Magnetometry

Transcription

Magnetometry

Magnetometry
M. Solzi
Dipartimento di Fisica – Università di Parma
Outline
Generation of magnetic fields
Measurement of magnetic fields
Measurement of magnetization and magnetic
susceptibility :
Induction techniques
Force methods
Measurement of magnetic anisotropy
(Some) applications
2
M. Solzi – Università di Parma
Magnetometry
Italian School on Magnetism
First step: you need to generate a magnetic field
Exploitation of direct or indirect magnetic field
effects of electric currents
Main methods:
Resistive solenoids
Electromagnets
Superconducting solenoids
Pulsed magnetic fields
Others (flux compression, permanent magnets)
3
Magnetometry
Class-lab: resistive solenoids/Helmholtz coils
Helmholtz coils: lateral access, high homogeneity
4
Magnetometry
How to increase the field produced by solenoids?
Magnetic circuit with a Joke and
two cores usually made of highpermeability carbon steel
The cores are wounded by two
copper-wired coils
The useful magnetic field H is
generated in the air gap between
the polar expansions
B = µH
5
µ(Fe)≈ 2000
Magnetometry
(Old-fashioned) Electromagnets
Production of DC magnetic fields up to
20 kOe (in some cases up to 30 kOe)
H depends on:
Current intensity
Core permeability and saturation induction
Gap width
Max current is limited by insulation of
copper wire of the coils
The coils, connected in series, are cooled
in air or oil or with flowing water to
avoid insulation damage: Joule heating
6
Magnetometry
High-field resistive solenoids: Bitter Magnets
3 coils in series
Inner coil consists of 2 coils in parallel
Cooling water flows axially through
holes
Elliptical holes minimize stresses
Conductor: Cu/Ag alloy
Insulation: Kapton
HFML Nijmegen: 30 T, 50 mm bore
7
Magnetometry
Superconducting solenoids
Eliminate Joule heating!
Solenoids with
superconducting alloy wires:
Nb-Sn, Nb-Zr, Nb-Ti
Wires permeated with epoxy
Low power (< kW)
Can be persistent
Large sample space
Should be kept at 4.2 K!
Extremely high inductance
→slow ramp rates
TML Tsukuba: 24 T (2011)
Double coil: NSC (17 T) +
HTCSC (GdBCO)
8
Magnetometry
An example of commercial superconducting solenoid
Closed superconducting circuit:
It can be feeded with a specific current
so that it operates in persistent mode,
without any external supply
You need to open the circuit for feeding a
current or changing the field:
By means of the heater switch
9
Magnetometry
Hybrid Magnets
HFML Nijmegen:30 T – 50 mm bore
Combined superconducting
and resistive magnets:
Superconducting outer
Resistive inner
Very expensive to run
Not “user friendly”
Days to prepare
Dangerous! Energy stored in
supercond. magn. is several
hundreds MJ
Max field: 50 T?
TML Tsukuba: 32 T
52 mm bore
10
Magnetometry
Pulsed Magnetic Fields
coil
RLC circuit: large capacity c
discharge
Limitations for obtaining large
fields H:
Mechanical strength:
Joule heat dissipation
Pulsed fields with short
duration: heat stored by the coil
heat capacity C
A source of stored energy (bank
of capacitors c) supplies total
energy E
11
Magnetometry
Crowbar
resistance
Tmax
t
∫ R(T )J (t ) dt < ∫ C (T )dT
2
t0
E=
T0
t max
∫
t0
=
 dΦ 

