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[[File:Magnetic Tunnel Junction.png|thumb|right|Magnetic tunnel junction (schematic)]]
- British Medical Journal: Emotional Distress in Infertile Women and Failure of Assistive Reproductive Technologies. If a woman wants to have a quick pregnancy, it's always handy to have an inexpensive ovulation test kit. Nonetheless, it may be possible to easily conceive by simply knowing the best day to get pregnant and by understanding how fertility works. Weak Sperm - Unhealthy or abnormal sperm can also affect pregnancy outcome. So in order to give your infant the best habitat for nine months, take care of your body. <br><br>Women must resort to a healthy diet on a regular basis. " Well, if you need to understand how to get pregnant fast, then you'll definitely should be a lady with a program. One fantastic program called Pregnancy Miracle offers a report for potential moms-to-be. Possibly the most important thing that you need to know during conception is when the right time to have intercourse is. com where you can ask questions, get information, or just let off a bit of steam. <br><br>Becoming in tune with the body's discreet signs that it transmits to you every month throughout the monthly period and fertile periods is one good way of boosting your possibilities of victory when trying to get pregnant. Epididymals obstruction is defined as the blockage of the passage of sperm to **** leading to low sperm count and increases the risk of infertility. This guide and her program has worked for her and quite a few other people, hopefully it will do the similar for you. Here are some fertility tips to get pregnant as fast as possible. Alcohol can reduce fertility by as much as 50% and decrease sperm counts. <br><br>The cleansing program, followed by optimal nutrition and vitamins supplementation, may enhance your fertility. It is just a matter of finding the perfect remedy for your situation. ” This guide on The Sims 3 Woo - Hoo will help to explain how you can get your Sims to Woo - Hoo, and where Woo - Hoo is able to happen. It was an interesting spiritual cleansing and as with all spiritual journeys, it just might have worked if there is enough belief. '''''''''''''''''''''''''''' Woman hoping to get pregnant should take a multivitamin that includes at least 400 micrograms (mcg) of folic acid (but no more than 1,000 mcg). <br><br>And these two divisions of the same type of DNA, this means the children of the same sex, and appearance. A detailed understanding of the many factors that cause infertility is the foundation on which a successful conception can be made to occur. If you are looking for the absolute simplest system for getting pregnant naturally, you will likely be truly pleased to understand that there's only a tiny number of points you'll want to complete so that you could conceive and give birth to a perfect and healthy child. Aside from a high quality fertility supplement, you should include your diet with fertility super foods to increase the rate of getting pregnant. You may also use subliminal messages to train your mind to block these negative stories, so you can focus on the positive things about your pregnancy.<br><br>If you have any inquiries concerning where and how to use [http://www.quebec-1759.info/ quickest way to get pregnant], you can call us at our own page.
 
'''Tunnel magnetoresistance''' (TMR) is a [[magnetoresistance|magnetoresistive effect]] that occurs in a '''magnetic tunnel junction''' (MTJ), which is a component consisting of two [[ferromagnet]]s separated by a thin [[Insulator (electrical)|insulator]]. If the insulating layer is thin enough (typically a few [[nanometer]]s), [[electron]]s can [[Quantum tunneling|tunnel]] from one ferromagnet into the other. Since this process is forbidden in classical physics, the tunnel magnetoresistance is a strictly [[Quantum mechanics|quantum mechanical]] phenomenon.
 
Magnetic tunnel junctions are manufactured in [[thin film]] technology. On an industrial scale the film deposition is done by magnetron [[sputter deposition]]; on a laboratory scale [[molecular beam epitaxy]], [[pulsed laser deposition]] and [[electron beam physical vapor deposition]] are also utilized. The junctions are prepared by [[photolithography]].
 
== Phenomenological description ==
 
The direction of the two [[magnetization]]s of the ferromagnetic films can be switched individually by an external [[magnetic field]]. If the magnetizations are in a parallel orientation it is more likely that [[electron]]s will tunnel through the insulating film than if they are in the oppositional (antiparallel) orientation. Consequently, such a junction can be switched between two states of [[electrical resistance]], one with low and one with very high resistance.
 
