Effect of spin fluctuations on the magnetic equation of state of ferromagnetic or nearly ferromagnetic metals

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Abstract
The authors present a quantitative model for the magnetic equation of state of nearly or weakly ferromagnetic metals at low temperatures which includes corrections to conventional Stoner theory arising from enhanced fluctuations in the local magnetisation. The model takes account of both longitudinal and transverse fluctuations in terms of four physically transparent parameters which may be determined independently from the equation of state in the T=0 limit and from inelastic neutron scattering, or calculated directly from a semi-empirical band structure model near the Fermi level fitted for example to experimental Fermi surface areas. For parameters of the same order of magnitude as those recently determined in the weakly spin-polarised metal Ni3Al, the model yields approximately a quadratic temperature dependence of the spontaneous magnetisation over a wide range well below the Curie temperature (Tc), a nearly linear inverse susceptibility well above Tc, and nearly linear magnetic isotherms (Arrott plots) at high magnetic fields. These results are qualitatively consistent with the behaviour observed in many magnetic metals near the ferromagnetic instability at low temperatures. For Ni3Al the model yields good quantitative agreement with experiment for the magnitude of the Curie temperature Tc, for the ratio peff/p0 of the high- to low-temperature effective magnetic moments, and for the coefficient of the quadratic (T2) variation of the magnetisation with temperature well below Tc, without the use of any free adjustable parameters. Finally the authors show that the model also provides a good quantitative description of the paramagnetic susceptibility and transition temperature of the more complex magnetic system MnSi, the only other unsaturated magnetic metal for which all of the microscopic parameters are well known.