ISSN:
1089-7550
Source:
AIP Digital Archive
Topics:
Physics
Notes:
We consider with temperature the exchange coupling of two identical ferromagnetic films separated by a paramagnetic metal of thickness d. The minority-spin band of the ferromagnets is matched to the band of the paramagnet. Majority-spin electrons experience a repulsive potential of maximum height equal to the exchange gap of the ferromagnets. A spin-flip current, which flows as a result of a virtual rotation of the ferromagnetic moments, is calculated at temperature T, assuming single-particle excitations only. This current, equated to the torque exerted by one ferromagnet on the other, defines the exchange energy as an infinite sum of terms with coefficients A12(d,T),B12(d,T),..., extending beyond the Heisenberg-like A12(d,T) term. For certain d, the biquadratic B12(d,T) term is of the proper magnitude and sign to cause intrinsic 90° coupling between the moments of the two ferromagnets. Additionally, we calculate the T dependence of A12(d,T) and B12(d,T) for different Fermi energy to exchange-gap ratios, showing that, in general, a nonmonotonic dependence of both A12(d,T) and B12(d,T) vs T is expected. Monotonic T dependence occurs in the asymptotic regime of large d.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.355445
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