FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0...

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Lake Ontario Lake Erie FePt Nanomaterials for FePt Nanomaterials for Future Magnetic Data Future Magnetic Data Storage Storage Hao Zeng Hao Zeng Department of Physics, Department of Physics, University at Buffalo University at Buffalo - - SUNY SUNY Summer School of Advanced Functional Materials 2006 Shenyang, China, July 6, 2006

Transcript of FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0...

Page 1: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Lake Ontario

Lake Erie

FePt Nanomaterials for FePt Nanomaterials for Future Magnetic Data Future Magnetic Data

Storage Storage

Hao ZengHao Zeng

Department of Physics, Department of Physics, University at BuffaloUniversity at Buffalo--SUNYSUNY

Summer School of Advanced Functional Materials 2006Shenyang, China, July 6, 2006

Page 2: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

What’s Enabling Google Earth? 200 TB of Hard Disk Drives

92% of new information stored on magnetic media!

Page 3: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

“Moore's Law” for Data Storage

?

Page 4: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Hard Disk Drive Technology

SNR ∝ 10log(N)

S S S SSSSN N N N NNN

Page 5: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Coherent Rotation-Stoner Wohlfarth Model

0 50 100 150 200-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

E

θ

ϕ =180°

EB

)cos(sin2 ϑϕϑ −−= VHMKVE s

Easy axis

H

θϕ

H

Ms

Setting EB =0,One get Hc = 2K/Ms

B.D. Cullity, Introduction to Magnetism and Magnetic Materials

Page 6: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Superparamagnetism

KV >> kTMs

Ms

Hc

MrFM

KV < 25kT

Ms

Ms

SP

1/τ = f0e -∆E/kT

Magnetic reversal is thermally activated,the probability of crossing over the energy barrier

∆E=kTln(f0 τ)

f0 –attempting frequency ~ 109 Hz, τ –measurement time ~ 100 s ∆E=25 kT

])25(1[2 2/1

VKTk

MKH

u

B

s

uc −=

u

BB

u

BB

KTkV

KTkV

60

,25

' =

= 100 s

10 year

Page 7: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Fighting SP Limit-Advanced Recording Schemes

AFC media

Ru

SNR∝Mrt∝(d1-d2)

Veff∝(d1+d2)

Page 8: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Perpendicular recording

Pack more data-same volume with smaller bit size

Stabilizes stored bits

Page 9: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

High Ku Media Materials

D. Weller et al., IEEE Trans. Magn. vol 36, No 1, January 2000, p. 10-15

Page 11: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Thermally Assisted Recording

Lower the energy barrier for reversal by laser heating

PRB 72, 172410, 2005

Page 12: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Origin of Magnetocrystalline Anisotropy of FePt

Origin of anisotropy is spin-orbit coupling

Fe has relatively moderate spin-orbit interactions. MAE is very small in the bulk Fe.

Pt has very large spin-orbit coupling constant, but has no magnetic moment in pure form.

FePt gets the best of two worlds: Fe has large magnetic moment, and induces sizable magnetic moment on Pt (0.4µB). Pt provides spin-orbit interactions. Because of these the anisotropy is not single ion in origin and depends on the interaction between Fe and Pt.

Page 13: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Anisotropy Calculations

∫=

∆+=

−=∆

∞−

ijij

E

easye

hardeanis

E

TtdETr

EEEF

]1[Im10

1

π

c

a

t∆ Is SO perturbation and T0 is a scattering T-matrix describing interactions

Page 15: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Achieving Texture Non-epitaxially

Fe55Pt45 annealed at 550 °C for 5 sec

• d⊥ ≈ 4. 5 nm

• d⊥ ≈ 6.3 nm

• d⊥ ≈ 6.7 nm

H. Zeng, M. L. Yan, N. Powers et al., Appl Phys Lett 80 (13), 2350-2352 (2002).

Page 16: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Three Stages in Texture Evolution

20 30 40 50 600

500

1000

1500

2000

2500

Inte

nsity

(a.u

.)

