Experimental verification of spin-wave theory in high fields (invited)

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Abstract
The magnetic moment of single crystals of nickel, iron, cobalt, and yttrium iron garnet have been measured between 1.6 and 288 K, in magnetic fields up to 180 000 Oe, along the different crystallographic axes with an accuracy of 0.01%. From these measurements are verified: (i) The H−1/2i Holstein‐Primakoff test on the (∂M/∂Hi,Hi) curves, where Hi is the internal field. (ii) The isothermal magnetization M(Hi,T) is represented by the equation M(Hi,T)=Ms(T)+A(T) ⋅ H1/2i+B(T) ⋅ Hi. (iii) The spontaneous magnetization Ms(T) is determined by fitting the experimental points M(Hi,T) with the above equation. (iv) From the Ms(T) variation we determine the absolute saturation moment M=0.619 μB/atom for Ni, 2.226 μB/atom for Fe, 1.729 μB/atom for Co (Hi∥c axis) and 1.72 μB/atom (H⊥c axis), 10.062 μB/mole 5Fe2O3⋅3Y2O3 for YIG. (v) Writing a priori Ms(T)=M0(1−anTn−an′Tn′−an″Tn″) the variation of the spontaneous magnetization with the temperature, and plotting the variation of log [M0−Ms(T)]/M0 as a function of log T, one proves n=3/2, n′=5/2, n″=0 for nickel and iron; for cobalt n=3/2 from points above 100 K; for YIG, n appears to be 5/2. (vi) From the a3/2 values are determined the stiffness coefficients D of iron, cobalt, and nickel which are in reasonable agreement with those determined by neutron diffraction. (vii) By subtracting the theoretical contribution of the spin waves as a function of magnetic field and temperature from the M(Hi,T) data, we obtain an additional superimposed susceptibility for iron, cobalt, and nickel as a function of the temperature, due to their metallic nature.