Effects of the Substitution of 20% Nd for La or Doping with 20% C on the Magnetic Properties and Magnetocaloric Effect in LaFe 11.5 Si 1.5 Compound

: The effects of element substitution and element doping on the magnetic properties and magnetocaloric effect of the LaFe 11.5 Si 1.5 compound were investigated. The crystals of the LaFe 11.5 Si 1.5 , La 0.8 Nd 0.2 Fe 11.5 Si 1.5 , and LaFe 11.5 Si 1.5 C 0.2 compounds all showed cubic NaZn 13 -type structures, but the lattice of the La 0.8 Nd 0.2 Fe 11.5 Si 1.5 shrank and the lattice of the LaFe 11.5 Si 1.5 C 0.2 expanded. All three compounds had the characteristic of ﬁrst-order magnetic transition due to the obvious itinerant-electron metamagnetic (IEM) transition occurring above Curie temperature ( T C ). For the LaFe 11.5 Si 1.5 , La 0.8 Nd 0.2 Fe 11.5 Si 1.5 , and LaFe 11.5 Si 1.5 C 0.2 compounds, the T C were approximately 194 K, 188 K, and 232 K, respectively. Meanwhile, the maximum magnetic entropy changes ( − ∆ S M ) under a magnetic ﬁeld change of 0–3 T were approximately 18.7 J/kg · K, 22.8 J/kg · K, and 16.4 J/kg · K, respectively. The T C was mainly affected by the lattice constant. Furthermore, the − ∆ S M was mainly affected by the latent heat of the ﬁrst-order magnetic transition.


Introduction
Recently, room-temperature magnetic refrigeration technology based on the magnetocaloric effect (MCE) has attracted extensive attention due to its significant advantages, such as its high efficiency, its energy saving, non-toxic and pollution-free qualities, its simple and compact structure, and its low noise [1][2][3][4][5][6]. This technology is expected to be used in devices that produce energy-efficient coatings.
The LaFe 13−x Si x (1.2 ≤ x ≤ 1.6) compound has become one of the preferred materials for magnetic refrigeration technology due to its large magnetocaloric effect, low cost, and environmental protection. Its refrigeration capacity depends on the temperature-induced ferromagnetic-paramagnetic transition and the magnetic-field-induced itinerant-electron metamagnetic (IEM) transition of NaZn 13 -type main phase near the Curie temperature (T C ). However, the T C of the compound is between 190 K and 250 K. It is difficult to meet the refrigeration demand at room temperature [7][8][9][10].
At present, the T C of LaFe 13−x Si x compound is regulated mainly by replacing part of the La with rare-earth elements [11,12], and by replacing part of the Fe with transition-metal elements [13,14], doping interstitial atoms [15,16], etc. For example, Fujieda et al. [17] found that the lattice constant a and T C gradually decreased with increasing Pr content in the La 1−z Pr z (Fe 0.88 Si 0.12 ) 13 compound. When z = 0, a = 1.468 nm and T C = 195 K. Meanwhile, when z = 0.5, a = 1.446 nm and T C = 186 K. Hu et al. [18] found that when x was taken as 0.04, 0.06, and 0.08, the T C of La(Fe 1−x Co x ) 11.9 Si 1.1 were 243, 274, and 301 K, respectively. The ferromagnetic ordering was accompanied by a negative lattice expansion. Balli et al. [19] found that the insertion of 1.3 nitrogen atoms per LaFe 11.7 Si 1.3 formula (i.e., the formation of LaFe 11.7 Si 1.3 N 1.3 ) can increase the lattice parameter and T C from 11.467 to 11.733 Å and from 190 to~230 K, respectively. However, the differences in magnetic properties caused by the different regulation methods have not been systematically compared. In this work, the effects of element substitution and element doping on magnetic properties and magnetocaloric effects are compared. For simplicity, the aim of the element substitution scheme is to replace 20% La with Nd in the LaFe 11.5 Si 1.5 compound (i.e., to form a La 0.8 Nd 0.2 Fe 11.5 Si 1.5 compound). Meanwhile, the aim of the element-doping scheme is to introduce interstitial C with an atomic coefficient ratio of 20% in the LaFe 11.5 Si 1.5 compound (i.e., to form the LaFe 11.5 Si 1.5 C 0.2 compound). This provides an experimental and theoretical basis for the application of the LaFe 13−x Si x compound.

