Techniques for inferring M at small scales

Transcription

1 Magnetism and small scales We ve seen that ferromagnetic materials can be very complicated even in bulk specimens (e.g. crystallographic anisotropies, shape anisotropies, local field effects, domains). Now we consider what happens when these materials are structured on the nm scale. Characterization techniques Interesting physics questions 2d effects (films) 1d effects (nanowires) Single-domain effects (nanoparticles) Techniques for inferring M at small scales Essential to progress in understanding micro- and nanomagnetic properties is the ability to determine experimentally M at these scales. Several techniques, each with its own appeal and limitations: Electronic transport Magneto-Optic Kerr Effect (MOKE) SEMPA Magnetic Force Microscopy (MFM) Magnetic Resonance Force Microscopy (MRFM) Spin-polarized STM Micro-SQUIDs Micro-Hall bars 1

2 Magneto-Optic Kerr Effect M causes rotation of plane of polarization of incident light. By varying geometry and plane of polarization, can build up picture of M as a function of position. Limited to optical resolution. Can be done in near-field limit, but very challenging. Images from Hubert and Schafer, Magnetic Domains, Spinger-Verlag SEMPA Scanning electron micropscopy with polarization analysis Has resolution of SEM - nice tool, but complicated to set up (UHV). Images from Tulchinsky et al., NIST 2

3 Magnetic Force Microscopy (MFM) Variant of AFM that uses a magnetically coated tip. Magnetic forces can be separated from atomic potential forces. Resolution nearly as good as straight AFM, but the stronger the coupling between the tip and the surface, the more likely the tip will influence sample (push domain walls around). Images from DI website Magnetic Resonance Force Microscopy (MRFM) Performed using MFM-style high-q cantilever in big magnetic field. Field from coated tip pushes some spins (electron or nuclear) into resonance with rf field + cantilever mechanical mode. Have succeeded in sensing single spins! (Nature 430, 329 (2004)) Images from AIP website 3

4 Spin-polarized STM Like regular STM, but using a magnetized tip (imbalance in tip spin species). Idea is to compare STM images at same tip bias, but with tip magnetized opposite directions. Just as tough as SEMPA. Images from Seoul National University, Korea MicroSQUIDs and scanning SQUID microscopy Uses local field from sample to change flux through superconducting ring with weak link. Resolution comparable to size of weak link. Needs low T and low background B fields! Images from Wernsdorfer habilitation thesis Image from Kirtley, IBM. 4

5 Micro and Scanning Hall magnetometry Uses 2deg Hall probes with very small (sometimes ballistic) active regions. Very flexible, but tough to get in close proximity to surface. Image from Lok et al., JMMM 204, 159 (1999). Image from Oral et al., APL 69, 1324 (1996). Interesting physics questions Now that we can probe M at small scales under a variety of conditions, what kind of questions are interesting? Many involve issues of domain walls and magnetization. What are the origins & excitations of the FM state, and how are they affected by geometric constraints? How do surfaces affect magnetization and domain dynamics? How do domains move and reorient? How do single domain particles behave? How do magnetic domains affect electrical conduction? 5

6 2d effects There is a large group of physics researchers who study magnetism in thin films, particularly in connection with fundamental physics questions (e.g. spin wave excitations and stability of FM order). Of more interest technologically are the dynamics of domains in thin films. A definition: A magnetic film of thickness t is effectively two-dimensional when any domain walls in the film lie perpendicular to the surface normal. 2d effects An additional physics ingredient: surface anisotropy. Recall that breaking translational symmetry of lattice potential in crystal led to surface states - single particle states with energies forbidden in the bulk. Breaking symmetry of magnetic environment can lead to surface magnetism not determined by same energetics as in bulk. 2 u s = K s [1 ( m n) Positive K s encourages m n, opposite of shape anisotropy. ] 6

7 2d effects Competition between all the different energy scales + disorder can lead to extremely complicated, hysteretic domain patterns. Why? Can have multiple ground state configurations that have very similar energies. Images from Hubert and Schafer, Magnetic Domains, Spinger-Verlag Pieces of permalloy thin film demagnetized under identical conditions. 2d effects Another example, this from a film with strong perpendicular anisotropy and low coercivity: Images from Hubert and Schafer, Magnetic Domains, Spinger-Verlag 7

