[PPT] - Phase transitions Experimental studies on magnetic materials Ekkes PowerPoint Presentation

SLIDE 1

27-08-11

Challenge the future

Delft University of Technology

Phase transitions

Experimental studies on magnetic materials

Ekkes Brück, Fundamental Aspects of Materials and Energy, TNW

SLIDE 2

2 Magnetic phase transitions

Outline

Basic magnetics (classical)
Origin of first order transition?
Magnetic materials
Gd5Ge2Si2 magnetic Rare-Earth
MnFe(P,Si) magnetic transition metals
TbFe4Al8 magnetic RE & TM

SLIDE 3

3 Magnetic phase transitions

Magnetization processes

no field no field no net moment no net moment

Magnetic (spin) moments

Effect of temperature. Classical statistical physics: Effect of temperature. Classical statistical physics: probability of finding atomic dipole in state with energy E: probability of finding atomic dipole in state with energy E:

µ

µ B B0

SLIDE 4

4 Magnetic phase transitions

Magnetization processes

B

N M

µ

B/T (T/K)

0 1 2 3 4

7 5 3 1

µ

µ B B0

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5 Magnetic phase transitions

Magnetization processes

from unmagnetized from unmagnetized state state

nce magnetized
nce magnetized

M MR

R

B BC

C

M MS

S

B B0

M M

M
MS

S

Hysteresis loop

SLIDE 6

6 Magnetic phase transitions

Magnetization processes

www.ee.umd.edu/~rdgomez/permalloy.htm www.ee.umd.edu/~rdgomez/permalloy.htm

Ferromagnetic domains

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7 Magnetic phase transitions

1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5

M (µ B/f.u.) B (T) at 310 K

MnFeP0.46As0.54 For example

Magnetization processes

Materials with field induced first

rder phase

transition.

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8 Magnetic phase transitions

Zeeman effect for state with total moment J J Jz 2 1

1
2

B

Ground state J is 2J+1 times degenerated: Jz=-J, -J+1, … J
Splits in magnetic field into sublevels
Spectroscopic splitting factor gLandee depends on L, S, and J
Splitting at B=1 Tesla in the order of meV
Atom behaves as if it has effective moment: µeff=-gLµBJ

B H

z P

⋅ − = ⋅ − = µ

B μ ) 1 ( 2 ) 1 ( ) 1 ( 2 3

+ + − + − =

J J S S L L gLande

z z B Lande P

B J g H E

µ > = = <

z B L

B g E

µ = ∆

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9 Magnetic phase transitions

When a system, in contact with a heat bath at temperature T can be in a state with energy E, the probability for this is given by the Gibbs rule: where k is Boltzmann's constant. Z is called the partition sum,

Statistical physics description

SLIDE 10

10 Magnetic phase transitions

Z is needed to have the proper normalization The strength of statistical physics is that by calculating Z a lot of information about the system can be derived. The Helmholtz free energy is: while the Gibbs free energy is:

SLIDE 11

11 Magnetic phase transitions

spins lattice

Basic magnetocalorics

E



Two energy reservoirs

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12 Magnetic phase transitions



E

Basic magnetocalorics

spins lattice

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13 Magnetic phase transitions

Magnetic cooling: Debye and Giauque 1926 61g Gd2(SO4)3·8H2O, ΔB=0.8T, 1.5K 0.25K → Nobel prize 1949

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14 Magnetic phase transitions

Thermodynamic relations:

( ) p B

T G p B T S

,

, ,

      ∂ ∂ − =

,

( ) p T

B G p B T M

,

, ,

      ∂ ∂ − =

,

( ) B T

p G p B T V

,

, ,

        ∂ ∂ − =

Differential of Gibbs free energy Entropy Magnetization Volume Differential of entropy dp p S dB B S dT T S dS

B T p T p B , , ,

        ∂ ∂ +       ∂ ∂ +       ∂ ∂ =

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15 Magnetic phase transitions