Experimental Procedure
The samples of nominal compositions of LaFe 11.5 Si 1.5 , La 0.8 Nd 0.2 Fe 11.5 Si 1.5 , and LaFe 11.5 Si 1.5 C 0.2 were prepared by arc-melting appropriate amounts of the raw materials of La (99.5% in purity), Nd (99.9% in purity), Fe (99.9% in purity), Si (99.999% in purity), and Fe-C alloy (carbon content: 3.5 wt.%) under a high-purity argon atmosphere. The obtained samples were repeatedly melted several times to ensure homogeneity. Each sample was approximately 100 g. The samples were subsequently sealed in a quartz tube under high vacuum. An annealing treatment at 1393 K for 20 days in a muffle furnace (NJ11-KBF-16Q-V, Zhongxi Huada Technology Co., Ltd., Beijing, China) was carried out; subsequently, the samples were quenched in liquid nitrogen. Finally, the powdered samples were obtained for subsequent testing.
A powder X-ray diffraction (XRD; D8-Advance, Bruker, Karlsruhe, Germany) was performed by using Cu Kα radiation at room temperature to identify the crystal structure and crystal lattice constants. A vibrating sample magnetometer (VSM; 7410, LakeShore, Westerville, OH, USA) was used to measure the thermomagnetic curves under an external magnetic field of 0.01 T and isothermal magnetization curves under an external magnetic field change of 0-3 T. The VSM-7410 is currently the most sensitive vibrating sample magnetometer in the world, and it can guarantee at least 5 × 10 −7 emu. The isothermal magnetic entropy change (−∆S) was obtained according to the Maxwell relation [20]:

Results and Discussion
The XRD patterns of the LaFe 11.5 Si 1.5 , La 0.8 Nd 0.2 Fe 11.5 Si 1.5 , and LaFe 11.5 Si 1.5 C 0.2 are shown in Figure 1. According to the comparison with the PDF card in Jade software, all these samples were crystallized in a single phase with a cubic NaZn 13 -type structure (the space group is Fm-3c). Compared with the LaFe 11.5 Si 1.5 , the fact that the Nd had a smaller atomic radius than the La may have caused the lattice shrinkage in the La 0.8 Nd 0.2 Fe 11.5 Si 1.5 and its XRD diffraction peaks to move to a slightly higher angle. Furthermore, the introduction of interstitial C atoms may have caused the lattice expansion in the LaFe 11.5 Si 1.5 C 0.2 and its XRD diffraction peaks to move to a slightly lower angle. By using Jade software, the XRD data were refined to obtain the lattice constants. The lattice constants of the LaFe 11.5 Si 1.5 , La 0.8 Nd 0.2 Fe 11.5 Si 1.5 , and LaFe 11.5 Si 1.5 C 0.2 were approximately 11.475 Å, 11.462 Å, and 11.484 Å, respectively. The different lattice constants could prove the shrinkage or expansion of the afore-mentioned lattices. Coatings 2022, 12, x FOR PEER REVIEW 3 of 7 The thermomagnetic curves (i.e., M-T curves) of the LaFe11.5Si1.5, La0.8Nd0.2Fe11.5Si1.5, and LaFe11.5Si1.5C0.2 under an external magnetic field of 0.01 T are shown in Figure 2. With the increase in temperature, the magnetic transition from the ferromagnetic state to paramagnetic state can be observed in all the samples. The TC can be defined as the temperature at which the first temperature derivative of the magnetization has its highest value in the heating process [21]. The TC of the LaFe11.5Si1.5, La0.8Nd0.2Fe11.5Si1.5, and LaFe11.5Si1.5C0.2 were approximately 194, 188, and 232 K, respectively. The difference in TC can be explained from the following two