Magnetic Properties and Magnetocaloric Effect in Gd100-xCox Thin Films

: We investigated the magnetic and magnetocaloric properties of Gd 100-x Co x ( x = 40 to 56) thin ﬁlms fabricated by the sputtering technique. Under an applied ﬁeld change ∆ H = 20 kOe , the magnetic entropy change ( ∆ S m ) decreases from 2.64 Jkg − 1 K − 1 for x = 44 to about 1.27 Jkg − 1 K − 1 for x = 56. Increasing the Co concentration from x = 40 to 56 shifts the Curie temperature of Gd 100-x Co x ( x = 40 to 56) thin ﬁlms from 180 K toward 337 K. Moreover, we extracted the values of critical parameters T c , β , γ , and δ by using the modiﬁed Arrott plot methods. The results indicate the presence of a long-range ferromagnetic order. More importantly, we showed that the relative cooling power (RCP), which is a key parameter in magnetic refrigeration applications, is strongly enhanced by changing the Co concentration in the Gd 100-x Co x thin ﬁlms. Our ﬁndings help pave the way toward the enhancement of the magnetocaloric e ﬀ ect in magnetic thin ﬁlms.


Introduction
The study of the magnetocaloric effect as a means for magnetic cooling has attracted rising interest due to the prospect of replacing conventional refrigeration systems [1,2]. Recently, various experimental and theoretical works have been carried out on magnetic materials showing a large magnetocaloric effect [3,4]. Moreover, many studies of the magnetocaloric effect (MCE) for ambient applications have been performed on rare-earth based compounds, since the latter show high magnetic moments. However, the MCE was found to be rather small for this class of material. Indeed, the largest MCE was reported for the rare-earth element Gd, where the ∆S M value goes up to −9.8 Jkg −1 K −1 and ∆T ad near T c = 293 K is about 11.6 K for a magnetic field change of 5T [5]. In 1997, Pecharsky and Gschneidner demonstrated in their pioneering work a giant MCE in the compound Gd 5 Si 2 Ge 2 [6], a discovery that reawakened interest in magnetic refrigeration for ambient applications. Later, several different classes of materials were found to exhibit giant MCEs near room temperature, such as MnAs 1-x Sb x [7],  and a temperature ranging from 150 to 290 K. The magnetization curves below the Tc show a non-linear behavior with a tendency towards saturation under the applied magnetic field, which indicates a ferromagnetic behavior. However, the magnetization above the Tc shows a linear behavior, which reflects a paramagnetic behavior. The latter is due to the thermal agitation which disarranges the magnetic moments. In order to determine the nature of the transition in Gd56Co44 alloy film, we used the Arrott plot method and employed the Inoue-Shimizu model [28]. According to the Banerjee criteria [29], the positive (resp. negative) slope of the M 2 (H/M) curves indicates a second-(resp. first-) order transition. As shown in Figure 2b, only positive slopes of the M 2 (H/M) curves were observed for the Gd56Co44 alloy film, indicating that the PM-FM transition is a second order transition. Based on the magnetization curves shown in Figure 2a, the isothermal magnetic entropy change caused by the variation of the applied magnetic field from 0 to 20 H kOe Δ = can be determined by using the Maxwell relation:

