  We elucidate a magnetic mass effect on a sphaleron energy that is crucial for
baryon number preservation needed for successful electroweak baryogenesis. It
is found that the sphaleron energy increases in response to the magnetic mass.
As an application, we study the sphaleron energy and electroweak phase
transition with the magnetic mass in a two-Higgs-doublet model. Although the
magnetic mass can screen the gauge boson loops, it relaxes a baryon number
preservation criterion more effectively, broadening the baryogenesis-possible
region. Our findings would be universal in any new physics models as long as
the gauge sector is common to the standard model.
