Temperature dependence of the spontaneous magnetization of Ni2MnGa and other ferromagnets. The superellipse equation

The temperature dependence of the spontaneous magnetization of Ni2MnGa and other ferromagnets can be described in reduced coordinates by the superellipse equation using a single dimensionless parameter. This critical exponent parameter equals 2.4 for Ni2MnGa, 2.7 for nickel and cobalt, 3.0 for iron and 2.05 for gadolinium. Because reduced magnetization and reduced temperature enter the equation symmetrically, the MS(T) dependence can be measured only in the low-temperature range, from 0 to 0.5TC. The magnetization curve from 0.5TC to TC can then be obtained by interchanging reduced magnetization and temperature in the superellipse equation. In this way, the experimentally challenging task of measuring spontaneous magnetization near TC  is avoided, as the behavior near TC is effectively determined from measurements performed near T = 0. The MS(T) dependence in a whole temperature range is fully determined by two parameters – the Curie temperature, TC and the critical exponent,