Vdp dB B S dT T C dS

p T p B

α −       ∂ ∂ + =

, ,

Identification of terms Adiabatic process at constant pressure

dB B S C T dT

p T p B , ,

      ∂ ∂ − =

∫

      ∂ ∂ =

B B m

dB T M S Δ

Magnetic entropy Maxwell relations

B T

T M B S

      ∂ ∂ =       ∂ ∂

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16 Magnetic phase transitions

From definition of specific heat S0 can be set to zero because it is not depending on field

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17 Magnetic phase transitions

B T T B T M B T M B T S

i i i i i i i m

∆ − − = ∆

∑

+ + +

1 1 1

) , ( ) , ( ) , (

Experimental determination from magnetic measurements

SLIDE 18

18 Magnetic phase transitions

Outline

Basic magnetics (classical)
Origin of first order transition?
Magnetic materials
Gd5Ge2Si2 magnetic Rare-Earth
MnFe(P,Si) magnetic transition metals
TbFe4Al8 magnetic RE & TM

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19 Magnetic phase transitions

Continuous phase transition

In the absence of an external field, H=0, the system with exchange interaction J/k=1may spontaneously order. T=0.3J/k T=0.25J/k T=0.2J/k

      − =

+m) ( +m)

m)+(

(

m)

(

NHm+NT

NJm F 2 1 ln 2 1 2 1 ln 2 1 2 1

2

SLIDE 20

20 Magnetic phase transitions

First order phase transition

      − =

+m) ( +m)

m)+(

(

m)

(

NHm+NT

NJm F 2 1 ln 2 1 2 1 ln 2 1 2 1

4 T=0.0225 J/k T=0.025 J/k T=0.02 J/k

If interactions with quartets play a role this may result in local minima in the free energy.

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21 Magnetic phase transitions

(Bean and Rodbell, 1962).

Ansatz TC = T0[1 + ß(V - V0)/V], TC Curie temperature, T0 Curie temperature if lattice incompressible. V0 volume in absence of exchange interaction, β effect of volume change on Curie temperature. Reason for first order transition

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22 Magnetic phase transitions

pV S S T V V V K B NkT j j G

l j C

+ + −         − + −         + − =

) ( 2 1 1 3 1

2 2

σ σ σ

N number of magnetic atoms per unit mass, k Boltzmann constant, σ0 saturation magnetization, σ relative magnetization, K the compressibility, Sj entropy of spin sublattice, Sl entropy of lattice subsystem Gibbs energy

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23 Magnetic phase transitions

. 2 606 . 867 . 2 / 867 . 2

5 3 2 σ α β σ σ σ σ η σ σ

T NkT B T T

− + + + − =

State equation α Thermal expansion Good agreement with exp. data Second order transition for η <1

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24 Magnetic phase transitions

Gibbs energy as function of σ Local minimum near Tc ⇒ First order transition

SLIDE 25

25 Magnetic phase transitions

Outline

Basic magnetics (classical)
Origin of first order transition?
Magnetic materials
Gd5Ge2Si2 magnetic Rare-Earth
MnFe(P,Si) magnetic transition metals
TbFe4Al8 magnetic RE & TM

SLIDE 26

26 Magnetic phase transitions

Phase transition in iron 0T 3T

C p [ J / m

l

· K ] T [°C] T [K] ∆T [K]

Magnetic ordering T 10 0.8T 3T 6T

SLIDE 27

27 Magnetic phase transitions

Total entropy vs reduced temperature of gadolinium in low field (blue) and high field 9T (purple) (Gschneidner et al) MCE in gadolinium

SLIDE 28

28 Magnetic phase transitions

Outline

Basic magnetics (classical)
Origin of first order transition?
Magnetic materials
Gd5Ge2Si2 magnetic Rare-Earth
MnFe(P,Si) magnetic transition metals
TbFe4Al8 magnetic RE & TM

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29 Magnetic phase transitions

Giant magnetocaloric effect in Gd5Ge2Si2 Magnetically dilute yet higher effect double transition?

