the magnetoelastic paradox m. rotter, a. barcza, ipc, universität wien, austria h. michor, tu-wien,...

The Magnetoelastic ParadoxM. 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

M. Zschintzsch, ISP TU-Dresden, Germany

B. Beuneu, LLB – Saclay, France

M el Massalami, UFRJ, Brazil

J. Prokleska, Charles University, Prague, CZ

A. Kreyssig, IOWA State University, Ames, US

2M.Rotter „The Magnetoelastic Paradox“ Lorena 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


Experimental Methods

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(patent submitted, optional use in PPMS, VTIs,...operated at 6 institutes in A, D, CZ, Brazil, US)

How to measure Magnetostriction ?


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


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


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 !


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


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


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


TN= 24 K q=(0 ½ 0)

GdCuSn


TN= 22.7 K

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

GdAu2

TN= 50 K

GdAg2

q=(0.362 0 1)


Gd3Rh TN=112 K

Large magnetostrictive effects on lattice constants – but NO distortion

Gd3NiTN=100 K


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

Volume Magnetostriction


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

|


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

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

GdNi2B2C

?


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


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(magnetoelasticparadox)

GdNi2B2C

Powder Xray Diffraction

.... FWHM determined by fitting

?

tan

d

d


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


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

?


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

Rotter et al. EPL 75 (2006) 160

Capacitance D

ilatometry

Exchange Striction Model

Status of Research on Magnetostriction in Gd based Antiferromagnets. Systems with a symmetry breaking magnetic propagation vector and large spontaneous magnetostriction demonstrate the existence of the magnetoelastic paradox and are marked by "MEP".

Symmetry Magnetic Anisotropic/ Single Forced / Propagation isotropic(dV/V) Crystal Magneto-Neel Spontaneous available -strictionTemp.(K) Magnetostriction (10-3)

GdIn3 cub./43 [12] (1/2 1/2 0) [13] MEP! 0.0/~-0.3 [14] yesGdCu2In cub./10 (1/3 1 0) [R18] 0.0/-0.1 [15]GdPd2In cub./10 [16] 0.0/0.0 [15]GdAs cub./25 (3/2 3/2 3/2) [17, 18, 19] [17]no MEP ?GdP cub./15 (3/2 3/2 3/2) [17] [17]GdSb cub./28 (3/2 3/2 3/2) [20] ? [21, 22]no MEP? Yes work in progressGdSe cub./60 (3/2 3/2 3/2) [20]GdBi cub./32 (3/2 3/2 3/2) [20] [21]no MEP ?GdS cub./50 (3/2 3/2 3/2) [20]EuTe cub./9.8 (3/2 3/2 3/2) [23] [23]GdTe cub./80 (3/2 3/2 3/2) [20]GdAg cub./133 (1/2 1/2 0) [24]GdBe13 cub./27 (0 0 1/3) [25]Gd2Ti2O7 cub./1 (1/2 1/2 1/2) [26] yesGdB6 cub./16 (1/4 1/4 1/2) [27] yesGd2CuGe3 hex./12 [28]GdGa2 hex./23.7 (0.39 0.39 0) [29]GdCu5 hex./26 (1/3 1/3 0.22) [29]Gd5Ge3 hex./79 [30] work in progress yes work in progressGd7Rh3 hex./140 [31, 32]Gd2PdSi3 hex./21 [33] yesGdCuSn hex./24 (0 1/2 0) [34] MEP! 1.9/-0.5 [35]GdAuSn hex./35 [34] (0 1/2 0) [36]GdAuGe hex./16.9 [37]GdAgGe hex./14.8 [38]GdAuIn hex./12.2 [38]GdAuMg hex./81 [39]GdAuCd hex./66.5 [40] (1/2 0 1/2) [40]GdAg2 tetr./23 (1/4 2/3 0) [R12] MEP! 1.2/0.0 [R19]Gd2Ni2-xIn tetr./20 [R19] 0.8/0.0 [R19]


Gd2Ni2Cd tetr./65 [41]Gd2Ni2Mg tetr./49 [42]Gd2Pd2In tetr./21 [43]GdNi2B2C tetr./20 (0.55 0 0) [44] MEP! 0.1/0.0 [R19, R20] yes [R4]GdAu2 tetr./50 (5/6 1/2 1/2) [R12] 0.0/0.0 [R19]GdB4 tetr./42 (1 0 0) [45]GdRu2Si2 tetr./47 [46] work in progress work in progress yes work in progressGdRu2Ge2 tetr./33 [46] work in progress work in progressGdNi2Si2 tetr./14.5 (0.21 0 0.9) [47]GdNi2Sn2 tetr./7 [48]GdPt2Ge2 tetr./7 [48]GdCo2Si2 tetr./45 [48]GdAu2Si2 tetr./12 (1/2 0 1/2) [R12]GdPd2Ge2 tetr./18 [48]GdPd2Si2 tetr./16.5 [49]GdIr2Si2 tetr./82.4 [49]GdPt2Si2 tetr./9.3 [49] (1/3 1/3 1/2) [50]GdOs2Si2 tetr./28.5 [49]GdAg2Si2 tetr./10 [48]GdFe2Ge2 tetr./9.3 [51, 52]GdCu2Ge2 tetr./15 [51]GdRh2Ge2 tetr./95.4 [51]GdRh2Si2 tetr./106 [49]GdCu2Si2 tetr./12.5 (1/2 0 1/2) [47]GdPt3Si tetr./7.5 [53] work in progressGdCu(FeB) orth./45 (0 1/4 1/4) [54] 19/-2 [54]Gd3Rh orth./112 [55] MEP ? 6.4/2.1 [56]Gd3Ni orth./100 [57] MEP ? 4.5/2.9 [56]Gd3Co orth./130 [58, 59]GdSi2 orth.(<818K)/? [60]GdSi orth./55 [61] work in progress work in progress yes work in progressGdCu6 orth./16 [62] work in progressGdAlO3 orth./3.9 [63]GdBa2Cu3O7 orth./2.2 (1/2 1/2 1/2) [64] [65]GdPd2Si orth./13 [66]