8 1d effects (nanowires) A system is 1d magnetically if domain wall normals tend to be along the wire axis. How does magnetization reverse itself in a 1d nanowire? Coherent rotation Domain wall propagation Some combination (nucleation + propagation) There are electrical transport signatures that can be used to infer M as well as magnetization measurements. 1d effects (nanowires) Images from Hong et al., JPCM 8, L301 (1996). Example: thermal activation vs. quantum tunneling of domain walls Discrete feature in MR corresponds to unpinning of single wall. Width of distribution of escape fields vs. T suggests escape mechanism. Width does not go away as T approaches 0. 8

9 1d effects (nanowires) Propagation of domain walls once depinned. What is propagation speed? What does it depend on? Use Giant MagnetoResistance (GMR) effect to study domain wall motion. Images from Ono et al., Science 284, 468 (1999). 1d effects (nanowires) Images from Ono et al., Science 284, 468 (1999). Investigators found that domain walls in this 1d system propagate at velocity linearly dependent on H. Also found that constant of proportionality (effective DW mobility) was temperature independent. Detailed physics of DW propagation is not understood - mobility from theory is much too high. 9

10 1d effects (nanowires) One way to try to understand systems like this is through micromagnetic modeling (finite element analysis). Here Ferre et al. examine a reversal mechanism in a model wire without crystalline anisotropy. Notice that this is much more complex than simple propagation of a single domain wall. Remember that Ono et al. were only inferring M from R. Images from Ferre et al., PRB 56, (1997). Magnetization reversal Additional language to describe domains from world of magnetic modeling: exchange stiffness constant, A u ex A has units of J/m. = A( m) 2 Recall that crystallographic anisotropies are characterized by K, = K(sinθ ) u ani K has units of J/m 3. Can therefore compute an exchange length, L ex A / K This is, to within a factor of order 1, the same as the domain wall thickness we d calculated before. Particles with L < L ex are effectively 0-dimensional - single domain. How these particles behave is very interesting and important. 10

11 Single domain reversal For a general particle on a plane in external magnetic field, with φ = 0 defined as direction of easy axis, u tot = g φ) µ H M cos φ µ H ( 0 s 0 M s sinφ To find equilibrium direction of M, minimize this wrt φ. Stability criterion involves second derivative of this. For a simple uniaxial anisotropy, 2 g( φ) = K sin φ g' ( φ) = 2K sinφ cos φ 2 2 g' '( φ) = 2K (cos φ sin φ) Setting u tot = 0 and solving for H gives us the critical field for switching the magnetization. Single domain reversal Result is called the Stoner-Wohlfarth astroid: H H H * * 2K = µ M 2K = µ M 0 0 s s 3 cos φ 3 sin φ This tells us when it s energetically favorable for a simple, uniaxial anisotropy particle to switch its magnetization. Doesn t tell us about mechanism of reversal. H 11

12 Single domain reversal From the astroid, can figure out magnetization curves by a geometric construction procedure. Quantities at right have been nondimensionalized. Note that when H > H *, magnetization no longer exhibits hysteresis - it s energetically most favorable from M to follow H all the time. Images from Hubert and Schafer, Magnetic Domains, Spinger-Verlag Single domain reversal - mechanisms Three possibilities: Incoherent reversal - analogous to domain wall formation and propagation. Coherent rotation - entire M rotates like one big spin. Curling mode: 12

13 Curling Can see curling (vortex) state in MFM images of permalloy disks. Top left, cores are up and down. Top right, cores are all down. Images from Shinjo et al., Science 289, 930 (2000). Single domain reversal - rates u ani = K(sinθ ) Energy barrier for single domain particle to flip ~ KV. For small enough particles, expect to see thermal activation over this barrier above a blocking temperature, ~ KV/k B. Notice that T b ~ V - smaller particles have lower blocking temperatures. High temperature result: superparamagnetism. 13

14 Single domain reversal - rates Simple treatment of superparamagnetism ignores dynamics, actual mechanism of domain reversal. Typical form: τ 1 = Ωexp( KV / kbt ) Attempt frequency can range from 10 9 Hz and up. Note that one can also consider quantum tunneling of the magnetization, though there are some serious subtleties. See literature on molecular magnets (Mn 12 acetate, for example). Summary A number of techniques exist for inferring M at submicron scales. Interplay between various energy scales leads to rich, complex behavior, especially once geometric constraints become significant. Domain wall dynamics and magnetization reversal are hot topics of research, especially now that numerical techniques have become good enough to do sophisticated modeling. Single domain particles can often be treated analytically as far as stability of M is concerned. Dynamics of reversals can be complicated. Thermal flipping of small single-domain particles can lead to superparamagetism. 14