== History ==
 
The effect was originally discovered in 1975 by M. Jullière (University of Rennes, France) in [[iron|Fe]]/[[germanium|Ge]]-[[oxygen|O]]/[[cobalt|Co]]-junctions at 4.2 K. The relative change of resistance was around 14%, and did not attract much attention.<ref>{{cite journal | author=M. Julliere | title=Tunneling between ferromagnetic films | journal=Phys. Lett.| year=1975 | volume=54A | pages=225–226|doi=10.1016/0375-9601(75)90174-7 |bibcode = 1975PhLA...54..225J }}</ref> In 1991 Terunobu Miyazaki ([[Tohoku University]], Japan) found an effect of 2.7% at room temperature. Later, in 1994, Miyazaki found 18% in junctions of iron separated by an [[amorphous]] [[aluminum oxide]] insulator <ref>{{cite journal | author=T. Miyazaki and N. Tezuka | title =Giant magnetic tunneling effect in Fe/Al<sub>2</sub>O<sub>3</sub>/Fe junction|title=Giant magnetic tunneling effect in Fe/Al<sub>2</sub>O<sub>3</sub>/Fe junction | journal=J. Magn. Magn. Mater. | year=1995 | volume=139 | pages=L231–L234|bibcode = 1995JMMM..139L.231M |doi = 10.1016/0304-8853(95)90001-2 }}</ref> and [[Jagadeesh Moodera]] found 11.8% in junctions with electrodes of CoFe and Co.<ref>{{cite journal | author=J. S. Moodera ''et al.'' | title=Large Magnetoresistance at Room Temperature in Ferromagnetic Thin Film Tunnel Junctions | journal=Phys. Rev. Lett. | year=1995 | volume=74 | pages=3273–3276 | doi=10.1103/PhysRevLett.74.3273 | pmid=10058155 | issue=16 | bibcode=1995PhRvL..74.3273M}}</ref> The highest effects observed to date with aluminum oxide insulators are around 70% at room temperature.
 
Since the year 2000, tunnel barriers of [[crystalline]] [[magnesium oxide]] (MgO) have been under development. In 2001 Butler and Mathon independently made the theoretical prediction that using [[iron]] as the ferromagnet and [[MgO]] as the insulator, the tunnel magnetoresistance can reach several thousand percent.<ref>{{cite journal | author=W. H. Butler, X.-G. Zhang, T. C. Schulthess, and J. M. MacLaren | title=Spin-dependent tunneling conductance of Fe/MgO/Fe sandwiches | journal=Phys. Rev. B | year=2001 | volume=63 | page=054416 | doi=10.1103/PhysRevB.63.054416|bibcode = 2001PhRvB..63e4416B | issue=5 }}</ref><ref>{{cite journal | author=J. Mathon and A. Umerski | title=Theory of tunneling magnetoresistance of an epitaxial Fe/MgO/Fe (001) junction | journal=Phys. Rev. B | year=2001 | volume=63 | page=220403 | doi=10.1103/PhysRevB.63.220403|bibcode = 2001PhRvB..63v0403M | issue=22 }}</ref> The same year, Bowen et al. were the first to report experiments showing a significant TMR in a MgO based magnetic tunnel junction [Fe/MgO/FeCo(001)].<ref>{{cite journal | author=M. Bowen ''et al''. | title=Large magnetoresistance in Fe/MgO/FeCo(001)… epitaxial tunnel junctions on GaAs(001…) | journal=Appl. Phys. Lett. | year=2001 | volume=79 | page=1655 | doi=10.1063/1.1404125|bibcode = 2001ApPhL..79.1655B | issue=11 }}</ref>
In 2004, Parkin and Yuasa were able to make Fe/MgO/Fe junctions that reach over 200% TMR at room temperature.<ref>{{cite journal | author=S Yuasa, T Nagahama, A Fukushima, Y Suzuki, and K Ando | title=Giant room-temperature magnetoresistance in single-crystal Fe/MgO/Fe magnetic tunnel junctions | journal=Nat. Mat. | year=2004 | volume=3 | pages=868–871 | doi=10.1038/nmat1257 | pmid=15516927 | issue=12|bibcode = 2004NatMa...3..868Y }}</ref><ref>{{cite journal | author=S. S. P. Parkin et al. | title=Giant tunnelling magnetoresistance at room temperature with MgO (100) tunnel barriers | journal=Nat. Mat. | year=2004 | volume=3 | pages=862–867 | doi=10.1038/nmat1256 | pmid=15516928 | issue=12|bibcode = 2004NatMa...3..862P }}</ref> In 2009, effects of up to 600% at room temperature and more than 1100% at 4.2 K were observed in junctions of CoFeB/MgO/CoFeB.<ref>{{cite journal | author=S. Ikeda, J. Hayakawa, Y. Ashizawa, Y.M. Lee, K. Miura, H. Hasegawa, M. Tsunoda, F. Matsukura and H. Ohno | title=Tunnel magnetoresistance of 604% at 300 K by suppression of Ta diffusion in CoFeB/MgO/CoFeB pseudo-spin-valves annealed at high temperature | journal=Appl. Phys. Lett. | year=2008 | volume=93 | page=082508 | doi=10.1063/1.2976435|bibcode = 2008ApPhL..93h2508I | issue=8 }}</ref>
 
