What Magnetic Measurements tell us What Magnetic Measurements tell - - PowerPoint PPT Presentation

What Magnetic Measurements tell us What Magnetic Measurements tell us about magnetism? about magnetism?

Viorel Pop

Babeş-Bolyai University, Faculty of Physics, Cluj-Napoca, Romania

Magnetic moment

An electrical current, I, is the source of a magnetic field B Idl

Current I

Magnetic field generated by a single-turn coil with

far from the origin:

is by definition the magnetic moment of the single-turn coil

m r θ µ

3

2 sin R I B = m r

I

V

∑

= m M r r

magnetisation M magnetic susceptibility χ magnetic permeability μ

( )

M H B r r r + = µ

μ0 = 4π⋅10-7 H/m

H M = χ

B=µ0(H+χH)= µ0(1+χ)H= µH

H B = µ

( )

χ 1 µ µ + =

C, Cu, Pb, H2O, NaCl, SiO2

M T χ χ H (a) (b)

Diamagnetic

m = r

χ < 0

C, Cu, Pb, H2O, NaCl, SiO2

M T χ χ H (a) (b)

Diamagnetic

Paramagnetic

m = r

χ < 0

m ≠ r

Jij = 0 χ > 0 χ ≠ f(H)

C

B eff

⋅ = 8 ) (µ µ C

B eff

⋅ = 466 4, ) (µ µ

) ( 1 + = J J g

B eff

µ µ

Na, Al, CuCl2

χ

M H 1/C

1/χ T

C T =

−1

χ

J

C N kB

eff

3 µ µ ⋅ =

if χ(emu/mole) if χ(µB/T∙f.u)

C, Cu, Pb, H2O, NaCl, SiO2

M T χ χ H (a) (b)

Diamagnetic

Paramagnetic Magnetic ordered

m = r

χ < 0

m ≠ r

Jij = 0 χ > 0

m ≠ r

Jij ≠ 0 χ >> 0 χ ≠ f(H)

C

B eff

⋅ = 8 ) (µ µ C

B eff

⋅ = 466 4, ) (µ µ

) ( 1 + = J J g

B eff

µ µ

Na, Al, CuCl2

χ

M H 1/C

1/χ T

C T =

−1

χ

J

C N kB

eff

3 µ µ ⋅ =

if χ(emu/mole) if χ(µB/T∙f.u)

a) ferromagnetic

j ij

J H S Si r r ⋅ − = 2 Jij > 0

Fe, Co, Ni, Gd…

Ms ≠ 0

1/χ

M T Tc θ θ χ − = T C T1<T2<Tc<T3 T1 T2 T3 M H Ms(0) = gJ µB J

Molecular field approximation

Curie – Weiss law

θ = Tc M N H

ii m =

b) antiferromagnetic

Ms=0

χ T

χ⎜⎜

χ⊥

TN 1/χ T TN θ θ < 0 θ χ + = + = T C H M M

B A

Η=0 Η Η Η Η

Jij < 0

B A

M M r r =

MnO, Mn, Cr…

c) ferrimagnetism Ms≠0

B A

M M r r ≠

Jij < 0

Fe3O4, ferrites, GdCo5,…

M=MA-MB M=MA-MB M=MA-MB M=⎜MA-MB⎜

T T T

MB MB MB MA MA MA M0 M0 M0

Tc Tc Tc Tcomp

M M M NAA≈NBB NAA<NBB NAA>NBB

T<Tc

T>Tc

1/χ T Tc θ

' θ σ χ χ − − + = T C T 1 1

1/χ

M T Tc θ θ χ − = T C

Ms(0)

M H Ms(T1) Ms(T2) Ms(T3) χp T1 T2 T3 T1 < T2 < T3

H M M

p s

χ + =

M H Ms(T1) Ms(T2) Ms(T3) χp T1 T2 T3 T1 < T2 < T3

H M M

p s

χ + =

1 2 3 4 5 6 100 200 300 400 500

Al5Mn3Ni2 Ms (µB/f.u.) T (K) Ms = 5.03 µB/f.u. Tc = 401 K 1 2 3 4 5 2 4 6 8 10

Al5Mn3Ni2 T = 10 K M(µB/f.u.) µ0H (T)

3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2 5 6 7 8 9 10

M(µB/f.u.) µ0H (T)

Ha

+ + + +++ +

• - - - -

Ms Hd + + + + + + +

• - - - -

Ms Hd

M H r r

d d

N − =

Ha

s d

M N H

II

=

s d

M N H

⊥

=

d a i

H H H H r r r r + = =

Ha = applied field

( ) ( )

a d d a d a

N N H 1 M M H H H H M χ χ χ χ χ + = − = + = = M H M Ha 1/Nd M H r r

d d

N − = The influence of the demagnetising field on the magnetisation curves

Ndx = Ndy = Ndz =1/3.

