A method for writing a memory device, comprising: providing a magnetic random access memory, herein after termed MRAM, cell comprising a magnetic tunnel junction with a storage layer having storage magnetization; a sense layer having a sense magnetization that is freely orientable; a spacer layer between the sense layer and the storage layer; and an antiferromagnetic layer that pins the storage magnetization direction below a threshold temperature (T B) and unpins it at a temperature above the threshold temperature; at least one of the storage layer and the sense layer having a magnetic anisotropy axis wherein the magnetic anisotropy axis is an intrinsic anisotropy; during a writing step to one of m logic states, wherein the storage magnetization is switchable between m different directions corresponding to m logic states, with m being greater than 2: applying a heating current pulse adapted for heating the magnetic tunnel junction to a temperature above the threshold temperature; and inducing a write magnetic field having a predetermined amplitude and a predetermined orientation with respect to the magnetic anisotropy axis for aligning the storage magnetization in a written direction; and characterized in that the method further comprises, performing an initialization step in response to a writing command to perform the writing step, the initialization step comprising: applying an initial heating current pulse adapted for heating the magnetic tunnel junction to a temperature above the threshold temperature; and providing an initial resultant magnetic field oriented along the magnetic anisotropy axis for adjusting the storage magnetization from a configuration where the storage magnetizations is oriented at a non-zero angle with respect to the magnetic anisotropy axis in an initial direction along the magnetic anisotropy axis; wherein the initialization step being performed prior to the writing step. providing a magnetic random access memory, herein after termed MRAM, cell comprising a magnetic tunnel junction with a storage layer having storage magnetization; a sense layer having a sense magnetization that is freely orientable; a spacer layer between the sense layer and the storage layer; and an antiferromagnetic layer that pins the storage magnetization direction below a threshold temperature (T B) and unpins it at a temperature above the threshold temperature; at least one of the storage layer and the sense layer having a magnetic anisotropy axis wherein the magnetic anisotropy axis is an intrinsic anisotropy; during a writing step to one of m logic states, wherein the storage magnetization is switchable between m different directions corresponding to m logic states, with m being greater than 2: applying a heating current pulse adapted for heating the magnetic tunnel junction to a temperature above the threshold temperature; and inducing a write magnetic field having a predetermined amplitude and a predetermined orientation with respect to the magnetic anisotropy axis for aligning the storage magnetization in a written direction; and characterized in that the method further comprises, performing an initialization step in response to a writing command to perform the writing step, the initialization step comprising: applying an initial heating current pulse adapted for heating the magnetic tunnel junction to a temperature above the threshold temperature; and providing an initial resultant magnetic field oriented along the magnetic anisotropy axis for adjusting the storage magnetization from a configuration where the storage magnetizations is oriented at a non-zero angle with respect to the magnetic anisotropy axis in an initial direction along the magnetic anisotropy axis; wherein the initialization step being performed prior to the writing step. applying a heating current pulse adapted for heating the magnetic tunnel junction to a temperature above the threshold temperature; and inducing a write magnetic field having a predetermined amplitude and a predetermined orientation with respect to the magnetic anisotropy axis for aligning the storage magnetization in a written direction; and characterized in that the method further comprises, performing an initialization step in response to a writing command to perform the writing step, the initialization step comprising: applying an initial heating current pulse adapted for heating the magnetic tunnel junction to a temperature above the threshold temperature; and providing an initial resultant magnetic field oriented along the magnetic anisotropy axis for adjusting the storage magnetization from a configuration where the storage magnetizations is oriented at a non-zero angle with respect to the magnetic anisotropy axis in an initial direction along the magnetic anisotropy axis; wherein the initialization step being performed prior to the writing step. applying an initial heating current pulse adapted for heating the magnetic tunnel junction to a temperature above the threshold temperature; and providing an initial resultant magnetic field oriented along the magnetic anisotropy axis for adjusting the storage magnetization from a configuration where the storage magnetizations is oriented at a non-zero angle with respect to the magnetic anisotropy axis in an initial direction along the magnetic anisotropy axis; wherein the initialization step being performed prior to the writing step.