== Applications ==
 
The [[Disk read-and-write head|read-heads]] of modern [[hard disk drive]]s 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&nbsp;nm.<ref name="white paper">Barry Hoberman [http://www.crocus-technology.com/pdf/BH%20GSA%20Article.pdf The Emergence of Practical MRAM]. Crocus Technologies</ref> There are two 2nd generation techniques currently being developed: [[Thermal Assisted Switching]] (TAS)<ref name="white paper"/> and [[Spin Torque Transfer]] (STT). Magnetic tunnel junctions are also used for sensing applications.
 
== Physical explanation ==
 
[[File:TunnelSchema TMR.png|thumb|right|Two-current model for parallel and anti-parallel alignment of the magnetizations]]
 
The relative resistance change—or effect amplitude—is defined as
 
:<math>\mathrm{TMR} := \frac{R_{\mathrm{ap}}-R_{\mathrm{p}}}{R_{\mathrm{p}}}</math>
 
where <math>R_\mathrm{ap}</math> is the electrical resistance in the anti-parallel state, whereas <math>R_\mathrm{p}</math> is the resistance in the parallel state.
 
The TMR effect was explained by Jullière with the [[spin polarization]]s of the ferromagnetic electrodes. The spin polarization ''P'' is calculated from the [[spin (physics)|spin]] dependent [[density of states]] (DOS) <math>\mathcal{D}</math> at the [[Fermi energy]]:
 
<math>P = \frac{\mathcal{D}_\uparrow(E_\mathrm{F}) - \mathcal{D}_\downarrow(E_\mathrm{F})}{\mathcal{D}_\uparrow(E_\mathrm{F}) + \mathcal{D}_\downarrow(E_\mathrm{F})}</math>
 
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, ''P<sub>1</sub>'' and ''P<sub>2</sub>'':
 
<math>\mathrm{TMR} = \frac{2 P_1 P_2}{1 - P_1 P_2}</math>
 
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 [[conservation law|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 [[coercivity|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 decreases with both increasing temperature and increasing bias voltage. Both can be understood in principle by [[magnon]] excitations and interactions with magnons.
 
It is obvious that the TMR becomes infinite if ''P<sub>1</sub>'' and ''P<sub>2</sub>'' 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 are called ''ferromagnetic half-metals''. Their conduction electrons are fully spin polarized. This property is theoretically predicted for a number of materials (e.g. CrO<sub>2</sub>, various [[Heusler alloy]]s) but has not been experimentally confirmed to date.
 
==Spin-filtering in Tunnel Barriers==
Prior to the introduction of epitaxial [[magnesium oxide]] (MgO), amorphous aluminum oxide was used as the tunnel barrier of the MTJ and typical room temperature TMR was in the range of tens of percent. MgO barriers increased TMR to hundreds of percent due to the ability to filter spin, which is complementary to the electrode spin polarization effect described above. The physical origin of this spin filtering is actually symmetry filtering because the electron wavefunctions of opposite spin originate from different bands at the Fermi level. These bands correspond to different orbitals for majority and minority spin and thus have different symmetries. The MgO conduction and valence bands have the same symmetry as majority spin electrons, so they experience a lower barrier height than minority spin electrons. This exponentially increases the tunneling probability so parallel configuration current exceeds anti-parallel current by a much larger amount.
 
==Spin-transfer torque in Magnetic Tunnel Junctions (MTJs)==
The effect of [[spin-transfer torque]] (STT) has been studied in MTJs where there is an tunnelling barrier sandwiched between a set of 2 ferromagnetic electrodes such that there is (free) magnetization of the right electrode, while assuming that the left electrode (with fixed magnetization) acts as spin-polarizer. This would then be pinned to some selecting transistor in an MRAM device.  
 
