Vis kilden til Giant magnetoresistance

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When magnetic fields are appplied to metals, most show an increase in resistance, known as magnetoresisitance (MR), but GMR exploits the fact that when these junctions is under a critical length the magnitude of this magnetoresistance is greatly amplified. This has been used as a way of packing data extremely dense, and most modern hard-drives (HDD) uses this technology.

== Theoretical background ==



=== Ordinary magnetoresistance ===
In the absence of an external field electrons travel through a solid in straight lines in between scattering events. For a free electron gas, the same is true even in the presence of an applied field. Althoug the applied field exerts a force (the Lorence force) on the electrons which deflects them from their path, the electric field created by the displaced electrons exactly balances the Lorentz force, and at equilibrium the electrons follow the same straight-line path.This is known as the Hall effect. However in a real metal the conduction electrons have different average velocities, and although on average the transverse Hall electric field exactly balances the magnetic field, individual electrons travel in a curved path and because of this they scatter more. Consequently the resistance in the presence of the field is larger than the resistance in the absence of the field.
This effect is, however, very small, and doesn't have technological applications.

=== Anisotropic magnetoresistance ===
Larger magnetoresistive effects, of around 2%, are observed in ferromagnetic metals and their alloys. The phenomenon is called anisotropic magnetoresistance (AMR) because the change in resistance when a field is applied parallel to the current direction is different from that when a field is perpendicular to the curren direction. In fact, the resistance for current flowing parallel to the field direction increases when a field is applied, whereas the resistance for current flowing perpendicular to the field direction decreases by approximately the same amount. The effect is significant even in small fields, and his origin lies in the spin-orbit coupling of the electrons.
From about 1993 until the late 1990s, anisotropic magnetoresistive materials were used almost exclusively as the read elements in recording heads.

=== Giant magnetoresistance ===
The magnetoresistive component in modern read heads operates on the giant magnetoresistive (GMR) effect, extremely larger than the previous effects. 

==== Mott's model and spin dependent transport====
In most metals, such as for instance copper, there is an equal number of spin-up and spin-down electrons. This causes the atom to be spin neutral. The ferromagnetic materials used most frequently in GMR applications are metals of the first transition series. For these elements it is energetically favourable for the d-electrons to have parallel spins in order to reduce their Coulomb repulsion. This is known as exchange splitting, and it gives rise to a net magnetic moment which makes the metal ferromagnetic. Moreover, exchange splitting means that the density of states is not the same for the spin-up and spin-down electrons at the Fermi energy.<ref name="H. Ehrenreich"> H.Ehrenreich, F. Spaepen, Solid State Physics Vol 56, pp. 113-237</ref>

GMR can be qualitatively understood using the Mott model, which was introduced as early as 1936 to explain the sudden increase in resistivity of ferromagnetic metals as they are heated above the Curie temperature, where the material is no longer ferromagnetic.<ref name="West">A. West, "Basic solid state Chemistry", 2nd edition, John Wiley & Sons 1999</ref>
Mott proposed that the resistivity of spin-up and spin-down electrons in a ferromagnet is different because of the exchange splitting effect. This is because the scattering rates of the spin-up and spin-down electrons are quite different in a ferromagnetic material. For this reason, conductivity in
metals can be described in terms of two largely independent conducting channels, corresponding to the spin-up and spin-down electrons. 

Using Mott’s arguments it is straightforward to explain GMR in magnetic multilayers. We consider collinear magnetic configurations, and assume that the scattering is strong for electrons with spin antiparallel to the magnetization direction, and weak for electrons with spin parallel to the magnetization direction. For the parallel-aligned magnetic layers, the spin-up electrons pass through the structure almost without scattering, because their spin is parallel to the magnetization of the layers. On the other hand, the spin-down electrons are scattered strongly within both ferromagnetic layers, because their spin is antiparallel to the magnetization of the layers. Since conduction occurs in parallel for the two spin channels, the total resistivity of the multilayer is determined mainly by the highly-conductive spin-up electrons and appears to be low. For the antiparallel-aligned multilayer, both the spin-up and spin-down electrons are scattered strongly within one of the ferromagnetic layers, because within the one of the layers the spin is antiparallel to the magnetization direction. Therefore, in this case the total resistivity of the multilayer is high. [need a figure!]

