The story so far: Today:

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1 The story so far: Devices based on ferromagnetism have found tremendous utility in technology. Ferromagnetism at the nm scale is increasingly important, and physical effects (e.g. superparamagnetism) not usually seen in large devices will become relevant imminently. Physics of carriers in ferromagnets is an active area of research - the interplay between magnetization and current is still being explored. Today: Extraordinary magnetoresistance Learning a lesson from a nanostructured material, and applying it to an engineered device. Magnetic Random Access Memory (MRAM) Using GMR and TMR in a 21st century form of core memory. Other applications of nanoscale magnetic particles Magnetorheological fluids Chemical or immunoassay Medical applications 1

2 Extraordinary Magnetoresistance In 1998, Thio and Solin at NEC were studying an extremely narrow band gap semiconductor, Hg x Cd 1-x Te. They discovered, much to their surprise, that this material exhibited an extremely large magnetoresistance at room temperature: EMR What is going on in this material? Electrons dominate transport in this material because µ e ~ 10 5 cm 2 /Vs even at room temperature (!) (very small electron effective mass), and µ e /µ h ~ 200. Compositional fluctuations on length scales < 1 micron can result in small inclusions of metallic material with much higher conductivity than the nominal semiconductor: 2

3 EMR - mechanism What do these high conductivity inclusions do? In substantial magnetic fields, B is perpendicular to E because the Hall field is very large. For very metallic inclusions, E is perpendicular to the surface of the inclusion. Result: In low magnetic fields, current flows mostly through inclusions - conductance is high. In high enough fields, current flows mostly around inclusions - conductance much lower. Image from Thio, NEC EMR - application Solin et al., Science (2000). Once the mechanism was understood, Solin et al. started engineering structures to magnify this effect. Now use n-type InSb film (again, high mobilities, largely because m * ~ m 0 ). Instead of accidental inhomogeneous pockets, deliberately introduce Au regions (Ohmic contact to n-insb). 3

4 EMR - application Solin et al., APL (2002). Nonmagnetic read head (!) with very narrow active region and large MR effects. Should be immune to magnetization noise, since contains no FM material. Magnetic Random Access Memory The same spin-dependent scattering that has been used to produce GMR and TMR materials for HDD read heads can be used for nonvolatile computer memory. Remember ferrite cores? Image from IBM website 4

5 MRAM Two possible architectures: GMR-based TMR-based Image from IBM website MRAM Image from IBM website IBM betting on TMR design. Refining tunnel junctions - 1 nm Al 2 O 3 tunnel barriers, FeCo alloy for ferromagnet layers. Imagine: As fast as DRAM. As nonvolatile as flashram. Instant-boot computers. Motorola, IBM trying to move this technology into production by Motorola has already demonstrated 1Mb MRAM chip (June 02). 5

6 Other applications of nanoscale magnetism Magnetoassay Magnetorheological fluids Medical applications Magnetoassay There is a big market for biocompatible FM nanoparticles. The basic idea: Functionalize outside of biocompatible FM particle with particular compound that binds to some analyte. Expose to bio system and see whether things bind to the magnetic particle. Image from Retrotech website 6

7 Magnetoassay Problems: Most magnetic materials aren t very biocompatible. Often researchers try to win by mixing materials with high M values into relatively inert polymer beads. Downside: beads end up being large. Tricky to handle FM particles without them sticking together. Magnetoassay Advantages: Cheap, fast, reliable, easy to detect w/o fancy optics. Image from Naval Industrial Partners website 7

8 Magnetorheological fluids Ferrofluids are colloidal suspensions of sub-micron FM particles (often Fe 3 O 4 ). Without an applied magnetic field, just act like a viscous fluid. With an applied magnetic field, effective viscosity can change by several orders of magnitude (!): Magnetorheological fluids Highly useful in things like magnetic clutches. Suggested for applications like body armor. Suggested for magnetic actuation in medical applications Image from Technorama.ch website 8