(111) (d)

0

200

400

600

800

1000

(002)(200)(001)

(111) (c)

0

100

200

300(002)(200)

(001)

(111)

(111)

(b)

0

50

100

150

200

250

(002)(200)

(001)(a)

t

Page 17: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Typical Hysteresis Loops

-15 -10 -5 0 5 10 15-0 .15

-0 .10

-0 .05

0 .00

0 .05

0 .10

0 .15

H (kO e)

-0 .10

-0 .05

0 .00

0 .05

0 .10

m (m

emu)

Top: 100 Å Fe55Pt45, 550 °C, 5 sec

Bottom: 100 Å Co55Pt45, 700 °C, 300 sec

//

//

Page 18: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

FePt-based Nanocomposite Films

-1200

-800

-400

0

400

800

1200

(a)

H (kOe)H (kOe)

out of plane in plane

M (e

mu/

cc)

(b)

-40 -20 0 20 40

-600

-300

0

300

600 (c)

-40 -20 0 20 40

(d)

(a) FePt single layer; (b) (FePt 32Å/B2O38Å)5; (c) (FePt 32Å/B2O3 12Å)5; and (d) (FePt 32Å/B2O3 48Å)5. These films were annealed at 550°C for 30 minutes.

(a) TEM image of (FePt 32Å/B2O3 12Å)5 and (b) HR-TEM image of (FePt 32Å/B2O3 20Å)5 annealed at 550°C for 30 minutes

C.P. Luo, Ph.D. dissertation

Hysteresis loops as a function of B2O3 thickness

Page 19: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Concept of Patterned Media

• x

“Single-domain magnetic pillar array of 35 nm diameter and 65 Gbits/in2

density for ultrahigh density quantum magnetic storage”S.Y. Chou, M.S. Wei, PR Krauss, PB Fischer JAP 76, 6673 (1994)

single grain per bit (elimination of random √N noise)superparamagnetic limit applicable to a single bit, not to each grains within a multigrain bitdensity/cost limited by lithographic technology

Page 20: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Building Patterned Media Bottom-up — SOMA

4 nm FePt

S. Sun et al., Science 287, 1989 (2000).

Page 21: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

FePt Nanoparticle Synthesis

FeCO

CO

CO

CO

OC

O

O

CH3

CH3

O

O

H3C

H3C

Pt

- COHeat,

FePt

COOH

NH2

reduction

Page 22: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

FePt Nanocrystal Recording Tests(A. Moser, D. Weller)

0 5 1 0 1 5 2 0 2 5- 2 0- 1 8- 1 6- 1 4- 1 2- 1 0

- 8- 6- 4- 2024

MR

signa

l [m

V]

x [µ m ]

1040 fc/mm

2140 fc/mm

5000 fc/mm

500 fc/mm

Reading

4 nm ferromagneticFePt particle assembly

Writing

Page 23: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Phase Transformation & Aggregation

25nm

(a)

25nm1nm

(b)

600 °C

Fe

Pt

fctHigh Ku

fccLow Ku

Page 24: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Aggregation and Magnetic Properties

-1.0

-0.5

0.0

0.5

1.0

-1.0

-0.5

0.0

0.5

1.0

-60 -40 -20 0 20 40 60

-1.0

-0.5

0.0

0.5

1.0

(a)

(b)

(c)

H (kOe)

0 5 10 15 20 25 30 35 40 45 50

0.0

0.5

1.0癈 700 60 min FG癈 600 60 min FG癈 550 60 min FG

δM

H (kOe)

H. Zeng, et al, APL, 80, 2583(2002).

600 °C, moderate aggregation

interparticle interactions550 °C, little aggregation

700 °C, severe aggregation

Page 25: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

L10 ordered FePt by RTA

Temperature for the onset of chemical ordering significantly loweredHowever, aggregation is not solved by reduction of ordering temp.