[[Bilde:Exchangecoupling.PNG|200px|thumb|right|Exchange coupling<ref name="H. Ehrenreich"> H.Ehrenreich, F. Spaepen, Solid State Physics Vol 56, pp. 113-237</ref>]]

==== GMR structures====
In GMR multilayer materials, thin layers of  of magnetic materials are separated by layers of non-magnetic materials. Depending on the thickness of the non magnetic layers, the magnetic layers couple either ferromagnetically (parallel) or antiferromagnetically (antiparallel). This is known as exchange coupling. Giant magnetoresistance occurs when the thicknesses are chosen such that the adjacent layers are antiferromegnetic in zero applied field. This results in a high-resistance state as spin-up electrons are scattered by regions of down spin magnetization and vice versa, as explained by the Mott model. 

By applying an external field magnetic field, the relative magnetization directions between adjacent magnetic layers can be changed. A low-resistance state is obtained when the magnetization of the layers is rotated to a ferromagnetic configuration. When the magnetic layers are ferromagnetically aligned, conduction electrons of compatible spin-type are able to move through the heterostructure with minimal scattering, and the overall resistance of the material is lowered.

Although the highest values of GMR were measured in antiferromagnetically-coupled magnetic multilayers, these multilayers are not the best materials for technological applications. This is due to the large magnetic fields which are required to saturate the magnetization of the multilayers and to obtain a sizeable change in the resistance. For example, as is evident from Fig.6, the saturation fields in the Fe/Cr multilayers are of the order of 10-20 kG which is three orders of magnitude higher than the fields required for applications. The sensitivity, which is defined as ΔR/R per unit magnetic field, is much too small.

Antiparallel alignment can also be obtained by introducing different coercivities of the successive ferromagnetic layers. In this case (pseudo spin valve structure) the magnetic moments of the soft and hard magnetic layers switch at different values of the applied magnetic field providing a field range in which they are antiparallel and the resistance is higher. 

Another structure which gives much better performances from the point of view if applications is the spin valve. In the spin valve the magnetization of one ferromagnetic layer is pinned by the exchange coupling with an adjacent antiferromagnetic layer, whereas the magnetization of the other ferromagnetic layer is free to rotate with the applied magnetic field. Although the measured values of GMR are higher in magnetic multilayers, spin valves are more attractive from the point of view of applications, because only small magnetic fields need to be applied to change the resistance.

== Materials ==
Since the discovery of GMR a large number of magnetic multilayer structures, which display the GMR effect, have been discovered. It was found that the magnitude of GMR varies considerably depending on the chemical constituents of the multilayer. The highest published values of GMR to date are 220% in Fe/Cr multilayers and 120% in Co/Cu multilayers. Moreover, values of GMR between 9% and 28% were also obtained in others multilayers such as Co/Ag, Ni/Ag, NiCu.


[[Bilde:Spinresistance.PNG|200px|thumb|left|Band structure matching <ref name="H. Ehrenreich"> H.Ehrenreich, F. Spaepen, Solid State Physics Vol 56, pp. 113-237</ref>]]

=====Band structure=====
Above, spin dependent scattering within the ferromagnetic layer has been described by the Mott model. However, in addition to this, there is also spin dependent scattering at the interface between magnetic and nonmagnetic layers. 

The electical conductivity across a junction between two metals will depend on the difference in band structure. A large difference in band structure leads to a high potential barrier, which increases the scattering probability and hence the resistance. Since the spin-up and spin-down electrons in a ferromagnet have different band structures due to the exchange splitting effect, as explained earlier, the transmission probability across the junction will be different for spin-up and spin-down electrons <ref name="H. Ehrenreich"> H.Ehrenreich, F. Spaepen, Solid State Physics Vol 56, pp. 113-237</ref>
Thus, in order to achieve high transmission of spin-up and not spin-down, for instance, it is necessary to select a nonmagnet whose band structure closely resembles the band structure of spin-up electrons in the ferromagnet. <ref name="Nobel article">"Scientific background on the Nobel Prize in Physics 2007. The Discovery of Giant Magnetoresistance", The Royal Swedish Academy of Sciences 2007</ref>

=====Lattice considerations=====
When building a superlattice of two or more crystalline materials it is important to consider the lattice parameters of the materials. If the lattice parameters differ significantly there would be significant strain at and near the interface, causing dislocations and imperfections which would scatter both the spin-up and spin-down electrons equally. This would be derogative to the total GMR effect. Hence, it is imperative that the lattice parameters are very closely matched. 

