一级磁结构相变材料Mn0.6Fe0.4NiSi0.5Ge0.5和Ni50Mn34Co2Sn14的磁热效应与磁场的线性相关性

磁熵变（△S_M）与磁场（μ₀H）的相关性已在很多二级相变材料中被研究并报道，但一级相变材料的磁热效应与磁场相关性还少有报道.本文在具有一级磁结构相变的Mn_0.6Fe_0.4NiSi_0.5Ge_0.5材料中研究发现△S_M与μ₀H存在线性相关性，并通过麦克斯韦关系式的数值分析详细讨论了这一线性相关性的来源.同时，进一步发现在低磁场时，△S_M近似正比于μ₀H的平方.该线性相关性同样在一级磁结构相变Ni₅₀Mn₃₄Co₂Sn₁₄材料中得到了印证.但由于一级磁弹相变LaFe_11.7Si_1.3材料相变温度具有更强的磁场依赖性，不具有△S_M的线性相关性，因此，本研究表明，当磁结构相变材料的相变温度具有弱磁场依赖性时，△S_M与μ₀H具有线性相关性.进而，在磁场未达到相变饱和磁场以下，利用△S_M与μ₀H的线性相关性可以有效推测更高磁场下的△S_M.

Linear dependence of magnetocaloric effect on magnetic field in Mn0.6Fe0.4NiSi0.5Ge0.5 and Ni50Mn34Co2Sn14 with first-order magnetostructural transformation

The study on the field dependence of magnetocaloric effect (MCE) is considered to be of fundamental and practical importance, since it not only guides us in understanding and optimizing the MCE, but also helps us estimate the MCE for higher magnetic field which is not available in some laboratories. The magnetic field (μ₀H) dependence of magnetic entropy change (△S_M) has been studied extensively in many materials with second-order magnetic transition. However, the field dependence of MCE for first-order magnetic transition (FOMT) materials has not been sufficiently studied due to their complexity and diversity. In the present work, polycrystalline Mn_0.6Fe_0.4NiSi_0.5Ge_0.5, Ni₅₀Mn₃₄Co₂Sn₁₄, and LaFe_11.7Si_1.3 compounds with FOMT are prepared, and the magnetic and magnetocaloric properties are investigated systematically. In order to avoid a spurious △S_M, the M-μ₀H curves are measured in a loop process. The M-μ₀H curves are corrected by taking into account the demagnetization effect, i.e. H_int=H_ext-N_dM. It is found that the -△S_M follows a linear relationship -△S_M=-△S₀ +κμ₀H with the variation of magnetic field in Mn_0.6Fe_0.4NiSi_0.5Ge_0.5 compound when μ₀H > 1 T. In addition, it is also noted that the △S_M is approximately proportional to the square of μ₀H at low field. The origin of this linear relationship between △S_M and μ₀H at high field and the deviation at low field are discussed by numerically analyzing the Maxwell relation. In addition to the △S_M peak value, it is found that other △S_M values at different temperatures also follow the linear relation at high field by performing the same numerical analysis. Moreover, it is found that the fitted △S_M curve matches the experimental data very well. This result indicates that the linear relationship between △S_M and μ₀H could be utilized to predict the △S_M for higher magnetic field change when the field is lower than the saturation field. The applicability of this linear relationship is also verified in other systems with first-order magnetostructural transformation, such as Ni₅₀Mn₃₄Co₂Sn₁₄. However, it fails to describe the field dependence of △S_M in LaFe_11.7Si_1.3, which exhibits a strong field dependence of transition temperature. Consequently, our study reveals that a linear dependence of △S_M on μ₀H could occur in magnetostructural transition materials, which show the field independence of transition temperature.