Departament d’Estructura i Constituents de la Matèria Universitat de Barcelona

Departament d’Estructura i Constituents de la Matèria Universitat de Barcelona

Structure and magnetism in the premartensitic and martensitic states

in Heusler shape-memory alloys

Fundamentals of the Magnetic Shape-Memory Effect: Material properties and atomistic simulations, Ringberg Castle (Germany), February 14-16, 2007

Antoni Planes

Collaborators: E. Bonnot, T. Castán, Ll. Mañosa, X. Moya, M. Porta, E. Vives (UB), A. Saxena, T. Lookman, J. Lashley (Los Alamos), M. Acet, T. Krenke, E.F. Wassermann, S. Aksoy (Duisburg), M. Morin (INSA). T.A. Lograsso, J.L. Zarestky (Ames)

Introduction

Magnetic shape-memory effect refers to the change of shape (deformation) of a magnetic material undergoing a martensitic transition caused by either:

inducing the transition or

rearranging the martensitic variantsby means of an applied magnetic field

Prototypical shape-memory alloy: Ni-Mn-Ga

Maximum induced deformation ~ 10% with an applied field ~ 10 kOe two orders of magnitude larger than in magnetosrictive Terfenol-D (Tb0.27Dy0.73Fe2)


Shape-memory properties


Superelasticity Shape-memory effect

Ela

stic

Sup

erel

astic

Ela

stic

Magnetic shape-memory properties


Magnetic superelasticity Magnetic shape-memory effect

H

H

Ela

stic

Sup

erel

astic

Ela

stic

La2-xSrxCuO4 Lavrov et al., Nature, 418, 385 (2002) (antiferro)

Magnetic shape-memory materialsHEUSLER

IRON-BASED

OTHER

Ni-Mn-X Ullakko et al., APL, 69, 1966 (1996) (Ga)

(X= Ga, Al, In, Sn, …) Fujita et al., APL, 77, 3054 (2000) (Al)

Sutou et al., APL, 85, 4358 (2004); Krenke et al., PRB, 72, 014412 (2005); 73, 174413 (2006) (In,Sn)

Co-Ni-Al Oikawa et al., APL, 79, 2472 (2001)

Ni-Fe-Ga Morito et al., APL, 81, 5201 (2002); 83, 4993 (2003)

Fe-Pd James & Wuttig, PMA, 77, 1273 (1998)

Fe-Pt Kakeshita et al., APL, 77, 1502, (2000)

Co-Ni Zhou et al., APL, 82, 760 (2003)


InterplayStructural degrees of freedom

Magnetic degrees of freedom

Unique pretransitional behaviour

Mesoscopic scaleElastic

domains(variants)

Magnetic domains

Microscopic scale

(spin-phonon interplay)

Magnetic shape-memory Magnetic superelasticity Magnetocaloric effect

Magnetostructural interplay


Outline

Phase diagram and general properties Pretransitional effects: Phonon anomalies and the intermediate transition

Conclusions


Magnetic properties

Heusler, L21 (Fm3m)

Ni

Mn

Ga

Ni2MnGa

• Ferromagnetic order (Tc~ 370 K)

• Total magnetic moment: µtotal 4.1 µB per f.u.

Non-stoichiometric Ni2Mn1+xGa1-x (µNi 0.3 µB per f.u.)• Weak magnetic anisotropy

BNitotal 3.5μx12μμ


Phase diagram

Ni2+xMn1-xGaIntermediate

Martensite

L21-ferro

L21-para

From: Vasil’ev et al., Physics-Uspekhi, 46, 559 (2003)

Phase diagram at constant Ga concentration


Phase diagram

7.0 7.2 7.4 7.6 7.8 8.0 8.20

300

600

900

1200

1500

L21

ferro

T (K

)

e/a

B2

martensitepara

L

L21

para

martensiteferrointermediate

ferro

Relative phase stability controlled (to a large extent) by the average number of valence electrons per atom, e/a


Other effects

From: Khan et al., J. Phys. Condens. Matter, 16, 5259 (2004)


Cubic

Martensitic transition mechanism

Transformation mechanism: Shear + Shuffle on {110} planes along <1-10> directions


10M ([32]2)

14M ([52])

Martensitic structure

From: Lanska et al., J. Appl. Phys., 95, 8074 (2004)

7,0 7,2 7,4 7,6 7,8 8,0 8,20

300

600

900

1200

1500

L 21ferro

T (K

)

e/ a

B 2

martensitepara

L

L 21para

martensiteferro

intermediate

ferro

7,5 7,6 7,7 7,8

200

300

400

500

T (K

)e/ a


By increasing e/a the following structures occur:

10M 14M NM (L10 )

Entropy change


Ni-Mn-SnNi-Mn-InNi-Mn-Ga

paraferro paraferr

o

paraferro

Magnetic properties

e/a

From: Enkovaara et al., PRB, 67, 212405 (2003).

From: Albertini et al., APL, 81, 4032 (2002).