( ) M

Hd r r ⋅ − − = θ cos 1 l

θ

O

M r

d

sphere

d << l Nd = 0 d >> l Nd = -1

M H Ms(T1) Ms(T2) Ms(T3) T1 T2 T3 T1 < T2 < T3

H M M

p s

χ + =

Hd ≠ 0

1 2 3 4 5 2 4 6 8 10

Al5Mn3Ni2 T = 10 K M(µB/f.u.) µ0H (T)

3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2 5 6 7 8 9 10

M(µB/f.u.) µ0H (T)

1 2 3 4 5 2 4 6 8 10

Al5Mn3Ni2 T = 10 K M(µB/f.u.) µ0H (T)

3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2 5 6 7 8 9 10

M(µB/f.u.) µ0H (T)

0,5 1 1,5 2 2,5 3 2 4 6 8 10

GdCo4Si T = 4 K M(µB/f.u.) µ0H (T)

H M M

p s

χ + =

0,5 1 1,5 2 2,5 3 2 4 6 8 10

GdCo4Si T = 4 K M(µB/f.u.) µ0H (T)

2,2 2,3 2,4 2,5 2,6 2,7 2,8 2,9 3 2 3 4 5 6 7 8 9 10

M(µB/f.u.) µ0*H (T)

H H a M M

p s

χ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = 1

Ms(T)

M H

Hsat = Ms

H H

NO MAGNETOCRYSTALLINE ANISOTROPY

Magnetic measurements give magnetisation (A/m)

Case study:

magnetic measurements on plate shape samples

M H

Hsat = Ha

H

M H

Hsat = Ms

H

PERPENDICULAR ANISOTROPY

Magnetic measurements give magnetisation (A/m) Magnetic measurements give magnetocrystalline anisotropy

M T Tc

Ms(0)

Ms(0) = gJ µB J0

T→0K

Ms(0) = gJ µB S0

T→0K

For 3d transition metals (Fe, Co, Ni…), the

• rbital moment is blocked by crystalline field:

For the rare earth (Gd for example): J0=Jp

?

B

• B

ii c

k J J Ng N T 3 1

2 2

) ( + = µ µ

Curie temperature evaluation T → Tc; T < Tc

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − + + + ⋅ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

c

T T J J J M T M 1 1 1 3 10

2 2 2 2

) ( ) ( ) ( ) (

2 4 6 8 10 200 400 600 800 1000 1200

ThFe11C1.5 M(a.u.) T(K)

10 20 30 40 50 300 350 400 450 500 550 600 650 700

M2 (a.u.) T(K)

• O. Isnard, V. Pop, K.H.J. Buschow,
• J. Magn. Magn. Mat. 256 (2003) 133

2 4 6 8 10 200 400 600 800 1000 1200

SmCo5+20 wt% Fe_8hMM M (a.u.) T(K) Tc(Fe)

1 2 3 4 5 6 7 8 200 400 600 800 1000 1200 M (a.u.) T(K)

Tc = 1119 K

MH M b M a M Fm

4 2

4 2 µ − ⋅ ⋅ ⋅ + + = ) (

In the low magnetisation region - for example T → Tc; T < Tc

= dM dFm H bM aM

3

µ = +

• r

b a b H M M − =

2

µ

( ) ( )

H M C J M T J J M T T T N

c c ii 3 2 2 2

1 10 1 2 2 3 µ µ µ = + + + + − ) (

molecular field approximations: Nii = Tc/C Hm = Nii M

( )

c c ii

T T T N a − = µ

( ) C

J M T J J b

2 2 2

1 10 1 2 2 3 + + + = ) ( µ

T < Tc T = Tc T > Tc. a < 0 a = 0 a > 0

20 40 60 80 100 120 0.2 0.4 0.6 0.8 1

ThFe11C1.5 M2 (µB/f.u.)2 µ0H/M (T*f.u./µB)

400 K 440 K 420 K

• O. Isnard, V. Pop, K.H.J. Buschow,
• J. Magn. Magn. Mat. 256 (2003) 133

M

2

T2 T3 Tc T4 T5 T1 H/M 1/χ Ms

2

H/M3 H/M4 H/Mc

2 s

M

T1 T2 T3 Tc T4 T5 T1 < T2 < T3 < Tc < T4 < T5.

