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S. Khmelevskyi, P. Mohn:
"First-principle based simulations of longitudinal spin-fluctuations in metals andintegration in classical space with variable spin amplitude";
AIP Advances, 8 (2018), S. 1014221 - 1014227.

The use of the classical Heisenberg model which incorporates only transverse spin
degrees of freedom has only limited success for description of the metallic magnetism
at finite temperature, since temperature and magnetic disorder induced longitudinal
variations of the atomic spin moments might become large in the itinerant electron
systems away from the limit of localized moments. In order to incorporate the longitudinal
spin fluctuations in finite temperature simulation schemes a simple extended
version of the Heisenberg model which allows for an on-site spin magnitude variation
controlled by the one-site energy terms is widely used during the recent decade
for ab-initio mapping and statistical simulations. Here, we apply and discuss such
ab-initio based scheme for the canonical itinerant ferromagnetic metals (Fe, Co, Ni)
and recently discovered high temperature antiferromagnet - V3Al, in conjunction with
standard spherical integration metrics in classical spin state and the recently proposed
linear one.We also examine the dependence of the results on the choice of the exchange
and correlation potential in ab-initio total energy calculations.We compare the respective
uncertainties in the calculated values of the magnetic ordering temperature and
temperature dependent spin moment magnitude to the difference in the results which
relate to the choice of the metrics.