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We report Dirac monopoles with polar-core vortex induced by spin-orbitcoupling in ferromagnetic Bose-Einstein condensates, which are attached to twonodal vortex lines along the vertical axis. These monopoles are more stable inthe time scale of experiment and can be detected through directly imagingvortex lines. When the strength of spin-orbit coupling increases, Diracmonopoles with vortex can be transformed into those with square lattice. In thepresence of spin-orbit coupling, increasing the strength of interaction caninduce a cyclic phase transition from Dirac monopoles with polar-core vortex tothose with Mermin-Ho vortex. The spin-orbit coupled Bose-Einstein condensatesnot only provide a new unique platform for investigating exotic monopoles andrelevant phase transitions, but also can preserve stable monopoles after aquadrupole field is turned off.

Dirac monopoles with polar-core vortex induced by spin-orbit coupling in spinor Bose-Einstein condensates