M2

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − =

3 4 4 3 3 4

M H M H M H M H T M H M H T T

c c c

Arrott plot

1/χ

M T Tc θ θ χ − = T C

Ms(0)

Ms(0) = gJ µB J0 ) ( 1 + =

p p B eff

J J gµ µ

T→0K T > Tc

Ms(0) = gJ µB S0 ) ( 1 + =

p p B eff

S S gµ µ

T→0K T > Tc

1 > = S S r

p For 3d transition metals (Fe, Co, Ni…), the

• rbital moment is blocked by crystalline field:

For the rare earth (Gd for example): J0=Jp

1 P.R. Rhodes, E.P. Wolfarth, Proc. R. Soc. 273 (1963) 347. 2 O. Isnard, V. Pop, K.H.J. Buschow, J. Magn. Magn. Mat. 256 (2003) 133 3 D. Bonnenberg, K.A. Hempel, H.P.J. Wijn, Landolt-B.orsntein new series, Vol. III, 19a,

Springer, Berlin, 1986, p. 142.

4 O. Isnard, N. Coroian, V. Pop (unpublished) 5 R. Ballou, E . Burzo, and V. Pop, J. Magn. Magn. Mat. 140-144 (1995) 945.

r = 1 local moment limit r →∞ total delocalisation limit →∞ 2.03 1.69 1.5 1.32 1.01 1.00 r YCo3B2

5

HoCo4Si4 Fe3C3 ThFe11C1.5

2

Co1 Fe1 Gd1

M H

H M = χ

Paramagnetic sample If there are some ferromagnetic impurity

s

cM H M + = χ

M H

H M = χ

Paramagnetic sample If there are some ferromagnetic impurity

s

cM H M + = χ H M c H M

s

+ = χ H M H 1

χ

T TN Tc Tc

θ χ + = T C θ χ − = T C

' θ σ χ χ − − + = T C T 1 1

T C = χ

θ θ θ

1/χ

θ

2 1 sin

K Ea ≈

K1 > 0

4 8 12 16 0,2 0,4 0,6 0,8 1 ∆M H, 10 A.m

6

• 1

M , 1 A . m

6

• 1

H c H c Ha

[111] [001] [110] [100]

M H Ha

[100]

H

[001]

H

[110]

H

K1 < 0 axial symmetry:

YCo5

low anisotropy energy spin – flop transition

H (z) (z) H (z) H Mb Ma Ma Ma Mb Mb M H (a) (b)

T < TN, antiferromagnetic materials, χ⊥ > χ ⎢⎢

• E. Du Trémolet de Lacheisserie (editor),

Magnetisme, Presses Universitaires de Grenoble, 1999

ex a c

H H H = Density of energy in magnetic field H,

E = -χµ0H2/2

M H (a) (b) (z) H Mb Ma H (z) Ma Mb H (z) Ma Mb

High anisotropy energy spin – flip transition

spin–flip and spin–flop also in ferrimagnetic materials metamagnetic transition

ex c

H H ≈

H M = χ

M H

χi χm

H

sat

M

st

M

χ0

Msat Ms dH dM

i =

χ

χ

H

T<Tc

M H

• Hc

Hc H Mr

• Mr

B B’ A C D E F O

reversible

µ >> 0

magnetic cores magnetic circuits

soft Hc – small~0,001÷10 A/m

permanent magnets

hard Hc – BIG ~102÷106 A/m

M H

• Hc

H c H M r

• M

r B B ’ A C D E F O

( )

M H B r r r + = µ

Curie temperature, Tc

Fundamental research

M

Application research

B

Hard magnetic materials

• H

B BH (BH)max P (BH)=const

Hysteresis measurements in soft magnetic materials

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3

• 8000 -6000 -4000 -2000

2000 4000 6000 8000

Ni3Fe f = 5 kHz B (T) H (A/m)

HSI = 103/4π·HCGS ≈ 80 HCGS

• 100
• 50

50 100

H(Oe)

0.01 0.1 1 10 0.01 0.1 1

P (W/cm^3)_1kHz; Ni3Fe_1-5_800 P (W/cm^3)_5kHz; Ni3Fe_1-5_800 P (W/cm^3)_10kHz; Ni3Fe_1-5_800 P (W/cm^3)_20kHz; Ni3Fe_1-5_800 P (W/cm^3)_50kHz; Ni3Fe_1-5_800

P (W/cm3) Bmax (T) 10 15 20 25 30 35

20 40 60 80 100 120 140

10 20 30 40 50 60

B=0.1T

µ; Ni3Fe_1_700 µ; Ni3Fe_1-5_600 µ; Ni3Fe_1-5_700 µ; Ni3Fe_1-5_800 µ; Ni3Fe_2_700 µ; Ni3Fe_3_700 P/f (J/m^3); Ni3Fe_1_700 P/f (J/m^3); Ni3Fe_1-5_600 P/f (J/m^3); Ni3Fe_1-5_700 P/f (J/m^3); Ni3Fe_1-5_800 P/f (J/m^3); Ni3Fe_2_700

