Abstract
Light emitting diodes made out of inverse spin valves of a ferromagnetic half metal sandwiched between two nonmagnetic metals are proposed. Based on a giant spin-dependent chemical potential difference created under an external bias, the inverse spin valves are possible to emit light when electrons with the higher chemical potential flip their spins and become the electrons of the opposite spin with the lower chemical potential. The frequency of this type of light emitting diodes is tunable by the bias.
Most light emitting diodes (LEDs) are made of either nonmagnetic semiconductors or organic semiconductors. The working principle of an LED is to create a situation where electrons occupy higher energy levels and some of the lower energy levels are unoccupied so that electrons can move to those lower energy levels by emitting photons. One of the popular ways to achieve this in the conventional LEDs is through a p-n junction where electrons are injected into the conduction band on one side and holes into the valence band on the other side (of the junction) when the LED is electrically biased in the forward direction of the junction. As long as an electron and a hole are spatially not too far apart, they can radiatively recombine and emit incoherent narrow-spectrum light. Thus, the emitted light depends largely on the energy difference between electrons and holes. This is also why a proper electronic structure is normally required for LED materials. How much the light frequency is tunable depends on the detail energy band structure of the LED material. On the other hand, all materials can emit light if they are in excited states. The question that we would like to ask is whether it is possible to make an LED out of materials that are normally not for LEDs. In this letter, we propose an inverse spin valve device in which the chemical potentials of spin-up (SU) and spin-down (SD) electrons split when an external bias is applied. The degree of the split is at the magnitude of applied bias, and is due to the spin-dependent electron transport. Thus the device can emit tunable light under an external bias. Interestingly enough, this inverse spin valve is made out of both nonmagnetic and magnetic metals. Traditionally, one will not relate LEDs with magnetism where one may be interested in the magnetization reversal [1–6]. Furthermore, the emitted light is not sensitive to the particular materials used, and thus it is an LED out of any material.
A conventional spin valve is a layered structure of a nonmagnetic spacer sandwiched between two ferromagnetic metals. An inverse spin valve is a layered structure with a ferromagnet sandwiched between two nonmagnetic metals. As illustrated in Figure 1(a), and are two nonmagnetic metals. To maximize the spin-related chemical potential split, the ferromagnetic spacer is chosen to be a half metal (HM) that acts as a conductor to electrons of one spin orientation (spin-up), but as an insulator to those of the opposite orientation (spin-down). Then only SU electrons can pass through the half metal when an external bias is applied on the inverse spin valve. SD electrons will be blockaded from the flow through the spacer. Similar to a giant magnetoresistance [7–9] or tunneling magnetoresistance [10, 11] device, electron transport of an inverse spin valve is spin-dependent.
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The spin-dependent electron transport of an inverse spin valve leads to spin-dependent Fermi levels in nonmagnetic metals near the nonmagnetic-magnetic interfaces under a bias. Consider one inverse spin valve connected to a battery of voltage . Let us assume that the electron chemical potential in is initially moved up by while that of is kept unchanged [12]. The electron flow diagram is shown in Figure 1(b). and each has two electron reservoirs. One is for SU electrons, and the other is for SD electrons (denoted by rectangular boxes). SU electrons in can flow into the empty SU electronic states in via the empty SU electronic states in the half metal, generating a current from to . There is no current between the SD-electron reservoir of and SD-electron reservoir of due to the spin blockade of the half metal. The same amount of electrons will be pumped back from to by the battery to keep the electron neutrality in and . However, a battery does not distinguish electron spin, and it pumps equal amounts of SU and SD electrons. In other words, SU electrons flow out of and into . In the meanwhile, an equal amount of electrons with half of them in the SU state and the other half in the SD state are drawn out of and are supplied into by a battery. As a result, accumulates more SD electrons, and accumulates more SU electrons. Thus, the chemical potential of the SD electrons is higher than that of the SU electrons in . Vice versa, the Fermi level of SU electrons is higher than that of SD electrons in . Figure 1(c) is an illustration of the Fermi levels (denoted by the dash lines) of SU and SD electrons in nonmagnetic metals and half metal. The electron density of states (DOSs) in the figure for nonmagnetic metals and half metal is just a sketch. and are the chemical potential differences between SU and SD electrons in and , respectively. is the chemical potential difference between the SU electrons in and the SU electrons in .
SD electrons in can only go to by first flipping their spins and changing to SU electrons. The only supply of the SD electrons to is from the conversion of the SU electrons in through spin flipping. As shown in Figure 1(b), these lead to the internal currents () in () between SD-electron and SU-electron reservoirs. Assume the spin flip occurs only near nonmagnetic-magnetic interfaces within a width of spin diffusion length () in (). This is justified because () is the length scale over which a chemical potential difference can maintain, and the conversion rate of SU and SD electrons from each other is the same when both SU and SD electrons have the same Fermi levels (chemical potentials). Let () be the spin flipping time (spin-relaxation time [13]) in (), corresponding to the flipping rate of (). The conversion rate from the SD (SU) electrons to the SU (SD) electrons in () is the product of the excess SD (SU) electrons () and the single electron flipping rate. Thus () iswhere () is the density of states of the SD electrons in () at the Fermi level. is the cross-section areas.
