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