perspectives. (1) The change in TC may have been related to the number of electrons contributed by the different 3d elements to the conduction band. The changes in the number of electrons in the conduction band may have led to changes in the 3d state density near the Fermi energy [22]. The substitution of La by Nd in the LaFe11.5Si1.5 may have reduced the number of 3d electrons, resulting in a lower TC. Correspondingly, the introduction of interstitial C in the LaFe11.5Si1.5 may have increased the number of 3d electrons, resulting in a higher TC. (2) The TC is closely related to the Fe-Fe bond length, especially the Fe Ⅰ (8b)-Fe Ⅱ (96i) bond length [23]. The substitution of the La by the Nd with a smaller atomic radius may have led to the lattice shrinkage, thus reducing the Fe-Fe bond length and weakening the Fe-Fe exchange interaction, resulting in a lower TC. Correspondingly, the introduction of interstitial C may have led to the lattice expansion, thus increasing the Fe-Fe bond length and enhancing the Fe-Fe exchange interaction, resulting in a higher TC. Moreover, the M-T curves of each sample show obvious thermal hysteresis. The thermal hysteresis can be estimated from the difference in the temperature of the magnetic transition between cooling and heating, and it is evidence of the first-order magnetic transition of materials. The thermal hysteresis of the LaFe11.5Si1.5, La0.8Nd0.2Fe11.5Si1.5, and LaFe11.5Si1.5C0.2 were approximately 2.8, 4.3, and 1.3 K, respectively. The thermomagnetic curves (i.e., M-T curves) of the LaFe 11.5 Si 1.5 , La 0.8 Nd 0.2 Fe 11.5 Si 1.5 , and LaFe 11.5 Si 1.5 C 0.2 under an external magnetic field of 0.01 T are shown in Figure 2. With the increase in temperature, the magnetic transition from the ferromagnetic state to paramagnetic state can be observed in all the samples. The T C can be defined as the temperature at which the first temperature derivative of the magnetization has its highest value in the heating process [21]. The T C of the LaFe 11.5 Si 1.5 , La 0.8 Nd 0.2 Fe 11.5 Si 1.5 , and LaFe 11.5 Si 1.5 C 0.2 were approximately 194, 188, and 232 K, respectively. The difference in T C can be explained from the following two perspectives. (1) The change in T C may have been related to the number of electrons contributed by the different 3d elements to the conduction band. The changes in the number of electrons in the conduction band may have led to changes in the 3d state density near the Fermi energy [22]. The substitution of La by Nd in the LaFe 11.5 Si 1.5 may have reduced the number of 3d electrons, resulting in a lower T C . Correspondingly, the introduction of interstitial C in the LaFe 11.5 Si 1.5 may have increased the number of 3d electrons, resulting in a higher T C . (2) The T C is closely related to the Fe-Fe bond length, especially the Fe I (8b)-Fe II (96i) bond length [23]. The substitution of the La by the Nd with a smaller atomic radius may have led to the lattice shrinkage, thus reducing the Fe-Fe bond length and weakening the Fe-Fe exchange interaction, resulting in a lower T C . Correspondingly, the introduction of interstitial C may have led to the lattice expansion, thus increasing the Fe-Fe bond length and enhancing the Fe-Fe exchange interaction, resulting in a higher T C . Moreover, the M-T curves of each sample show obvious thermal