# Magnetic Anisotropy and Damping Constant of Ferrimagnetic GdCo Alloy near Compensation Point

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{4}J m

^{−3}. By analyzing the transient dynamics of magnetization as a function of time, we estimate the damping constant to be 0.08–0.22.

## 1. Introduction

^{4}J m

^{−3}at the compensation point. To investigate damping, we measure the transient dynamics of magnetization, triggered by sudden change of anisotropy energy. Analyzing the relaxation of the magnetization precession, we determine the enhanced damping of 0.22 at the compensation point.

## 2. Materials and Methods

^{−1}. The deposition rate of each layer is predetermined with a single thick layer, whose thickness is determined by X-ray reflectivity measurements, then the thickness of each layer is controlled by deposition time. All layers are deposited at room temperature.

_{AHE}) in the presence of the charge current (I

_{c}) and magnetization (M) as ${\overrightarrow{V}}_{\mathrm{AHE}}\propto {\overrightarrow{I}}_{\mathrm{c}}\times \overrightarrow{M}$ [24]. When I

_{c}and M are along the x and z directions, respectively, V

_{AHE}is along the y direction. Because the AHE originates from the electrons near the Fermi level, it does not provide the absolute magnitude of magnetization but accurately measures the relative magnitude of the out-of-plane magnetization, ${m}_{z}={M}_{z}/\left|M\right|$, because of the large signal-to-noise ratio of V

_{AHE}. We connect wire bonding at the four corners of the square-shaped sample, size of 1.27 × 12.7 cm

^{2}, to measure V

_{AHE}in the van der Pauw geometry. We measure V

_{AHE}, with a DC charge current of 1 mA, as a function of the magnetic field with an oblique angle in the z-direction.

## 3. Results

#### 3.1. Basic Magnetic Properties

#### 3.2. Determination of Magnetic Anisotropy

_{z}= cos θ

_{M}, where θ

_{M}is the angle of magnetization from the sample normal (Figure 2). The AHE reading is advantageous over VSM reading in terms of signal-to-noise ratio. As the GST method analyze many m

_{z}data with different applied fields (B

_{app}), it is more accurate than the analysis based on one data point at the saturation field. In addition, as the GST method analyze the gradual change in m

_{z}with respect to B

_{app}, its field requirement is smaller than the saturation field.

_{z}using AHE with applying B

_{app}at an oblique angle of θ

_{H}= 0° or 85° (Figure 2). At θ

_{H}of 0°, m

_{z}is nearly independent of B

_{app}because AHE signal, which is linearly proportional to M, dominates the ordinal Hall signal, which is linearly proportional to B

_{app}. With a large θ

_{H}of 85°, m

_{z}gradually decreases with B

_{app}as the in-plane component of B

_{app}tilts the magnetization (Figure 3). (θ

_{H}should be less than 90° to have an out-of-plane component of B

_{app}, which suppresses multidomain formation.) According to the GST method, the relationship between m

_{z}and B

_{app}can be expressed as [22],

_{1}and K

_{2}are the first and second-order uniaxial anisotropies, M

_{S}is the saturation magnetization of the GdCo alloy, and F is given by

_{1}and K

_{2}can be determined independently of the intercept and slope, respectively (Figure 3). (For the Gd = 24%, the measured range of the $1-{m}_{z}^{2}$ is small because the maximum B

_{app}of 1.7 T is much smaller than the saturation field of ${B}_{\mathrm{sat}}\approx \frac{2{K}_{\mathrm{tot}}}{{M}_{\mathrm{S}}}$, where K

_{tot}is the total anisotropy.) The determined values of K

_{1}and K

_{2}with Gd concentrations of 18%, 21%, 24%, and 27% are summarized in Table 1. The maximum K

_{tot}= K

_{1}+ K

_{2}of 2.8 × 10

^{4}J m

^{−3}is obtained at the compensation point of Gd = 24%. Previously reported values of K

