TORQUE METHOD FOR THE THEORETICAL DETERMINATION OF MAGNETOCRYSTALLINEANISOTROPY

We propose a torque method for the theoretical determination of the ma gnetocrystalline anisotropy (MCA) energy for systems with uniaxial sym metry. While the dependence of the total energy on the angle between t he magnetization and the normal axis (theta) can be expressed as E(the ta) = E(0) + K(2)sin(2)(theta) + K(4)sin(4)(theta), we show that the M CA energy [defined as E(MCA) = E(theta = 90 degrees) - E(theta = 0 deg rees) = K-2 + K-4] can be easily evaluated through the expectation val ue of the angular derivative of the spin-orbit coupling Hamiltonian (t orque) at an angle of theta = 45 degrees. Unlike other procedures, the proposed method is independent of the validity of the MCA force theor em, or of the absolute accuracy of two total energy calculations. Calc ulated MCA energies for the free Fe monolayer with different lattice c onstants are analyzed and compared with results of other ab initio cal culations, especially those obtained with our previously reported stat e tracking method.