idt +
 dt 
imax
tmax
0
t0
∫ Lidi +
∫
t max
2
Ri
∫ dt =
t0
 dL  2
 i dt +
 dt 
t max
2
Ri
∫ dt
t0
Pulsed fields properties
Useful magnetic energy
1
1
Em = ∫ H ⋅ BdV = µ0 ∫ H 2 dV =
2
2
imax
1 2
∫ Lidi = 2 Limax
0
imax
Efficiency
Em
=
E
This term should be reduced to 0
dL/dt comes from:
•Mechanical strains
•Current expulsion from the conductor
12
Magnetometry
∫ Lidi
0
imax
t max
0
t0
∫ Lidi +
∫
 dL  2
 i dt +
 dt 
t max
2
Ri
∫ dt
t0
Pulsed fields (short-pulse): solenoids
Non-destructive, short pulse
Wire: Cu/Ag and Cu/Nb alloy
Kapton insulation
Reinforcement: glass/carbon
fiber – armored solenoid
Coil consists of few turns
keep inductance low
Magnet cooled to 77 K prior to
pulse
increases conductivity
13
Magnetometry
Pulsed fields (short pulse) characteristics
Example: specifications
Capacitor driven
1.5 MJ at 10 kV
Imax= 20 kA
Max field 70 T
63 T, 15 mm, 7/35 ms
50 T, 24 mm, 6/30 ms
42 T, 24 mm, 100/500 ms
1 pulse/hour to 63 T
500-800 pulses, then …
Steel shell
14
Magnetometry
Long-pulse pulsed fields
Non-destructive, long pulse:
Motor/generator
260 tons flywheel
Can deliver 750 MJ
Magnet uses only 90 MJ
Shaped-pulse magnets
60 T for 0.1 s
50 T for 0.5 s
32 mm bore
1 shot/hour
60T LP sound
15
Magnetometry
Magnetic flux compression
Single stage
Magnet is destroyed
Max field: ≈200 T
Samples often survives
16
Magnetometry
Magnetic flux compression
Los Alamos National Laboratory (NHMFL), USA and Sarov, Russia
17
Magnetometry
Permanent magnets: Halbach array
18
Magnetometry
Magic cylinders - spheres
19
Magnetometry
Technically feasible magnetic fields (2011)
Method
Intensive laser irradiation of solids
(sample is in plasma state)
Explosive flow compression
(Experimental set-up will be
destroyed)
Electromagnetic flux compression
(coil will be destroyed)
Coil with one or a few convolutions
(will be destroyed)
Pulsed coils
Hybrid magnet (resistive +
superconducting)
Resistive electro magnets
Superconducting magnet systems
(conventional and high temperaturesuperconductor)
Superconducting magnets
(conventional)
Coils with iron yoke
20
Field value
Duration
34 000 T
10 ps
2 800 T
μs
Sarov
620 T
μs
Tokyo
300 T
μs
Tokyo, Toulouse, Los Alamos
91 T
10-3
to 1 s
Laboratory (assortment)
Dresden (91,4 T), Los Alamos (97,4 T),
Toulouse (82,0 T), Tokyo, Wuhan, Leuven,
Oxford
45 T
static
Tallahassee
33 T
static
Grenoble, Tallahassee, Nijmegen
30 T
static
Tallahassee (planned)
22 T
static
commercial
2T
static
commercial
Magnetometry
Methods for magnetic field measurement
Hall Probes
Fluxgate Magnetometers
Flux Measurements with Pick Up Coils
Magnetoresistors
Nuclear Magnetic Resonance (NMR)
Electron Paramagnetic Resonance (EPR)
21
Magnetometry
Hall probe gaussmeter
Charge carriers experience a Lorentz
force in the presence of a magnetic
field
This produces a steady state voltage in
a direction perpendicular to the
current and field
22
High spatial resolution
Depends on T
Typical Range: < 1 mT to 30 T
Typical Accuracy ~ 0.01% to 0.1%
Typical dimensions ~ mm
DC – 30 kHz
Magnetometry
VHall
B
= µ 0 RH I ×
l xl y l z
Fluxgate magnetometer
Excitation Coil: AC current
drives a pair of ferromagnetic
needles to saturation
Detection Coil: Detects Zero
field condition
Bias Coil: Maintains a zero field
condition
Highly sensitive, linear,
directional device.
Typical field range ~ a few mT.
Bandwidth: DC to ~ 1 kHz.
23
Magnetometry
Sensitivity: ~ 20pT (~1nT
commercial).
Accuracy: ~ 0.1%
Search coil
Flux measurement:
induction law
Flux through a coil defined
by the surface S is
Φ = ∫ B ⋅ dS
S
If the flux linked varies
with time, a loop voltage is
induced, given by