Another lattice consideration is that the magnetization direction in a ferromagnet is related to crystallographic directions within the lattice. This is something which must be taken into consideration in the synthesis process.<ref name="West">A. West, "Basic solid state Chemistry", 2nd edition, John Wiley & Sons 1999</ref>

=== Other important factors for GMR effect ===

=====Purity=====
High impurity or high internal strains in a ferromagnet increases its coercivity. Recall that a high coercivity means that a high magnetic field must be applied to change the direction of magnetization. Good purity control is therefore essential to tailor a structure with the desired properties <ref name="Kittel">C. Kittel, "Introduction to Solid State Physics", John Wiley & Sons; 8th Edition, 2004</ref>

In an ideal GMR structure, one type of spin electrons experience zero resistance while the other has infinite resistance. Hence, in order to maximize the GMR effect, we generally want to minimize the spin-independent scattering events and maximize the spin-dependent scattering of either spin-up or spin-down electrons. Material imperfections such as dislocations, stacking faults and grain boundaries can lead to both spin-dependent and spin-independnet scattering, depending on a number of factors. Therefore, imperfections can be a severe disadvantage or a powerful tool, depending on whether they are present by design or by random. <ref name="Gurney et.al.">B.A. Gurney, V.S. Speriosu, J.P. Nozi~res, H. Lefakis, D.R. Wilhoit and O.U. Need, Phys. Rev. Lett 71 (1993) 4023.</ref>

=====Ferromagnetic layer thickness=====
[[Bilde:Thicknessofgmr.PNG|300px|thumb|right|Thickness dependence of relative GMR effect. NM = nonmagnetic, FM = ferromagnetic. <ref name="Sato">M. Sato, S. lshio and T. Miyazaki, J. Magn. Magn. Mater. 126 (1993) 460.</ref><ref name="Dieny2">B. Dieny, V.S. Speriosu, S. Metin, S.S.P. Parkin, B.A.
Gurney, P. Baumgart and D. Wilhoit, J. Appl. Phys. 69
(1991) 4774</ref> ]]

As the ferromagnetic layer thickness is ''reduced'', there will obviously be less bulk scattering events. The critical thickness is at the mean free path of the strongly scattered electrons. If the layer is any thinner than this, the GMR effect drops dramatically. Experiments show that not only bulk scattering, but also interface scattering depends on the layer thickness. If the layer is thinner than approximately two monolayers, the scattering is not optimal. <ref name="Parkin"> S.S.P. Parkin, Phys. Rev. Lett. 71 (1993) 1641</ref>

As the ferromagnetic layer thickness is ''increased'', current will be shunted towards the center of the channel. This leads to a higher current density, with a resultant inrease in resistance and a drop of GMR. <ref name="Dieny"> B. Dieny, Journal of Magnetism and Magnetic Materials 136 (1994) 335-359</ref>

=====Nonferromagnetic layer thickness=====
Again, as the nonferromagnetic layer thickness is ''increased'', current will be shunted towards the center of the channel. This leads to a higher current density, with a resultant inrease in resistance and a drop of GMR. Moreover, a thicker layer leads to more bulk scattering events. Hence the GMR effect drops monotonically with increasing laer thickness.<ref name="Dieny"> B. Dieny, Journal of Magnetism and Magnetic Materials 136 (1994) 335-359</ref> 

If the nonmagnetic layer gets too thin, pinholes will cause a strong ferromagnetic coupling of the magnetic layers, which reduces the GMR effect dramatically. Normally, therefore, the nonmagnetic layer must be at least 15Å thick. <ref name="Dieny"> B. Dieny, Journal of Magnetism and Magnetic Materials 136 (1994) 335-359</ref>

