The document discusses magnetic properties and their temperature dependence. It describes how saturation magnetization decreases with increasing temperature and disappears at the Curie point, above which materials become paramagnetic. It also discusses magnetic domains and how they form to minimize demagnetization fields. Hysteresis loops are described for soft and hard magnets, and their different applications and optimization. Superconductivity is introduced, noting the Meissner effect and resistance dropping to zero below the critical temperature.

1. Today’s objectives - Magnetic Properties II Temperature dependence of saturation magnetization Be able to sketch B vs. H for a ferromagnet and describe why it is hysteretic and nonlinear. Lots and lots of domains… Be able to sketch and describe hysteresis loops for soft and hard magnets. How are each applied? How are each optimized? Sketch resistance vs. Temp for a superconductor. Why is there a transition, and what are the magnetic properties above and below T C ?

2. Temperature dependence The saturation magnetization is a measure of the maximum magnetization (assumes perfect alignment of all individual atomic magnetic dipoles). As temperature increases, M s diminishes, decreasing to 0 at a critical temperature (T c ). Beyond T c a ferromagnet becomes paramagnetic. Beyond T n a ferrimagnet becomes paramagnetic. The same is true for antiferromagnetic materials. Ferromagnets are usually metals. Ferrimagnets are usually ceramics. paramagnetic T c T n

3. Temperature dependence T C or T n Above a critical temperature called the Curie point ( TC ), ferro- and ferrimagnetic materials no longer possess a spontaneous magnetization. They become PARAMAGNETIC . So do anti-ferromagnetic materials. ferromagnetic anti-ferromagnetic ferrimagnetic T=0K paramagnetic

4. Lots and lots of domains… Domains form for a reason in ferro- and ferrimagnetic materials. They are not random structures.

5. Brown’s Paradox; lots of questions??? Take a simple iron needle. Iron is ferromagnetic , it should possess a spontaneous magnetization. The name ferromagnetic means magnetic like iron . It should attract another iron needle depending on the orientation of the magnetization vector. But it does not; Brown’s Paradox . Why??? Only if the “magnetic” iron is magnetized by a permanent magnet or an electromagnet, it will attract other pieces of iron . But this attraction disappears in a short while. Why??? How come lodestone (Fe 3 O 4 ) can stay “magnetic” for much longer times?

6. Why do Domains Form? H D H D M S Domains form to minimize (and in some cases to completely eliminate) demagnetization fields ( H D ). They are not random structures.

7. Magnetic Domains In reality, a ferro- or ferrimagnet is comprised of many regions (“domains”) with mutual alignment of the individual atomic magnetic dipole moments. These domains are not necessarily aligned with respect to each other. Domain walls between the domains are characterized by a gradual transition from one orientation to the next. The overall magnetization of the material (M) is the vector sum of the magnetization vectors for all of the individual domains. If not magnetized, the overall magnetization is simply zero. sum

8. Domain Walls Bloch Wall Bloch Wall and N è el Wall

9. Domain orientation (poling) Ferromagnets are simply considered to have extremely high and linear permeabilities (the same is true for susceptibilities). But, this simple picture ignores the domain structure of magnetic materials. Reality is more complex: Initially, domains are randomly oriented and B=0. Application of an external field (H) grows any domains with a similar orientation as H, shrinking the others. Eventually, only a single domain remains. Ultimately, something near the saturation magnetization is reached (M s or B s ).

10. Magnetic Hysteresis Once a magnetic material is saturated, decreasing H again does not return M (or B) to the same position. This hysteresis in the magnetic response is related to a) the mechanism (the last domain switched may not be the first to switch back the other direction) b) drag of domain wall motion For no external magnetic field, a remanent induction ( ± B r ) will remain. Some domains remain aligned in the ‘old’ direction. A ‘negative’ field, the “ Coercive Field ( ± H c ) ,” must be applied to eliminate all B r . The opposite mechanism occurs for increasing the external field after total saturation in the reverse direction.

11. Partial hysteresis If the applied external field sweeps through a portion of the hysteresis loop, there will be some finite hysteresis in the B response even if the field does not reach the coercive field: due to the same mechanisms as cause hysteresis in general domain wall drag, and the order of domain reorientation. -H c H c

12. Unmagnetized vs. magnetized H=External magnetic field ( magnetic field strength ) . B=magnetic induction ( magnetic flux density ) . µ=permeability (depends on the material, often referred to in terms of the relative permeability or the susceptibility) This equation for the magnetic induction is explicitly for an unmagnetized ferromagnet. M=magnetization , representing the magnetic moments within a material in the presence of a magnetic field of strength H. Once the material has been poled, though, the equation must be modified. B r accounts for any remanent magnetic induction (domain orientation).

13. Magnet types Magnets are categorized depending on the shape of the magnetic hysteresis loop. Soft magnet = narrow in H Hard magnet = broad in H The area of the loop represents energy lost in moving the domain walls as the magnet is poled from one extreme to the other and back again. Energy may also be lost due to local electric currents generated within the material caused by the external field. AC electric field causes a magnetic field, and vice versa.

