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Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Departament d’Estructura i Constituents de la Matèria Universitat de Barcelona
Magnetocaloric and shape-memory properties in
ferromagnetic Heusler alloysAntoni Planes
Collaborators: Ll. Mañosa, X. Moya * (ECM, U. Barcelona)X. Batlle, A. Labarta, F. Casanova ** (FF, U. Barcelona) M. Acet, S. Aksoy, T. Krenke ***, E. Wasserman (U. Duisburg-Essen)
Present address: * Cambridge University** Univ. San Diego *** ThyssenKrupp
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Thermodynamics
.......ΩσdεΩHdMµTdSdU +++= 0
Elastocaloricproperties
S
T
HσMε
Magnetocaloricproperties
Shape-memory properties
),(
),(
MS
SMM
εεε
==
Coupling
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Outline
• Shape-memory properties
• Magnetic shape-memory and magnetostructural coupling
• First order transitions and magnetocaloric effect
• Results: Ni-Mn-Ga
• Other Heuler alloys
• Conclusions
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Shape-memory propertiesShape-memory properties refers to the ability of a material undergoing a martensitic transition to recover from severe deformations:
• in the martensitic phase upon heating above the transition: Shape-memory effect
• upon loading and unloading a large strain associated with the stress-induced martensitic transformation: Superelasticity
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Magnetic shape-memory properties
Magnetic shape-memory: Field induced deformation caused by rearranging the martensitic variants.
Requires:
Large magnetic anisotropy
+ High twin boundary mobility
Magnetic superelasticity: Field induced deformation caused by inducing the martensitic transition.
Requires:
Significant shift of the transitionwith magnetic field.
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Coupling
Structure Magnetism
Microscopic scale Mesoscopic scale
Interplay
Controlled by the change of J
Controlled by the change of A
Magnetic superelasticity Magnetic shape-memory
Magnetocaloric effect
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Magnetocaloric effect: General features
Magnetic system (T, H independent variables):
...dHH
SdT
T
SdS
T,...H,...
+
∂∂+
∂∂=
When magnetic field H is applied/removed:
Adiabatic Temperature change:
Isothermal Entropy change:
∫
∂∂−=
f
i
H
H THadi dH
H
S
C
T∆T
∫
∂∂=
f
i
H
H Tiso dH
H
S∆S
isoH
adi ∆SC
T∆T −≈
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
∫
∂∂=
∂∂=
∂∂ ⇒
f
i
H
H Hiso
HT
dHT
M∆S
T
M
H
SMaxwell relation
Magnetocaloric effect: Determination• Directly from calorimetric measurements
• Indirectly from magnetization curves
• ⇒ ∆Siso< 0 when Hf – Hi > 0 ⇒ Cooling by adiabatic demagnetization
• ⇒ ∆Siso< 0 when Hf – Hi > 0 ⇒ Heating by adiabatic demagnetization
0<
∂∂
HT
M
0>
∂∂
HT
M
MCE is expected to be large in regions where M shows a fast change with T ⇒vicinity of phase transitions
Considerations
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
∆Siso
M
TTt(0) Tt(H)
T
( )[ ]HTT∆M hM t−=
h(x) is the Heaviside function
[ ][ ]
∉
∈−=
∂∂= ∫
(H)),T(TT for
(H)),T(T for Tα
∆M
dHT
M∆S
tt
tt
H
iso
00
0
0
For ∆M > 0 (dTt /dH > 0) ⇒ ∆Siso < 0 (for 0 → H)