Pecharsky & Gschneidner PRL 78 (1997) 4494

ΔT a

d (

K )

SLIDE 30

30 Magnetic phase transitions

Crystal growth Crystal growth

D=4mm Sphere was cut by spark erosion from as grown rod Crystal was grown in a mirror furnace by means

f traveling solvent floating zone method

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31 Magnetic phase transitions

Extraordinary magnetic behavior: first-order character of the

paramagnetic-ferromagnetic transition.

Unusual behavior Unusual behavior

50 100 150 200 250 300 350 400 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Gd5Si1.65Ge2.35 Crystal Sphere d=4mm B=0.05T Stepwise heating mode

a b c M (µ B /f.u.)

T (K)

1 2 3 4 5 10 20 30 40

Gd5Ge2.35Si1.65 crystal Sphere d=4mm at 5K

a b c M ( µ B/f.u)

B (T)

20 40 60 80 100 120 140 160 180 200 220 240 260 50 100 150 200 250 300 350 400 450 500 550 600

C (J/mol ·K) T (K)

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32 Magnetic phase transitions

The high temperature paramagnetic monoclinic phase transforms to the

low temperature ferromagnetic orthorhombic phase. The low temperature phase has a higher symmetry than the high temperature, which is the opposite of what is normally observed for other polymorphic systems.

Unusual behavior Unusual behavior

Crystallographic data comes from W Choe PRL v84, n20, p4617, 2000

>Tc: P1121/a, No.14 <Tc: Pnma, No.62

b b

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33 Magnetic phase transitions

1

1 2 3 4 5 6 7 8

heating cooling

a-axis

∆ L/L (10

3)
2.0
1.5
1.0
0.5

0.0 0.5

cooling heating

∆ L/L (10

3)

b-axis

180 200 220 240 260 280

1.5
1.0
0.5

0.0 0.5

cooling heating

T (K)

∆ L/L (10

3)

c-axis

thermal expasion of Gd5Ge2.4Si1.6

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34 Magnetic phase transitions

Volume decreases when cooling through the transition, i.e., the cell

volume in the low-temperature ferromagnetic phase is smaller ( ∆v>0.4%) than in the high-temperature paramagnetic one. This is in contrast with the general physical picture of the magnetovolume effects which are transtions from a low-volume low-moment to a high-volume high-moment state.

Unusual behavior Unusual behavior

Normal: Unusual:

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35 Magnetic phase transitions

Gd5Si4 based

rthorhombic

Pnma Ferro magnet Q.L.Liu et al.

Recent XRD investigation

reported that Gd5(SixGe1-x)4 alloys form a completely miscible solid-solution crystallized in the Gd5Si4-type Pnma structure below TC regardless of the

composition. Ground state is

low temperature (Gd5Si4– based) orthorhombic ferromagnet

Temperature of structural

phase transition always coincides with Curie temperature TC.

Unusual behavior Unusual behavior

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36 Magnetic phase transitions

x > 0.5 0.4 < x < 0.5 x < 0.3 Gd5Si4 type Pnma Gd5Si2Ge2 type P1121/a Gd5Ge4 type Pnma T=Si, Ge (Gd3+)5(T2

6-)2(3e-) (Gd3+)5(T2 6-)1.5(T4-)(2e-) (Gd3+)5(T2 6-) (T2 6-)2 (1e-)

V. K. Pecharsky and K. A. Gschneidner, Jr., J. Alloys Compd. 260, 98-106 (1997)

b a

What is responsible for the unusual behaviors? What is responsible for the unusual behaviors?

Breaking and making bond RKKY or superexchange Breaking and making bond RKKY or superexchange Breaking and making bond RKKY or superexchange Breaking and making bond RKKY or superexchange

SLIDE 37

37 Magnetic phase transitions

Outline

Basic magnetics (classical)
Origin of first order transition?
Magnetic materials
Gd5Ge2Si2 magnetic Rare-Earth
MnFe(P,Si) magnetic transition metals
TbFe4Al8 magnetic RE & TM

SLIDE 38

38 Magnetic phase transitions

MnFeP1-xSix Hexagonal Fe2P type of structure

Bacmann, JMMM 1994 Space group: P62m Mn 3g sites Fe 3f sites P/Si 1b&2c sites _

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39 Magnetic phase transitions

