直接利用磁场和温度精确确定磁性材料La0.67Ca0.33MnO3和Pr0.7Sr0.3MnO3的电阻率

电阻率是研究钙钛矿结构锰氧化物磁性材料的重要参数之一,它与温度和外加磁场有密切关系.本文的工作之一是寻找合适的方法,确定在金属-绝缘体转换过程中,不同磁场情况下,材料La0.67Ca0.33MnO3和Pr0.7Sr0.3MnO3的电阻率随温度变化的数学解析关系.通过非线性数值拟合,找到了满足这一关系的函数为双曲正切修正的高斯函数.同时,获得金属-绝缘体转换时居里温度Tc满足的微分方程以及与该温度对应的最大电阻率ρmax.本文的另一个工作是寻求最大电阻率ρmax和磁场之间的函数关系,发现采用玻尔兹曼函数可以精确反映两者之间的数学联系.两项工作得到的数学拟合结果与实验数据之间的最小相关系数为0.998,最大平均相对误差4.35％,说明数据拟合的结果与实验结果十分符合.

Prediction of the magneto-resistivity of manganese oxides La0.67Ca0.33MnO3 and Pr0.7Sr0.3MnO3 via temperature and magnetic field

The resistivity related to temperature and magnetic field is a crucial parameter for determining the physical properties of the perovskite-type manganese oxide. The first task of this work is to find out a suitable method to predict the resistivities of La_0.67Ca_0.33MnO₃ and Pr_0.7Sr_0.3MnO₃ in the process from insulator phase to the metal phase via the temperature and the magnetic field. Based on the nonlinear numerical fitting, an analytical expression showing the dependence of the resistivity on temperature both less than and higher than the metal-insulator transition Curie temperature (T_C) at different magnetic fields, and the maximum resistivity (ρ_max) corresponding to each Curie temperature is acquired. The second task of this work is to trace a mathematical relationship between the magnetic field and the maximum resistivity, and the Boltzmann function can be used successfully by numerical fitting. The lowest correlation coefficient and the largest average relative error between the actual and the calculated data are 0.998 and 4.35% in all considered cases respectively.