µ

P/f (J/m3) f (kHz)

5 10 15 20 25 30 35

1 2 3 4 5 6

10 20 30 40 50 60

Ni3Fe_1_700; µ' Ni3Fe_1-5_600; µ' µ'; Ni3Fe_1-5_700 µ'; Ni3Fe_1-5_800 µ'; Ni3Fe_2_700 Ni3Fe_1_700; µ'' Ni3Fe_1-5_600; µ'' µ''; Ni3Fe_1-5_700 µ''; Ni3Fe_1-5_800 µ''; Ni3Fe_2_700

µ' µ'' f (kHz)

B = 0.1 T

• I. Chicinas, O. Geoffroy, O. Isnard, V. Pop
• J. Magn. Magn. Mat. 290-291 (2005) 1531

h h h

K A / π δ =

Dcr = soft phase critical dimension δh = width of domain wall in the hard phase Ah and Kh are the exchange and anisotropy constants

Hard Magnetic Nanocrystalline Materials

h

cr D δ 2 ≈

exchange-spring magnets Hard phase exchange Soft phase high anisotropy large magnetisation

+

EXPERIMENTAL criteria for the presence of the exchange spring mechanism Large reversible demagnetization curve Enhanced remanence mr > 0.5 (mr = Mr/Ms)

+

}

Hard Magnetic Nanocrystalline Materials

• 100
• 50

50 100

• 4
• 3
• 2
• 1

1 2 3 4

SmCo5 + 20Fe/8h MM

as milled 450oC 0.5h 500oC 1.5h 550oC 1.5h 600oC 0.5h 650oC 0.5h SmCo5/2h MM

M (emu/g) H (T)

• V. Pop, O. Isnard, I. Chicinas, D. Givord, Proceedings of Euro PM2005, Prague

• 100
• 50

50 100

• 4
• 3
• 2
• 1

1 2 3 4

SmCo5/20%Fe

8h_M (emu/g) 8h+450C/0.5h 8h+550C/1.5h 8h+650C/0.5h

M (emu/g) H (T)

20 40 60 80

• 1
• 0.8
• 0.6
• 0.4
• 0.2

SmCo5/20%Fe

8h_M (emu/g) 8h+450C/0.5h 8h+550C/1.5h 8h+650C/0.5h

M (emu/g) H (T)

• 100
• 50

50 100

• 4
• 2

2 4

SmCo5/20Fe T = 300 K

8h+550C/1.5h 2h_MM 2h+450C/0.5h

M (emu/g) H (T)

N.H. Hai, N.M. Dempsey, D. Givord, JMMM262 (2003) 353

• E. Girgis et al, J. Appl. Phys. 97 (2005) 103911

Exchange bias

Major hysteresis loops with a selection of minor re-magnetization curves (broken lines) and recoil loops for ( a) single-phase Sm2Fe14Ga3C2 and ( b) two-phase Sm2Fe14Ga3C2/40vol% -Fe.

(Feutril et al, J. Phys.D: Appl. Phys. 29 (1996) 2320)

recoil loops

• 20
• 10

10 20 30 40 50

• 2
• 1.5
• 1
• 0.5

SmCo5+20%Fe 2h_450C30min T = 4 K M (emu/g) H (T)

• 50

50

• 2
• 1.5
• 1
• 0.5

SmCo5+20%Fe 6h_450C30min T = 4 K M (emu/g) H (T)

• 50

50

• 2
• 1.5
• 1
• 0.5

6h+450C/0.5h 2h+450C0.5h

M (emu/g) H (T) T = 4 K

• V. Pop, O. Isnard, I. Chicinas, D. Givord, (be published)

3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 10 20 30 40 50 60

4 K 295 K

M

s (µ B/f.u.)

Tem ps de broyage (h) recuit

10 20 30 40 50 60 28.0 28.5 29.0 29.5 30.0

Mean hyperfine field (T) Milling time, t m (hours)

MECHANICAL ALLOYING soft magnetic materials

Intensité (u.a.) 2 t h e ta

Ni3Fe Ni

1h 1h+ 330°C/1h 2h 2h+ 330°C/1h 3h 3h+ 330°C/1h 4h 4h+ 330°C/1h 6h 6h+ 330°C/1h 8h 8h+ 330°C/1h 10h 10h+ 330°C/1h 12h 12h+ 330°C/1h ss

90 91 92 93 94 95

2 θ (°)

Intensity (a.u.)