15 Next time Interplay between current and magnetization Demands of the data storage / magnetoelectronics industry 15

16 Ferromagnetism and Electronic Transport There are a number of effects that couple magnetization to electrical resistance. These include: Ordinary magnetoresistance (OMR) Anisotropic magnetoresistance (AMR) Giant magnetoresistance (GMR) Tunneling magnetoresistance (TMR) Ballistic magnetoresistance (BMR) Colossal magnetoresistance (CMR) We ll look briefly at the physics taking place in each of these. Ordinary magnetoresistance (OMR) This is the same magnetoresistance that comes about in normal metals. (Total internal) magnetic induction affects orbits of electrons at Fermi surface. Result of tightening orbits at higher fields is a positive magnetoresistance. H J has a weaker effect than H perp. to J. In polycrystalline materials and those where boundary scattering is important, again can have interplay between magnetic induction and disorder. In clean metals, OMR typically ~ B 2, and can be ~ 10% at 10 Tesla 1

17 Anisotropic magnetoresistance (AMR) Pointed out experimentally as early as 1930s (though really solidly confirmed in 1960s) that FM material measured resistance depends on relative directions of M and J. Figure from HP Data from bulk permalloy (80% Ni, 20% Fe). Resistance lower if M perpendicular to J. Resistance higher if M parallel to J. Anisotropic magnetoresistance Physical origin: spin-orbit coupling leads to spin-dependent scattering of conduction electrons. Conduction in (for ex.) Ni due to 4s and 3d electrons. Crudely, the 3d orbitals are affected by M, and are mixed (slightly reoriented) so that they present a larger scattering cross-section to electrons moving parallel to M. More scattering = higher resistance. M M 2

18 Anisotropic magnetoresistance Typical size of effect: ~ 1%. Typical field scale: determined by physics of reorienting M. In bulk permalloy, 5-10 Oe. In permalloy wires with large aspect ratios, ~ 1 T. Weak temperature dependence (competition between this scattering and other scattering mechanisms) - effect gets slightly larger at lower T. Nickel nanowire Cobalt nanowire Figure from Fert et al., JMMM 200, 338 (1999). Giant Magnetoresistance Discovered in laboratory c Not a trait of pure FM materials! Requires nanostructured composites of FM and nonmagnetic metals. Superlattice of very thin alternating layers of FM and N metals. Original configuration = current in plane Figure from Baibich et al., PRL 61, 2472 (1988). FM N 3

19 Giant Magnetoresistance Physical origin: spin-dependent transmission of carriers at interfaces between N and FM metals. There is some net spin polarization of the carriers. Density of states as a function of spin orientation is affected by M. Spins that are the majority species in one orientation of M are the minority species (lower DOS at Fermi level) in regions when M is oppositely directed. aligned = low resistance antialigned = high resistance Giant Magnetoresistance Typical size of effect: ~ 100%. Depends on percentage of spin polarized carriers at Fermi level, and zero-field coupling between neighboring FM layers. Note that relative directions of M and J not directly relevant. Typical field scale: determined by physics of reorienting relative directions of adjacent FM layer magnetizations. Usually arranged to be low. Interface quality is crucial. Coupling between adjacent FM layers oscillates with thickness of N layers: layer thicknesses and roughness must also be controlled. Effect gets larger at lower T and for cleaner metal layers as other scattering contributions are reduced. 4

20 Device geometries Original device was current-in-plane (CIP). If interfaces really dominate, GMR effects should be substantial in current-perpendicular-to-plane (CPP) devices, and they are. How are these systems actually used? Spin-valve geometry. Use antiferrromagnetic pinning layer to lock magnetization of one FM layer. Other FM is made to be magnetically soft - M easily realigns in small fields. Image from Leeds Univ. Tunneling magnetoresistance Spin-dependent density of states should have other consequences. Is possible to make FM-I- FM tunnel junctions. Tunneling conductance depends strongly on relative densities of states of spin species. In fact, tunneling magnetoresistance (TMR) is used to determine spin polarization at Fermi level. 5

21 Tunneling magnetoresistance Define spin polarization P as N P = N Model of Julliere (1975): N + N Here the Ns are proportional to the relevant densities of states at the Fermi level. Tunneling conductance will be proportional to tunneling rates, and tunneling rates will be proportional to number of carriers trying to tunnel (DOS of one FM) and number of available states (DOS of other FM). Assume that tunneling preserves spin (clean interfaces, etc.). G 2 ~ ( N ) + ( N ) 2 G ~ 2N N Tunneling magnetoresistance G 2 ~ ( N ) + ( N ) 2 G ~ 2N N Combining with definition of P, G ~ (1 + P )( N + N ) G ~ (1 P )( N + N ) 2 Compute ratios, and unknown factors drop out: G G G 2 R 2P = R 1+ P (1/ R ) (1/ R = (1/ R ) 2 2 ) R 2P = = R 1 P Some measured numbers: (from Meservey et al., Phys. Rep. 238, 173 (1994) Ni: 23% Fe: 40% Co: 35% NiFe: 32% 2 6

