The Magnetoelastic Paradox

M. Rotter, A. Barcza, IPC, Universität Wien, Austria

H. Michor, TU-Wien, Austria

A. Lindbaum, FH-Linz, Austria

M. Doerr, M. Loewenhaupt, IFP TU-Dresden, Germany

B. Beuneu, LLB – Saclay, France

M el Massalami, UFRJ, Brazil

2M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

1. Magnetostriction Measurements

2. Magnetostriction in the Standard

Model of Rare Earth Magnetism

3. The Magnetoelastic Paradox (MEP)

4. Experimental Evidence for the MEP

in Gd Compounds

5. Application of Magnetic Fields - the

case of GdNi2B2C

6. Outlook

3M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

Experimental Methods1cm

Capacitance Dilatometry

X-ray Powder Diffraction

• Good resolution (10-9 in dl/l)• 45 T Magnetic Fields - forced magnetostriction

• requires single crystals

• Anisotropic Effects on Polycrystals (Expansion, Symmetry-Changes)• bad resolution (10-4 in dl/l)

Rotter et.al. Rev. Sci. Instr. 69 (1998) 2742

Magnetostriction Measurements

4M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

X Axis

0 30 60 90 120 150 180 210 240 270

a [Å

]

4,154

4,156

4,158

4,160

4,162

T(K)

0 30 60 90 120 150 180 210 240 270

c [Å

]

9,600

9,604

9,608

9,612

9,616

9,620

Debye fit for T > 47 K

Debye fit for T > 47 K

TN=47 KGdRu2Si2

95,7 96,0 96,3 96,6 96,9

50

100

150

200

250

300

Inte

nsi

ty (

cou

nts

)

2*Theta(deg)

60K 10K(008)

GdRuSi

5M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

55,6 55,8 56,0 56,2

25

50

75

100

125

150

Inte

nsi

ty (

cou

nts

)2*Theta(deg)

60K 10K

(202)

74,4 74,7 75,0 75,3 75,6

50

100

150

200

250

300

Inte

nsi

ty (

cou

nts

)

2*Theta(deg)

60K 10K(220)

GdRu2Si2

? ?

No sign of distortion of the tetragonal plane !

6M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

Crystal Field

T

e-

+

+

L0

T<TC(N)

Spontaneous Magnetostriction

STANDARD MODEL OF RARE EARTH MAGNETISMMicroscopic Origin of Magnetostriction:

Strain dependence of magnetic interactions

Exchange

T<TC(N) L=0, L0

„exchange-striction“

T

Gd3+, S=7/2, L=0

7M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

No distortion (dJ1/d)

ij

jimag ijJH JJ),(2

1

kT k i i

k i i JH J J,

) , (

...)0()(

magH

magel HEH

cEel 2

1

}{ / TkH BeTrZ ZTkF B ln 0

F

Ferromagnet: J1>0dV/V<0

J1J1

Exchange striction on a Square Lattice

8M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

No distortion (dJ1/d)

Anti-Ferromagnet withNN exchange: J1<0dV/V>0

Tetragonal Distortion (dJ1/d) !!!

Anti-FerromagnetWith small |J1|J2<0dV/V=0

J1J1

J2

J1

J2

J1

THE MAGNETOELASTIC PARADOX

Antiferromagnets with L=0 below TN:

Symmetry breaking distortions are expectedbut

have NOT been found

.... but in ALL experiments: distortion <10-4

9M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

TN= 24 K q=(0 ½ 0)

GdCuSn

10M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

TN= 22.7 K

<TR1=21.2K M||[001]<TR2=10.8K M||[110]

GdAu2

TN= 50 K

GdAg2

q=(0.362 0 1)

11M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

Gd3Rh TN=112 K

Large magnetostrictive effects on lattice constants – but NO distortion

Gd3NiTN=100 K

12M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

Spontaneous Magnetoelastic Effects in Gd Compounds A. Lindbaum, M. Rotter Handbook of Magnetic Materials Vol 14 (Buschow, Elsivier,NL)

Volume Magnetostriction

13M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

Spontaneous Magnetoelastic Effects in Gd Compounds A. Lindbaum, M. Rotter Handbook of Magnetic Materials Vol 14 (Buschow, Elsivier,NL)

Anisotropic Spontaneous Magnetostriction

FerromagnetAntiferromagnetε

TC(N)[K]

cbas V

dV

s

ds

,,

|3

|

14M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

TN= 20 K: M||[010] <TR= 14 K: M||[0yz] q = (0.55 0 0)

small magnetostriction, therefore cap.-dilatometry ....