Neglecting the tunneling by the SD electrons through the half metal and assuming a resistance for the SU electrons, the current from to isIn the steady state, there is no net electron build up anywhere in the circuit. Since the current through the battery is unpolarized, half of the current is made up by the SU electrons and the other half is from the SD electrons. Balance conditions and external constraint requireSolving (1)–(3), the spin-dependent chemical potential differences and areIt is interesting to see that the largest chemical potential splits occur at , a short circuit for SU electrons! The chemical potential splits are largely determined by the applied bias. Thus they could be the order of if the steady current (controlled by the relaxation time and bias) is not too large to cause an electric breakdown. The half metal may also be replaced by an ordinary ferromagnet. In this case, SD electrons in can also flow directly into . As long as there is a spin-dependent electron transportation, the spin-related chemical potential differences in and always exist but their values will be reduced by a factor of , where is the resistance of the ferromagnetd for the SD electrons (minority carriers).
Results of (4) mean the population inversion of the electrons in the electrically biased inverse spin valves. As shown in Figure 2(a) for , SU electronic states below their Fermi level are fully occupied (at zero temperature) while the SD electronic states in the energy range of between SU electron Fermi level and SD electron Fermi level are empty. Thus an SU electron can go to a lower empty SD electronic state and emit a photon. One can then apply standard theory of LED to the inverse spin valve device to make an LED or even a laser by incorporating the device with a cavity [14]. However, unlike the usual light source of atoms and semiconductors where spin does not involve in the electron transitions, the light source here is spin resolved. For example, in the case that the magnetization of the half metal is along the +z-direction, the spin-up (+z-direction) electrons in are in higher energy levels, and they can only go to spin-down states. Due to the angular momentum conservation, the spin of the emitted photon must be along the +z-direction. In other words, the light out of an inverse spin valve is polarized. Its polarization depends on the light propagation direction and magnetization of the half metal. As shown in Figure 2(b), the light emitted in the +z-direction is right-hand circularly polarized light, and left-hand circularly polarized light in the -direction. Because of the two-component nature of photons (angular momentums must be parallel to light propagation direction), no light can emit in the direction perpendicular to the magnetization of the half metal (xy-plane).
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It should be clear that electroluminescence in a spin-flip transition does not violate any fundamental principles, such as energy, angular momentum, and linear momentum conservations. The energy and angular momentum conservations are satisfied by emitting a photon with a proper frequency and angular momentum. Linear momentum conservation is easily satisfied, just as all radiative transitions in vapors or liquids or solids that can absorb readily any negligible linear momentum of a photon (this is why a good optical semiconductor should have a direct band gap). In a normal LED, radiative transitions occur between two states in two different bands with opposite parities. To have a finite dipole-induced electroluminescence, one needs a nonzero dipole matrix element where and are the initial and finite electronic states (in the same band). Thus, this is only possible in a metal without inversion symmetry! This requirement is similar to that in a cascade laser [15] of superlattices. Electroluminescence in a spin-flip transition is also supported by the fact that magnetization dynamics can be manipulated by the laser of femtosecond time-scales [16]. This fact indicates a strong coupling between photons and electron spin-flipping. Furthermore, in a conventional semiconductor, an electron decay within the same energy band is dominated by nonradiative one due to the electron-photon interaction whose time scale is typically picoseconds in comparison with nanoseconds for a radiative one. The nonradiative decay is expected to be greatly suppressed in our system because the direct photon-electron and electron-electron interactions cannot flip electron spins. Thus, radiative decay from occupied SU electron states to empty SD electron states should be the favored channel. Of course, nonradiative decay is still possible when the spin-orbital coupling is strong.
In comparison with the usual semiconductor LEDs, there are a few nice features about the proposed LED. (1) Photons have a well-defined polarization because both occupied and unoccupied states have well defined spins. (2) The population inversion is not very sensitive to the detail electronic structure, thus the physics is very robust, and one can in principle use any conducting materials, magnetic or nonmagnetic and organic or inorganic, to make LEDs. (3) The spin-dependent chemical potential difference is controlled by an external bias, thus the light frequency can be electrically tuned over very broad range.
Zero temperature is assumed in (1). For a finite temperature, electron distribution is no longer described by a step-function, and (1) should be modified. Also, the spatial variation of the Fermi level is neglected in the present work. In principle, Fermi levels of both SU and SD electrons vary in space because of electron diffusion, spatial distribution of electrons, and spin flipping. The spatial variation of the Fermi levels may also modify (1). For practical applications, it is interesting to work out a more careful analysis by taking into account the electron distribution in both energy and space although one should not anticipate any change in physics.
The working principle of currently proposed LED device is different from the traditional ones. Unlike many previous LEDs where electron spin degrees of freedom were not used, the LED devices here is largely based on manipulating electron spins through the spin-dependent electron transport in inverse spin valves so that it is possible to create higher occupied SU (SD) electron levels and lower unoccupied SD (SU) levels. The population inversion does not occur between states of the same spin, but for opposite spin instead. However, it should be pointed out that concept of spin-LED is not new [17, 18].
In conclusion, we propose a very robust LED device made of almost any material. Unlike the usual LEDs that rely on detail energy spectrum of the material, the proposed technology uses electron spin blockage to create a population inversion of electrons.
Acknowledgments
The author would like to thank Professor Yongli Gao and Professor John Xiao for the useful discussions. This work is supported by Grants no. RPC07/08.SC03, RGC/GRF603508, RGC/CERG603007, and SBI07/08.SC09.