  In Dec. 2011 PSR B0540-69 experienced a spin-down rate transition (SRT),
after which the spin-down power of the pulsar increased by ~36%. About 1000
days after the SRT, the X-ray luminosity of the associated pulsar wind nebula
(PWN) was found to brighten by 32+/-8%. After the SRT, the braking index n of
PSR B0540-69 changes from n=2.12 to n=0.03 and then keeps this value for about
five years before rising to n=0.9 in the following years. We find that most of
the current models have difficulties in explaining the measured braking index.
One exceptive model of the braking index evolution is the increasing dipole
magnetic field of PSR B0540-69. We suggest that the field increase may result
from some instabilities within the pulsar core that enhance the poloidal
component at the price of toroidal component of the magnetic field. The
increasing dipole magnetic field will result in the X-ray brightening of the
PWN. We fit the PWN X-ray light curve by two models: one assumes a constant
magnetic field within the PWN during the brightening and the other assumes an
enhanced magnetic field proportional to the energy density of the PWN. It
appears that the two models fit the data well, though the later model seems to
fit the data a bit better. This provides marginal observational evidence that
magnetic field in the PWN is generated by the termination shock. Future
high-quality and high-cadence data are required to draw a solid conclusion.