9 Medical applications Similar to magnetoassay, only this time for treatment. Coat nanoscale FM particles with compound that binds to desired analyte (e.g. prostate specific antigen). Allow biocompatible FM particles into body. Locate analyte by FM resonance. Cook tumors by FM resonance heating. MRI contrast agents 9

10 Spintronics Basic idea: use spin as well as charge of electron for information processing / useful devices. Problems: Need to get spin-polarized electrons - would like to do so without enormous magnetic fields. Would like to manipulate spin degree of freedom, again without big magnets if possible. Upside: can drag spin along with charge. Downside: spin is not conserved, per se. Want to read out spin information somehow. Sources of spin polarized carriers Two main ways of getting carriers with net spin polarization: Ferromagnetic contacts Recall our numbers for polarization in some common ferromagnets: (from Meservey et al., Phys. Rep. 238, 173 (1994) N P Ni: 23% Fe: 40% Co: 35% NiFe: 32% N Optical pumping with circularly polarized light N + N Image from Awschalom group, UCSB 1

11 Definitions Much of the language used to discuss dynamics of electron spins in solids is taken from NMR community. T 1 : the time for a nonthermal net spin polarization to relax back to its equilibrium value. B z B x Mz t T 1 T 1 times are set by relaxation mechanisms that can exchange angular momentum with carriers: spin-lattice relaxation time. Can vary quite a bit because of different relaxation mechanisms. Ex: thin gold films: ~ 45 ps. Definitions T 2 : the time for a population of coherently prepared spins to dephase. Due to local inhomogenaieties plus spin-spin interactions, the precessing spins gradually get further and further out of step. This process goes on simultaneously with T 1 processes. In dirty (lots of scattering) systems, can have τ << T 1, T 2, so not much difference between the two. In clean systems (semiconductors), however, the distinction can be important! 1/T 2* = 1/T 1 + 1/T 2. 2

12 Spin relaxation mechanisms Things get more complicated in metals because the electrons move. Image from Fabian, Karl-Franzen Univ., Austria Because of spin-orbit coupling, z-component of spin is no longer a good quantum number. Correct single-particle Bloch eigenstates are lin. comb. of spin-up and spin-down. Result: changes of wavevector k have some chance to flip particular carrier from a mostly spin-up state to a mostly spin-down state, and vice-versa. Mathiesson s rule Image from Fabian, Karl-Franzen Univ., Austria Since any momentum relaxation scattering process can cause spin flips with some likelihood, expect T 1 ~ τ with some coefficient, expected to depend only on material. Note that impurities of different Z and phonons (which locally modulate lattice structure) also cause changes in spin-orbit coupling, and can scatter carriers from one spin state into another. 3

13 Spin relaxation mechanisms Image from Fabian, Karl-Franzen Univ., Austria Materials with no inversion symmetry complicate matters. With SO scattering, carriers act like there is an effective internal magnetic field that depends on momentum, B(k). Result: spins precess in that internal field. Relaxation results because of momentum scattering; T 1 ~ τ again, though this effect is washed out at large applied magnetic fields. Spin relaxation mechanisms Image from Fabian, Karl-Franzen Univ., Austria This mechanism is exchange between electrons and holes. Recall, holes have considerably different spin-orbit interactions than electrons; coupling them together via exchange effectively shortens lifetime of spin states of electrons. Only relevant in semiconductors, where electron and hole wavefunctions are comparatively larger (lower carrier density) and have more overlap. 4

14 Spin lifetime and diffusion Image from Fabian, Karl-Franzen Univ., Austria In disordered materials, it s often more useful to talk about a spin diffusion length, L s, rather than a lifetime. Typical distance diffused by a carrier before a spin-flip event. Spin injection in an all-metal system Ohmic injection of spin-polarized carriers seems intuitively like it should be readily achievable: electrons FM N Expect to find an excess spin polarization in the normal metal that decays ~ exponentially moving away from the FM-N interface. Typical decay length: L s, spin-flip scattering length. In Au, D ~ 0.01 m 2 /s, giving L s ~ (D T 1 ) 1/2 = 0.6 microns. 5