Magnetocaloric Effect Properties
Figure 2a shows isothermal magnetization M (H) curves measured for Gd 56 Co 44 alloy film under an applied magnetic field up to ∆H = 20 kOe and a temperature ranging from 150 to 290 K. The magnetization curves below the T c show a non-linear behavior with a tendency towards saturation under the applied magnetic field, which indicates a ferromagnetic behavior. However, the magnetization above the T c shows a linear behavior, which reflects a paramagnetic behavior. The latter is due to the thermal agitation which disarranges the magnetic moments. In order to determine the nature of the transition in Gd 56 Co 44 alloy film, we used the Arrott plot method and employed the Inoue-Shimizu model [27]. According to the Banerjee criteria [28], the positive (resp. negative) slope of the M 2 (H/M) curves indicates a second-(resp. first-) order transition. As shown in Figure 2b, only positive slopes of the M 2 (H/M) curves were observed for the Gd 56 Co 44 alloy film, indicating that the PM-FM transition is a second order transition.  and a temperature ranging from 150 to 290 K. The magnetization curves below the Tc show a non-linear behavior with a tendency towards saturation under the applied magnetic field, which indicates a ferromagnetic behavior. However, the magnetization above the Tc shows a linear behavior, which reflects a paramagnetic behavior. The latter is due to the thermal agitation which disarranges the magnetic moments. In order to determine the nature of the transition in Gd56Co44 alloy film, we used the Arrott plot method and employed the Inoue-Shimizu model [28]. According to the Banerjee criteria [29], the positive (resp. negative) slope of the M 2 (H/M) curves indicates a second-(resp. first-) order transition. As shown in Figure 2b, only positive slopes of the M 2 (H/M) curves were observed for the Gd56Co44 alloy film, indicating that the PM-FM transition is a second order transition. Based on the magnetization curves shown in Figure 2a, the isothermal magnetic entropy change caused by the variation of the applied magnetic field from 0 to 20 H kOe Δ = can be determined by using the Maxwell relation: Based on the magnetization curves shown in Figure 2a, the isothermal magnetic entropy change caused by the variation of the applied magnetic field from 0 to ∆H = 20kOe can be determined by using the Maxwell relation: We compared the values of -∆S M obtained for the investigated Gd 100−x Co x alloys with x = 56, 52, 48, 44, and 40 with those obtained for a 100 nm-thick Gd layer, as depicted in Figure 3b. The maximum values of the -∆S M peak (T) curves are obtained close to T c . The peak temperature in -∆S M (T) is shifted towards high temperature by increasing x, which is most likely due to the enhancement of the Gd-Co indirect interaction. Figure 3b shows the evolution of the peak entropy change value and its full width at half maximum (FWHM) as a function of the Co concentration x. It can be clearly seen that the decrease in peak -∆S M is accompanied by an increase of the FWHM. The maximal entropy change is observed for x = 44, and is about 2.65 J/kg.K. Figure  We compared the values of -ΔSM obtained for the investigated Gd100−xCox alloys with x = 56, 52, 48, 44, and 40 with those obtained for a 100 nm-thick Gd layer, as depicted in Figure 3b. The maximum values of the -∆SM peak (T) curves are obtained close to Tc. The peak temperature in -∆SM (T) is shifted towards high temperature by increasing x, which is most likely due to the enhancement of the Gd-Co indirect interaction. Figure 3b shows the evolution of the peak entropy change value and its full width at half maximum (FWHM) as a function of the Co concentration x. It can be clearly seen that the decrease in peak -∆SM is accompanied by an increase of the FWHM. The maximal entropy change is observed for x = 44, and is about 2.65 J/kg.K. Figure 3c shows the evolution of -∆SM peak as a function of Tc −2/3 for the investigated Gd100-xCox alloys (x = 40, 44, 48, 52, 56) under the applied magnetic field of 2 T. It can be seen from Figure 3b that -∆SM peak changes linearly with Tc −2/3 (or (708.8-8.83x) −2/3 with a linear correlation coefficient above 0.992), indicating that -∆SM peak of the Gd100−xCox alloys can be easily tailored by adjusting x. In addition to the isothermal entropy change, the relative cooling power (RCP) is also a key parameter to evaluate the magnetocaloric performance. The RCP considers both the isothermal magnetic entropy change and the working temperature range of magnetocaloric materials, and it is given by the following formula:

Magnetocaloric Effect Properties
where TFWHM is the full width at half maximum obtained from the temperature at half the maximum peak value of the ΔSM curve. Figure 4 shows the evolution of the RCP of the Gd100-xCox thin films as a function of the applied magnetic field. The RCP value increases with the applied magnetic field. Moreover, all the studied Gd100−xCox alloys present a large RCP value around 140 J/kg for In addition to the isothermal entropy change, the relative cooling power (RCP) is also a key parameter to evaluate the magnetocaloric performance. The RCP considers both the isothermal magnetic entropy change and the working temperature range of magnetocaloric materials, and it is given by the following formula: where T FWHM is the full width at half maximum obtained from the temperature at half the maximum peak value of the ∆S M curve. Figure 4 shows the evolution of the RCP of the Gd 100-x Co x thin films as a function of the applied magnetic field. The RCP value increases with the applied magnetic field.
Moreover, all the studied Gd 100−x Co x alloys present a large RCP value around 140 J/kg for ∆H = 20 kOe, which is significantly higher than the RCP of the Gd thin films. Table 1 shows a summary of the present results, the MCE properties of the GdCo thin films, as well as some others reported in the literature. The high values of the RCP and -∆S m (T) obtained for the Gd 100−x Co x thin film alloys is very promising for magnetic refrigeration applications with a wide temperature range.

Universal Scaling Analysis
Universal scaling analysis indicates that the Co helps to homogenize the magnetic properties in GdCo thin films [25]. Such a method should remove the temperature and field dependence of the set of ( , ) S H T Δ Δ curve (for fixed H Δ ), so that all curves processed with the same scaling protocol collapse onto a single universal curve. A failure to display this universal collapse can be attributed to material inhomogeneity [31], likely in the form of a distribution of exchange energies. Figure 5 shows the universal curve construction for each of the studied Gd100−xCox thin films by plotting ΔS' against θ, where is the rescaled entropy change and θ is the rescaled temperature variable as follows: with Tr1 and Tr2 are reference temperatures chosen at 50% of max S Δ above Tc. As shown in Figure 5, the curves do not collapse into one single curve. Moreover, one can see from Figure 5 that the degree of collapse increases with the Co concentration. It has been shown that a failure to collapse (such as seen for x = 44) can be attributed to inhomogeneity within the material.