14. Soft magnets Strong induction for a relatively weak external field. High saturation field (B s ), High permeability ( μ ), low coercive field (H c ) Therefore a low energy loss per poling cycle. Applied when rapid, lossless switching is required; usually subjected to ac magnetic fields: Transformer cores

15. Soft magnet optimization Saturation field is determined by the composition Coercivity is a function of structure (related to domain wall motion) For the best soft magnet, minimize defects such as particles or voids as they restrict domain wall motion. Lower energy loss per loop if non-conducting (no eddy currents). Form a solid solution such as Fe-Si or Fe-Ni to improve resistivity by a factor of 4 or 5 (from 1*10 -7 to 4*10 -7 ). Use a ceramic ferrite to improve resistivity by 10 to 14 orders of magnitude (insulators instead of metals) . (MnFe2O4, ZnFe2O4: 2000), (NiFe2O4, ZnFe2O4: 10 7 )

16. Hard magnets High saturation induction, remanence, and coercivity. High hysteresis losses It is ‘hard’ to repole a hard magnet. Book talks about the “energy product”—forget the definition—it simply allows us to describe how strong the magnet is in terms of the amount of energy required to repole it. Standard and high energy hard magnets. Standard are simple tungsten steel; FeNiCu alloys High energy hard magnets are 100 times ‘stronger.’ SmCo 5 , Nd 2 Fe 14 B is the most common

17. Hard magnet optimization As for soft magnets, the microstructure is related to the energy required to move magnetic domains and thus how ‘hard’ the magnet is. Now, though, we want a wide hysteresis loop so we may want to: Introduce defects such as second phase particles. Optimize size, shape, and orientation of crystallites in a polycrystalline magnet. Have a conducting material (eddy current losses).

18. Magnetic hard drives The magnetic disk has a soft magnet (easy to pole and repole with little energy loss. The read/write head is a hard magnet, or an electromagnet. Concept is the same as for an audio tape or video tape. Magnetics have thus far ruled for computer hard drives. Flash (solid state, Si based) is coming on strong Ferroelectrics are also increasingly being applied Thermo-mechanical methods may also be used in the future

19. Microstructure Magnetic recording media used to include needle shaped particles. Now, extremely flat thin films are used to diminish surface roughness.

20. Magnetic Storage Media Bits on magneto-optical disk. Topography reveals grooves that delineate tracks. MFM shows written bits as well as finer domain structure in un-aligned grooves. 5µm scan. Digital Instruments 25 µm scan of magnetic domains in three topographically identical regions of 50 nm thick Permalloy film (used for read heads). William Challener, 3M Corporation

21. More magnetic domains http://www.veeco.com/nanotheatre/nano_view.asp?CatID=3&page=2&recs=20&CP=# antiferromagnetically coupled [Co/Pt/Ru] multilayer Magneto-optical: DVD-RW terfenol

22. Many thanks to Prof. Barry Wells, UConn-Physics.

23. WHAT IS SUPERCONDUCTIVITY?? For some materials, the resistivity vanishes at some low temperature: they become superconducting . Superconductivity is the ability of certain materials to conduct electrical current with no resistance. Thus, superconductors can carry large amounts of current with little or no loss of energy. Type I superconductors: pure metals, have low critical field, sudden transition from super to normal conductivity. Type II superconductors: primarily of alloys or intermetallic compounds, gradual transition from super to normal.

24. HISTORY

26. APPLICATIONS: Power Superconducting Transmission Cable From American Superconductor. The cable configuration features a conductor made from HTS wires wound around a flexible hollow core. Liquid nitrogen flows through the core, cooling the HTS wire to the zero resistance state. The conductor is surrounded by conventional dielectric insulation. The efficiency of this design reduces losses.

27. APPLICATIONS: Medical Superconducting coils can carry a lot of current. They thus produce a very strong and uniform magnetic field inside the patient's body. MRI (Magnetic Resonance Imaging) scans produce detailed images of soft tissues.

28. MEISSNER EFFECT B T >T c T < T c B When you place a superconductor in a magnetic field, the field is expelled below T C . Magnet Superconductor Below T C , the superconductor is diamagnetic, so fields within it are opposite to that of the magnetic field to which it is exposed.

29. A superconductor displaying the MEISSNER EFFECT If the temperature increases the sample will lose its superconductivity and the magnet cannot float on the superconductor .

30. APPLICATIONS: Superconducting Magnetic Levitation The Yamanashi MLX01MagLev Train The track are walls with a continuous series of vertical coils of wire mounted inside. The wire in these coils is not a superconductor. As the train passes each coil, the motion of the superconducting magnet on the train induces a current in these coils, making them electromagnets. The electromagnets on the train and outside produce forces that levitate the train and keep it centered above the track. In addition, a wave of electric current sweeps down these outside coils and propels the train forward.

31. 1-2-3 Superconductors (YBa 2 Cu 3 O 7-x )

32. Superconductivity There are some limitations, though: In addition to temperature sensitivity, superconductivity is also a function of current density and the external magnetic field. The material goes non-superconducting if T C , H C , or J C are exceeded.

33. Magnet type review large coercivity --good for perm magnets --add particles/voids to make domain walls hard to move (e.g., tungsten steel: H c = 5900 amp-turn/m) • Hard vs Soft Ferro or Ferri-magnets small coercivity--good for elec. motors (e.g., commercial iron 99.95 Fe) and hard drive media. --remove defects to make domain wall motion as easy as possible. Adapted from Fig. 20.16, Callister 6e . (Fig. 20.16 from K.M. Ralls, T.H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering , John Wiley and Sons, Inc., 1976.)

34. SUMMARY Reading for next class Optical Properties, Chapter sections: 21.1-4 Temperature dependence of saturation magnetization Be able to sketch B vs. H for ferromagnets and describe why it is hysteretic and nonlinear. Be able to sketch and describe hysteresis loops for soft and hard magnets. How are each applied? How are each optimized? Sketch resistance vs. Temp for a superconductor. Why is there a transition, and what are the magnetic properties above and below T C ?