Japan. Applications The read-heads of modern hard disk drives work on the basis of magnetic tunnel junctions. TMR, or more specifically the magnetic tunnel junction, is also the basis of MRAM, a new type of non-volatile memory. The 1st generation technologies relied on creating cross-point magnetic fields on each bit to write the data on it, although this approach has a scaling limit at around 90–130 nm. There are two 2nd generation techniques currently being developed: Thermal Assisted Switching (TAS) and Spin-transfer torque. Magnetic tunnel junctions are also used for sensing applications. Today they are commonly used for position sensors and current sensors in various automotive, industrial and consumer applications. These higher performance sensors are replacing Hall sensors in many applications due to their improved performance. Physical explanation The relative resistance change—or effect amplitude—is defined as where is the electrical resistance in the anti-parallel state, whereas is the resistance in the parallel state. The TMR effect was explained by Jullière with the spin polarizations of the ferromagnetic electrodes. The spin polarization P is calculated from the spin dependent density of states (DOS) at the Fermi energy: The spin-up electrons are those with spin orientation parallel to the external magnetic field, whereas the spin-down electrons have anti-parallel alignment with the external field. The relative resistance change is now given by the spin polarizations of the two ferromagnets, P1 and P2: If no voltage is applied to the junction, electrons tunnel in both directions with equal rates. With a bias voltage U, electrons tunnel preferentially to the positive electrode. With the assumption that spin is conserved during tunneling, the current can be described in a two-current model. The total current is split in two partial currents, one for the spin-up electrons and another for the spin-down electrons. These vary depending on the magnetic state of the junctions. There are two possibilities to obtain a defined anti-parallel state. First, one can use ferromagnets with different coercivities (by using different materials or different film thicknesses). And second, one of the ferromagnets can be coupled with an antiferromagnet (exchange bias). In this case the magnetization of the uncoupled electrode remains "free". The TMR becomes infinite if P1 and P2 equal 1, i.e. if both electrodes have 100% spin polarization. In this case the magnetic tunnel junction becomes a switch, that switches magnetically between low resistance and infinite resistance. Materials that come into consideration for this