dΦ
d 
V (t ) = −
= −  ∫ B ⋅ dS 
dt
dt  S

24
Magnetometry
Search coil
The change in flux is given by
t end
Φ end − Φ start = − ∫ V (t )dt
t start
and can be measured by
integrating the voltage signal
25
Simple, passive, linear, drift-free
devices
Require change in flux ⇒ ramp
field with static coil or move coil in
a static field
Measure flux, not field.
⇒Calibration of geometry very
important; limits accuracy
Magnetometry
Magnetization and susceptibility measurement
Measurements in closed magnetic circuit
Fluxmetric method:
Hysteresigraph, Permeameter
Measurements in open magnetic circuit
Induction method:
Vibrating sample Magnetometer (VSM)
Extraction magnetometer – SQUID magnetometer
Ac Susceptometer
Force methods:
Faraday and Gouy balance, lateral pendulum
Reed Magnetometer, AGFM
Other:
KerrMagnetometer
Hall Magnetometer
26
Magnetometry
Open-circuit measurements: correction for
demagnetizing field
Magnetic poles induced on the
sample surface: shape anisotropy
The demagnetizing field depends on
the shape of the sample and on the
relative direction of H and M :
Perp. thin films.: Hd= −M
Long. thin films/needles: Hd≈0
Sphere: Hd= −(1/3) M
27
Magnetometry
Fluxmetric/induction method
Faraday Law:
Point dipole
dΦ
dB
V = −N
= − NS
dt
dt
pick-up coil
Measurement of the flux Φ through
the coil section
S area
Stationary coil: B measurement by
integration
1
B=−
Vdt
∫
Problem: drift
NS
The applied field Ha should not
contribute to Φ ⇒ pick-up design:
N wounds
Uniform Ha: 2 cylindrical coils coaxial
or Helmholtz pair
28
Magnetometry
Extraction magnetometer
Magnetic point-dipole initially placed in
the center of a coil and then moved to a
“large” distance from it: voltage V
induced in the coil circuit
two series-opposition coils to
compensate the changes of magnetizing
field (1st order gradiometer)
to measure the difference of the
magnetic induction in a space region
dΦ
V =−
with and without sample
dt
Flux variation deduced by signal
Φ = − ∫ V (t )dt
integration
M = αΦ
29
Magnetometry
Vibrating sample magnetometer (VSM)
Direct measurement of M
The oscillating sample magnetic
moment induces an alternating
e.m.f. in the pick-up coils circuit
Lock-in amplifier:
Measurement of in-phase signal
High signal-to-noise ratio
Reference pick-up with a
permanent magnet: reference
input for the lock-in amplifier
Alternatively: vibrating (or
rotating) coil magnetometer
30
Magnetometry
Vibrating sample magnetometer (VSM)
31
Magnetometry
SQuID Magnetometry
Superconducting Quantum Interference Device
Based on two parallel Josephson junctions
Great sensitivity: measure of magnetic field changes of the
order of a quantum flux
Operating at cryogenic temperature
SQUID function based on:
Flux quantization in a sc ring
Josephson effect
32
Magnetometry
Josephson junction
DC Josephson effect: a current
with intensity proportional to the
phase difference between the wave
functions can flow through the
junction without an applied
voltage;
The magnitude of this current,
(critical current Ic) is a periodic
function of the magnetic flux
present in the junction
33
Magnetometry
Dc-SQuID: magnetic field sensor
Applied current (bias current)
Ib > Icrit ⇒
produces V to the SQuID ends
Characteristic I(V) curves: modulated by the
magnetic flux Φ
the constant increase of magnetic flux ΦB
through the ring leads first to a decrease and
then to an increase of Icrit
Icrit max for ΦB= 0, nΦ0
