Material Property By Dr. Cherdsak Bootjomchai (Dr. Per)
Chapter IV Magnetic Properties
Objectives - Magnetic Properties I 1. Equations describing magnetic field strength, induction (several versions), relative magnetic permeability, magnetic susceptibility, magnetization of a solid, and saturation magnetization. 2. Origins of magnetic moments. 3. Magnetic types of materials, their relative magnetic permeabilities, and why they behave as they do (diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic, ferrimagnetic). 4. Temperature dependence of magnetization and why it occurs.
Objectives - Magnetic Properties 5. Temperature dependence of saturation magnetization 6. Be able to sketch B vs. H for a ferromagnet and describe why it is hysteretic and nonlinear. 7. Lots and lots of domains 8. Be able to sketch and describe hysteresis loops for soft and hard magnets. How are each applied? How are each optimized? 9. Sketch resistance vs. Temp for a superconductor. Why is there a transition, and what are the magnetic properties above and below T C?
Magnetic dipoles Magnetic forces develop when a charged particle moves. Magnetic dipoles exist within certain magnetic materials. Just like bar magnets with North and South poles. The magnetic dipoles point from South to North by convention. (Compare to Electric fields, which go from + to -) The force of a magnetic field exerts a torque on the dipole that tends to align it. Compass needle
Earth s Magnetic Field A magnetic field is generated every time an electrically charged object moves. Most of the planets in the Solar System are known to generate magnetic fields. The Earth's magnetic field is generated in its fluid, outer core. This is because the heat of the inner core drives the fluid in the outer core up and around in a process called convection. Because this outer core is made of metal, which can be electrically charged, the convection causes a magnetic field to be generated.
A bit of History Mt. Olympus Troy Greece Magnesia, Manisa Turkey
The Stone from Magnesia - Magnetite Spinel Structure Atom x y z Fe(tet).125.125.125 Fe(oct).5.5.5 O.2549.2549.2549 Magnetite (or lodestone): opaque, black, ceramic crystal. Magnetite (FeO Fe 2 O 3 ) is an oxide of iron which, unlike Fe 2 O 3, is strongly magnetic.
Magnetic Vectors A magnetic field, either induced or permanent, generates a magnetic force. The direction of the force is drawn (blue lines). Density of field lines indicates the field strength. H=External magnetic field NI H = in units of H for Henry s L Also called magnetic field strength. a vector B=magnetic induction (Magnitude of internal magnetic field strength within a material exposed to an H field) in units of T for Tesla Also called magnetic flux density. also a vector B = µh
Comparison: magnets and dielectrics µ=permeability (depends on the material, similar to a dielectric constant where ε was related to electronic polarizability). B = µh A strong permeability means the material is made of something which can align strongly to an external magnetic field. This leads to a strong magnetic induction (or flux density). A good dielectric has charges which can polarize in an external field (opposite to it). electrons vs protons in nucleus cations and anions polar molecules interfaces q A ε (or k) ε ε q A
Magnetic Permeability Since the permeability influences the magnetic induction (flux density), It impacts how good of a magnet you can make. In a vacuum, the permeability is a universal constant, µ o = 1.257*10-6 H/m. B = µh Bo = µ oh
Other magnetic terms The relative permeability (µ r ) is sometimes used to describe the magnetic properties of a material (like ε for dielectrics). The magnetization (M) represents the magnetic moments within a material in the presence of a magnetic field of strength H (akin to polarization, P, for a dielectric). The magnitude of M is proportional to the applied field according to the magnetic susceptibility (χ m ). There are thus four main ways to represent B, the magnetic induction (also called the flux density). Note that units get very confusing. Just stick with one system (SI). B B B µ B B D = E+ r M = χ mh χ = µ 1 m B= µ H = µ µ H r B= µ H = = µ H = o µ µ r o = µ µ H o o = µ o H + µ om o P dielectric ( 1+ χ ) µ H r + µ M m polarization o o
Magnetic Orbital Moments Magnetic moments arise due to two mechanisms: Orbital motion of an electron around the nucleus. Essentially a small current loop, generating a very small magnetic field. A magnetic moment is established along the axis of rotation. m l is the magnetic quantum number for the electron. magnetic moment orbital = m l µ b b 24 µ = 9.27*10 A* m 2 The magnetic quantum number indicates the type of orbital (shape and usually orientation). Orbital m Total orbitals Total electrons s 0 1 2 p -1,0,1 3 6 d -2,-1,0,1,2 5 10
Magnetic Spin Moments 2 nd source of a Magnetic Moment Direction that an electron spins. Only two directions are possible. The moment resulting from these spinning electrons are along the spin axis, either UP or DOWN. magnetic moment spin =± µ b The combination of orbital and spin moments for every electron throughout a crystal define its magnetic properties.
