# SMM Magnetic Materials

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Semi-conducting & Magnetic Materials1968 Ampex Corporation Research department -Hired recent Ph.D. graduate from MIT Robert P. Hunt -Initial assignment: -Find something new & useful in magnetic storage technology. -Shortly after, he invented the Magneto-resistive head (MRH). At Ampex Research there also was Irving Wolf inventor of the Wolf permalloy electroplating bath. Bob asked Irving, Can you fabricate a Magneto-resistive head? Irving replied: Sure, Ill make it out of evaporated permalloy Serendipity: If Bob & Irving had not been in such close proximity, there would be no MRHs even today. Not only did the first MRHs use Permalloy, but, even today all Manufacturing companies use Permalloy as the sensor.

Semi-conducting & Magnetic MaterialsdH = 0.1Idl/R2H is in oersteds, I is in amperes, l & R are in cms.Consider a very straight, long conductor:

Integrating the above equation, we see that the magnetic field produced circles the conductor. The magnetic field is tangential: - orthogonal to current direction & radius vector, r. Direction of the magnetic field is given by the right-hand rule. Magnitude of the field is given by: H = 0.2I/r

Semi-conducting & Magnetic MaterialsdH = 0.1Idl/R2H is in oersteds, I is in amperes, l & R are in cms.Suppose the conductor is coiled to form a solenoid:

Magnetic field inside a long solenoid is given by: H = 0.4N I /l N is the number of turns, l is the solenoid length.Let us now define the Magnetic Moment:

1 = H .dV 4

is the magnetic moment in emu & V is the volume in cc.

For any solenoid, = 0.1NIA, where A is the cross-sectional area of the solenoid.

Semi-conducting & Magnetic MaterialsElectron spin: Magnetization is a property that arises from the motion of electrons within atoms. Magnetization of free space is by definition zero. Atoms: Electrons orbiting a nucleus made up of protons and neutrons. Electrons have 2 separate motions:

Orbits the nucleus Spins on its own axis.Both lead to magnetic moments: Orbital magnetic moments Electron spin magnetic moments

Semi-conducting & Magnetic MaterialsElectron spin: Magnetic moments of a spinning electron is called Bohrs magneton & its magnitude is given by:

eh B = 4 m

= 0.93 x 10 -20 emu

Where, e is the electrons charge in emu (1.6 x 10 -20), h is Plancks constant (6.6 x 10 -27) m is the electrons mass in grams (9 x 10 -28)Spinning electron has a quantum spin number, Can be oriented in in only 2 directions.

1 s= 2

Semi-conducting & Magnetic MaterialsElectron spin:Consider an atom of iron in free space: atomic number is 26, thus, 26 electrons

In shell 1s, 2s, 2p, 3s, 3p & 4s: total spin is zero: equal number of electrons spin up & down. In shell, 3d, uncompensated spin moment of 4B exists: 5 spin up & 1 down. When iron atoms condense to solid state, the electronic distribution changes: uncompensated spin moment lowers to 2.2B

Semi-conducting & Magnetic MaterialsElectron spin:Consider the magnetic behaviour of iron atoms in an iron crystal: - bcc structure with a0 = 2.86 Quantum effect occurs, called exchange coupling, forces all the iron atoms magnetic moments to point in nearly the same direction. Exchange coupling lowers the systems energy by aligning the uncompensated moments. At absolute zero, the ordering is perfect, higher temperatures causes increasing disorder. At the Curie temperature, 780C for Fe, thermal energy equals the exchange energy & all long-range order breaks down spin moments random directions. this state is called Paramagnet. Below the Curie temperature, the parallel alignment is called ferromagnetism.

Semi-conducting & Magnetic MaterialsElectron spin:Exchange coupling depends on the ratio of interatomic distance to the atomic size.

When atoms are relatively closely spaced, like Cr & Mn, the Exchange coupling is negative & the adjacent spins are aligned in an antiparallel manner called Antiferromagnets zero magnetic moment. For larger spacing ratios, the Exchange coupling is positive, spins are aligned parallel Ferromagnetic metals Fe, Co & Ni.

Semi-conducting & Magnetic MaterialsElectron spin:Intermediate ordering can occur number of spins in each direction is unequal -Fe2O3 and ferrites Ferrimagnetism.

Three common types of magnetic ordering

Semi-conducting & Magnetic MaterialsMagneto-Crystalline Anisotropy K:Orientation of the net magnetic moment with respect to the crystal axes? Ferromagnetic-ordered magnetic moments aligned parallel to the body-centered cube edges. In Fe, the cube edges are the easy, or lowest energy directions while the body diagonals are the hard, or highest energy, directions of the magnetic moment.