22 Tunneling magnetoresistance Typical size of effect: ~ 100%. As in GMR. depends on percentage of spin polarized carriers at Fermi level. Note that relative directions of M and J not directly relevant. Typical field scale: determined by physics of reorienting relative directions of adjacent FM layer magnetizations. Usually arranged to be low. Interface quality is again crucial - growing good tunnel barriers is very tough without doing odd things to the magnetic properties at the interface. Should be ~ temperature independent. Ballistic magnetoresistance GMR (1988) > BMR (1988) >> Nano- or atomic-scale point contacts between FM electrodes Magnetization apparently changes direction on length scale shorter than (elastic?) scattering length. Result: very large magnetoresistive effects, postulated to be for similar physics reasons as TMR. 7

23 Ballistic magnetoresistance Garcia et al., PRL 82, 2923 (1999). First measured using mechanical break junction technique. Effect can be large factor of 3 change in conductance! Unanswered questions: Truly ballistic? Magnetic dead layer? Magnetostriction? How large can effect be? Colossal magnetoresistance von Helmolt et al., PRL 71, 2331 (1993) Lin et al., Science 264, 413 (1994) (Re)discovered in Takes place in specific family of compounds, perovskites of the form A 1- xb x MnO 3, where A = (La, Pr, Nd, Sm), B = (Ca, Sr, Ba). Physical mechanism is completely different than any described so far. 8

24 Colossal magnetoresistance Size of effect: ~ % (!) Extremely temperature and doping dependent - challenging to get useful, reproducible behavior at room temperature. Mechanism: phase transition between conductive FM ordering of Mn ions and insulating AFM ordering of Mn ions. Replacing rare earths with light metals changes some of the Mn from Mn 3+ to Mn 4+. Charge can hop from Mn to Mn via the oxygen anions. Strong FM exchange favors hopping of aligned spins (high conductance). Still not well understood! Of much interest because of large effects and very high spin polarization of carriers. Spin currents and magnetization We ve been talking about how M affects J, ability to transport charge, as manifested through magnetoresistive effects. One can also consider the converse: can a current J of carriers with a net spin polarization affect M? Yes! A current with a net spin polarization means a flow of angular momentum from one region to another. This results in a net torque on the spins in those regions, and for high enough torques, it can be energetically favorable for domains to rearrange themselves. 9

25 Spin currents and magnetization Myers et al., Science 285, 867 (1999) Here s an example, involving current flow into a GMR multilayer. Change in magnetization direction of one of the layers is detectable by GMR effect - change in electrical resistance. Note, should be asymmetric in current direction! Spin currents and magnetization Katine et al., PRL 84, 3149 (2000) Clear demonstration of current-induced magnetization reversal. Ability to manipulate M without applying external fields is potentially very attractive technologically. One example of spintronics that we ll cover soon. 10

26 Spin currents and magnetization Krivorotov et al., Science 307, 228 (2005) Can do more - time-domain studies! Direct measurements of current-induced torques. Spin currents and magnetization Krivorotov et al., Science 307, 228 (2005) Can do more - time-domain studies! Direct measurements of current-induced torques. 11

27 Summary Magnetization can affect electronic conduction through several mechanisms: Local B field (OMR) Band structure and scattering (AMR) Spin-dependent transmission and scattering (GMR, TMR) Coupling between charge and magnetic order (CMR) Current can also affect magnetization, as shown in currentinduced magnetization reversal experiments. Next time Demands of data storage industry, particularly magnetic. 12

28 Needs of the data storage industry Focus on magnetic media first, and, as in the lecture on the electronics industry, will try to keep an eye on areas where nano will be relevant. Historic trends State-of-the-art Media Read and write mechanisms Scaling concerns Nonvolatile approaches Where it all began 1878 Oberlin Smith invents magnetic recording - patterns of domains in steel wire Valdemar Poulsen invents reel-to-reel metal tape recording, and the telephone answering machine Sony introduces reel-to-reel recorder using coated tape RCA introduces stereo tape - cartridge needs special player Phillips introduces cassettes Motorola, RCA introduce 8-tracks Cassette outsell LP records. 1