H. Zeng , Shouheng Sun, R. L. Sandstrom and C. B. Murray, JMMM 266, 227 (2003).

Page 26: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Discrete fct Ordered FePt Nanoparticle Arrays

-40000 -20000 0 20000 40000

-1.0

-0.5

0.0

0.5

1.0

m (a

rb. u

nit)

H (Oe)

8 nm, 560 °C 30 min N2

• highly ordered• nonexchange-coupled• thermally stable

H. Zeng et al, unpublished

Page 27: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Size and Surface Effects of FePt NPs

⎟⎠⎞

⎜⎝⎛ −∞=

dtMdM ss

61)()( (unpublished)

Both isotropic exchange (single ion) and anisotropic exchange (two-ion) stabilize ferromagnetic order!

(present theory does not explain the drastic decrease in Ms with decreasing size!)

Page 28: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Mossbauer Spectra of FePt NPs

F 298K652000656000660000664000668000 FePt - 298K - 4nm

645000650000655000660000665000 FePt - 78K - 4nm

162000164000166000168000170000 FePt - 4.2K - 4nm

-10 -5 0 5 10750000800000850000900000950000

1000000 Fe - 298K

Velocity(mm/s)

2000025000300003500040000 FePt - 298K - 8nm

740000

750000

760000

770000FePt, 78K, 8nm

Hhf (T) Qs (mm/s) Is (mm/s)4 nm 27.5 0.29 0.208 nm 27.5 0.26 0.20Fe 33

H. Zeng, unpublished results

Page 29: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Curie Temperature

v

c

cc

dd

TdTT

/1

0)()()(

⎟⎟⎠

⎞⎜⎜⎝

⎛=

∞−∞

No phase transition below 3 nm!

Page 30: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

How to Make a Perfect Patterned Media

Magnetic easy axis

High orderingHigh densityAligned easy axisCorrect symmetry

Page 31: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Magnetic Nanodot Array in Self-Assembled Porous Template

Page 32: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Thickness Tunable Porous Templates

Page 33: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Co Nanodot Arrays

Page 34: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Magnetic Properties of Co Nanodots vs. Films

-2000-1500-1000 -500 0 500 1000 1500 2000-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

m (m

emu)

H (Oe)

10 K 300 K

-2000-1500-1000 -500 0 500 1000 1500 2000

-0.10

-0.05

0.00

0.05

0.10

m (m

emu)

H (Oe)

10 K 300 K

Dot Array Film

Page 35: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

FePt Nanodots

Page 36: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

001 Texture and Perpendicular Anisotropy Achieved

2 0 4 0 6 0

Inte

nsity

(a.u

.)

2 θ (d e g .)

5 5 0 , g la s s s u b s tra te

G 6

G 5

G 4

(001) (002)

-20000 0 20000

-0.00008

-0.00006

-0.00004

-0.00002

0.00000

0.00002

0.00004

0.00006

0.00008

m (e

mu)

H (Oe)

//

Page 37: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Future Work

Templates with smaller diameter and Higher Density

20 nm pitch would lead to 250 Gb/cm2 (or 1.6 Tb/in2)10 nm pitch – 6.4 Tb/in2

Dot array with the “correct” symmetry

Page 38: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Alternative technology-MTJ MRAM Architecture

Potential Advantages:Non-volatile high density memory (∼ DRAM)Short access time (∼ SRAM)Low power consumption

Reading a bitWriting bits“0” “1”

-+

+

+ + ++++

Courtesy of Arunava Gupta, U. Alabama

Page 39: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Domain Wall Memory

Write head read head

Iin Iout

Density comparable to HDDNo moving partsCompatible with Si technology

Page 40: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

Acknowledgment

Chaeyun Kim, Bi-ching Shih-UBYucheng Sui, D.J. Sellmyer-UNLShouheng Sun-Brown U., Ping Liu, UTAGanping Ju-SeagateArunava Gupta-U Alabama

NSF and IRCAF for financial support

Page 41: FePt Nanomaterials for Future Magnetic Data Storage · Coherent Rotation-Stoner Wohlfarth Model 0 50 100 150 200-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 E θ ϕ=180° E B E=KVsin2ϑ−MVHcos(ϕ−ϑ)

41

Research

Department of Physics: Taxonomy

2005-2006 2122

1190706

Distinguished professors Full professors

Associate professorsAssistant professorsGraduate students

Physics MajorsStaff positions

2006-20072131

13110756