How do we Classify Magnetic Properties of Materials? The Faraday Experiment
The Faraday Experiment The coil induces an inhomogeneous magnetic field. The sample is suspended from one of the arms of a sensitive balance into the magnetic field H. Certain materials are weakly expelled from this field (along x direction). These are DIAMAGNETS. PARAMAGNETS are weakly attracted to this field (along x direction). FERROMAGNETIC, ANTI-FERROMAGNETIC and FERRIMAGNETIC materials are strongly attracted to this field.
Classification via Magnetic Susceptibility χ m χ m µ r B = µ H µ B H r = µ / µ o = µ rµ o M = χ H χ m m = µ r 1
Diamagnetism Nonmagnetic (only occurs in the presence of an external magnetic field, H) Even in an external magnetic field, very weak form of magnetism Non-permanent Occurs opposite to external field. Relative permeability < 1 ( 0.99999) Found in all materials, just usually too weak to matter. So weak that only noticed if no other form of magnetism exists for the atom and/or crystal. Most common for atoms with completely filled orbitals (no unmatched electrons that could have spin moments). Inert gases Some ionic structures (H 2 O, Al 2 O 3 ) Noble metals (Au, Cu, Ag, Hg, Zn) B µ r µ oh
Paramagnetism B µ r µ oh If the orbitals are not completely filled or spins not balanced, an overall small magnetic moment may exist. Without an external magnetic field, the moments are randomly oriented. No net macroscopic magnetization. NonMagnetic In an external field, the moments align with the field, thus enhancing it (only a very small amount, though). There is no interaction between adjacent dipoles. Permeability (µ r ) > 1 (barely, 1.00001 to 1.01. Examples include Al, Cr, Cr 2 Cl 3, MnSO 4 )
Ferromagnetism Unlike paramagnetism with incompletely balanced orbital or spin moments which are randomly aligned, for some materials unbalanced spin can lead to significant permanent magnetic moments. Fe (BCC alpha), Co, Ni, Gd. The permanent moments are further enhanced by coupling interactions between magnetic moments of adjacent atoms so that they tend to align even without an external field. Maximum possible magnetization for these materials is the saturation magnetization (M s, usually quoted per volume). There is a corresponding saturating flux density (B s ). M B s s = = M µ o per atom M per atom *atoms *atoms M per atom Fe Co Ni µ B 2.22 1.72 0.6
Anti-Ferromagnetism Magnetic moment coupling (for each individual atom) does not always align constructively as for ferromagnetism. For some materials, the alignment of the spin moments of adjacent atoms is in opposite directions. MnO O 2- has no net moment. Mn 2+ have a spin based net magnetic moment. Overall, there is no net magnetic moment even though at the atomic level there is a local moment.
Ordered arrangement of spins of the Mn 2+ ions in MnO determined by neutron diffraction. The 0 2- ions are not shown. Anti-Ferromagnetism
Ferrimagnetism Ferrimagnets are similar to ferromagnets. There is a net magnetic moment. They are also similar to antiferromagnets. The net magnetic moment is not as large as if all of the magnetic atoms coupled constructively. Essentially, ferrimagnetism entails some of the magnetically active atoms coupling constructively, and an unequal number coupling destructively. Examples include Fe 3 O 4 (Fe.Fe 2 O 4 ), NiFe 2 O 4, ZnFe 2 O 4. Unlike ferromagnets, they are not electrically conductive. Used in high frequency applications such as microwave devices, circulators, phase shifters.
Ferrimagnetism All Fe 2+ have a spin magnetic moment. Half of Fe 3+ have a spin moment in on direction, the other half in the other (decreasing the overall moment to just that contributed by the Fe 2+ ions). Common for inverse spinel materials and garnets. Usually, 2+ ions of Ni, Mn, Co, and Cu are the active ones. Simpler picture showing a net magnetic moment.
µ r> >>1 B Comparisons χ > 0 µ r >1.001 µ r =1 µ r =.99999 H To be quantitative, there are 4 options (magnetic permeability, relative permeability, or susceptibility): µ r µ o vacuum χ = 0 χ < 0 χ measures the material response relative to a vacuum. ( ) H B= 1+ χm µ o µ = χ m µ 1 B B B = µ H = µ µ H r o o = µ H = r + µ M o Type Mag Induction (B) Relative Permeability (µ r ) Susceptibility (χ m ) diamagnetic Small, opposite H <1 (barely, so µ µ o- ) Negative, -10-5 paramagnetic Small, with H >1 (this time µ µ o+ ) Positive, 10-3 to 10-5 ferromagnetic Large, with H >>1 >>1 -
Temperature dependence Saturation magnetization M S is the maximum magnetization in a material assuming perfect magnetic dipole alignment. This happens only at T=OK. Increasing T increases thermal vibrations and decreases M S due to diminished (exchange) coupling between dipoles. This is VERY important for ferro-, ferri-, and antiferromagnets. Thermal vibrations also cause the dipoles to spend more time pointing in the wrong direction, reducing M s. Above a critical temperature called the Curie (or Neèl) point (T C or T n ), ferro- and ferrimagnetic materials no longer possess a spontaneous magnetization. They become PARAELECTRIC.