A measure of this energy difference is the Magneto-Crystalline Anisotropy K: It is the energy required (ergs/cm2) to rotate the magnetic moments from the easy to the hard direction.

Semi-conducting & Magnetic MaterialsMagnetization M:Consider a volume of iron that has several million atoms. The magnetization is, by definition, the volume average of the atomic moments:

1 M = m V 1N

V is the volume in cc m is the atomic moment in emu N is the number of atomic moments in the volume V. M is in magnetic moment per unit volume (emu/cm3).

In a large enough magnetic field, the magnetization of all parts of the magnetic material is parallel. At lower fields, magnetization subdivides into domains. Within a single domain magnetization is parallel & uniform - value is called saturation magnetization, Ms that depends on temperature. At absolute zero, it is maximum and vanishes at the Curie temperature.

Semi-conducting & Magnetic MaterialsMagnetization M:Calculation of Ms at 0K for bcc Fe: Each Fe atom has 2.2 B of magnetic moment. 2 Fe atoms/unit cell, a0 = 2.86.

M s (T = 0) =

2.2. B .2

(2.86 x10 )

8 3

= 1700emu / cm3

At room temperature, Ms is only slightly reduced by thermal energy & pure Fe: Ms = 1700 emu/cm3; 4Ms = 21,000 G & s = 21.6 emu/g, where s is called the specific saturation magnetization. The value of 4Ms for other materials of interest: Co: 18,000 G Ni: 6000 G Permalloy (81Ni/19Fe): 12,500 G

Semi-conducting & Magnetic MaterialsFlux density B & Flux :We have seen magnetic field H & magnetization M. The flux density B is defined as: B = H + 4M B is in gauss, H is the total field in oersteds & M is in emu. All field vector quantities & addition is done vectorially. Spacing between lines is inversely proportional to the field magnitude. Closer the lines, higher the field strength. The magnetic flux, is given by:

= B.dA

Semi-conducting & Magnetic MaterialsMagnetic RecordingIn 1956, IBM introduced the 305 RAMAC computer. - IBM 350 magnetic disk drive 4.4 Mbytes - size of 2 large refrigerators ! -weight of 2 tons ! Todays laptops, disk drives of 160 Gbytes, & size notebook ! Increase in areal density of 8 orders of magnitude: Number of bits/sq. in of disk surface. 0.002 Mbits/in2 to 100 Gbits/in2. ! Basic recording principle Longitudinal Magnetic Recording (LMR) remained same. The next figure shows the basic concepts of LMR: Writing, storage & reading.

Semi-conducting & Magnetic Materials

Recording medium & Recording Head (separate Read & Write elements). Granular microstructure magnetic transition meanders between the 8nm grains W = track width (210 mm) t = thickness of medium (14 nm) SH = stripe height (100 nm) B = bit length (20 nm) d = gap between head & disk surface ( 10 nm) Head is said to fly over the disk.

Semi-conducting & Magnetic Materials

Inductive Write Head miniature Electromagnet time-varying current in a conductor wrapped around a ferromagnetic yoke - provides a time-varying magnetic field in the gap of this yoke. -This field in turn, magnetizes regions of the disk as they pass under the gap. Data is stored as horizontal magnetic patterns ones and zeros correspond to the presence or absence of magnetic reversals. Basic process of writing & storage has not changed, but the read process has changed dramatically.

Semi-conducting & Magnetic Materials

Scaling laws of magnetic recording: If areal density increases by s2, then all dimensions & current decrease by s. From the IBM350 to today: areal density has increased by s2 = 5 x 107. implies that critical dimensions have scaled by s~7000. t= d= IBM 350 30 m 20 m Scaling Law 4.3 nm 2.9 nm Actual today 14-20 nm 10 nm

Semi-conducting & Magnetic Materials

t= d=

IBM 350 30 m 20 m Bulk materials

Scaling Law 4.3 nm 2.9 nm

Actual today 14-20 nm 10 nm

Thin Films & Interface Effects Practical Nanotechnology

Semi-conducting & Magnetic Materials

Magnetization vs Field Hysteresis loop of a recording medium.

When the write current is held constant, the magnetization written in the Recording medium is at one of the remanent levels, MR. When the write current is suddenly changed from one polarity to the other, the written magnetization undergoes a transition from one polarity of MR to the other.

Semi-conducting & Magnetic MaterialsThe transition has the form:

M ( x) =

x M R tan 1 f 2

f is the so-called transition-slope parameter. Maximum slope occurs at M=0, and is 2MR/f Geometry of Recording Head

Straight line approximation leads to the transition width of f It can be shown that

2 Hc f = 2 t (d + t / 2) 3 MR

1/2

Semi-conducting & Magnetic MaterialsIn 1857, William Thompson (later became Lord Kelvin), discovered that the Electrical resistance of

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