Ni49.5Mn24.5Ga25.1Ni56.2Mn18.2Ga25.5

Ni50Mn35Sn15 Ni50Mn34In16

ΔSΔM

dHdTM

0ΔS independent of H

Effect of a magnetic field


0 1 2 3 4 5-60

-40

-20

0

20

Ni2MnGa

Ni53.5

Mn19.5

Ga27

Ni50

Mn35

Sn15

Ni50.3

Mn33.8

In15.9

T (K

)

0H (T)

Precursors in phase transitions• Nanoscale structures which occur above phase transitions. They announce that a system is preparing for the phase transition before it actually takes place.

• Often observed in ferroic and multiferroic materials.

• Revealed by high-resolution imaging techniques well above the (expected) phase transition.

• Detected as anomalies in diffraction experiments (intense diffuse scattering) and in the response to certain exitations.

• Not expected in systems undergoing first-order transions (which are expected to occur abruptly).

• In martensites, related to low restoring forces in specific lattice directions (transition path).


Structural precursors in Ni-Al (similar phenomenology in Fe-Pd, ….., shape-memory alloys)

TEM Neutron Diffraction

From, S.M. Shapiro et al., PRL, 57, 3199 (1986)

Cross-hatched striations (tweed) parallel to {110} planes observed above TM.

(020

)

Example: tweed

(60 nm)


Phonons in Ni-Mn-Ga

L21 5M L21 7M

Acoustic-phonon dispersion curves for the cubic phase of Ni2MnGa. From: Zheludev et al., 54, 15045 (1996).

TA2 branch at selected temperatures.

The position of the dip depends on the selected martensite structure.

From: Mañosa et al. PRB, 64, 024305 (2001)


• The softening is enhanced at the Curie point.

• For systems transforming to the 5M structure, the softening is nearly complete at TI > TM. Upon further cooling the frequency increases.

• At TI the system undergoes the intermediate transition.

TML21 → 5M (low e/a)

TI (higher e/a)

Ni-Al (from Shapiro et al., PRL, 62, 1298 (1989); PRB, 44, 9301 (1991)

Slopes in the two phases

Phonon softening


Elastic constants

L21 5M L21 7M


Diffraction experiments(100)

J. Pons, private communication

T > TI T < TI (111)T < TI

TEM

Neutrons

From A. Zheludev et al., PRB, 54, 15045 (1996)

Elastic scattering along the (ξξ0) direction The transition at TI is associated with the lock-in of the pseudoperiodic tweed phase into a commensurate phase due to the freezing of the anomalous phonon.


Modulation of {110} planes with wave number 1/3 along <1-10> direction.

Preserve cubic symmetry.

Magnetic and thermal anomalies

Further results which prove the existance of the premartensitic transition.

A.c. magnetic susceptibility Calorimetry

Latent heat= 9 J/mol(Martensitic transition:~ 100 J/mol)A. Planes et al., PRL 79, 3926 (1997)

TI

200 220 240 260 280

-80

-70

-60

-50

Latent heat

[Differential] heat capacity (MDSC)

DSC thermal curve

dQ/d

T (m

J/g K

)

T (K)

The intermediate transition is first-order


Effect of external fields

210 220 230 240 250 260

-0.16

-0.12

-0.08

-0.04

0.00

C

44/C

44

T (K) 0 2 4 6 8 10

230

232

234

236

238

240

(b)

T I (K

)

Stress (MPa)0 1 2 3 4 5

226

228

230

232

234

236

(a)

T I (K

)

Stress (MPa)

Elastic constantTransition temperatures:

STR

ES

SM

AG

NE

TIC

FIE

LD

From: W.H. Wang et al., J. Phys. Condens. Matter, 13, 2607 (2001)

From: Gozàlez-Comas et al., PRB , 60, 7085 (1999)

[001] direction

[1-10] direction

[1-10] direction

0 MPa1 MPa

4.5 MPa

TI ~ M2


Comparison with non-magnetic SMA

High temperature phase (cubic)

Ttw ?

Tweed

TI

Modulated (or intermediate) phase

TM

Martensite

Ni-Mn-Ga Ni-Al


Amplitude of the relevant phonon mode

Order parameters:

Magnetization M

Free energy:

Expansions:

Landau model

ηMFF(M)F(ηF )

...BM41AM

21F(M) 42

22ηM Mη

21F 1χ

6422* cη61bη

41ηωm

21)F(


Minimization with respect to M gives the following effective free-energy:

where:

M0 is the magnetization of the high temperature phase ( = 0):

