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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
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 3
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
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 4
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
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 5
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
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 6
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
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 7
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
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 8
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
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 9
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
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 12
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 13
“Global” measurement:TOTAL magnetic moment
“Local” measurement:magnetic induction
DC measurement:frequency independent part
M0
AC measurement:frequency - resolved M()
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 14
DC Magnetization
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 15
M(H) loops - ferromagnet
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 16
influence of domain structure
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 17
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
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 18
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
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 19
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
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 21
local measurement
undergrad experiment
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 22
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.
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 23
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
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 24
• 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
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 25
AC/DC measurements
H
lock-in
acVt
H
PASSIVE! pick-upcoils (no current)
M(t) M=const
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 26
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
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 27
examples
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 28
extraction coil magnetometer
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 29
QD extraction - coil magnetometer
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 30
torque magnetometer
τ M B
advantages?- fast- small samples
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 31
Vibrating-sample magnetometer
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 32
VSM – QD versalab
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 33
Lakeshore cryotronics VSM
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 34
QD SQUID-VSM magnetometer
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 35
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 36
QD MPMS
February 2014 Basics of Magnetic Measurements. Prof. Ruslan Prozorov 37