Icrit min for ΦB= (n/2) Φ0
the oscillation period isΦ0
Typical measurements of variations ΦB <Φ0
34
Magnetometry
Planar SQuID sensor
35
Magnetometry
DC SQuID detection circuit
T≤5K
A large superconducting loop,
which is exposed to the magnetic
field being measured, is
connected to
a multiturn signal winding that is
magnetically coupled directly to
the SQUID sensor
The signal winding magnifies the
flux that is applied to the SQUID
Flux Locked Loop (FLL):
linearizes the V-Φ characteristics
and enables a high dynamic range
36
V ∝Φ
Magnetometry
Magnetic shield
SQuID Gradiometer
1st order gradiometer
configuration: for measuring
spatially inhomogeneous
magnetic fields:
⇒Flux transformer
37
Magnetometry
SQuID magnetometer
38
Magnetometry
SQuID magnetometer: second-order gradiometer
The detection coils are placed in the centre of the sc
magnet
A single sc wire is wounded in a 3-coils set with a
2nd order gradiometer configuration (second-order
derivative)
⇒ Aim:
Reduction of the noise in the detection circuit
due to the fluctuations of the magnetic field
generated by the sc magnet
Minimization of the drift in the detection circuit
due to the magnetic field relaxation
The coils set measure the local variations of the
magnetic flux density produced by the dipole field
of a sample moving through the coils
39
Magnetometry
Special applications: Micro-SQuID
40
Magnetometry
Towards nano-SQuID
41
Magnetometry
AC Magnetometry
A small AC biasing field is superimposed to the DC field: this originates a timedependent magnetic moment in the sample
The magnetic field produced by the time-
dependent moment induces a current in
the pick-up coils, without need of moving
the sample
For low frequency the sample moment
follows the M(H) curve as for DC
measurements
Induced AC moment:
M AC
42
dM
=
H AC sin ωt = χH AC sin ωt
dH
χ = slope of M(H)= susceptibility
Magnetometry
AC Magnetometry
AC measurement is very sensitive to small variations of M(H), even if the
intensity of M is large
At higher frequencies:
The sample AC moment does not follow the M(H) curve: dynamic
effects (M may delay with respect to the driving field)
The AC moment measurement gives:
Amplitude χ
Phase shift φ (w respect to driving field)
Otherwise:
In-phase component
χ ′ = χ cos φ χ = χ ′2 + χ ′′2
(real) χ’
 χ ′′ 
Out-of-phase component
′
′
χ = χ sin φ φ = arctan 
(imaginary) χ”
 χ′ 
43
Magnetometry
AC Susceptometer
The technique was originally
44
based on the use of a bridge
circuit for mutual inductance
measurement (Hartshorn bridge)
A primary coil is feeded with
alternating current (ac)
Without sample an identical
signal is induced in the two
secondary coils, so that v1−v2=0
If a sample is present inside one
of the two coils: change of
inductance L ⇒ off-balance
induced voltage V
Differential ac susceptibility
Magnetometry
dM
V ∝ χ ac =
dH
AC susceptometer
Lock-in amplifier:
Oscillator
in phase: real component χ’
Out-of-phase: imaginary component χ”
Calibration of both amplitude and sign
of χ’ and χ” :
sample
II type superconductor sample (Nb, Pb):
χV′ = −1 ⇒ χV′ =
(for T< Tcr)
45
αX
Vfh
χV′′ = 0 ⇒ χV′′ = −
αY
Vfh
= −1
=0
Magnetometry
Lock-in Ampl.
X,Y
Force methods: magnetic interaction force and torque
Torque acting on a magnetic dipole in a
magnetic field H
(
r r
τ = µ0 m × H
r
)
m= magnetic moment
Force acting on a magnetic dipole in a
inhomogeneous field H
r
r
r
F = µ 0 (m ⋅ ∇ )H