100 150 200 250 300 50 100 150

x = 1.90 x = 1.93 x = 1.95 x = 1.40 x = 1.50 x = 1.80 x = 1.20 x = 1.25 x = 1.30

M (Am

2kg

1)

Temperature (K)

Magnetic response of MnxFe2-xP0.5Si0.5 in 1T

SLIDE 40

40 Magnetic phase transitions

290 300 310 320 330 340 350 360 50 100 150

H e a t i n g

M (Am

2kg

1)

T (K)

5 T 4 T 3 T 2 T 1.5 T 1 T 0.5 T 0.05 T

Mn1.24Fe0.71P0.46Si0.54

C

l

i n g

1 2 3 4 5 315 320 325 330 335

T

C (K)

B (T) 3.5 K/T

Different fields

SLIDE 41

41 Magnetic phase transitions

1 2 3 4 5 20 40 60 80 100 120

dem agnetizing

Mn1.24Fe0.71P0.46Si0.54

M (A m

2kg

1)

B (T)

m agnetizing

342 K 303 K

∆ T=3 K

Magnetization isotherms

SLIDE 42

42 Magnetic phase transitions

240 260 280 300 320 10 20 30 x=1.40 x=1.30 x=1.25

− ∆ S

m(Jkg

1K
1)

Temperature (K)

x=1.20 Gd

MCE of MnxFe2-xP0.5Si0.5 in 1 and 2 T

SLIDE 43

43 Magnetic phase transitions

0.03 0.06 0.09 5 10 15

x=1.50 x=1.40 x=1.30 x=1.25

M

2(x10 3 A 2m 4kg

2)

µ

0H/M (TkgA

1m
2)

x=1.20

Arrot plots of MnxFe2-xP0.5Si0.5

SLIDE 44

44 Magnetic phase transitions

Temp dep. X-ray of MnxFe2-xP0.5Si0.5

x=1.30 51 53 55 200 300 400

(300) (211) (002)

Temperature (K) 2θ (deg.) x=1.40 51 53 55 x=1.50 200 300 400

x=1.20

50 52 54 56 100 200 300 400

Hex

(a) (b)

(161) (251) (400) (242) (213) (312) (060) (033) Hex Bco (300) (211) (002) Temperature (K) 2θ (deg.) x=1.95

0.0 0.5 1.0

SLIDE 45

45 Magnetic phase transitions

Phases of MnxFe1.95-xP0.5Si0.5

1.1 1.3 1.5 1.7 1.9 100 200 300 TS TC PM-Bco PM-Hex

Tem perature (K)

x

FM-Hex

SLIDE 46

46 Magnetic phase transitions

200 220 240 260 280 300 320 340 360 380 400 20 40 60 80 100 120 140

T (K) M (Am

2/Kg)

x=1.40, y=0.40 x=1.34, y=0.42 x=1.38, y=0.42 x=1.34, y=0.44 Mn1-xFexP1-ySiy 1 T

Sweeping rate: 1 K/min

Mn2-xFexP1-ySiy 30-40% extra iron

320 330 340 350 360 370 380 390 400

3 6 9 12 15

− ∆ sM (J/kgK)

Mn1-xFexP1-ySiy

x=1.34 y=0.44 x=1.38 y=0.42 x=1.34 y=0.42

T (K)

x=1.4 y=0.4

∆ B = 2 T

Magnetic entropy change for a field change of 2 T. M vs. T

SLIDE 47

47 Magnetic phase transitions

50 100 150 220 240 260 280 300 320 340 360 4 8 12 16 20

x=1.24, y=0.56 x=1.22, y=0.58

B = 1 T 1 K/min

x=1.30, y=0.50 x=1.28, y=0.52 x=1.26, y=0.54

M (A m

2kg

1)

∆ B = 0-1T

Mn

xFe 2-xP 1-ySi y

− ∆ S (Jkg

1K
1)

T (K)

∆ B = 0-2T

E D C B A

Partial phase-diagram

SLIDE 48

48 Magnetic phase transitions

Theoretical progress

Novel type of magnetism: Intercallation of strong and weak magnetism

SLIDE 49

49 Magnetic phase transitions

4.55 x 10-5 electrons/Å3

9.1 x10-5 electrons/Å3

Change in electron density at the phase transition ferromagnetic density subtracted from paramagnetic density.