hysteresis. The thermal hysteresis can be estimated from the difference in the temperature of the magnetic transition between cooling and heating, and it is evidence of the first-order magnetic transition of materials. The thermal hysteresis of the LaFe 11.5 Si 1.5 , La 0.8 Nd 0.2 Fe 11.5 Si 1.5 , and LaFe 11.5 Si 1.5 C 0.2 were approximately 2.8, 4.3, and 1.3 K, respectively. The isothermal magnetization curves (i.e., M-H curves) of the La La0.8Nd0.2Fe11.5Si1.5, and LaFe11.5Si1.5C0.2 measured in a wide temperature range und ternal magnetic field change of 0-3 T are shown in Figure 3. For the temperatu measured in Figure 3, the temperature step is 2 K in the vicinity of TC and 5 K for t far away from TC. For all the samples, at temperatures well below TC, the magn increased rapidly with the increasing magnetic field and approached saturation magnetic fields. At temperatures well above TC, an approximately linear relation tween the magnetization and the magnetic field can be observed. It is noteworth the samples underwent a magnetic-field-induced IEM transition from the para state to the ferromagnetic state at temperatures slightly higher than TC. For the hysteresis, the La0.8Nd0.2Fe11.5Si1.5 was the most obvious, the LaFe11.5Si1.5 was the sec the LaFe11.5Si1.5C0.2 was the weakest. The greater magnetic hysteresis was not cond the effective refrigerating efficiency of the samples [11]. In addition, for the th pounds, since the magnetic transition was accompanied by a sudden change in the volume (magnetoelastic coupling), there was latent heat in the phase transition d magnetic transition. The appearance of thermal hysteresis and magnetic hystere M-T and M-H curves further proves that these three compounds are typical first-or netic transition materials. The isothermal magnetization curves (i.e., M-H curves) of the LaFe 11.5 Si 1.5 , La 0.8 Nd 0.2 Fe 11.5 Si 1.5 , and LaFe 11.5 Si 1.5 C 0.2 measured in a wide temperature range under an external magnetic field change of 0-3 T are shown in Figure 3. For the temperature range measured in Figure 3, the temperature step is 2 K in the vicinity of T C and 5 K for the range far away from T C . For all the samples, at temperatures well below T C , the magnetization increased rapidly with the increasing magnetic field and approached saturation at lower magnetic fields. At temperatures well above T C , an approximately linear relationship between the magnetization and the magnetic field can be observed. It is noteworthy that all the samples underwent a magnetic-field-induced IEM transition from the paramagnetic state to the ferromagnetic state at temperatures slightly higher than T C . For the magnetic hysteresis, the La 0.8 Nd 0.2 Fe 11.5 Si 1.5 was the most obvious, the LaFe 11.5 Si 1.5 was the second, and the LaFe 11.5 Si 1.5 C 0.2 was the weakest. The greater magnetic hysteresis was not conducive to the effective refrigerating efficiency of the samples [11]. In addition, for the three compounds, since the magnetic transition was accompanied by a sudden change in the unit-cell volume (magnetoelastic coupling), there was latent heat in the phase transition during the magnetic transition. The appearance of thermal hysteresis and magnetic hysteresis in the M-T and M-H curves further proves that these three compounds are typical first-order magnetic transition materials.
