elements of magnetism and magnetic measurements

Elements of magnetism and magnetic measurements

Ruslan Prozorov

19, 21 and 24 February 2014

Physics 590B

Magnetic moment of a closed loop carrying current I:2

i

C

Id IS

c M r l n

Total magnetic moment: iM M

Magnetic field on the axis of a loop of radius R at a distance z is:

3/ 22 2

2 iz

MH

R z

(superposition principle)

magnetic moment of free currents

Remember, M is a vector!

February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 2

ion Bg

M J J

J L S

total angular momentum

orbitalspin

- gyromagnetic ratiog – Landé factor

1 1 11

2 1

J J S S L Lg

J J

free electron:

2.0023 2.00g

219.27410 102

B

e erg

mc G Bohr

magneton

Magnetic moment:

e BM

(J=S=1/2)

atomic and electronic moments

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magnetic moment in numbers

it measures a total magnetic moment in cgs (emu)

1 emu is:• M of a 1 m2 loop carrying a 1 mA current• M of a loop of radius 1.78 cm carrying a 1 A current• Typical permanent magnet (1 mm3) ~ 1 emu

• M of a neutron star ~ 1030 emu• The Earth’s magnetic moment ~ 8x1025 emu• An electron spin: B~10-20 emu• Proton and neutron: N~10-23 emu

• One Abrikosov vortex (0.1 mm long) ~ 10-10 emu• Change in M due to d-wave gap < 10-10 emu/K• Hard superconductors ~ 0.1 emu

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the basics

emu

Gauss Oersted3

cm

4 ,B H m

B H

4

1 4

B HH H H

m H

this is ONLY true for homogeneous, uniform para- or dia- magnetic systems

erg/

Gm M V

magnetic permeability magnetic susceptibility

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in SI

Tesla ,A

A mm

B H m

B H

1

B HH H H

m H

erg/

Gm M V

magnetic permeability magnetic susceptibility

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magnetic susceptibility

2 3J erg1 Amp m 1 10

T G

Magnetic moment

3

3

A 4 10 A A1 0.013 , 1 80

10 4Oe Oe Oe

m m m

Magnetic field

41 10T G

Magnetic induction

NOTE: QD MPMS measures M [emu], not 4M

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magnetic susceptibility

/m H - dimensionless!

some other quantities are used:

1

m

ccg

cc g

1

mol m m

gM mol

g mol

4SI cgs

H

B

x

erg/

Gm M V

paramagnetic: 0, 1

non-magnetic: 0, 1

diamagnetic: 0, 1

4 1

perfect diamagnetism:1

, 04

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often used simplification

4B r H m r

B H

MH

V

this is used for superconductors and in micromagnetic calculations

34V

M B r H d r

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magnetism in a periodic table

http://www.1tvg.com/magsep_u_pu.htmFebruary 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 10

superconductivity in a periodic table

superconductor.orgFebruary 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 11

most general form of magnetic susceptibility

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“Global” measurement:TOTAL magnetic moment

“Local” measurement:magnetic induction

DC measurement:frequency independent part

M0

AC measurement:frequency - resolved M()

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DC Magnetization

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M(H) loops - ferromagnet

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influence of domain structure

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type-I superconductor

-600 -400 -200 0 200 400 600-400

-300

-200

-100

0

100

200

300

400

4m

(G

)

T (K)

a "perfect"

Pb sphere

T = 4.5 K

Hc=490 Oe

Hc(1-N)=327 Oe

Hc(1-N)

N=1/3

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hysteresis is a generic feature

-600 -400 -200 0 200 400 600

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

full M(H) loop

partial M(H) loops

field cooling

M (

em

u)

H (Oe)

Pb single crystal

T = 4.5 K

Hc=500 Oe

Hp = H

c(1-N)=220 Oe

N=0.55

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typical type-II superconductor

-20000 -10000 0 10000 20000

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15M

(e

mu)

H (Oe)

February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 20

m(r) in a superconductor after ZFC+H(pulse)

-1.0 -0.5 0.0 0.5 1.00.0

0.5

1.0

0.0

0.5

1.0B

/H

x/d

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local measurement

undergrad experiment

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magnetometer

Popular definition (Wikipedia):

A magnetometer is a scientific instrument used to measure the strength and/or direction of the magnetic field in the vicinity of the instrument. Magnetism varies from place to place and differences in Earth's magnetic field (the magnetosphere) can be caused by the differing nature of rocks and the interaction between charged particles from the Sun and the magnetosphere of a planet. Magnetometers are often a frequent component instrument on spacecraft that explore planets.

Rotating coil magnetometer Hall effect magnetometer Proton precession magnetometer Gradiometer Fluxgate magnetometer

Lab definition:A device to measure magnetic moment or magnetic induction of finite – volume samples at fixed temperature and magnetic field. Magnetic moment is a vector, but only one component is measured at a time.

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types of GLOBAL magnetic measurements

• Use Faraday law of induction,

– extraction from the coil

– MPMS SQUID

– Vibrating sample magnetometer (VSM)

– AC susceptibility

– pulse

• Use the force or torque

– Faraday balance (force)

– torque magnetometer

• Use sample as a nonlinear element of the cirquit

– cavity perturbation (MW)

– tunnel – diode resonator (RF)

dV

dt

cosW B μBEnergy:

F grad W grad μBForce:B

torque:

τ μ B

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• Surface probes

– Kerr – effect magneto-optics

– Faraday – effect magneto-optics

– miniature Hall-probes

– Bitter decoration

– magnetic force microscope

– miniature SQUID

• Bulk local probes

– muon spin rotation

– polarized neutron reflectometry

– nuclear magnetic resonance

– neutron scattering

• Menascale probes

– mechanical resonant imaging

– nanoSQUIDs

– fluorescent confocal microscope

– optical magnetometry of NV-centers in diamonds (NEW project at AmesLab!)

local probes

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AC/DC measurements

H

lock-in

acVt

H

PASSIVE! pick-upcoils (no current)

M(t) M=const

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use the force – Faraday balance magnetometer

Faraday pole caps have the property that in vertical direction z on the symmetry axis of the magnet, where the field, let us say, is in x-direction, the product Bx*dBx/dz is constant over a considerable range in z.

U

MB

F MB

22 x

z x x x x

dBd dF M B B B

dz dz dz

,0,0xB zBif

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examples

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extraction coil magnetometer

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QD extraction - coil magnetometer

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torque magnetometer

τ M B

advantages?- fast- small samples

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Vibrating-sample magnetometer

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VSM – QD versalab

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Lakeshore cryotronics VSM

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QD SQUID-VSM magnetometer

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QD MPMS

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