_{tot}of the GdCo alloy are in the range of 10

^{4}J m

^{−3}, depending on the Gd concentration and deposition method [1,2,20]. We note that the anisotropy energy of the GdCo alloy is about two orders of magnitude smaller than that of FePt, a well-known ferromagnet for strong magnetic anisotropy [22,23]. Such a low magnetic anisotropy of the GdCo alloy limits the application to memory devices. Interestingly, K

_{2}becomes larger than K

_{1}at the compensation point. This observation is surprising because K

_{1}is usually much larger than K

_{2}for typical ferromagnets [22,23]. To understand the physical origin for the strong enhancement of K

_{2}at the compensation point, further theoretical and experimental works are required.

#### 3.3. Determination of Damping Constant

_{app}along the z/x direction for the in-plane/out-of-plane anisotropy sample. We apply a B

_{app}of 0.3 T along the x direction for the Gd

_{18}Co

_{82}, Gd

_{24}Co

_{76}, and Gd

_{27}Co

_{73}samples and B

_{app}of 0.5 T along the z direction for the Gd

_{12}Co

_{88}sample. The magnitude of B

_{app}is chosen to be larger than the saturation field along the hard axis, so that the initial magnetization aligns along the x or z direction (Figure 1). (This is not the case for the Gd = 24%, in which the saturation field is much larger than B

_{app}of 0.3 T.) Such an alignment makes the damping analysis to be simple. The equilibrium direction of magnetization is determined by the balance between the uniaxial anisotropy, demagnetization field, and external field. When a pump pulse induces an ultrafast demagnetization via sudden heating, the balance is suddenly disturbed, and a precessional motion of magnetization is triggered [25]. Indeed, the TRMOKE shows a precessional motion on top of an ultrafast demagnetization (Figure 4). We separate the precessional motion by subtracting the demagnetization background signal from the raw data. The precessional motion can be described by the Landau–Lifshitz–Gilbert equation based on the mean-field model [26,27,28,29],

_{eff}is the net magnetization of the GdCo alloy, γ

_{eff}is the effective gyromagnetic ratio of the GdCo alloy, H

_{eff}is the effective field combining the exchange field, anisotropy field, demagnetization field, and external field, and α

_{eff}is the effective damping of the GdCo alloy. Alternatively, α

_{eff}can be obtained as ${\alpha}_{\mathrm{eff}}=1/\left(2\pi f\tau \right)$, where f is the precession frequency, and τ is the relaxation time of the damped cosine function of $\mathrm{cos}\left(2\pi ft\right)\times \mathrm{exp}\left(-t/\tau \right)$.

_{tot}(K

_{1}+ K

_{2}) and α

_{eff}in Figure 5. Both K

_{tot}and α

_{eff}maximize at the compensation point of Gd = 24%. Here, α

_{eff}is not the intrinsic parameter, but depends on B

_{app}. For the Gd

_{18}Co

_{82}and Gd

_{27}Co

_{73}alloys, when magnetization aligns nearly to the x direction by B

_{app}, the intrinsic damping (α

_{int}) is related to α

_{eff}as [30],

_{1}= B

_{app}+ B

_{K}, B

_{2}= B

_{app}, and B

_{K}= (2K

_{1}− μ

_{0}M

_{S}+ 4K

_{2})/M

_{S}. For the Gd

_{24}Co

_{76}alloy, magnetization aligns nearly to the z direction by strong B

_{ani}, then α

_{int}≈α

_{eff}. The variation of α

_{eff}of the Gd

_{24}Co

_{76}alloy with different B

_{app}is shown in Appendix A. Using the B

_{K}information in Table 1, we show that α

_{int}also maximize at Gd = 24% with a peak value of 0.22. Our result of α = 0.22 is consistent with previous reports of 0.2–0.3 of the GdCo and GdFeCo alloys from the ferromagnetic resonance and TRMOKE measurements [26,27,28]. However, much low α of 0.007 of the GdFeCo alloy was reported from the measurement of the domain wall motion [31]. Further studies are required to resolve this discrepancy between measurement techniques.