The following compounds are not expected to show a change in lattice symmetry at the transition from the paramagnet to the antiferromagnet, because the propagation vector does not break the symmetry of the lattice and there is only one atom in the primitive crystallographic unit cell. Therefore they cannot exhibit themagnetoelastic paradox.


GdNi2Ge2 tetr./27 (0 0 0.79) [67]GdCo2Ge2 tetr./37.5 [51] (0 0 0.93) [68]

In the following compounds the propagation does not break the crystal symmetry and there are more than one atom in the primitive crystallographic unit cell. In this case it depends on the relative orientiation of the moments in the unit cell, whether a symmetry breaking distortion is predicted by the exchange striction model or not. Therefore these compounds can in principle exhibit the magnetoelastic paradox although the propagation does not break the crystal symmetry of the lattice.


Gd2Sn2O7 cub./1 (0 0 0) [69] yesGd2In hex./100 (0 0 1/6) [70] 0.0/0.0 [R19]Gd2CuO4 tetr./6.4 (0 0 0) [71]GdCu2 orth./42 (1/3 0 0) [R21] 4.6/0.6 [72] yes [R22]Gd5Ge4 orth./130 [11] (0 0 0) [73] ?/<0.1 [74] yes [74]GdNi0:4Cu0:6 orth./63 (0 0 1/4) [75] 0.0/0.8 [76]Gd2S3 orth./10 [77] (0 0 0) [78] 0.0/0.0 [79] yes [79]GdNiSn orth./11 [80] (0 0 0) [81] yes


THE MAGNETOELASTIC PARADOX

Antiferromagnets with L=0 below TN:

Symmetry breaking distortions are expectedbut

have NOT been found

• GdNi2B2C: large distortion at small fields - is this common to all Gd AFM ? ... implication on magnetostrictive technology ?

• Magnetoelastic Coupling = long wave length limit of electron phonon interaction ... relevance for superconductivity ?

• Note: MnO shows trigonal spontaneous distortion at TN

Summary and outlook


New Methods• Imaging of AFM domains with XRMS

GdNi2Ge2 ab-plane T = 17 K

Mom

ent d

irect

ion

200 µm

• Anisotropy Measurements by ESR•Neutron Scattering on Transparent Gd Compounds

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

WorkshopMagnetostrictive Materials and Magnetic Refrigeration (MMMR)

13.-15. August 2007,Vienna, Austria

http://www.univie.ac.at/MMMR/


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



TN=47 K

GdRu2Si2

H(T)0 2 4 6 8 10 12 14 16

L/L

B||a da/aB||a' da/a

2x10-5

GdRuSi

GdRu2Si2

TN=47 Kq=(3/4 0 0)

35.7 35.8 35.9

0

500

1000

1500

2000

2500

3000

3500

4000

(1 1 2) 60K 20K

Inte

nsi

ty (

cou

nts

)

2 (deg)

Note: ε=4.10-5 ... ΔFWHM=0.0015 deg


2 T

heta

FW

HM

(°)

0,09

0,10

0,11

0,12

a (n

m)

0,4154

0,4156

0,4158

0,4160

0,4162

c (n

m)

0,9604

0,9608

0,9612

0,9616

0,9620V

(nm

3)

0,1658

0,1660

0,1662

0,1664

GdRu2Si2

T(K)

0 50 100 150 200 250 300

c/a

2,310

2,311

2,312

2,313

2,314

TN

(112)


GdSbStructure NaCl typeType II AFM order q=(111)TN=24.4 K

http://www.ill.fr/dif/3D-crystals/images/mnom.gif

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


H <0

Crystal Field

e-

+

+

Exchange - Striction

H

H>0

Forced Magnetostriction

L0 L=0, L0

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


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


TN= 42 K M [010]TR= 10 K q = (2/3 1 0) Magnetic Structure from

Neutron Scattering

GdCu2

kT i i

k i i JH J J, 1

) , (

Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281

0 -7-7-7-7+7

the magnetoelastic paradox m. rotter, a. barcza, ipc, universität wien, austria h. michor, tu-wien,...

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