15 Direct detection of magnetization? electrons FM N How much excess magnetization are we talking about? Could we measure it directly, by something like MFM? Number of excess spins pumped in per second: P (I/e). Lifetime of spins ~ T 1 for the normal metal. Suppose FM = iron ( P = 0.4 ) and N = Au (T 1 = 40 ps). For 1 microamp current, N = P (I/e) T 1 = 100. Very hard to find 100 excess spins spread out over ~ w x 0.6 microns. Other ways of detecting magnetization The numbers don t work out well for the direct detection (via magnetic fields) of the injected magnetization. Have to use other properties of that magnetization to infer its presence and magnitude. Signatures in conductance = Hanle effect, spin accumulation Signatures in optical response = Faraday rotation Signatures in optical emission = circularly polarized light 6

16 Spin injection in an all-metal structure Basic idea of Johnson and Silsbee (1985) (note: pre-gmr). Use one FM contact as an injector of electrons, and a closely spaced second FM contact as a detector ( analyzer ) (permalloy). Normal paramagnetic underlayer (aluminum). Johnson and Silsbee, PRL 55, 1790 (1985) Idea is that nonequilibrium magnetization in paramagnet produces a voltage difference between detector and ground. Pηµ BM V = Here η is an efficiency of injection at interface. χe Hanle effect Idea is to use applied transverse field to cause injected spins to precess. Projection of injected M along direction of detector M is what goes into determining the voltage detected. Since distance L is fixed, expect voltage to oscillate with orientation of B. Note: this experiment actually measures T 2* rather than T 1. 7

17 Hanle effect Johnson and Silsbee, PRL 55, 1790 (1985) Actually works. Johnson and Silsbee arrive at T 2 numbers that agree well with those obtained in ESR experiments. First solid demonstration of spin injection. Found that η defined above typically << 1: interfaces matter critically in spin injection experiments. Faraday rotation Kikkawa et al., Science (1997) Optical pump to produce lots of spin-polarized e-h pairs. Kerr angle oscillates as polarized carriers precess in applied magnetic field. ZnCdSe quantum well material used in this experiment. 8

18 Faraday rotation Much longer lifetimes (T 2* ) seen in doped quantum wells when compared with undoped ones. Why? Holes (rapid spin relaxing anyway due to SO) recombine with spinunpolarized electrons already present due to doping! Result is that remaining (spinpolarized) electrons are not severely hurt by recombination with holes. Long lifetimes and long coherence are potentially very useful for quantum computation. Kikkawa et al., Science (1997) Faraday rotation Kikkawa et al., Nature (1999) More advanced experiment does same thing but spatially resolved, in doped GaAs. This time, can watch cloud of spin-polarized electrons as it spreads (diffusion), drifts in an applied electric field, and shrinks (spin relaxation). 9

19 Optical emission Ohno et al., Nature (1999) Spin injection from magnetic semiconductor into nonmagnetic semiconductor. Built-in LED structure. Annihilation of spin-polarized electron with (unpolarized) hole can only happen in optical emission case if the resulting light is circularly polarized. Optical emission Ohno et al., Nature (1999) Optical signature shows FM hysteresis, and coincides precisely with FM signature of GaMnAs as seen in SQUID measurements. 10

20 Next time: The ugliness of electrical spin injection. Spin valves and spin transistors. 11

21 Spin injection For devices, all-electrical spin injection is desirable. Three materials combinations: FM Metal - N metal FM Metal - semiconductor FM semiconductor - semiconductor FM N Will look at these, and explain the difficulties associated with each. At same time, will get a sense of proposed spintronic devices. Spin injection from metals into metals Johnson, Semicond Sci Tech (2002). Charge current drags excess spin population into N metal. Electrostatic potential adjusts itself for appropriate equilibrium. 1