_{in}is the incident fluence of the pump of 12 J m

^{−2}, A

_{tot}is the absorption coefficient by the total metal layers of ≈ 0.3, C

_{V}is the typical heat capacity of metals of 3 × 10

^{6}J m

^{−3}K

^{−1}, and d

_{tot}is the total thickness of metal layers of 21 nm, the temperature rise of the sample would be approximately 60 K (ignoring the slow heat transfer to the substrate). Because the alloy concentration for the magnetic compensation depends on temperature, the Gd

_{24}Co

_{76}alloy may not be the magnetic compensation point during TRMOKE. We claim that the increase in α

_{eff}is caused by the angular momentum compensation between the Gd and Co sublattices. Such enhancement of α

_{eff}near the compensation point has been previously reported for the GdFeCo and GdCo alloys, and the mean-field model was used to explain the physical origin [26,27,28]. According to the mean-field model, α

_{eff}of the GdCo alloy is expressed as [29],

_{Co}/α

_{Gd}is the damping constant of the Co/Gd sublattice, M

_{Co}/M

_{Gd}is the magnetization of the Co/Gd sublattice, and γ

_{Co}/γ

_{Gd}is the gyromagnetic ratio of the Co/Gd sublattice. Accordingly, α

_{eff}diverges at the compensation of the angular momentum, $M/\gamma $. Typically, the angular momentum compensation temperature is 50–100 K higher than the magnetization compensation temperature [13,15,27].

## 4. Discussion

^{4}J m

^{−3}at the compensation point, Gd concentration of 24%. Surprisingly, we find that the second-order uniaxial anisotropy becomes larger than the first-order one at the compensation point. We expect that this anisotropy inversion is related to the magnetization compensation. Measuring the magnetization dynamics using TRMOKE, we determine the damping constant. An enhanced damping constant of 0.22 is observed at the compensation point. This enhancement is consistent with previous reports and can be understood by the angular momentum compensation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

_{24}Co

_{76}alloy with three different B

_{app}of 0.2, 0.3, and 0.4 T. From the fittings with a damped cosine function, we determine the same α

_{eff}of 0.22 ± 0.02 for all three conditions.

**Figure A1.**The B

_{app}dependence on α

_{eff}. The precessional motion in the Gd

_{24}Co

_{76}alloys with B

_{app}of (

**a**) 0.2, (

**b**) 0.3, and (

**c**) 0.4 T along the x-direction. The black circles are obtained by subtracting the demagnetization background from the raw data of TRMOKE. The red lines are fittings by damped cosine function of $\mathrm{cos}\left(2\pi ft\right)\times \mathrm{exp}\left(-t/\tau \right)$. The fitted f values are 6.0, 8.9, and 11.8 GHz for (