where α = |dTt /dH|
Example: Ideal first-order phase transition
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
( )[ ]HTT∆M hM t−=
h(x) is the Heaviside function
For ∆M > 0 (dTt /dH > 0) ⇒ ∆Siso < 0 (for 0 → H)
where α = |dTt /dH|
Example: Ideal first-order phase transition
M
TTt(H)∆Siso
T
Tt(0)
[ ][ ]
∉
∈−=
∂∂= ∫
(H)),T(TT for
(H)),T(T for Tα
∆M
dHT
M∆S
tt
tt
H
iso
00
0
0
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
∆M
T
Real first-order phase transition
H = 0
H ≠ 0 • The transition spreads over a range of temperatures
• It displays hysteresis
∫∆
∆∆
=∆T
dTHTMHT
HS ),()(
)( 0µ
∫∆
∆∆
−=∆Tt
t dTHTMHS
HT ),()(
)( 0µ
∆T(H)
)()(
)(
)(
HT
HT
HS
HSt
t ∆∆−=
∆∆
⇒
∆Tt(H)
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Materials
Ni2MnGa
Mn
Ni50Mn50-xSnx
Ni50Mn50-xInx
Ni50Mn50-xSbx
Ni50Mn50-xAl x
Prototypical Heusler SMA: Ni2MnGa Other Heusler alloys:
Ni
Ga
Ni-Mn-Sn Ni-Mn-In Ni-Mn-Ga
Cubic 10 M or 5 M (other 7 M, …)
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Effect of a magnetic field on the transition
200 250 300
-0,6
-0,4
-0,2
0
240 270 300 330
100 200 300
50 100 150 200-0,6
-0,4
-0,2
0
∆l/l
(%
)
N i50M n27Ga23
µ0H (T )
0 2 5
(a)
(d)
T (K )
N i50.3M n35.9Sb13.8
(b)
Ni50M n34In16
(c)
Ni49.8M n34.7Sn15.5
∆l/l
(%
)
T (K )
Ni-Mn-Ga:• Negligeablelength change at zero field• Negligible shift of the transition• Strong effect of the field on ∆l/l (< 0, easyaxis: short axis)
Black: H = 0 Blue: H = 2 T Red: H = 5 T
Ni-Mn-Sn :• Similar to Ni-Mn-In (smaller changes)
Ni-Mn-In :• Significant shift of the transition with the field• Noticeable length change at zero field • ∆l/l > 0 (easy axis: long axis)
Ni-Mn-In /Sn good candidates to display (reverse) magnetic superelasticity
Ni-Mn-Ga good candidate for magnetic shape-memory effect
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
0 10 20 30 40 500
0.1
<∆S
> (
J/K
mol
)
H (kOe)
170 175 180 185
0
0.2
0.4
0.6 100 Oe 500 Oe 1 kOe 2 kOe 4 kOe 10 kOe 20 kOe 30 kOe 40 kOe
∆S (
J/m
ol K
)
T (K)
Ni49.5Mn25.4Ga25.1
0 5 10 15 200
1
2
3
4
5
6
T=160K T=170K T=174K T=176K T=177K T=177.5K T=178K T=178.5K T=179K T=179.5K T=180K T=182K T=184K T=186K T=190K
M (
emu/
mol
)
H (kOe)
∫
∂∂=
H
0 H
dHTM
∆S
Magnetocaloric effect: Ni2MnGa
170 175 180 185
0
0.2
0.4
0.6 H=10 kOe
∆T
∆S (
J/K
mol
)
T (K)
Inversemagnetocaloriceffect!
Marcos et al., Phys. Rev. B,66, 224413 (2002)
∫=∆T
H)dH∆S(T,∆T1
∆S
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
A region exists where (∂M/∂T)H >0
Cubic Tetragonal
170 175 180 185
0
1
2
3
4
5
6
M (
103 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
∆M ~ 0
∆M < 0
∆M > 0
Explanation
0 1 0 2 0 3 0 4 0
-1 .5
-1 .0
-0 .5
0
¢M
(10
3 em
u/m
ol)
H ( k O e)
(a) (b) (c)
∆M
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Contributions
Marcos et al., Phys. Rev. B, 68, 094401 (2003)
Low and intermediate fields: thedominant contribution is related tothe magnetostructural interplayat mesoscale (magneticanisotropy). Gives rise to aninverse magnetocaloric effect .
High fields: the dominantcontribution is related to themicroscopic magnetostructuralcoupling (change of TM with anapplied field). Gives rise to a conventional magnetocaloriceffect.
