Methods are provided for operating a magnetic random access memory device including a memory cell having a magnetic tunnel junction structure on a substrate. In particular, a writing current pulse may be provided through the magnetic tunnel junction structure, and a writing magnetic field pulse may be provided through the magnetic tunnel junction structure. In addition, at least a portion of the writing magnetic field pulse may be overlapping in time with respect to at least a portion of the writing current pulse, and at least a portion of the writing current pulse and/or at least a portion of the writing magnetic field pulse may be non-overlapping in time with respect to the other. Related devices are also discussed.