physics 590 ruslan prozorov magnetic measurements Nov 9,

Transcription

1 physics 590 ruslan prozorov magnetic measurements Nov 9,

2 magnetic moment of free currents Magnetic moment of a closed loop carrying current I: Magnetic field on the axis of a loop of radius R at a distance z is: Total magnetic moment: M = M i (superposition principle) I Mi = d = IS 2c r l n C H z = 2M i 2 2 ( R + z ) 3/2

3 atomic moments M = γ J = gµ J ion J = L+ S spin orbital total angular momentum B γ - gyromagnetic ratio g Landé factor e µ B = mc 21 erg G ( + 1) + ( + 1) ( + 1) 2J( J + 1) J J S S L L g = 1+ Bohr magneton free electron: g = Magnetic moment: M µ e B (J=S=1/2)

4 the basics [ ] [ ] emu B Gauss = H Oersted + 4 π m 3, cm B B m = µ H = µ H µ H = H + 4πχ H = χh = 1+ 4 µ πχ erg m= M / V G this is ONLY true for homogeneous, uniform para- or dia- magnetic systems

5 magnetic susceptibility Magnetic moment 2 J 3 erg 1 Amp m = 1 = 10 T G χ = M / H - dimensionless! χ SI = 4πχ cgs some other quantities are used: χ χ m χ cc 1 = g ρ = cc g g = χ M = g mol mol m m mol 1 B H x

6 Extensions global (total) magnetic moment ( ) = + 4 ( ) B r H π m r B = µ H 4 ( ( ) ) 3 π = M Br H dr V M V = χh

7 most general form of magnetic susceptibility

8 demagnitization

9 spatial distribution of a magnetic induction

10 infinite cylinder (or slab) demagnetization = 0

11 ellipsoid (non-zero demag, H uniform)

12 non-zero demag, non-uniform H

13 confusing? in general, we cannot assume uniform field distribution validity of equations depend on geometry and particular system the process of measurement involves applying an external field, so you only measure properties at that field! there is ALWAYS a total magnetic moment, but its relation to the applied field may be very complicated Let s demonstrate: paramagnet: ½ + ½ = 1 superconductor ½ + ½ = ¾

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15 critical state model

16 inhomogeneous B In many cases 1. B is not spatially uniform 2. there is magnetic hysteresis M 4π M = ( B H ) dv V B(x) χ = M χ = dm / H / dh - has no meaning - differential magnetic susceptibility can be used

17 rectangular slab

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20 M(H) loops - ferromagnet

21 AC/DC magnetization loop

22 influence of domain structure

23 type-i superconductor 4πm (G) a "perfect" Pb sphere T = 4.5 K T (K) H c (1-N)=327 Oe N=1/3 H c (1-N) H c =490 Oe

24 hysteresis is a generic feature Pb single crystal T = 4.5 K H p = H c (1-N)=220 Oe N=0.55 M (emu) full M(H) loop partial M(H) loops field cooling H c =500 Oe H (Oe)

25 typical type-ii superconductor M (emu) H (Oe)

26 types of M(H) loops (Co-122) M (emu) H (Oe)

27 fishtail M (emu) H (Oe)

28 distribution of the magnetic induction B/H x/d

29 are the profiles real? undergrad experiment

30 magnetic moment in numbers it measures a total magnetic moment in cgs (emu) 1 emu is: M of a 1 m 2 loop carrying a 1 ma current M of a loop of radius 1.78 cm carrying a 1 A current Typical permanent magnet (1 mm 3 ) ~ 1 emu M of a neutron star ~ emu The Earth s magnetic moment ~ 8x10 25 emu An electron spin: µ B ~10-20 emu Proton and neutron: µ N ~10-23 emu One Abrikosov vortex (0.1 mm long) ~ emu Change in M due to d-wave gap < emu/k Hard superconductors ~ 0.1 emu

31 magnetometer Popular definition: 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 of small samples at fixed temperature and magnetic field. Magnetic moment is a vector, but only one component is measured at a a time.

32 types of magnetic measurements global total magnetic moment local B(x) Magnetometers extraction Faraday balance SQUID Vibrating sample magnetometer AC susceptibility Surface probes magneto-optics Hall-probes decoration magnetic force microscope scanning probes (SQUIDs, Hall probes etc)

33 magnetic moment in a magnetic field torque: τ = μ B θ µ B Energy: Force: W = μb = µ Bcos( θ) F = grad ( W ) = grad ( μb) for example, for Bμ= Bx( x ),0,0, = ( µ x, µ y,0) μb = µ B x x and dbx F = µ x dx in inhomogeneous magnetic field µ > 0 µ < 0 x x F B F changes sign however torque aligns along the field B

34 PASSIVE! pick-up coils (no current) AC/DC measurements H H M(t) V ac Φ = t M=const lock-in

35 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 B x *db x /dz is constant over a considerable range in z. U = MB if F = B = MB ( ) ( B ( z),0,0) x d d ( ) ( 2 db ) x Fz = MxBx = χ Bx = χ 2B x dz dz dz

36 examples

37 extraction coil magnetometer

38 QD extraction - coil magnetometer

39 torque magnetometer advantages? - fast - small samples τ= M B

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41 Vibrating-sample magnetometer

42 VSM QD versalab

43 Lakeshore cryotronics VSM

44 QD SQUID-VSM magnetometer

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47 QD MPMS

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49 Josephson effect

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52 Superconducting Quantum Interference Device (SQUID) flux-voltage convertors DC SQUID AC (RF) SQUID

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56 DC SQUID

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59 rf-squid one junction

60 rf-squid

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62 rf-squid

63 rf (10-20 MHz) current source rf-amp flux transformer resonant tank circuit

64 gradiometers

65 Zimmerman rf SQUID

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67 combinations

68 MPMS longitudinal and transverse coil sets

69 MPMS: longitudinal coil set

70 transverse coil set

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72 transverse component

73 sensitivity of transverse coil set to longitudinal moment

74 compare to

75 gradiometer measurements

76 how does MPM measure magnetic moment?

77 regression

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79 basic principles

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85 measuring large moments

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88 background subtraction

89 Practical MPMS - background

90 background is displaced from the signal by 1 mm

91 magnetic field variation

92 Remanent (remnant) field

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98 field non-uniformity and superconductors

99 another example & literature will be available for download