From the FORC analysis discussed in

Figure 7, the planar-patterned MnGa is expected to have negligibly small bit edge damage. However, for a more detailed discussion, the anisotropy field of the irradiated MnGa with ion doses around 10

^{13} ions/cm

^{2}, which is a transition region from ferromagnetic to paramagnetic as noted in

Figure 2, should be investigated. We measured the time resolved magneto-optical Kerr effect (TRMOKE) of the ion-irradiated MnGa films to investigate the anisotropy field and its distribution. A high-power fiber laser with a central wavelength of 1041 nm, a pulse width of 500 fs, and a repetition frequency of 100 kHz was used to obtain the TRMOKE. The frequency-doubled and linearly polarized probe beam was incident normal to the film surface to monitor the perpendicular component of the magnetization after the illumination of the pump beam. The fluences of the pump and probe beams were 0.2 and 0.04 mJ/cm

^{2}, respectively. The external field up to

H_{ext} = 14 kOe was applied at an angle of

θ_{H} = 60 deg from the film normal direction. Details of the TRMOKE setup are described in Refs. [

31,

32,

33,

34,

35]. The sample stack used for the TRMOKE was SiN (5 nm)/MnGa (50 nm)/Cr (10 nm)/MgO(001), and after ion irradiation, an additional SiN (35 nm) layer was deposited to enhance the Kerr rotation of the MnGa.

Figure 8 shows the decaying magnetization precessions of the MnGa before and after ion doses of 5 × 10

^{12}, 1 × 10

^{13}, and 2 × 10

^{13} ions/cm

^{2} under

H_{ext} = 14 kOe. The raw data, measured by the TRMOKE, contain the signals of laser-induced demagnetization at the delay time of the probe beam

t = 0 and exponential decay due to the recovery of the magnetization as described in Ref. [

31]. These unnecessary signals were subtracted to extract the decaying precession triggered by the pump illumination as shown in

Figure 8. The closed circles and solid lines in

Figure 8 indicate the measured data and fitted curves with the damped oscillation function,

A exp(–

t/

τ) sin

ωt, respectively, where

τ is the relaxation time and

ω the angular frequency of the oscillation. A clear oscillation due to the magnetization precession of the as-prepared MnGa can be seen in

Figure 8, and the precessions of the MnGa after the ion dose were confirmed to relax faster than those of the MnGa before the ion dose.

The effective anisotropy field

H_{keff} and g-factor

g were estimated by fitting the

H_{ext} dependence of

ω shown in

Figure 9a with the following expressions [

36,

37]:

where

$\gamma ={\mu}_{\mathrm{B}}g/\hslash =1.105\times {10}^{5}g[\mathrm{m}/\mathrm{A}\xb7\mathrm{s}]$ is the gyromagnetic constant, and

θ is the stable magnetization angle from the film normal estimated by minimizing the following magnetic energy:

Figure 9b shows the

ω dependence of the inverse of the relaxation time 1/

τ for the ion-dosed MnGa films. As shown in

Figure 9b, 1/

τ increased with increasing

ω, and the slope for the MnGa without the ion dose is quite small, whereas the slope was found to increase after ion irradiation. 1/

τ is influenced by Gilbert damping α, anisotropy distribution Δ

H_{keff}, anisotropy axis distribution Δ

θ_{H}, and two-magnon scattering (TMS) [

37,

38,

39,

40], and is expressed as,

if we neglect the contribution from spin pumping [

41]. When the TMS and Δ

θ_{H} are negligible and

H_{θθ}_{0} ≈

H_{φφ0}, Equation (3) is simply expressed as:

indicating that 1/

τ is roughly proportional to α [

37]. From the data in

Figure 9b, the slope and

y-intercept for the MnGa without the ion dose are estimated to be 0.01 and 1.3 Grad/s, respectively, suggesting small α ~0.01 and Δ

H_{keff} ~150 Oe. The TMS contribution is calculated as [

38,

39,

40]:

where

**k** is the magnon wave vector,

k its amplitude,

N_{0} the scattering intensity,

C(

k) the correlation function,

ω_{k} the spin wave dispersion, and

δω_{k} the inverse lifetime of the spin wave. These are expressed as [

38,

39]:

where

ξ is the correlation length, and

H_{θθ}(

**k**) and

H_{φφ}(

**k**) are given by [

38]:

where

µ_{0} is the permeability of vacuum,

A_{ex} the exchange stiffness, and

φ_{k} the azimuth angle of the spin wave.

N_{k} is the wave number dependent demagnetizing factor which is given by [

38]:

where

d is the film thickness. 1/

τ^{TMS} increases with increasing

ω; i.e., it increases the slope in

Figure 9b, since the increase of

H_{ext} increases

θ. From Equations (5) and (6), 1/

τ^{TMS} is proportional to Δ

H_{keff}^{2}, and thus the increase of Δ

H_{keff} results in the increases of the slope of the curve of 1/

τ vs.

ω. The increase of Δ

H_{keff} also increases the

y-intercept of

Figure 9b from Equation (4). In

Figure 9b, the solid lines show fitted curves with Equation (3), where we assumed Δ

θ_{H} = 0, since the second term in Equation (3) for the MnGa without ion irradiation was negligibly small, and the second term is considered not to increase after ion irradiation. We also assumed that the Gilbert damping stayed constant after ion irradiation, since the ion irradiation will not contribute to an increase in the intrinsic damping.

Figure 10 shows the ion dose dependence of

H_{keff}, Δ

H_{keff},

α, and

ξ of the ion-irradiated MnGa films. The g-factor of all MnGa films was estimated to be 2.0 irrespective of ion implantation.

α of the as-prepared MnGa is estimated to be 0.008, which is consistent with the previous result [

42].

H_{keff} of the MnGa before the irradiation was 20 kOe, which roughly agrees with that estimated from

M–

H loops shown in

Figure 1.

H_{keff} increased after the ion dose and stayed constant at

H_{keff} ~23 kOe. This suggests that the ion irradiation does not cause the reduction of the average value of the anisotropy, which is in accordance with the small bit edge damage in the patterned MnGa. On the other hand, Δ

H_{keff} significantly increased from 0.2 kOe to 3 kOe with an increase in the ion dose. Accordingly,

ξ decreased from 10 nm to 3 nm after the ion irradiation. These trends are explained by the microstructure discussed in

Figure 2 and

Figure 3. After the ion irradiation, L1

_{0} MnGa nano-crystals are expected to be surrounded by the paramagnetic A1 MnGa matrix. This results in a large distribution of the effective field acting in the nano-crystals, since each L1

_{0}-MnGa nano-crystal has different shape anisotropy. For the thin-film MnGa, the demagnetizing field is estimated to be 7.5 kOe, whereas the demagnetizing field of an isolated MnGa nano-crystal with an aspect ratio of 1 will be 2.5 kOe. The microstructure also explains the reduction of

ξ by the ion irradiation.

ξ corresponds to the length of disorder in the film, and

ξ ~10 nm for an as-prepared MnGa film is thought to be related to the grain size of the MnGa, which is expected to be a few tens of nanometers from the AFM image in

Figure 6a. After ion irradiation,

ξ will be reduced by the ion irradiation. The ion dose of 1 × 10

^{13} ions/cm

^{2} corresponds to 1 ion per 3 nm × 3 nm, which agrees well with

ξ after ion irradiation.