**a**–

**c**), respectively. The fitted τ values are 120, 80, and 60 ps for (

**a**–

**c**), respectively.

## References

- Esho, S.; Fujiwara, S. Growth Induced Anisotropy in Sputtered GdCo Films. In Magnetism and Magnetic Materials, Proceedings of the First Joint MMM-Intermag Conference, Pittsburgh, PA, USA, 15–18 June 1976; AIP Publishing: College Park, MD, USA, 1976; Volume 34, pp. 331–333. [Google Scholar]
- Taylor, R.; Gangulee, A. Magnetization and magnetic anisotropy in evaporated GdCo amorphous films. J. Appl. Phys.
**1976**, 47, 4666–4668. [Google Scholar] [CrossRef] - Mizoguchi, T.; Cargill, G., III. Magnetic anisotropy from dipolar interactions in amorphous ferrimagnetic alloys. J. Appl. Phys.
**1979**, 50, 3570–3582. [Google Scholar] [CrossRef] - Ostler, T.A.; Evans, R.F.L.; Chantrell, R.W.; Atxitia, U.; Chubykalo-Fesenko, O.; Radu, I.; Abrudan, R.; Radu, F.; Tsukamoto, A.; Itoh, A.; et al. Crystallographically amorphous ferrimagnetic alloys: Comparing a localized atomistic spin model with experiments. Phys. Rev. B
**2011**, 84, 024407. [Google Scholar] [CrossRef][Green Version] - Stanciu, C.D.; Hansteen, F.; Kimel, A.V.; Kirilyuk, A.; Tsukamoto, A.; Itoh, A.; Rasing, T. All-optical magnetic recording with circularly polarized light. Phys. Rev. Lett.
**2007**, 99, 047601. [Google Scholar] [CrossRef][Green Version] - Kirilyuk, A.; Kimel, A.V.; Rasing, T. Laser-induced magnetization dynamics and reversal in ferrimagnetic alloys. Rep. Prog. Phys.
**2013**, 76, 026501. [Google Scholar] [CrossRef] [PubMed] - Hansen, P.; Clausen, C.; Much, G.; Rosenkranz, M.; Witter, K. Magnetic and magneto-optical properties of rare-earth transition-metal alloys containing Gd, Tb, Fe, Co. J. Appl. Phys.
**1989**, 66, 756–767. [Google Scholar] [CrossRef] - Jiang, X.; Gao, L.; Sun, J.Z.; Parkin, S.S.P. Temperature dependence of current-induced magnetization switching in spin valves with a ferrimagnetic CoGd free layer. Phys. Rev. Lett.
**2006**, 97, 217202. [Google Scholar] [CrossRef][Green Version] - Yang, Y.; Wilson, R.B.; Gorchon, J.; Lambert, C.-H.; Salahuddin, S.; Bokor, J. Ultrafast magnetization reversal by picosecond electrical pulses. Sci. Adv.
**2017**, 3, e1603117. [Google Scholar] [CrossRef][Green Version] - Mishra, R.; Yu, J.; Qiu, X.; Motapothula, M.; Venkatesan, T.; Yang, H. Anomalous current-induced spin torques in ferrimagnets near compensation. Phys. Rev. Lett.
**2017**, 118, 167201. [Google Scholar] [CrossRef][Green Version] - Cai, K.; Zhu, Z.; Lee, J.M.; Mishra, R.; Ren, L.; Pollard, S.D.; He, P.; Liang, G.; Teo, K.L.; Yang, H. Ultrafast and energy-efficient spin–orbit torque switching in compensated ferrimagnets. Nat. Electron.
**2020**, 3, 37–42. [Google Scholar] [CrossRef] - Sala, G.; Krizakova, V.; Grimaldi, E.; Lambert, C.-H.; Devolder, T.; Gambardella, P. Real-time Hall-effect detection of current-induced magnetization dynamics in ferrimagnets. Nat. Commun.
**2021**, 12, 1–9. [Google Scholar] [CrossRef] [PubMed] - Kim, K.-J.; Kim, S.K.; Hirata, Y.; Oh, S.-H.; Tono, T.; Kim, D.-H.; Okuno, T.; Ham, W.S.; Kim, S.; Go, G.; et al. Fast domain wall motion in the vicinity of the angular momentum compensation temperature of ferrimagnets. Nat. Mater.
**2017**, 16, 1187–1192. [Google Scholar] [CrossRef] [PubMed][Green Version] - Siddiqui, S.A.; Han, J.; Finley, J.T.; Ross, C.A.; Liu, L. Current-induced domain wall motion in a compensated ferrimagnet. Phys. Rev. Lett.
**2018**, 121, 057701. [Google Scholar] [CrossRef] [PubMed][Green Version] - Caretta, L.; Mann, M.; Büttner, F.; Ueda, K.; Pfau, B.; Günther, C.M.; Hessing, P.; Churikova, A.; Klose, C.; Schneider, M.; et al. Fast current-driven domain walls and small skyrmions in a compensated ferrimagnet. Nat. Nanotechnol.