SLIDE 50

50 Magnetic phase transitions

Summary Mn & Fe rich Si compounds

Magneto-elastic and magneto-structural transition 1st order
Increased Mn or Fe content strongly reduces hysteresis
Increased Si content strongly reduces hysteresis
Ferromagnetic state prefers hex structure?
Combining variation of Mn and Si content results in desired

properties

TC of (Mn,Fe)2+z(P,Si) compounds above 400 K

SLIDE 51

51 Magnetic phase transitions

Outline

Basic magnetics (classical)
Origin of first order transition?
Magnetic materials
Gd5Ge2Si2 magnetic Rare-Earth
MnFe(P,Si) magnetic transition metals
TbFe4Al8 magnetic RE & TM

SLIDE 52

52 Magnetic phase transitions

Magnetic properties of single-crystalline TbFe4Al8

Fe- or Co-rich 1:12 compounds candidates for permanent-magnet materials Preferential occupation of different sites R-R interactions AF Fe-Fe interactions

SLIDE 53

53 Magnetic phase transitions

2a (Tb) 8f (Fe) 8i (Al) 8j (Al)

TbFe4Al8 ThMn12 type

SLIDE 54

54 Magnetic phase transitions

Magnetic structure @ 8K

Schobinger-Papamantolos et al 1999

canted spiral with ferromagnetic component

nly half of the

moments shown

SLIDE 55

55 Magnetic phase transitions

Temperature dependence of magnetisation with B//c-axis

SLIDE 56

56 Magnetic phase transitions

50 100 150 200 250 300 350

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

FC ZFC TbFe4Al8 single crystal [100] 0.05T

Magnetisation (µ B/f.u.) Temperature (K)

0.00 0.01 0.02 0.03 0.04

Temperature dependence of magnetisation with B//a-axis Spin glass? Tmax ~ 60K

SLIDE 57

57 Magnetic phase transitions

5
4
3
2
1

1 2 3 4 5

4
3
2
1

1 2 3 4

TbFe4Al8 (100) axis at 5K

Magnetisation (µ B/f.u.)

Field (T)

“Hysteresis” loop of ZFC sample

SLIDE 58

58 Magnetic phase transitions 10 20 30 40 50 60 70 80 0.0 0.5 1.0 1.5 2.0 2.5

TbFe4Al8 single crystal [100]

µ 0Hc (T)

Temperature (K)

Temperature dependence

f coercive field

SLIDE 59

59 Magnetic phase transitions

8
6
4
2

2 4 6 8

4
3
2
1

1

B//[100] measured along [010]

dL/L0 (10

4)

B (T)

1

1 2 3 4

B//[100] measured along [100]

longitudinal and transversal magnetostriction B//[100]

SLIDE 60

60 Magnetic phase transitions

Four relevant energies: TN iron = 160 K TO terbium = 110 K Tc coercivity = 70 K TF ferrimagnetic = 25 K Peculiar magnetization not related to AF order or CantedSpiral order. Magnetoelastic effect (orthorhombic)

10 20 30 40 50 60 70 80 0.0 0.5 1.0 1.5 2.0 2.5

TbFe4Al8 single crystal [100]

µ 0Hc (T)

Temperature (K)

8
6
4
2

2 4 6 8

4
3
2
1

1 B//[100] measured along [010]

dL/L0 (10

4)

B (T)

1

1 2 3 4 B//[100] measured along [100]

SLIDE 61

61 Magnetic phase transitions

People involved in project

Senior scientists: Jürgen Buschow, Niels van Dijk
Pos docs: Lian Zhang, Luana Caron, Cam Thanh Dinh
PhD students: Thanh Trung Nguyen, Zhiqiang Ou, Huu Dung

Nguyen, Jose Leitao

Technician: Anton Lefering