22 Spin injection from metals into metals Here s a more recent demonstration of this idea. Now use nanofabricated permalloy (F1, F2) and copper (N). Many possible measurement configurations. Py pieces small enough to be single domain. Py pieces have differing geometric anisotropies: magnetization can be controllably flipped one at a time! Jedema et al., Nature 410, 345 (2001) Spin injection from metals into metals Conventional spin-valve geometry: I in 1 and out 7; V btw. 4 and 9. Analogous to CPP GMR device. Does not work well here - AMR and Hall effects in the Py strips are too big. Jedema et al., Nature 410, 345 (2001) Instead, Jedema et al. use nonlocal geometry as described above. I in 1 and out 5; V between 6 and 9. Antiparallel M: should see higher voltage (effective 4-terminal resistance) because of nonequilibium spin buildup in Cu cross region. 2

23 Nonlocal spin valve effect Jedema et al., Nature 410, 345 (2001) When sweeping in-plane field, shorter Py piece flips first. As predicted, higher voltages measured when Py magnetizations are antialigned. Note that this works even at room temperature! Can do quantitative analysis by modeling spin diffusion process in device. Quantitative analysis (signs and portents) Jedema et al. do simple 1d diffusion analysis, where they allow the electrons to freely pass back and forth across the F-N interfaces (can get spin flip scattering w/in the Py, for example). Results work fairly well; get sensible results for P and L s. Note long values of L s even at room temperature! 2 Ls P exp( L / 2Ls ) σ N wt R = ( M + 1)[ M sinh( L / 2L ) + cosh( L / 2L )] Lsσ F M L σ sf N (1 P 2 ) s s 3

24 Quantitative analysis (signs and portents) Johnson, Semicond Sci Tech (2002). Johnson points out that interpreting data in this system is actually quite subtle. Need to worry about where spin injection really happens. Need to worry about 2d diffusion of spin in lateral arms all the time. Disagreement over treatment of interface scattering. Sign of things to come: even in an allmetal system (high carrier densities, generally negligible Hall effects), it s hard to get agreement on what constitutes unambiguous spintronic action. Spin injection from metals into semiconductors Things get even uglier when worrying about spin injection from FM metals into semiconductors. Why do people care about this? Potential integration with existing semiconductor technology. Low carrier densities permit gating for further device possibilities. Clean materials mean much longer spin lifetimes and distances. Very clever device designs exist that take advantage of physics present in semiconductors. 4

25 A spin transistor One example: the Datta-Das spin transistor Datta and Das, Appl. Phys. Lett. 56, 665 (1990) Working principle: because of relativistic effects (!), electric fields look, to the moving electrons, like they have a small magnetic field component. This is enhanced in materials with strong spin-orbit scattering (no inversion symmetry = III-V) - the Rashba Effect. Datta-Das transistor Applied gate voltage changes local electric field in channel. That is seen by the moving carriers as a slight magnetic field causing precession of the spins. Depending on amount of precession, should get improved conduction or not. Das Sarma, Amer. Sci. 89, 516 (2001). 5

26 Spin injection from metals into semiconductors Why hasn t anyone gotten this to work yet? 1) It s very hard to inject net spin polarization directly from a metal into a semiconductor! Two spin channels add in parallel, assuming negligible spin flip scattering in semiconductor. Can solve this problem and compute the spin polarization of the current in the semiconductor, P sc, and compare it with P, the polarization in the FM. Schmidt et al., Semi. Sci. Tech (2002). Spin injection from metals into semiconductors R FM 2R = 1 P 2R R FM = 1+ P R = 2R SC = R SC SC P SC R = P R FM SC 2( R FM 2 / R ) + (1 P SC 2 ) So, while spin polarization of current in semiconductor is proportional to that in FM, it s reduced by a factor of (R FM /R SC ), which can be ~ 10-4! Conductance mismatch between materials will cause big suppressions of spintronic effects. 6

27 Spin injection from metals into semiconductors 2 2 R P RFM 4 = R 1 P R 4( R / R ) + 2( R / R ) + (1 P SC FM SC FM SC 2 ) Spin valve type effects are reduced quadratically in the mismatch! Spin injection from metals into semiconductors Why hasn t anyone gotten this to work yet? 2) It s very hard to eliminate local Hall effects in systems with very low carrier densities! For example, Monzon et al. at Cal Tech spent several years trying to do these experiments, only to eventually decide that they could not see anything that couldn t be explained by Hall effects from stray fields. 7

