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Magnetized Domain Walls in the Deconfined Sakai-Sugimoto Model at Finite Baryon Density

The magnetized pure pion gradient ($\mathcal{5}ϕ$) phase in the deconfined Sakai-Sugimoto model is explored at zero and finite temperature. We found that the temperature has very small effects on the phase. The thermodynamical properties of the phase shows that the excitations behave like a scalar solitonic free particles. By comparing the free energy of the pion gradient phase to the competing multiquark-pion gradient (MQ-$\mathcal{5}ϕ$) phase, it becomes apparent that the pure pion gradient is less thermodynamically preferred than the MQ-$\mathcal{5}ϕ$ phase. However, in the parameter space where the baryonic chemical potential is smaller than the onset value of the multiquark, the dominating magnetized nuclear matter is the pion gradient phase.