  Using XMM-Newton and Chandra, we measure period derivatives for the second
and third known pulsars in the class of Central Compact Objects (CCOs) in
supernova remnants, proving that these young neutron stars have exceptionally
weak dipole magnetic field components. For the 112 ms PSR J0821-4300 in Puppis
A, Pdot = (9.28 +/- 0.36)E-18. Its proper motion, mu = 61 +/- 9 mas/yr, was
also measured using Chandra. This contributes a kinematic term to the period
derivative via the Shklovskii effect, which is subtracted from Pdot to derive
dipole Bs = 2.9E10 G, a value similar to that of first measured CCO PSR
J1852+0040 in Kes 79, which has Bs = 3.1E10 G. Antipodal surface hot spots with
different temperatures and areas are deduced from the X-ray spectrum and pulse
profiles. Paradoxically, such nonuniform surface temperature appears to require
strong crustal magnetic fields, probably toroidal or quadrupolar components
much stronger than the external dipole. A spectral feature, consisting of
either an emission line at approximately 0.75 keV or absorption at
approximately 0.46 keV, is modulated in strength with the rotation. It may be
due to a cyclotron process in a magnetic field on the surface that is slightly
stronger than the dipole deduced from the spin-down. We also timed anew the 424
ms PSR J12010-5226, resolving previous ambiguities about its spin-down rate.
Its Pdot = (2.22 +/- 0.02)E-17, corresponding to Bs = 9.8E10 G. This is
compatible with a cyclotron resonance interpretation of its prominent
absorption line at 0.7 keV and harmonics. These results deepen the mystery of
the origin and evolution of CCOs: why are their numerous descendants not
evident?
