region is attached to the left ferromagnetic electrode (modeled as semi-infinite tight-binding chain with non-zero Zeeman splitting) and the right N electrode (semi-infinite tight-binding chain without any Zeeman splitting), as encoded by the corresponding self-energy terms. Discrepancy between theory and experiment Theoretical tunnelling magneto-resistance ratios of 10000% have been predicted. However, the largest that have been observed are only 604%. One suggestion is that grain boundaries could be affecting the insulating properties of the MgO barrier; however, the structure of films in buried stack structures is difficult to determine. The grain boundaries may act as short circuit conduction paths through the material, reducing the resistance of the device. Recently, using new scanning transmission electron microscopy techniques, the grain boundaries within FeCoB/MgO/FeCoB MTJs have been atomically resolved. This has allowed first principles density functional theory calculations to be performed on structural units that are present in real films. Such calculations have shown that the band gap can be reduced by as much as 45%. In addition to grain boundaries, point defects such as boron interstitial and oxygen vacancies could be significantly altering the tunnelling magneto-resistance. Recent theoretical calculations have revealed that boron interstitials introduce defect states in the band gap potentially reducing the TMR further These theoretical calculations have also been backed up by experimental evidence showing the nature of boron within the MgO layer between two different systems and how the TMR is different. See also Quantum tunneling Magnetoresistance Giant Magnetoresistance (GMR) Spin-transfer torque References Electric and magnetic fields in matter Spintronics Magnetoresistance