29 Where it all began Core memory - use magnetization of ferrite cores as computer memory. $6000 per 1kb bit line 6.6 kb in 8 x8 x8 word line Image from Columbia Univ. ACIS Image from pcbiography.net Where it all began Image from pcbiography.net RAMAC (1956) First hard disk drive disks Stored a total of 5 MB of information. Areal density = 2kb/in 2 Data rate = 70 kb/sec. 2

30 Historical trends Image from IBM presentation Historical trends Image from IBM presentation 3

31 Historical trends Image from IBM presentation Magnetic storage: state-of-the art Image from IBM website Disk medium: 2.5 diameter, 34 Gb/in 2 (typical size ~ 140 nm) CoPtCr alloy (M sat = 4 x 10 5 A/m, H c = 2.7 x 10 5 A/m, K = 1.5 x 10 5 J/m 3 ) Layered structure, including special AFM layer: 4

32 Magnetic media Why the AFM layer? Consider superparamagnetism for this disk material. Individual grain in a bit ~ 10 nm on a side. Energy barrier = KV ~ 1.5 x J. Attempt frequency ~ 10 9 leads to effective rate of τ 1 ~ Ω exp( KV / k T ) ~ Means typical timescale for a particular grain to thermally reverse itself would be 2 months. B 7 s 1 Need some way of reducing superparamagnetic effects! Magnetic media Image from IBM website Antiferromagnetic pixie dust layer stiffens disk medium without strongly altering its coercivity (write-ability). 5

33 Hard drives - read heads Permalloy yoke with integrated, microfabricated Cu coils. Shield of high permeability material between yoke and GMR sensor - guides B to prevent record head from affecting GMR FM layers. Minimum size of transverse bit set by write-gap width. Head attached to end of piezoactuated arm. Aerodynamics keeps head suspended above surface at flight height. Images from IBM website Hard drives - read heads Image from IBM website Basic spin valve design. Exchange layer pins one of the GMR FM layers. Note that this is a standard current-in-plane geometry. 6

34 Where are we headed? Image from IBM presentation Advances coming: Different media Thermally assisted recording Vertical recording Patterned media Different read heads CPP GMR heads CPP magnetic tunnel junction heads CMR? EMR? Different technology altogether MRAM Millipede Holographic storage 7

35 Thermally assisted recording Image from IBM website Simple idea: use media with significantly higher anisotropies. Benefit: added thermal stability against superparamagnetism. Downside: harder to write bits. Solution: locally heat medium (optically) to drop coercive field. Tricky - need short thermal relaxation times. Vertical media 8

36 Vertical media Potential advantages: Can get better thermal stability by larger bit volumes without sacrificing bit area density. Better signal to noise under some circumstances because fringing fields over larger area tend to influence read head. Disadvantages: Textured growth of medium on substrate can be quite tricky. Patterned media image from Nat. Univ. Singapore Don t rely just on film growth: make nanostructured media with prearranged bit locations - single domain particles. Several different approaches: E-beam lithography (far too slow) Ion beam patterning through mask Nanoimprint lithography Electrochemistry through porous mask Self-organization / self-assembly Real possibility of > 1TB/in 2! 9

37 CPP read heads Competing storage technologies Other approaches (nonmagnetic): AFM-based storage ( Millipede - IBM) Electron-based storage (HP) STM-based storage (IBM) Holographic storage 10

38 Millipede AFM storage Image from IBM website Millipede AFM storage Array of 1024 piezoresistively sensed AFM cantilevers. Physical deformation of polymer medium to write, using integrated resistor to heat individual tip by ~ 100 degrees. Healed by local heating to erase. Demonstrated density of 200 Gb/in 2, with an eye toward 1Tb by summer, Can this ever be cheap and reliable? IBM really seems to think so. Think 300 DVDs in a space the size of a credit card. 11

39 Electron-based storage image from Scientific American, May 2000 HP plan: nanofabricated field emission tips. In principle, can get very high resolution, approaching atomic scale. Holographic storage image from Bell Labs Use phase-sensitive interference patterns from lasers to write data pages into an optically changeable medium. Can be read pages at a time. Different pages can be stored at different depths in medium. Potential storage densities and speeds are enormous! Problems: Needs serious lasers and optics. Materials problems with media. 12

40 Conclusions Magnetic data storage still has a lot of life left to it, but progress rates are so fast they make Moore s law look relaxed. Physics (superparamagnetism) demands changes in media soon. New read head technologies also likely to be relevant. Competing technologies have incredible potential, and will eventually supplant magnetic storage for certain applications. 13