The Curie (or Neèl) Temperature T C (Fe) T n (Fe 3 O 4 )
Temperature dependence ferromagnetic anti-ferromagnetic T C or T n T=0 K ferrimagnetic paramagnetic 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.
MAGNETIC MOMENTS FOR 3 TYPES No Applied Magnetic Field (H = 0) Applied Magnetic Field (H) (1) diamagnetic none opposing Adapted from Fig. 20.5(a), Callister 6e. (2) paramagnetic random aligned Adapted from Fig. 20.5(b), Callister 6e. (3) ferromagnetic ferrimagnetic aligned aligned Adapted from Fig. 20.7, Callister 6e.
What about Ferri- and Anti-FerroMagnets? What about ferrimagnetic? Similar to Ferromagnets What about antiferromagnetic? Similar to Paramagnets
Classification Summary
Temperature dependence The saturation magnetization is a measure of the maximum magnetization (assumes perfect alignment of all individual atomic magnetic dipoles). T n T c 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
Temperature dependence ferromagnetic anti-ferromagnetic T C or T n T=0K ferrimagnetic paramagnetic 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.
Lots and lots of domains Domains form for a reason in ferro- and ferrimagnetic materials. They are not random structures.
Why do Domains Form? H D M S H D Domains form to minimize (and in some cases to completely eliminate) demagnetization fields (H D ). They are not random structures.
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
Domain Walls Bloch Wall Bloch Wall and Nèel Wall
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 ). Bsat Magnetic induction (B) 0 H = 0 H H H H B= µ µ H B= ( 1+ χ ) µ H H Domains with aligned magnetic moment grow at expense of poorly aligned ones! Applied Magnetic Field (H) r o m o
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 remagnet 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.
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
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). B = µ H + µ M + o o B B = µh = µ o H + µ om B r
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.
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
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 )
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
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).
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
Microstructure Magnetic recording media used to include needle shaped particles. Now, extremely flat thin films are used to diminish surface roughness. ~60nm
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
More magnetic domains antiferromagnetically coupled [Co/Pt/Ru] multilayer terfenol Magneto-optical: DVD-RW http://www.veeco.com/nanotheatre/nano_view.asp?catid=3&page=2&recs=20&cp=#
Many thanks to Prof. Barry Wells, UConn-Physics.
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.
HISTORY
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.
APPLICATIONS: Medical MRI (Magnetic Resonance Imaging) scans produce detailed images of soft tissues. Superconducting coils can carry a lot of current. They thus produce a very strong and uniform magnetic field inside the patient's body.
MEISSNER EFFECT When you place a superconductor in a magnetic field, the field is expelled below T C. B B T >T c T < 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.
A superconductor displaying the MEISSNER EFFECT If the temperature increases the sample will lose its superconductivity and the magnet cannot float on the superconductor.
APPLICATIONS: Superconducting Magnetic Levitation 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. The Yamanashi MLX01MagLev Train
1-2-3 Superconductors (YBa 2 Cu 3 O 7-x )
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.
Magnet type review Hard vs Soft Ferro or Ferri-magnets large coercivity --good for perm magnets --add particles/voids to make domain walls hard to move (e.g., tungsten steel: Hc = 5900 amp-turn/m) Hard Soft B Hard 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.) Applied Magnetic Field (H) 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.
SUMMARY 1. Equations describing magnetic field strength, induction (several versions), relative magnetic permeability, magnetic susceptibility, magnetization of a solid, and saturation magnetization. 2. Origins of magnetic moments. 3. Magnetic types of materials, their relative magnetic permeabilities, and why they behave as they do (diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic, ferrimagnetic). 4. Temperature dependence of magnetization and why it occurs.
SUMMARY 1. Temperature dependence of saturation magnetization 2. Be able to sketch B vs. H for ferromagnets and describe why it is hysteretic and nonlinear. 3. Be able to sketch and describe hysteresis loops for soft and hard magnets. How are each applied? How are each optimized? 4. Sketch resistance vs. Temp for a superconductor. Why is there a transition, and what are the magnetic properties above and below T C?
End of Chapter IV Magnetic Properties