**2018**, 13, 1154–1160. [Google Scholar] [CrossRef] [PubMed] - Ikeda, S.; Miura, K.T.; Yamamoto, H.; Mizunuma, K.; Gan, H.D.; Endo, M.; Kanai, S.; Hayakawa, J.; Matsukura, F.; Ohno, H. A perpendicular-anisotropy CoFeB–MgO magnetic tunnel junction. Nat. Mater.
**2010**, 9, 721–724. [Google Scholar] [CrossRef] - Ohmori, H.; Hatori, T.; Nakagawa, S. Perpendicular magnetic tunnel junction with tunneling magnetoresistance ratio of 64% using MgO (100) barrier layer prepared at room temperature. J. Appl. Phys.
**2008**, 103, 07A911. [Google Scholar] [CrossRef] - Yoshikawa, M. Tunnel magnetoresistance over 100% in MgO-based magnetic tunnel junction films with perpendicular magnetic L10-FePt electrodes. IEEE Trans. Magn.
**2008**, 44, 2573–2576. [Google Scholar] [CrossRef] - Rahman, M.T.; Liu, X.; Morisako, A. TiN underlayer and overlayer for TbFeCo perpendicular magnetic recording media. J. Magn. Magn. Mater.
**2006**, 303, e133–e136. [Google Scholar] [CrossRef] - Ceballos, A.; Pattabi, A.; El-Ghazaly, A.; Ruta, S.; Simon, C.P.; Evans, R.F.L.; Ostler, T.; Chantrell, R.W.; Kennedy, E.; Scott, M.; et al. Role of element-specific damping in ultrafast, helicity-independent, all-optical switching dynamics in amorphous (Gd,Tb)Co thin films. Phys. Rev. B
**2021**, 103, 024438. [Google Scholar] [CrossRef] - Sucksmith, W.; Thompson, J.E. The magnetic anisotropy of cobalt. R. Soc. Lond. Ser. A Math. Phys. Sci.
**1954**, 225, 362–375. [Google Scholar] - Okamoto, S.; Kikuchi, N.; Kitakami, O.; Miyazaki, T.; Shimada, Y.; Fukamichi, K. Chemical-order-dependent magnetic anisotropy and exchange stiffness constant of FePt (001) epitaxial films. Phys. Rev. B
**2002**, 66, 024413. [Google Scholar] [CrossRef] - Choi, G.-M.; Min, B.-C.; Shin, K.-H. L1
_{0}Ordering of FePtB Films on a Thin MgO Layer. Appl. Phys. Express**2011**, 4, 023001. [Google Scholar] [CrossRef] - Nagaosa, N.; Sinova, J.; Onoda, S.; Macdonald, A.H.; Ong, N.P. Anomalous hall effect. Rev. Mod. Phys.
**2010**, 82, 1539–1592. [Google Scholar] [CrossRef][Green Version] - Van Kampen, M.M.; Jozsa, C.C.; Kohlhepp, J.J.; LeClair, P.P.; Lagae, L.L.; De Jonge, W.J.M.; Koopmans, B.B. All-optical probe of coherent spin waves. Phys. Rev. Lett.
**2002**, 88, 227201. [Google Scholar] [CrossRef] [PubMed][Green Version] - Binder, M.; Weber, A.; Mosendz, O.; Woltersdorf, G.; Izquierdo, M.; Neudecker, I.; Dahn, J.R.; Hatchard, T.D.; Thiele, J.-U.; Back, C.H.; et al. Magnetization dynamics of the ferrimagnet CoGd near the compensation of magnetization and angular momentum. Phys. Rev. B
**2006**, 74, 134404. [Google Scholar] [CrossRef][Green Version] - Stanciu, C.D.; Kimel, A.V.; Hansteen, F.; Tsukamoto, A.; Itoh, A.; Kirilyuk, A.; Rasing, T. Ultrafast spin dynamics across compensation points in ferrimagnetic GdFeCo: The role of angular momentum compensation. Phys. Rev. B.
**2006**, 73, 220402. [Google Scholar] [CrossRef][Green Version] - Kato, T.; Nakazawa, K.; Komiya, R.; Nishizawa, N.; Tsunashima, S.; Iwata, S. Compositional dependence of g-factor and damping constant of GdFeCo amorphous alloy films. IEEE Trans. Magn.
**2008**, 44, 3380–3383. [Google Scholar] [CrossRef] - Wangsness, R.K. Sublattice effects in magnetic resonance. Phys. Rev.
**1953**, 91, 1085–1091. [Google Scholar] [CrossRef] - Mizukami, S. Fast magnetization precession obsereved in L1
_{0}-FePt epitaxial thin film. Appl. Phys. Lett.**2011**, 98, 052501. [Google Scholar] [CrossRef] - Kim, D.-H.; Okuno, T.; Kim, S.K.; Oh, S.-H.; Nishimura, T.; Hirata, Y.; Futakawa, Y.; Yoshikawa, H.; Tsukamoto, A.; Tserkovnyak, Y.; et al. Low magnetic damping of ferrimagnetic GdFeCo alloys. Phys. Rev. Lett.
**2019**, 122, 127203. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**VSM results. Magnetization hysteresis of the Gd

