Pyromagnetic Test of Spin Wave Theory in Metallic Nickel

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Abstract
The temperature dependence of the spontaneous magnetization of metallic nickel has been studied between 4.2° and 120°K by a pyromagnetic technique developed by the authors. Fractional changes in magnetization as small as a few parts per million could be detected near 4.2°K. The resultant data were fitted by the method of least squares to a theoretical equation containing terms descriptive of thermal excitation of spin waves in the presence of an effective magnetic field plus a T2 term descriptive of collective electron behavior. The best fit of the data to this equation is obtained using the spin wave terms alone, provided an intrinsic energy gap is assumed in the spin wave dispersion law of 2.7°K for magnetization parallel to the [111] axis and 1.9°K parallel to the [100] axis. Enhancement of this gap by an externally applied field follows theoretical predictions. It is noted that the measured difference between the gap temperature along the two principal axes has the value theoretically predicted from previous measurements of magnetic anisotropy energy, however the isotropic contribution observed in this experiment has not been theoretically anticipated. A possible origin for the isotropic gap is proposed in terms of interaction of polarized s and d electrons. It is also pointed out, however, that the ``isotropic effective field'' may be a spurious result, originating in thermal expansion effects not included in the theoretical equation to which the data were fitted. Finally, a new type of pyromagnetic measurement is described which can be used to determine the temperature dependence of the magnetic anisotropy.