The Arrott plots of the LaFe 11.5 Si 1.5 , La 0.8 Nd 0.2 Fe 11.5 Si 1.5 , and LaFe 11.5 Si 1.5 C 0.2 are shown in Figure 4. According to studies on the Landau theory and Arrott plots [24], the phase transition properties can be inferred from the Arrott plot near the T C . The fourthorder coefficient of the Landau free-energy expansion is negative when the metamagnetic transition behavior occurs, which is manifested by the appearance of an inflection point or a negative slope on the Arrott plot [21,25]. Both the inflection and the negative slope on the Arrott plots can be observed in Figure 4, which once again proves that obvious first-order magnetic transition occurred. In addition, the inclination degree of the negative slope could largely predict the intensity of the lowest maximal value of −∆S (i.e., −∆S M ) [21]. the LaFe11.5Si1.5C0.2 was the weakest. The greater magnetic hysteresis was not conducive to the effective refrigerating efficiency of the samples [11]. In addition, for the three compounds, since the magnetic transition was accompanied by a sudden change in the unit-cell volume (magnetoelastic coupling), there was latent heat in the phase transition during the magnetic transition. The appearance of thermal hysteresis and magnetic hysteresis in the M-T and M-H curves further proves that these three compounds are typical first-order magnetic transition materials.  The Arrott plots of the LaFe11.5Si1.5, La0.8Nd0.2Fe11.5Si1.5, and LaFe11.5Si1.5C0.2 are shown in Figure 4. According to studies on the Landau theory and Arrott plots [24], the phase transition properties can be inferred from the Arrott plot near the TC. The fourth-order coefficient of the Landau free-energy expansion is negative when the metamagnetic transition behavior occurs, which is manifested by the appearance of an inflection point or a negative slope on the Arrott plot [21,25]. Both the inflection and the negative slope on the Arrott plots can be observed in Figure 4, which once again proves that obvious first-order magnetic transition occurred. In addition, the inclination degree of the negative slope could largely predict the intensity of the lowest maximal value of −ΔS (i.e., −ΔSM) [21]. The −ΔS of the LaFe11.5Si1.5, La0.8Nd0.2Fe11.5Si1.5, and LaFe11.5Si1.5C0.2 as a function of temperature for an external magnetic field change of 0-3 T are shown in Figure 5. The −ΔSM values are 18.7 J/kg·K for LaFe11.5Si1.5, 22.8 J/kg·K for La0.8Nd0.2Fe11.5Si1.5, and 16.4 J/kg·K for LaFe11.5Si1.5C0.2. These results verify the previous inference of the Arrott plots. The negative slope of the La0.8Nd0.2Fe11.5Si1.5 compound is the largest in Figure 4 and its −ΔSM is also the largest. The MCE value in a variable magnetic field can be determined by the −ΔSM value. The La0.8Nd0.2Fe11.5Si1.5 compound has the largest −ΔSM value, indicating it has the maximum MCE. The main magnetic properties of the LaFe11.5Si1.5, La0.8Nd0.2Fe11.5Si1.5, and LaFe11.5Si1.5C0.2 are summarized in Table 1. In the near future, the use of comprehensive utilization of element substitution and element doping is expected to obtain magnetic refrigeration materials with high TC and −ΔSM.  Table 1. In the near future, the use of comprehensive utilization of element substitution and element doping is expected to obtain magnetic refrigeration materials with high T C and −∆S M . largest. The MCE value in a variable magnetic field can be determined by the −ΔS The La0.8Nd0.2Fe11.5Si1.5 compound has the largest −ΔSM value, indicating it has t mum MCE. The main magnetic properties of the LaFe11.5Si1.5, La0.8Nd0.2Fe11.5S LaFe11.5Si1.5C0.2 are summarized in Table 1. In the near future, the use of compr utilization of element substitution and element doping is expected to obtain mag frigeration materials with high TC and −ΔSM.

Conclusions
In this work, the magnetic properties and magnetocaloric effect of the LaFe 11.5 Si 1.5 , La 0.8 Nd 0.2 Fe 11.5 Si 1.5 , and LaFe 11.5 Si 1.5 C 0.2 compounds were studied. All the compounds crystallized in a single phase with a cubic NaZn 13 -type structure. The substitution of 20% Nd for La in LaFe 11.5 Si 1.5 can cause lattice shrinkage, accompanied by lower T C and higher −∆S M . Furthermore, doping with 20% C in LaFe 11.5 Si 1.5 can cause lattice expansion, accompanied by higher T C and lower −∆S M . The La 0.8 Nd 0.2 Fe 11.5 Si 1.5 compound had the most obvious first-order magnetic transition characteristics, including the most obvious IEM phenomenon, while the LaFe 11.5 Si 1.5 C 0.2 compound had a T C that was relatively close to the room temperature. The use of comprehensive utilization of element substitution and element doping is expected to obtain magnetic refrigeration materials with high T C and −∆S M .

Conflicts of Interest:
We declare that we have no conflict of interest other than the above-mentioned project funds.