20

6422*eff AM

41ηc

61ηb

41ηωm

21F ~~~

ccAMbb

)T(TaMωmωm20

u20

2*2*

~

~

~~~

21

1

χ

χ

c

20

cc

TT for 0 M

TT for T)μ(TBA

Tc is the Curie temperature


Landau model

• If 12/B is large, can be negative, and a first-order transition is

possible. The transition temperature is:

• The temperature dependence of the anomalous phonon frequency:

1 > 0 softening is enhanced.

• Clausius-Clapeyron equation:

Results in agreement with the experiments if 1 > 0

b~

u

2

I Tca16

b3T ~~~

0BMaΔS

ΔMdHdT

0

I ~1χ


Landau model: results

0.5 1.0 1.5 2.0 2.5

200

240

280

320

360

400

TI

Tc

T (K

)

x (at. Fe %)

Ni50.85

Mn23.88-x

Ga25.27

Fex

Ms

When an intermediate transition occurs?


Results for Ni-Mn-Ga(Fe)

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

200

240

280

320

360

400

Ms

Tc

Ni51.7

Mn22.9

Ga25.23-x

Fex

T (K

)

x (at. Fe %)0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

80120160200240280320360400

TIMs

Tc

Ni52.21-x

Mn22.56

Ga25.23

Fex

T (K

)

x (at. Fe %)

120 160 200 240 280 320

0.0

0.4

0.8

1.2

(a.

u.)

T (K)

' ''

x=1.93

80 120 160 200 240

0.0

0.4

0.8

(a.

u.)

T (K)

' ''

x=3.91

270 300 330 360 390 420

-1000

0

1000

dQ/d

T (J

/K k

g)

T (K)

x=2.06 Tc

Ms

In Heusler alloys the relative phase stability is (to a large extent)

controlled by e/a.

Compared to other shape-memory alloys, Ni-Mn-Ga shows unique pretransitional behaviour which is a consequence of spin-phonon coupling.

Strong softening of the 1/3[110]TA2 phonon and large magnetisation is required for a first-order intermediate transition to occur.

The intermediate phase almost preserves cubic symmetry and results from the freezing of 1/3[110]TA2 phonon.


Conclusions

• Transition at zero-field: Formation of twin related variant.

• The magnetic easy axis changes from one twin to the other

Cubic → Martensite (twinned)

• Effect of a magnetic field

Twin related variants and magnetic stripe domains inside

From: Ge et al., JAP, 96, 2159 (2004).

Weak anisitropy Strong anisitropy

In systems with strong anisotropy and highly mobile boundaries, field induced rearrangement of martensitic variants is possible Magnetic Shape-Memory


Magnetic shape-memory effect

Field induced deformation in a Ni-Mn-Ga alloy

The residual deformation remaining when the field is removed can be removed by:

1. Heating up through the transition

2. Application of a magnetic field perpendicular to the original

3. Application of a stress that opposes the applied field

From: Likhachev et al., Proc SPIE, 4333, 197 (2001)


Example

0 1 2 3 4 5-60

-40

-20

0

20

Ni2MnGa

Ni50.3

Mn33.8

In15.9

T (K

)0H (T)


Magnetic superelasticity

From: Krenke et al., PRB, (2007)

Magnetic superelasticity in Ni-Mn-In alloy

ΔSΔM

dHdTM

0

Adiabatic Temperature change, Tadi

Isothermal Entropy change, Siso

when a magnetic field H is applied/removed

H ΔM

ΔM(H)dHΔS(H)e

H

e

H

H TTdH

TM

00

1It is given by:

∆Te is the range over which the transition extends.


Magnetocaloric effect

Controlled by the change of magnetization at the transition

ΔM = MM – MP > 0, Conventional magnetocaloric effect

ΔM = MM – MP < 0, Inverse magnetocaloric effect

170 175 180 1850123456

M (1

03 e

mu/

mol

)

T (K)

0 100 200 300 400 500 700 1 kOe 2 kOe 4 kOe 6 kOe 10 kOe 20 kOe 40 kOe

0 10 20 30 40

-1.5

-1.0

-0.5

0.0

M (1

03 e

mu/

mol

)

H (kOe)

Ni49.5Mn25.4Ga25.1

∆M = MM - MP


Magnetocaloric effect in Ni2MnGa

0 10 20 30 40 500

0.1

<S

> (J

/K m

ol)

H (kOe)

170 175 180 185

0

0.2

0.4

0.6 H=10 kOe

T

S (J

/K m

ol)

T (K)

Inverse magnetocaloric effect

0 10 20 30 40

-1.5

-1.0

-0.5

0

¢M

(103 e

mu/

mol

)

H (kOe)

(a) (b) (c)Cubic Tetragonal


Physical picture

Historical

• Magnetostructural characterization, Ziebeck’s group [Philos.Mag. B, 49, 295 (1984)]

• Martensitic Transformation and Shape-Memory Properties (Martynov, Kokorin, …)

• Phonon anom. & Intermediate trans., Shapiro’s group PRB, 51, 11310 (1995)

• Magnetic Shape-Memory Effect, O´Handley’s group at MIT, APL, 69, 1966 (1996)

• Magnetoelastic coupling. Vordervisch, Trivisono, UB group (phonons/elas. cnts, 1997)

• Modelling: O’Handley (JAP, 1998), James & Wuttig (PMB, 1998), …..

• First.Principles Calculations: Helsinski group, Duisburg group, …

• Further developments, MIT group, Helsinki group, …..

• Development of other M-SMA: Ishida’s group, Kakeshita’s group, ….

• Magnetic superelasticity: Duisburg & Barcelona, PRB, 2007


Departament d’Estructura i Constituents de la Matèria Universitat de Barcelona

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