∂H y
 ∂H x
∂H z 
∂ r r

m ⋅ H = µ 0  mx
+ my
+ mz
 Fx = µ 0
∂x 
∂x
∂x
∂x


∂H y

 ∂H x
∂ r r
∂H z 

+ my
+ mz
m ⋅ H = µ 0  mx
 Fy = µ 0
∂y
∂y
∂y
∂y 



∂H y
 ∂H x
∂ r r
∂H z 

+ my
+ mz
m ⋅ H = µ 0  mx
 Fz = µ 0
∂z
∂z
∂z
∂z 


46
(
)
(
)
(
)
Magnetometry
Force methods: Faraday and Gouy balance
(
)
∂ r r
∂H z
∂H z
Fx = µ 0
m ⋅ H = µ 0 mz
= Vµ 0 χV H
∂x
∂x
∂x
z
m = MV = VχV H
Fx
• Force Fx should not depend on
sample position in the magnetic
field region
• Electromagnets with suitably
shaped poles to keep constant the
product
∂H x
H
∂x
47
Magnetometry
Fx
Stationary pendulum magnetometer
The field gradient is
perpendicular to sample-holder
bar (that is, horizontal)
F tends to move away sample
from the equilibrium position
No need for Archimede’s
correction
(
)
∂ r r
∂H z
∂H z 

Fx = µ 0
m ⋅ H = µ 0 mz
= Vµ 0 χV  H z

∂x
∂x
∂
x


z
x
Fx
48
Magnetometry
Force methods: reed and AGFM
Sample fixed to a thin metal
wire (Au reed)
Alternating Field Gradient
(series-opposition coils)
Mechanical Resonance of the
vibrating reed
Vibration amplitude ∝Q×F
gradH
H
49
Magnetometry
Cantilever magnetometer
Very thin Si cantilever
Parallel plates capacitor
Measurement of capacity
variation ∆C(H)
Two different operating
modes:
Force mode
Torque mode
50
Magnetometry
Cantilever magnetometer
Force mode
Torque mode
∆C(H ) = β ′τ (H )
r
r
r
τ (H ) = µ0 m(H )× H
∆C(H ) = βF (H )
r
r
r
F = µ0 (m(0) ⋅ ∇)H
r
r
r r
m // H ⇒ F = µ0 (m(H ) ⋅ ∇)H → ∀z
∆C(H )
m(H ) =
β∇H (H )
51
(
)
τ (H ) = µ0m(H )H sinθmH
∆C(H ) = β ′µ0m(H )H sinθmH
∂θmH
∂m
<< 1 ⇒
= cost ⇒ m
∂H
∂θmH
(H ) =
Magnetometry
∆C(H )
β ′µ0 H sinθmH
Anomalous Hall Effect (AHE) Magnetometry
Measurement of very thin
magnetic films
M outside the film plane
In addition to the ordinary Hall
effect (OHE) ⇒ extra voltage ∝M
in magnetic materials, due to spin
dependent scattering mechanisms
The Hall voltage is inversely
The AHE depends on the ⊥
proportional to the film thickness
component of M, and produces an
The contribution of the Planar Hall
E ⊥ Mz and the current density
Effect (PHE) has to be subtracted
52
Magnetometry
Measurement of magnetic anisotropy
Measurement of the magnetization curve:
Underlying Area
Sucksmith and Thompson Method
Approach to saturation
Torque methods:
Torque Magnetometer
Torsion Pendulum – TOM
Vector -VSM
Measurement of susceptibility(SPD)
Ferromagnetic resonance (FMR)
53
Magnetometry
Magnetic anisotropy
Magnetic potential energy
Anisotropy field:
HA =
W=
Ms
∫ H ⋅ dM
0
2 K1
µ0 M s
c
Hexagonal symmetry
M
ϑ
Emca = K1 sin 2 ϑ + K 2 sin 4 ϑ + K 3 sin 6 ϑ
54
Magnetometry
Torque measurement
Torque which should be applied to
a crystal to obtain a rotation of an
c
angle φ in a field H→∞
Uniaxial crystal rotated around z⊥c
ϑ
axis:
1
τ = (K1 + K 2 )sin 2φ − K 2 sin 4φ
2
In practice H≠∞ ⇒ M not aligned
with H ⇒ torque exerted by H on
Ms:
τ = µ0 HM s sin Φ
= torque exerted by M on the crystal
M
∂Emca ∞
τ=
= ∑ an sin nφ
∂φ
n =1
φ = f (ϑ )
an = f ( K i )
z
φ
c
Φ
ϑ
H
M
55
Magnetometry
Torque Magnetometer
Problem: instability if k< K1V
Solution: application of an
electromagnetic torque as
feedback
Sample: single crystal disc/sphere
Need of knowing the wire torsion constant k
The torque τH exerted from H on the sample is
counter-balanced by the torque tE produced by the torsion
of a wire/fiber: τH ∝ twisting angle
H must saturate the sample: in principleτH does not
depend on H
56
Magnetometry
Torsion pendulum
Samples with very large
magnetocrystalline anisotropy:
difficulty of obtaining saturation along
the hard direction
One can only measure the magnetic
stiffness around the easy direction,
along which the field He is applied
Equilibrium position= stiffness
against the rotation, due to the
anisotropy, He and M
d 2 Emca
µ0 H e M s
∂ 2 Et
dϑ 2 = µ 0 H A H e M s
=
H A + He
∂φ 2
d 2 Emca
+
H
M
µ
0 e
s
dϑ 2
57
Magnetometry
z
c
ϑ
Φ
M
φ
H
Et = Emca (ϑ ) − µ0 H e M s cos(φ − ϑ )
∂Et dEmca
=
− µ0 H e M s sin (φ − ϑ ) = 0
∂ϑ
dϑ
dEmca
1
φ → 0⇒φ =
−ϑ
µ0 H e M s dϑ
d 2 Emca
= µ0 H A M s
2
dϑ
Torsion-oscillation magnetometer (TOM)
Resonance frequency of the
torsion pendulum
I= sample moment of inertia
V= sample volume
k= torsion constant

