Model of magnetostrictionModel of magnetostriction

Magnetoelastic behavior of rare earth based intermetallics in high magnetic fields up to 33 T

M. Doerra, M. Rotterb , J. Brooksc,d, E. Jobiliongd, A. Lindbaumb, R. Vasicd, and M. Loewenhaupta

a Institute of Solid State Physics (IFP), TU Dresden, D-01062 Dresden, GERMANYb Institute of Physical Chemistry, University Vienna, Währingerstr. 42, A-1090 Vienna, AUSTRIA

c Department of Physics, Florida State University, Tallahassee, FL 32306-5350, USA d National High Magnetic Field Laboratory (NHMFL), Tallahassee, FL 32310-3704, USA

• Magnetostriction measurements are a powefull tool to study the magnetoelastic interactions and magnetic phase transitions.

• The magnetoelastic behavior can be calculated using a theoretical model which takes into account the crystal field striction as well as the exchange striction.

• Magnetostrictive measurements in resistive. water cooled high field magnets give good results. The resolution is still limited to 10-6 by mechanical vibrations.

Summary Summary

We acknowledge support by the Austrian Science Foundation (FWF) within the projects P16957 and P17226 and by the Deutsche Forschungsgemeinschaft (DFG) within the Sonderforschungsbereich 463. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by NSF Cooperative Agreement No. DMR-0084173, by the State of Florida, and by the DOE.

MagnetostrictionMagnetostrictionin high magnetic fieldsin high magnetic fields

The capacitive miniature-dilatometer.... measures thermal expansion at H=const. and

magnetostriction at T=const. with a resolution of 10-7 (in supercond. magnets)

....uses a tilted plate capacitor made from Ag

....has small dimensions: diameter d=22mm, height h=40mm

[1] M.Rotter et al., Rev.Sci.Instrum. 69 (1998) 2742.

MagnetsThe dilatometer was successfully used in ....... a superconducting 17 T-magnet (Oxford Instruments)

with a 4He-gas flow cryostat or a 3He insert (T = 0.3...300 K).

....water-cooled resistive magnets with 4He bath cryostats

Rare earth intermetallicsRare earth intermetallics ... R ... RCuCu22

Sample stick with the capacitive miniature dilatometer (Ag-cell, right)(installation at NHMFL)

33T-BITTER-magnetNHMFL Tallahassee

Magnetostriction Phase diagram (easy direction)

Miniature dilatometer [1](a,p....shielding electrodes, b,o....capacitor plates, c...screen, d...distance piece,e...sample, f...sapphire rings, q,r....holder)

Experimental methods

• X-ray or neutron diffraction (spontaneous effects, H=const., sensitivity 10-5)

• Extensometers (using strain gauges, spontaneous and field induced effects, successfully tested in pused fields, sensitivityf 10-6)

• Interferometry (spontaneous effects H=0, sensitivity 10-7)

• Capacitive dilatometry (spontaneous and field induced effects, sensitivity 10-9 - but practically only 10-7)

The RCu2 compounds magnetostriction result from ...

the single ion crystal field (CEF) contribution and

the two ion exchange interaction.

The mean field – Monte Carlo simulation program McPhase (www.mcphase.de) allows to model the magnetostriction.

The elastic constants – important for applications - can be calculated.

[2] M.Rotter, M. Doerr, M. Loewenhaupt, P. Svoboda: J. Appl. Phys. 91 (2002) 8885.

[3] M. Doerr, A. Lindbaum, M. Rotter: Adv. Phys. 54 (2005) 1.

23T-BITTER-magnetGHMFL Grenoble

Sample stick with the capacitive miniature dilatometer (Ag-cell, right)(installation at GHMFL)

4f

R = Ce

Pr

Nd

Pm

Sm

Eu

Gd

Tb

Dy

Ho

Er

Tm

Yb

0 1 2 3 4-4.0x10-4

-3.0x10-4

-2.0x10-4

-1.0x10-4

0.0

1.0x10-4

b

NdCu2 H || b T = 2 K

i

0H (T)

0 5 10 15 20 25 30-3.0x10-3

-2.0x10-3

-1.0x10-3

0.0

1.0x10-3

2.0x10-3

3.0x10-3

4.0x10-3

SmCu2 H || b T = 4 K

c

b

a

i

0H (T)

0 5 10 15 20 25 300

5

10

15

20

25

30

35

40

NHMFLF

LT

AF2

AF3AF1 0H (

T)

T (K)

0 5 10 15 20 25 300

1

2

3

4

H || a

F1

AF1 AF2

FM

Magnetization Magnetostriction

0H (

T)

T (K)

0 10 20 30 40 500

1

2

3

4

5

6

7

8

9

10

H || abc

F´ c

c

c

b

b

a

a

a Magnetization Th. Expansion

0H (

T)

T (K)

0 2 4 6 80

2

4

H || b

F2

AF2 AF3

FM

F1

AF1

0H (

T)

T (K)

Noise levels in BITTER-magnets

Technical precautions to avoid electrical or mechanical noise

Noise level in l/l before the

improvement

Electrical isolation between dilatometer and cryostat / magnet / pump

5x10-5

Ground free power lines 1x10-5

Short and loop free wiring in the dilatometer cell 3x10-6

Damping the dilatometer mechanically to avoid vibrations caused by strong water flow

1x10-6

Possible resolution in BITTER-magnets <1x10-6

Magnetostriction measurements on RCu2 were performed up to the highest available steady magnetic fields. They show the transitions between different magnetically ordered phases clearly. Together with magnetization measurements the allow to

construct the magnetic phase diagrams. Especially, the influence of magnetic transitions on the crystalline structures via magnetoelastic interaction can be studied.

It may result in lattice distortions, giant magnetostrictive effects = GMS [3] and symmetry changes or low dimensional lattice expansion.

i

HTiHTiCF JOBJOA

N

,

22,

02

1

HTaii

HTcbaiiHTiii

EX

JJM

JJLJJKN

,

,2/2/2/,

1

0 1 2 3 4

0.0

5.0x10-4

1.0x10-3

1.5x10-3

2.0x10-3

a

DyCu2 H || a T = 2 K

i

0H (T)

0 1 2 3 4 5 6 7 8 9 10-1.0x10-3

0.0

1.0x10-3

2.0x10-3

3.0x10-3

4.0x10-3

5.0x10-3

6.0x10-3

0 5 10 15 20 25 300.0

1.0x10-3

2.0x10-3

3.0x10-3

4.0x10-3

5.0x10-3

6.0x10-3

a

GdCu2 H || a T = 4 K

i

0H (T)

NHMFL