The STT vector, driven by the linear response voltage, can be computed from the expectation value of the torque operator:
 
<math> \mathbf{T} = \mathrm{Tr}[\hat{\mathbf{T}} \hat{\rho}_\mathrm{neq}] </math>
 
where <math> \hat{\rho}_\mathrm{neq} </math> is the [[Gauge theory|gauge-invariant]] nonequilibrium [[density matrix]] for the steady-state transport, in the zero-temperature limit, in the linear-response regime,<ref>[F. Mahfouzi, N. Nagaosa, and B. K. Nikolić, ''Spin-orbit coupling induced spin-transfer torque and current  polarization in topological-insulator/ferromagnet vertical heterostructures'',  Phys. Rev. Lett. '''109''', 166602 (2012).  Eq. (13)]</ref> and the torque operator <math> \hat{\mathbf{T}} </math> is obtained from the time derivative of the spin operator:
 
<math>
\hat{\mathbf{T}} = \frac{d\hat{\mathbf{S}}}{dt}= -\frac{i}{\hbar}\left[\frac{\hbar}{2}\boldsymbol{\sigma},\hat{H}\right]
</math>
 
Using the general form of a 1D tight-binding Hamiltonian:
 
<math> \hat{H}=\hat{H}_0 - \Delta (\boldsymbol{\sigma} \cdot \mathbf{m})/2 </math>
 
where total magnetization (as macrospin) is along the unit vector <math> \mathbf{m}</math> and the Pauli matrices properties involving  arbitrary classical vectors <math> \mathbf{p},\mathbf{q} </math>, given by
 
<math> (\boldsymbol{\sigma} \cdot \mathbf{p})(\boldsymbol{\sigma} \cdot \mathbf{q}) = \mathbf{p} \cdot \mathbf{q} + i(\mathbf{p}\times\mathbf{q})\cdot \boldsymbol{\sigma}  </math>
 
<math> (\boldsymbol{\sigma} \cdot \mathbf{p}) \boldsymbol{\sigma} = \mathbf{p} + i \boldsymbol{\sigma} \times \mathbf{p} </math>
 
<math>  \boldsymbol{\sigma}  (\boldsymbol{\sigma} \cdot \mathbf{q}) = \mathbf{q} + i \mathbf{q} \times  \boldsymbol{\sigma} </math>
 
it is then possible to first obtain an analytical expression for <math> \hat{\mathbf{T}} </math> (which can be expressed in compact form using  <math> \Delta, \mathbf{m} </math>, and the vector of Pauli spin matrices <math> \boldsymbol{\sigma}=(\sigma_x,\sigma_y,\sigma_z) </math>).  
 
The STT vector in general MTJs has two components: a parallel and perpendicular component:
 
A parallel component:
<math> T_{\parallel}=\sqrt{T_x^2+T_z^2} </math>
 
And a perpendicular component:
<math> T_{\perp}=T_y </math>
 
While in symmetric MTJs (made of electrodes with the same geometry and exchange splitting), the STT vector has only one active component, as the perpendicular component disappears:
 
<math> T_{\perp} \equiv 0 </math>.<ref>[S.-C. Oh ''et. al.'', ''Bias-voltage dependence of perpendicular spin-transfer torque in a symmetric MgO-based magnetic tunnel junctions'', Nature Phys. '''5''', 898 (2009). [http://www.nature.com/nphys/journal/v5/n12/abs/nphys1427.html &#91;PDF&#93;]</ref>
 
Therefore, only <math> T_{\parallel} </math> vs. <math> \theta </math> needs to be plotted at the site of the right electrode to characterise tunnelling in symmetric MTJs, making them appealing for production and characterisation at an industrial scale.
 
Note:
In these calculations the active region (for which it is necessary to calculate the retarded [[Green's function (many-body theory)|Green's function]]) should consist of the tunnel barrier + the right ferromagnetic layer of finite thickness (as in realistic devices). The active region is attached to the left ferromagnetic electrode (modeled as semi-infinite tight-binding chain with non-zero [[Zeeman effect|Zeeman splitting]]) and the right N electrode (semi-infinite tight-binding chain without any Zeeman splitting), as encoded by the corresponding self-energy terms.
 
==References==
{{reflist|35em}}
 
==See also==
 
* [[Quantum tunnelling]]
* [[Magnetoresistance]]
* [[Giant Magnetoresistance]]
* [[Spin-transfer torque]]
 
{{DEFAULTSORT:Tunnel Magnetoresistance}}
[[Category:Electric and magnetic fields in matter]]
[[Category:Spintronics]]

Latest revision as of 18:11, 13 July 2014

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