User:Stt 2009

"When an electric current passes from one ferromagnetic layer via a non-magnetic layer into another ferromagnetic layer, the spin polarization and subsequent rotation of this current can induce a transfer of angular momentum that exerts a torque on the second ferromagnetic layer."

This torque transfer is called spin torque transfer.

General discussion
If WKB-approximation is assumed, a transfer of vectorial spin accompanies an electric current perpendicular to two parallel magnetic films connected by a normal metallic spacer. Such a junction with two ferromagnetic electrodes is shown below:



It is build of several layers and each has its own function. The bottom layer for example consists of tantal in order to fix the Cu-seed-layer on the Si-Waver. The FeMn layer above is used to pin the ferromagnetic layer (NiFe). The Spacer consists of Cu, followed by the NiFe-non-pinned ferromagnet. On top of this, the MTJ (magnetic tunnel junction) consists of a back with variable height, caped with a last tantal-layer. The typical height of the single layers is given in the draft.

The material of the spacer and the ferromagnets is widly spread, common combinations are (Co/Cu/Co) or (CoFeB/MgO/CoFeB). The constitution of the junction affects the critical current by which the magnetic orientation of the thin layer is totally reorientated. Typical values are 107 A/cm2for the Co/Cu/Co alloys and 106 A/cm2 for the CoFeB/MgO/CoFeB alloys.

If a voltage is applied between the two electrodes, the electrons flow trough the pinned layer and become spin-polarized. They tunnel through the spacer, reach the second magnetic electrode and transfer a part of their angular momentum onto the electrons in the second electrode. When enough electrons transfer theri spin onto the second FM, its netto magnetic moment points along the polarization of the electrons. The effect of switching the orientation of the second ferromagnet by passing through electrons with a known angular momentum is called "spin torque transfer". The whole process is also called "current induced magnetic switching" (CIMS).

Every system which shows the GMR or TMR effect will also show the CIMS effect because it is a consequence of the additional torque exerted on the magnetization, which itself is a result of the spin transfer from the conduction electrodes to the locatized magnetic moments. The amount of transferred torque depends on several variables like the angle between the magnetic moments of the ferromagnets, the barrier height and thickness and of course the spin polarization of the electrons.

Short physical derivation
We now look at the spin and charge transport in a biased planar tunnel junction with two ferromagnetic electrodes assuming the free-electron-like model.

The left electrode is semi-infinite with a fixed magnetic orientation $$S_l$$ (in-plane). The right electrode is relativly thin with a free magnetic orientation. Two coordinate systems are given, each for one ferromagnet. The z-axis of each coordinate system points along the netto magnetic moment of its ferromagnet. If the electron (spin) is between the two electrodes, it is decribed by the left system. The x-axis are orientated along the plane in which the netto magnetic moments are. As a result, the y-axis are perpendicular to both (orthonormal basis) and point right into the ferromagnets. To calculate the in-plane (x') and out-of-plane (y'=y) components of the spin torque in the right film a positive definition of the charge current is presumed when the currents flows from the thinner to the thick layer. For this positive (bias-)voltage the electrons (and their spins) flow from the left ferromagnet to the right one.

As prooved in, the spin-torque $$T$$ can be written as an out-of-plane component $$T^l_{||}     =-\frac{\hbar}{2}J^{sl}_x $$ and an in-plane component $$T^l_{\perp}=-\frac{\hbar}{2}J^{sl}_y$$ for the left (thicker)ferromagnet and $$T^r_{||}=\frac{\hbar}{2} \left( J^{sr}_{x'} - \overline{J^{sr}_{x'}} \right)$$ respectively $$T^r_{\perp}=\frac{\hbar}{2} \left( J^{sr}_{y} - \overline{J^{sr}_{y}} \right)$$ for the right (thinner) one. $$J$$($$\overline J$$) denotes the $$\mu^{th}$$ component of the spin current density calculated in the barrier near to the left (right) ferromagnet. Both in-plane and out-of-plane components are on a comparable magnitude.

These components represent the spin current density which is not absorbed in the left FM. It tunnels through the barrier and reaches the right FM. When this layer is thick (or semi-infinite) the x' and y componets are absorbed, $$\overline J$$ vanishes and the out-of-plane exerted torques on both layers are the same. $$ T^l_{\perp}=T^r_{\perp}$$

To determine the spin torque needed for further calculation, the spin current componets arise interest. After a long (and painful) calculation and serveral assumptions (free-electron-like model, zero temperature limit) the $$\mu^{th}$$ component of the the right ferromagnetic-induced spin current density is supposed to be $$J_{\mu}^s(y)=\frac{4\pi^2m^2}{h^4}\sum_{\sigma}\left( \int_{E_{l\sigma}}^{E_F-eV}d\epsilon_{\perp} \frac{eV}{k_{l\sigma}(\epsilon_{\perp})}j_\mu^s(y,\epsilon_{\perp}) + \int_{E_F-eV}^{E_F}d\epsilon_{\perp} \frac{E_F-\epsilon_{\perp}}{k_{l\sigma}(\epsilon_{\perp})}j_\mu^s(y,\epsilon_{\perp})\right)$$

$$E_F$$ is the fermi-energy in the left(source) electrode. The integration is performed over the energy associated with the motion perpendicular to the layer planes and the summation is over the two spin-subbands.

The single torque components can even change their sign, when the barrier is thick enough.

Application
The STT is also used as writing technology where data is written by re-orienting the magnetisation of a thin magnetic layer in a tunnel magnetoresistance (TMR) element using a spin-polarised current. At very small device scales it is possible that a spin polarised current can transfer its spin angular momentum to a small magnetic element. Spin torque transfer magnetic RAM (STT-MRAM) has the advantage of lower power-consumption and better scalability over conventional MRAM. Spin torque transfer technology has the potential to make possible MRAM devices combining low current requirements and reduced cost, however the amount of current needed to re-orient the magnetisation is, at present, too high for commercial applications and the reduction of this current density alone is the basis for a lot of current academic research in spin-electronics. In order to lower the critical current some investigation on synthetic ferrimagnetic layers is done.

Hynix Semiconductor and Grandis formed a partnership in April 2008 to explore commercial development of STT-RAM technology.