Tham khảo tài liệu 'physics of magnetism magnetic materials 2011 part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | SECTION . THE CURIE LAW 13 Substitution of this result into Eq. leads to d ị 4 l x g Jx M Ngq-B-y- I In-------- p--- dx ex - 1 die to- ax I e T i e - e ix Since sinh X ex e 2 one obtains . d I M Ngựfí In ax I sinh sinh After carrying out the differentiation one finds M TVgKB JBj y with Bj y the so-called Brillouin function given by 2J 1 2J l y 1 __iL y B1W 27 27 - 27 2Ĩ with T rr y ĩ -. It is good to bear in mind that in this expression H is the field responsible for the level splitting of the 2J 1 ground-state manifold. In most cases H is the externally applied magnetic field. We shall see however in one of the following chapters that in some materials also internal fields are present which may cause the level splitting of the 2 J 1 -mainfold. Expression makes it possible to calculate the magnetization for a system of N atoms with quantum number J at various combinations of applied field and temperature. Experimental results for the magnetization of several paramagnetic complex salts containing Cr3 Fe3 and Gd3 ions measured in various field strengths at low temperatures are shown in Fig. . The curves through the data points have been calculated by means of Eq. . There is good agreement between the calculations and the experimental data. . THE CURIE LAW Expression becomes much simpler in cases where the temperature is higher and the field strength lower than for most of the data shown in Fig. . In order to see this we will assume that we wish to study the magnetization at room temperature of a complex salt of Nd3 in an external field H 80 kA m-1 which corresponds to an external flux density B i oH T 1O 4it X 10-7 T AnT1 more details about units will be discussed 14 CHAPTER 3. PARAMAGNETISM OF FREE IONS Figure . Magnetization M in HB atom of several paramagnetic complex salts containing Gd3 Fe3 and Cr3 plotted versus ịLtỳH T in T K . After Henry 1952 . in Chapter 8 . For Nd3 one .