== GMR-based hard drives ==



=== How it works ===

==== Hard disk drives (HDD) ====
[[Bilde:harddrv.jpg |300px|thumb|right|A cutaway view of an HDD. Image courtesy of [http://www.cybercollege.com/frtv/www2.htm Cybercollege]]]

In GMR Hard disk drives (HDD) data is stored on magnetically coated platters made of metal or glass that revolve at several thousand rotations per minute (RPM), driven by an electric motor. It is extremely important that these platters are completely flat (less than a few nanometers in height-difference on the entire disk), because the read-write head is scanning the surface at a relative speed of 10-30 m/s at ~15 nm distance. This is also the reason why you should never move a HDD in use, because the read-write heads might come in contact with the disks and scratch the surface, which would leave the disk useless. The capacity of the drive depends on the number of platters, typically from 4 to 8 and the type of magnetic coating. The magnetic coating is divided into small areas called bits, where one bit represent either a 1 or a 0, depending on the direction of the magnetization. 
When the disks spin the data is read and written by read-write heads located on the "arms". The position of the read-write heads is controlled by an actuator operating the arm.

==== Read-write head ====
[[Bilde:gmr3.gif|300px|thumb|right|Basic layout of a GMR read-write head. Image courtesy of [http://www.promconversia.com/eng/magnet/gmr Promconversia]]]
A GMR read-write head is located on the arm sweeping over the revolving platters typically separated from the platters by a mere 15 nm. The read head measures the resistance, and depending on the magnetization the resistance is measured as either high or low, corresponding to 1's and 0's which is provided back to the computer by the means of a control circuit. The write part of the read-write head consist of an electro-magnet which is able to shift the polarization of the mentioned bits and thereby writing the 1's and 0's.

=== Problems ===

==== Superparamagnetic effect (SPE) ====

The energy needed to flip between the different magnetization directions is related both to the physical size of the bit and the properties of the material. And simply described, SPE is a physical phenomenon that occurs in data storage when the energy that holds the magnetic spin in the atoms making up a bit either a 0 or 1 becomes comparable to the ambient thermal energy. When this happens bits become subject to random flipping between 0’s and 1’s, corrupting the information they represent. One way of reducing this problem is by keeping the bit-size large, but since the scaling tends to go toward smaller bit-sizes and higher densities, manufacturers try to increase the flip-energy per area by making different microstructures, such as the Current-Perpendicular to plane (CPP) or Tunnel Magnetoresistance (TMR). Even though low coercivity is preffered in GMR devices, materials with higher coercivity might be used to be able to decrease the bit size without experiencing SPE.

=== Emerging technologies ===

====Tunneling magnetoresistance (TMR) ====
TMR occurs when current flows through two ferromagnets separated by a thin (~1nm) insulator. The resistance is dramatically changed from the parallel to the anti-parallel alignment of the two ferromagnets, which gives higher signal-to-noise ratio for the TMR than GMR and possibility of higher density. The increase in resistance for TMR is in the orders of 200% and often much more. Today, almost all HDD's produced is based on TMR.

==== Current-perpendicular-to-plane GMR (CPP-GMR) ====
[[Bilde:Layercake.jpg|300px|thumb|right|Reference structure of GMR-CPP. Image courtesy of ref <ref name="Keiichi ">Keiichi Nagasaka, CPP-GMR technology for magnetic read heads of future high-density recording systems, Journal of Magnetism and Magnetic Materials Volume 321, Issue 6, March 2009, Pages 508-511 </ref>]]
According to newer research <ref name="Keiichi ">Keiichi Nagasaka, CPP-GMR technology for magnetic read heads of future high-density recording systems, Journal of Magnetism and Magnetic Materials Volume 321, Issue 6, March 2009, Pages 508-511 </ref> TMR is approaching an upper density-limit of 300–400 Gbit/in2. This means that if new technologies are not invented, the ongoing evolution of capacity increase will come to a halt. The CPP-GMR, also called vertical bits because of the reading heads sending a sensing current perpendicular to the disks, promises higher density because of the smaller surface area needed for a single bit.

== References ==

<references/>

*[http://nobelprize.org/nobel_prizes/physics/laureates/2007/phyadv07.pdf The Discovery of Gigant Magnetoresistance, Scientific background for the 2007 Nobel prize in physics.]