Journal of Magnetism and Magnetic Materials 42 (1984) 163-166 163 North-Holland, Amsterdam THE TEMPERATURE DEPENDENCE OF MAGNETIZATION OF Gd-Tb ALLOYS W.D. CORNER, B. SZPUNAR * Physics Department, University of Durham, South Road, Durham DH1 3LE, UK D. FORT and D.W. JONES Centre for Materials Science, University of Birmingham, Birmingham B15 2TT, UK Received 1 August 1983; in revised form 26 October 1983 It is shown that a mean field theory can describe very closely the variation of magnetization with temperature found in a series of Gd-Tb alloys. The proportionality of the exchange constants to the density of the states at the Fermi energy has been confirmed. The values for the densities of states for Gd and Tb required for satisfactory fitting of the experimental results are in agreement with values calculated from electronic specific heat measurements. 1. Introduction It has been shown for rare earth-transition metal (RE-T) alloys [1] that the mean (molecular) field theory with properly chosen exchange inter- action constants can describe well the variation of magnetic moment with temperature. The exchange interaction constant between a and b atoms in a ferromagnetic alloy can be expressed in the follow- ing form, Jab = --JaJbPalloy(ef), (1) where Ja and Jb are constants characterizing the pure materials. An assumption of this kind of interaction was also very successful in a calcu- lation of the Curie temperature in RE-RE alloys. Assuming that the density of states at the Fermi level panoy(ef)changes linearly with concentration it was possible [2] to explain the empirical 2/3 power law which represents deviations from the de Gennes scaling of the transition temperatures for RE-RE, RE-Y, RE-Lu and RE-Sc alloys. Mea- surements of magnetization as a function of tem- perature can be made with high accuracy, particu- * On leave from: Department of Solid State Physics, Academy of Mining and Metallurgy, Cracow 30-059, Poland. larly in the low temperature region. In this paper we analyse the temperature dependence of magne- tization in Gd-Tb alloys. 2. Details of theoretical model In writing down an expression for the local Hamiltonian for Tb we introduce a second term to allow for the effects of anisotropy ~Tb = iso aniso ~4bJvb + V;b . (2) The first term may be written as, = - 1) Palloy(~f)JTb CKJK<J ~ , x g / (3) where g~ is the gyromagnetic ratio for Tb, c r is the concentration, p represents the density of states and <J~:> is defined by eq. (6). For single ion hexagonal anisotropy with basal plane easy direc- tion the second term takes the form, v¢ iso ,0 o = -~B2(O ~ > (4) with B2 ° as the crystal field parameter and (O °> is an average value of the Stevens operators. Follow- 0304-8853/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)