28 Possible solution to FM-SC interface problem How do you avoid the conductance mismatch problem? Make tunnel junctions rather than direct Ohmic contacts! In last 1-2 years, people have made much more progress in allelectrical spin injection into semiconductors. Hall problems and interpretation of results continue to be problematic. Spin Hall effect Because of spin-orbit coupling, it s possible for a pure spin current to be produced in response to an electric field. Can be intrinsic due to strain + band structure. Can be extrinsic due to impurity scattering. New MOKE measurements in GaAs and InGaAs Kato et al., Science (on-line, 11/11/04) 8

29 Spin Hall effect Definite accumulation of spin species at opposite edges of sample! Apparently independent of crystalline axes suggests that this is the extrinsic spin Hall effect. 30 years of hunting pay off. Possible source of spins for manipulation without external fields, magnetic dopants, etc. Next time Magnetic semiconductors Spins for quantum computation Wrap-up 9

30 Magnetic semiconductors We saw last time that: We d like to do spintronics in semiconductors, because semiconductors have many nice properties (gateability, controllable spin-orbit effects, long spin lifetimes). Injecting spin efficiently into semiconductors from FM metals is hard because of the conductivity mismatch between materials, and the best way to do it is with tunnel barriers. Ideally, want FM semiconductors: Ohno et al., Nature (1999) (Dilute) Magnetic semiconductors Getting FM in semiconductors is not trivial. Recall why we have FM in metals: Band structure leads to enhanced exchange interactions between (relatively) localized spins (d- or f-shell electrons). Conduction electrons can play a very important role. In semiconductors, Carriers present are only there because of doping, and at much lower concentrations. No natural localized spins. Situation today: Add localized spins by doping (e.g. with Mn). Mechanism of FM still not clear. Curie temperatures still not great 1

31 Magnetic semiconductors - description Main family: III-V compound semiconductors. Most common magnetic dopant in Mn (group II). Result: III(Mn)-V compounds are p-type. Grown by low-temperature MBE - not thermodynamically stable. Typical concentration something like Ga 0.95 Mn 0.05 As. Ohno et al., Science (1998) Note that these materials are quite heavily doped! II-VI materials have been much harder to work with (unable to dope; exchange interaction difficult to control). DMS: magnetic properties Koshihara et al., PRL 78, 4617 (1997). In 0.95 Mn 0.05 As has T c ~ 30 K. Ga 0.95 Mn 0.05 As has T c ~ 110 K. Magnetic order depends very strongly on carrier density! Can therefore be manipulated. Light-induced ferromagnetism! 2

32 DMS: magnetic properties Sensitivity to carrier concentration means it s possible to have gateable ferromagnetism! Potentially very exciting for spintronics applications. Major problems: Temperature range is poor. Materials compatibility is not very good, either. Ohno et al., Nature (2000) DMS: group IV possibilities Recent progress in Mn x Ge 1-x growth. Again, low T ferromagnetism, with gate modulation as hole concentration is varied. Park et al., Science (2002) 3

33 Quantum Computation - a very quick intro A prime motivation for manipulation of spins in semiconductors is to perform quantum information processsing. What is quantum computation? Using the quantum properties of quantum-bits (qubits) to perform calculations more rapidly (in principle) than is possible with classical computers. Why should this be possible? Imagine a collection of N bits that can be 1 or 0. With these N bits one can represent any integer from 0 up to 2 N -1. Now suppose these bits are quantum mechanical objects. = New Roadmap for QIP. Qubits and their properties Consider N spin-1/2 particles, with spin up corresponding to 1 and spin down corresponding to 0. The quantum mechanical state of these states for 1 such qubit is written 1> or 0>. 1 Now, though, we can consider superpositions: ( ) 2 More conventional to think of these spins as column vectors: / 2 1 ( ) 2 1/ 2 Logic operations are now actually unitary operations on the spins (though in general this requires a dial-a-hamiltonian box). 4