_{x}Co

_{1-x}alloy, x from 12% to 27%, applying the magnetic field (

**a**) out-of-plane and (

**b**) in-plane directions. (

**c**) The saturation magnetization of the Gd

_{x}Co

_{1-x}alloy. (

**d**) The coercivity field of the out-of-plane anisotropy Gd

_{x}Co

_{1-x}alloy.

**Figure 2.**Angle definition for AHE measurements. The normal to the sample plane is defined as the z axis. When a magnetic field (B

_{app}) is applied at the angle of θ

_{H}with respect to the z axis, the magnetization (M) tilts at an angle of θ

_{M}, which is determined by the balance between the uniaxial anisotropy energy and Zeeman energy.

**Figure 3.**AHE results. The normalized AHE voltage (m

_{z}) of the (

**a**) Gd

_{18}Co

_{82}, (

**b**) Gd

_{21}Co

_{79}, (

**c**) Gd

_{24}Co

_{76}, and (

**d**) Gd

_{27}Co

_{73}alloys. The magnetic field is applied with an oblique angle, θ

_{H}, with respect to the film normal direction. The black/red color corresponds to the θ

_{H}of 0°/85°. The GST analysis of the (

**e**) Gd

_{18}Co

_{82}, (

**f**) Gd

_{21}Co

_{79}, (

**g**) Gd

_{24}Co

_{76}, and (

**h**) Gd

_{27}Co

_{73}alloys. The black squares are the data obtained from (

**a**–

**d**) with θ

_{H}of 85°. The red lines are fittings with Equation (1). The fitted values of the uniaxial anisotropy are summarized in Table 1.

**Figure 4.**TRMOKE results. The magnetization dynamics triggered by a pump pulse in the (

**a**) Gd

_{12}Co

_{88}, (

**b**) Gd

_{18}Co

_{72}, (

**c**) Gd

_{24}Co

_{76}, and (d) Gd

_{27}Co

_{73}alloys. A magnetic field of 0.5 T/0.3 T is applied along the z/x direction for (

**a**)/(

**b**–

**d**). The black circles are the measure data. The red lines are the background demagnetization signal. The extracted precessional motion in the (

**e**) Gd

_{12}Co

_{88}, (

**f**) Gd

_{18}Co

_{72}, (

**g**) Gd

_{24}Co

_{76}, and (

**h**) Gd

_{27}Co

_{73}alloys. The black circles are obtained by subtracting the demagnetization background from the raw data of (

