Spin dynamics simulations of body-centered cubic iron
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The longstanding controversy about the existence, or otherwise, of spin waves in para-magnetic body-centered cubic (BCC) iron is investigated with a classical Heisenberg ferro-magnetic model. To account somewhat realistically for the exchange couplings between iron spins, four shells of interacting neighbors are considered with exchange parameters derived by electronic structure calculations. Periodic boundary conditions are applied to BCC lattices and Monte Carlo methods are used to study static properties, to equilibrate the systems, and to generate initial congurations for spin dynamics. Large scale spin dynamics simulations are performed below, at, and above Curie temperature Tc to determine the dynamic structure factor S(q, É) from the measured correlation functions, and high resolution infor-Spin Dynamics Simulations of Body-ECSepninteDreydnaCmubicisc SIrimqon ulscataionnss(ooff Bneoudtyr-oCnensctearettderiCnug)biacrIeron Spin Dynamics Simulations of Body-Centered Cubic Ironant-E scans and three peaks Spin DynamicqsSpSiinmDulyantiaomnsicosfSBimoduyla-tCioennsteoref dBCoduyb-iCceInrtoenred Cubic Irononstant-q scans shows that the two symmetric peaks centered at nonzero energies are due to propagating modes for moderate and large |q|. These results indicate that spin wave excitations persist above T, and the dispersion curves are generally in agreement with experiments that rst c revealed spin waves in iron. Moreover, the degree of magnetic short-range order (SRO) is obtained directly from the behavior of static correlation functions. For T = 1.1Tc, the correlation length is approximately only 2a (» 6 neighbor shells with a ' 2.87A as iron lattice constant), indicative of only limited SRO. Consequently, extensive SRO is not required to support spin-wave-like structures in S(q, É) of iron.