Universal Scaling Analysis
Universal scaling analysis indicates that the Co helps to homogenize the magnetic properties in GdCo thin films [25]. Such a method should remove the temperature and field dependence of the set of ∆S(∆H, T) curve (for fixed ∆H), so that all curves processed with the same scaling protocol collapse onto a single universal curve. A failure to display this universal collapse can be attributed to material inhomogeneity [30], likely in the form of a distribution of exchange energies. Figure 5 shows the universal curve construction for each of the studied Gd 100−x Co x thin films by plotting ∆S against θ, where ∆S = ∆S M /∆S peak M is the rescaled entropy change and θ is the rescaled temperature variable as follows: with T r1 and T r2 are reference temperatures chosen at 50% of ∆S max above T c . As shown in Figure 5, the curves do not collapse into one single curve. Moreover, one can see from Figure 5 that the degree

Critical Exponents
The second-order ferromagnetic to paramagnetic transition near the Curie temperature can be characterized by a set of critical exponents, where β corresponds to the spontaneous magnetization, γ corresponds to the initial susceptibility, and δ corresponds to the critical magnetization isotherm These steps are therefore repeated until the iterations converge to the optimum values of β , γ , and Tc. Therefore, the MAPs shown in Figure 6a yielded the following results: β = 0.47 ± 0.009 and γ = 1.15 ± 0.1. Figure 6b depicts the modified Arrott plots, which show that all lines are parallel to

Critical Exponents
The second-order ferromagnetic to paramagnetic transition near the Curie temperature can be characterized by a set of critical exponents, where β corresponds to the spontaneous magnetization, γ corresponds to the initial susceptibility, and δ corresponds to the critical magnetization isotherm at T c . The critical exponents possess the following power-law dependences [31]: where ε = (T − T c )/T c is the reduced temperature, and m 0 and h 0 m 0 are the critical amplitudes. Initial values of β = 0.4 and γ = 1.33 are selected, then a plot of M 1/β as a function of (H/M) 1/γ was obtained [12]. The high field linear region (H > 1) is used for the analysis, because the Modified Arrott Plots (MAPs) tend to deviate from linearity at low field due to the mutually misaligned magnetic domains. The values of M s and χ −1 0 can be then determined from the intersection of the linearly extrapolated curves with the M 1/β and (H/M) 1/γ , respectively. Figure 6a shows the temperature dependence of χ −1 0 (T) and M s (T), which are fitted with Equations (1) and (2). The fitting enables us to obtain new values of β and γ, which are then used to construct new MAPs. These steps are therefore repeated until the iterations converge to the optimum values of β, γ, and T c . Therefore, the MAPs shown in Figure 6a yielded the following results: β = 0.47 ± 0.009 and γ = 1.15 ± 0.1. Figure 6b Figure 6c shows the magnetic field dependence of magnetization at T c for Gd 56 Co 44 alloy film, while the critical isotherm on a log-log scale is shown in the inset. The extracted value of δ is 3.37 ± 0.001. δ can also be extracted via the Widom scaling relation [32]: By using the critical parameters β and γ obtained via the MAPs, we deduce from the Widom scaling relation a δ value of 3.44, thus confirming the reliability of the critical exponents extracted from the experimental data. Moreover, the reliability of β and γ can be confirmed via the following scaling hypothesis: where f ± are regular analytical functions with f + and f − for above and below T c , respectively. The scaling relation indicates that M(H, ε)ε −β as a function Hε −(β+γ) should yield two universally different branches, one for T > T c and the other for T < T c . By using the values of β, γ, and T c from the MAPs method in Figure 6d, one can clearly see that magnetization data falls into two universal curves, one for T > T c and the other for T < T c , which agrees with the scaling theory and confirms that the obtained values for the critical exponents and T c are reliable. Moreover, these critical exponents are very similar to the theoretical values from the mean field model (γ = 1.0, β = 0.5, and δ = 3) [33]. We also analyzed the critical behavior of magnetic phase transition using Arrott plots for Gd 100−x Co x (x = 40, 48, 52, and 56), which follows the mean field model. Consistent with the existence of long-range ferromagnetic interaction, the critical behavior analysis in the vicinity of T c demonstrates that the magnetism of the GdCo thin films is governed by the long range nature of ferrimagnetism in this system.

Conclusions
In summary, we fabricated Gd 100−x Co x alloy films on a silicon substrate using sputtering techniques. The magnetic and magnetocaloric effect of Gd 100-x Co x (x = 44, 48, 52, 56) thin films were investigated. The Curie temperature increases with the Co concentration, and the maximal magnetic entropy change reaches a maximum at the Curie temperature. Under an applied magnetic field of ∆H = 20 kOe, the value of -∆S M is found to be 2.64 for x = 44. Moreover, the studied Gd 100−x Co x alloy films present an important relative cooling power (RCP) higher than 140 J/kg. Moreover, the investigation of the critical properties of the second-order ferromagnetic transition of the Gd 100−x Co x alloy films demonstrate that the magnetic interaction around T c can be described with the mean field model corresponding to long-range interaction.