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Anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) arerecognized as the most promising magnetar candidates, as indicated by theirenergetic bursts and rapid spin-downs. It is expected that the strong magneticfield leaves distinctive imprints on the emergent radiation both by affectingthe radiative processes in atmospheres of magnetars and by scattering in theupper magnetospheres. We construct a self-consistent physical model thatincorporates emission from the magnetar surface and its reprocessing in thethree-dimensional (3D) twisted magnetosphere using a Monte Carlo technique. Thesynthetic spectra are characterized by four parameters: surface temperature kT,surface magnetic field strength $B$, magnetospheric twist angle $\Delta\phi$,and the normalized electron velocity $\beta$. We also create a tabular model(STEMS3D) and apply it to a large sample of XMM-Newton spectra of magnetars.The model successfully fits nearly all spectra, and the obtained magnetic fieldfor 7 out of the 11 sources are consistent with the values inferred from thespin-down rates. We conclude that the continuum-fitting by our model is arobust method to measure the magnetic field strength and magnetosphericconfiguration of AXPs and SGRs. Investigating the multiple observations ofvariable sources, we also study the mechanism of their spectral evolution. Ourresults suggest that the magnetospheres in these sources are highly twisted($\Delta\phi > 1$), and the behavior of magnetospheric twisting and untwistingis revealed in the 2002 outburst of 1E 2259+586.

X-ray Perspective of the Twisted Magnetospheres of Magnetars