0 10 20 30 40-0.1
0
0.1
0.2
⟨¢S⟩
(J/K
mol
)
H (kOe)
∆
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
e/a
(K)
7.4 7.6 7.80
200
400
600
800
TC
L21
ferro-
T
TM
M ferro-
L21
para-
Effect of compositionMarcos et al., Phys. Rev. B, 68, 094401 (2003)
Tc-TM = 0 K
Tc-TM = 26 KTc-TM = 51 KTc-TM = 150 K
Tc-TM ~ 201 K
TC−TM ~ 201 K
TC−TM = 150 K
TC−TM = 26 K
TC−TM ~ 0 K
TC−TM = 51 K
0 10 20 30 40 50-2.0
-1.5
-1.0
-0.5
0
0.5
1.0
1.5
∆M (
103 e
mu/
mol
)
H (kOe)
Alloy 1 Alloy 2 Alloy 3 Alloy 4 Alloy 5
0 1.0 2.0 3.0 4.0-4
-2
0
2
4
6
<∆S
> (
10-2
J/K
mol
)
H (kOe)
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Other Heusler shape-memory alloy
Ni49.5Mn24.5Ga25.1Ni56.2Mn18.2Ga25.5
Ni50Mn35Sn15 Ni50Mn34In16
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Results: Ni-Mn-SnKrenke et al., Nature Mater. 4, 450 (2005); Phys Rev. B, 72, 014412 (2005)
285 300 315 330
0
10
20
165 180 195
0
10
20
b)
T (K)
x = 0.13
Mf
Ms T A
C
Ms
a)
∆S
(J
kg-1 K
-1)
T (K)
1 2 3 4 5
x = 0.15µ
0 H (T)
Mf
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Results: Ni-Mn-InMoya et al., Phys. Rev. B, 75, 184412 (2007); Krenke et al., Phys. Rev. B, 73, 174413 (2006)
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Results: Ni-Mn-InMoya et al., Phys. Rev. B, 75, 184412 (2007); Krenke et al., Phys. Rev. B, 73, 174413 (2006)
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Comparison
0 10 20 30 40 50-0.4
-0.2
0
0.2
0.4
0.6
0.8
1.0
⟨∆S⟩/|
∆St|
Ni49.5
Mn25.4
Ga25.1
Ni56.2
Mn18.2
Ga25.6
Ni50
Mn35
Sn15
Ni50.3
Mn33.8
In15.9
H (kOe)
Ni49.5Mn24.5Ga25.1 Ni56.2Mn18.2Ga25.5
Ni50Mn35Sn15 Ni50Mn34In16
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
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)
µ0H (T)
Magnetocaloric effect vs. Clausius-Clapeyron
∆St independent of H
0 10 20 30 40 50-0.4
-0.2
0
0.2
0.4
0.6
0.8
1.0
⟨∆S⟩/|
∆St|
Ni49.5
Mn25.4
Ga25.1
Ni56.2
Mn18.2
Ga25.6
Ni50
Mn35
Sn15
Ni50.3
Mn33.8
In15.9
H (kOe)
)()(
)(HT
HS
HSt
t
∆−∝∆∆
∫∆
∆∆
=∆T
dTHTMHT
HS ),()(
)( 0µ∫
∆
∆∆
−=∆Tt
t dTHTMHS
HT ),()(
)( 0µ
Kim et al., Acta Mater., 54, 493 (2005)Jeong et al., Mater. Sci. Engng. A, 359, 253 (2003)
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
• Heusler alloys show large magnetocaloric effect in the vicinity of the martensitic transition.
• The physics of magnetocaloric effect is controlled by the behaviour of the magnetization change at the transition.
• In nearly stoichiometric Ni2MnGa inverse magnetocaloric effect occurs at low applied fields due to the high magnetic anisotropy of the martensitic phase.
• In non-stoichiometric Ni-Mn-Sn and Ni-Mn-In giant inverse magnetocaloric effect is a consequence of the tendency of the excess of Mn atoms to introduce antiferromagnetic coupling.
Conclusions
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Dissipative effects
∫ −=⇒≤ iδSdST
δq
T
δq0
0 → H : Adibatic change of T
C
TS∆S
C
T ∆T
∆SC
T∆T
iirr
rev
+−=
−=
where
∫
∂∂=
H
H
dHT
M∆S
0∆
Tirr
∆T
rev
Ni-Mn-InMoya et al., Phys. Rev. B, 75, 184412 (2007)
Delft Days on Magnetocalorics, Delft, Netherlands October 30-31, 2008
Entropy and magnetization changeNi50Mn35Sn15Krenke et alPhys.Rev.B72 (2005) 14412
Ni50Mn34In16Krenke et alPhys. Rev B 73(2006) 174413
Ni49.5Mn24.5Ga25.1Marcos et al., Phys.Rev.B 66(2002) 224413
Ni56.2Mn18.2Ga25.5L. Pareti et al., Eur. Phys.J B 32(2003) 303
Ni-Mn-In
Ni-Mn-Sn
Ni-Mn-Ga
Moya et al., Mat. Sci. Engn. A 438 (2006) 913