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Thermodynamic properties of strange quark matter (SQM) in a nonuniformmagnetic field are studied within the phenomenological MIT bag model under thecharge neutrality and beta equilibrium conditions, relevant to the interior ofstrange quark stars. The spatial dependence of the magnetic field strength ismodeled by the dependence on the baryon chemical potential in the exponentialand power forms. The total energy density, longitudinal and transversepressures in magnetized SQM are found as functions of the baryon chemicalpotential. It is clarified that the central magnetic field strength in astrange quark star is bound from above by the critical value at which thederivative of the longitudinal pressure with respect to the baryon chemicalpotential vanishes first somewhere in the interior of a star under varying thecentral field. Above this upper bound, the instability along the magnetic fieldis developed in magnetized SQM. The change in the form of the dependence of themagnetic field strength on the baryon chemical potential between theexponential and power ones has a nonnegligible effect on the critical magneticfield strength while the variation of the bag pressure within the absolutestability window for magnetized SQM has a little effect on the critical field.

Anisotropic pressure in strange quark matter in the presence of a strong nonuniform magnetic field