1  d 2 Emca

V
+
k
ω = 
2

I  dϑ

2
V d Emca
ω 2 − ω02 =
I dϑ 2
2
1
I
=
ω 2 − ω02 µ0 M sV
58
ω02 =
k
I
α
 1
1 


+
 He H A 
ω 2 − ω02
tan α =
I
µ0 M sVH A
Magnetometry
I
µ0 M sV
H e−1
Vector VSM
Measuring magnetization
curves for different
orientations of a sample
with a VSM is an indirect
method of studying the
anisotropy field
Vector coils can be used to
simulate a torque
measurement
59
Magnetometry
SPD technique (rev. parallel susceptibility, RPS)
M
c
Single crystal – H ⊥ easy
H
Ms
direction (c axis)
Singularity
0
(II order transition) M
Isotropic policrystalline sample
HA
H
Ms
H
Singularity disappears
Analysis of the nth derivatives
(dnM/dHn): Singular Point
Detection
The order of derivative depends
on the symmetry of the hard
direction (uniaxial, cubic, …)
60
Magnetometry
d 2 M dχ p
=
dH
dH 2
Cuspid at H=HA
0
HA
d2M/dH2
H
0
HA
H
Ms
SPD technique in pulsed field
Direct derivation of the dM/dt signal
The peak position does not depend on
the grain size (if they are single
domain!)
The peak shape depends on the
distribution of grain orientations
61
SPD theory: is based on the
Stoner-Wohlfarth model – coherent
rotation of non-interacting SD particles
Magnetometry
Reversible transverse susceptibility (RTS)
The motion of domain walls hides the RTS response
Particelle SD
Particelle MD
Hc
HA Hc
Stoner-Wohlfarth model (SD particles)
62
Magnetometry

Magnetometry

Transcription

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