**a**–

**d**). The red lines are fittings by damped cosine function of $\mathrm{cos}\left(2\pi ft\right)\times \mathrm{exp}\left(-t/\tau \right)$. The fitted f values are 3.4, 7.2, 8.9, and 9.4 GHz for (

**e**–

**h**), respectively. The fitted τ values are 600, 160, 80, and 160 ps for (

**e**–

**h**), respectively.

**Figure 5.**Summary of the uniaxial anisotropy (K) and damping constant (α). (

**a**) The K values of the GdCo alloy. The black square/red circle/blue triangle corresponds to the first order (K

_{1})/second order (K

_{2})/total (K

_{1}+ K

_{2}) anisotropy. The error range in the K

_{1}and K

_{2}determination is 20% considering the 10% uncertainty in M

_{S}of VSM measurements and ±1° error in θ

_{H}of AHE measurements. (

**b**) The α values of the GdCo alloy. The black square/red circle corresponds to the effective damping (α

_{eff})/intrinsic damping (α

_{int}). The α

_{eff}is obtained from the fitting of the precession motion. The α

_{int}is obtained using Equation (4) for the Gd = 12%, 18%, and 27%. For the Gd = 24%, we assume α

_{int}is the same as α

_{eff}. The error range in the α

_{eff}determination is 10% considering the fitting uncertainties of f and τ.

**Table 1.**The first-order (K

_{1}) and second-order (K

_{2}) uniaxial anisotropy of the GdCo alloy, with the Gd concentration of 18%, 21%, 24%, and 27%. The K

_{1}

^{eff}and K

_{2}values are determined from the linear fitting of Figure 2e–h. The K

_{1}values are obtained from K

_{1}

^{eff}by K

_{1}= K

_{1}

^{eff}+ μ

_{0}M

^{2}/2.

Colume Heading | Gd_{18}Co_{82} | Gd_{21}Co_{79} | Gd_{24}Co_{76} | Gd_{27}Co_{73} |
---|---|---|---|---|

K_{1}^{eff} (J m^{−3}) | 7.9 × 10^{3} | 15.3 × 10^{3} | 8 × 10^{3} | 3.9 × 10^{3} |

μ_{0}M^{2}/2 (J m^{−3}) | 5.6 × 10^{3} | 1.1 × 10^{3} | 0.1 × 10^{3} | 2.3 × 10^{3} |

K_{1} (J m^{−3}) | 13.5 × 10^{3} | 16.4 × 10^{3} | 8.1 × 10^{3} | 6.2 × 10^{3} |

K_{2} (J m^{−3}) | 2.3 × 10^{3} | 3.1 × 10^{3} | 20 × 10^{3} | 4.5 × 10^{3} |

K_{1} + K_{2} (J m^{−3}) | 15.8 × 10^{3} | 19.5 × 10^{3} | 28.1 × 10^{3} | 10.7 × 10^{3} |

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**MDPI and ACS Style**

Joo, S.; Alemayehu, R.S.; Choi, J.-G.; Park, B.-G.; Choi, G.-M. Magnetic Anisotropy and Damping Constant of Ferrimagnetic GdCo Alloy near Compensation Point. *Materials* **2021**, *14*, 2604.
https://doi.org/10.3390/ma14102604

**AMA Style**

Joo S, Alemayehu RS, Choi J-G, Park B-G, Choi G-M. Magnetic Anisotropy and Damping Constant of Ferrimagnetic GdCo Alloy near Compensation Point. *Materials*. 2021; 14(10):2604.
https://doi.org/10.3390/ma14102604

**Chicago/Turabian Style**

Joo, Sungjung, Rekikua Sahilu Alemayehu, Jong-Guk Choi, Byong-Guk Park, and Gyung-Min Choi. 2021. "Magnetic Anisotropy and Damping Constant of Ferrimagnetic GdCo Alloy near Compensation Point" *Materials* 14, no. 10: 2604.
https://doi.org/10.3390/ma14102604