34 Qubits and their properties A generic unitary operator: U θ cos( θ / 2) sin( θ / 2) sin( θ / 2) cos( θ / 2) So, U π inverts a qubit (up to a phase): U π 0 = Uπ 0 = = = 1 U π 1 = = = So, U π/2 produces a superposition: U π ( 0 1 ) 1 / 2 0 = + 2 What can this do for us? Imagine a string of N qubits, starting out in 0000 >. Use the state of each qubit to represent a binary number, a. Now apply the linear operator U π/2 to each qubit in this state. Result: 1 1 N a N 2 a= 0 We ve now prepared the qubits in a superposition of all their possible values! From a linear number of operations N, we ve produced a superposition with an exponentially large number of terms, 2 N. 5

35 What can this do for us? Now suppose we had two such strings. Suppose we had an operator O that, when operating on a string a returned a particular function f(a). That is, O a; 0 a; f ( a) Consider applying this operator to our big superposition: O 1 2 N 1 N a= 0 a;0 1 2 N 1 N a= 0 a; f ( a) Now with a single operation we ve computed f(a) for an exponentially large number of possible a. That s the crux of quantum computation! Because of this kind of quantum parallelism, it s possible to do certain computations much faster than with classical computers. What kinds of applications? There are already quantum algorithms (well-defined series of operations) for: Searching databases (Lov Grover) Factoring large numbers (Peter Schor) This is an extremely hot field in computer science right now. Big funding: DARPA, NSA Big players: IBM, Microsoft, Intel 6

36 What do we need to accomplish all this? Requirements according to David DiVincenzo (IBM): 1. Be a scalable physical system with well-defined qubits 2. Be initializable to a simple fiducial state such as > 3. Have much longer decoherence times 4. Have a universal set of quantum gates 5. Permit high quantum efficiency, qubit-specific measurements Universal quantum gates: can be proven that one only needs two kinds of gates (NOT and XOR) operating on 2 qubits at a time to do general quantum computations (with some other subtleties). Why is this difficult? One needs to be able to go in and couple qubits together with great precision, almost aribitrarily. How can one manipulate one particular qubit without accidently decohering the entire system? System must be isolated from the environment so that coherence times are long compared to operation times. One really wants to do this in a way that s scaleable. 7

37 How are people trying to implement QIP? Several approaches: Optical trapping / manipulation of atoms and ions NMR (liquid, solids) Quantum dots Superconducting qubits Everyone would love to do this in the solid state, because it would scale well and interface with existing technology. NMR Idea is to use nuclear spins in some system as qubits. Problem: you don t really have pure quantum states. Solution: with qubits, you can fudge things and have effective pure states. Ex: investigators at MIT have used 13 nuclear spins in a molecule to factor the number 15 = 5 x 3. NMR in molecules does not scale well: Individual chemical shifts of NMR frequencies are too limited - can t individually flip 8456th spin out of 10000, for example. 8

38 NMR hybrid - solid state possibility Kane., Nature (1998) Use P dopants in Si as qubits. Big hyperfine + Starck effects = dialable NMR frequencies to address individual qubits. Could be read out electrostatically. Quantum dots Idea of Divincenzo and Loss: use electron spins as qubits. Each qubit is a single electron in a quantum dot. Use gates to manipulate exchange interaction between neighboring qubits. Use SETs to read out states of qubits when done. Univ. of Wisconsin 9

39 Superconducting qubits Group in Delft exploring using superconducting loops as qubits. When 1/2 flux quantum is through loop, current clockwise is degenerate with current counterclockwise (can act like spin 1/2 system). Readout, manipulation all use nanofab. SQUIDs and SETs. QIP summary: Very intriguing ideas Number of possible technologies, but it s not clear if any of them will work well in a practical manner. Many implementations would depend critically on nanofabrication and nanotechnology. Progress has been much more rapid than I imagined two years ago, particularly in the superconducting qubits and semiconductor quantum dot approaches. 10