GdNi2B2C

?

15M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

Thermal Expansion

5 10 15 20 25

0T

2T||a

TN

1.5T

0.75T

T (K)

Forced Magnetostriction

Orthorh.distortion !

10-4

a/a

TN= 20 K: M||[010] <TR= 14 K: M||[0yz] q = (0.55 0 0)

GdNi2B2C

16M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

At H=0: Domains ?

distortion =3x10-4 would lead to FWHM (204)+ 0.1° FWHM (211)+ 0.05°

at H=0 no distortioncan be found

GdNi2B2C

Powder Xray Diffraction

.... FWHM determined by fitting

?

17M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

McPhase - the World of Rare Earth MagnetismMcPhase is a program package for the calculation of

magnetic properties of rare earth based systems.          Magnetization                       Magnetic Phasediagrams

    Magnetic Structures            Elastic/Inelastic/Diffuse                                               Neutron Scattering

                                             Cross Section

www.mcphase.de

18M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

iiBJ

ijji

ijjimag

g

ijJ

ijJH

CD

HJ

JJ

JJ

)(2

1

),(2

1

The magnetic Hamiltonian

Isotropic exchange (RKKY,...)

Classical Dipole Interaction

Zeeman Energy

5

22

||

||))((3)()(

ji

jijijiBJ

RRRRgijJ

CD RR

RR

0 5 10 15 20 25 30

0,0

0,5

1,0

1,5 Experiment McPhase Calc. GdNi

2B

2C

c P/T

(J/m

olK

2 )

T(K)

Angle 2(°)

4 6 8 10 12 14 16 18 20

Inte

nsi

ty (

co

un

ts)

-2000

0

2000

4000 T=2.2K

nuc

(0.4

55 1

2)

(0.5

45 1

2)

(0.4

55 0

3)

(0.5

45 0

2)

(0.6

36 0

1)(0

.455

0 1

)(0

.545

0 0

)

magT=2 K0 2 4 6 8 10 12 14

0

1x10-4

2x10-4

3x10-4

0

-5

-10

-15

-20

-25

T = 2 K

a- b

0H||a (T)

Hmag

+McPhase

?

20M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

0 2 4 6 8 10 12 14

0

1x10-4

2x10-4

3x10-4

0

-5

-10

-15

-20

-25

T = 2 K

a- b

0H||a (T)

Orthorhombic Distortion

Standard Model of RE Mag... McPhase Simulation

HH JJJJ

JJJJ

JJJJ

,)010(,)100(

)010()100(

)010()100(

~

))((

))((

TiiTiibbaa

iiiibbaa

iiiiibbaa

elmag

B

A

EHH

?

The Magnetoelastic Paradox for L=0

.... demonstrated at GdNi2B2C

Capacitance D

ilatometry

Exchange Striction Model

21M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

• Transmutation of Gd

New Methods

Neutron Scattering

• Imaging of AFM domains with XRMS

GdNi2Ge2 ab-plane T = 17 K

Mom

ent d

irect

ion

200 µm

• Anisotropy Measurements by ESR

More Experiments• Powder X-ray Diffraction• Magnetic Neutron / X-ray

Scattering• Dilatometry in high

Fields

ToDo

More Theory• Apply Standard model

of RE Magnetism• Ab initio Calculation on

MEP

Anharmonicity of lattice dynamics

+ Small contribution of band electrons

anharmonic Potential

Harmonic potential

with Debye function

)/(22

1 TTDKTK Dphonel

z

xe

dxx

zzD

0

3

3 1

3)(

Normal thermal Expansion

23M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

H <0

Crystal Field

e-

+

+

Exchange - Striction

H

H>0

Forced Magnetostriction

L0 L=0, L0

Gd3+, S=7/2, L=0

24M.Rotter „The Magnetoelastic Paradox“ Planneralm 2006

Theory of Magnetostriction

lmi

iml

mlcf OBH

,

)()( J ij

jiex ijJH JJ),(2

1

Crystal field Exchange

k

T k i i

k i i JH J J,

) , (

lm

Tml

ml B

H J O, ) (

+

...)0()0()(

excf HH

excfel HHEH

cEel 2

1with

}{ / TkH BeTrZ ZTkF B ln 0

F