lorenz type absorption peaks are observed for all samples.The permeability values for the 400 ºC annealed film are small compared with those of the other two films.This is possibly due to the enhanced in-plane anisotropy field (70 Oe) of the 400 ºC annealed film compared with the other films (30 Oe).Complex permeability measurements are carried out by changing the external static magnetic field from 0 to 1 kOe.Examples of absorption peaks are shown in Fig. 3. Resonant frequency is defined at the frequency where shows a maximum value.Solid lines show the calculated using best fitting parameters of M s , K 1 , and [7], where g-factor is fixed at 2.07 [2].There are very good agreements between the experiments and the calculations for the as-deposited film and the film annealed at 300 ºC for the applied static magnetic field range, whereas for the film annealed at 400 ºC, good agreements are recognized only for more than 300 Oe.As shown in Fig. 1, magnetic saturation is already reached at 200 Oe in the static magnetic field characteristic, but the FMR measurement indicates that more than 300 Oe magnetic field is required to excite the spin wave in the uniform mode in radio frequency region.
Figure 4 shows the static magnetic field dependence of resonant frequency, f r , for three FePd thin films.Solid lines are the fitting curves by formula (3) using best fitting parameters of M s , H in , and H out .There is no difference of magnetic field dependence of f r between for the as-deposited film and for the 300 ºC annealed film, which suggests that any observable perpendicular anisotropy is not developed in the 300 ºC annealed film though a small partial L1 0 structural ordering is observed.The perpendicular anisotropy field is estimated to be 1.5 kOe by the fitting for the 400 C annealed film.
The app values obtained by the fitting for each absorption peak are shown in Fig. 5 as a function of resonant frequency reciprocal, 1/f r .The app values tend to become small as the frequency reciprocal, 1/f r , becomes small.The app values are almost similar for the as-deposited and for the 300 ºC annealed films, whereas app is large for the 400 ºC annealed film compared with other films.Gilbert damping constant, , defined in the LLG equation should be frequency independent.Therefore, we tried to separate the measured magnetic relaxation into the frequency independent part and the frequency dependent part as denoted in formula (1) using the measured . is defined by a parabolic fitting using the reciprocal of near the resonance peak.H is calculated by formula (2) using the measured .Frequency dependences of H are shown in Fig. 6.Gilbert damping constant, , is calculated by using the slope of the straight line and H 0 , which means H caused by inhomogeneous effect, is defined as an intercept at y-axis.These Gilbert damping constants, , and H 0 values are shown in the insets of the figure .H values for the as-deposited and for the 300 ºC annealed films are almost similar.However, H values for the 400 ºC annealed film are much larger than those of other films.
The value for the as-deposited film is 0.010 and 0 is 10 Oe.The value for the 400 ˚C annealed film is 0.013, which is slightly larger than that for the asdeposited film.However, 0 for the annealed film is 85 Oe, which is much larger than that for the as-deposited film.The results suggest that the magnetic relaxation of partially L1 0 ordered FePd film with perpendicular anisotropy is mainly dominated by 0 which is caused by magnetic in-homogeneity in the film.As shown in figures 1, 4 and 5, there is little difference in the magnetic relaxation between the as-deposited film (S=0) and the 300 ˚C annealed film with partial L1 0 ordering (S=0.21).The result indicates that the small structural inhomogeneity without perpendicular anisotropy shows almost no effect on magnetic relaxation but the magnetic in-homogeneity caused by the appearance of perpendicular anisotropy shows significant effect.Such magnetic in-homogeneity may cause frequency independent relaxation like two magnon process [10].

Conclusions
Magnetic relaxation of FePd epitaxial thin films with very flat surfaces is measured by broadband FMR.Measured magnetic relaxation is evaluated by separating into a frequency independent part, H 0 , and a frequency dependent part.Gilbert damping constant, , is calculated by using the slope of frequency dependent part.The value for the FePd film deposited at 200 ˚C, which shows disorder A1 structure, is 0.010 and H 0 , is 10 Oe.Meanwhile, the value for the 400 ˚C annealed film, which shows partially L1 0 ordered structure (S=0.32), is 0.013, which is slightly larger than that of the disorder A1 structure film.However, H 0 for the 400 ˚C annealed film is 85 Oe, which is much larger than that for the disorder A1 structure film.The results show that the magnetic relaxation of partially L1 0 ordered FePd film is mainly dominated by H 0 , which is related with magnetic in-homogeneity developed by perpendicular anisotropy in the film during ordering process.