Magnetic superelasticity and inverse magnetocaloric effect in Ni-Mn-In
Thorsten Krenke, Eyüp Duman, Mehmet Acet, and Eberhard F. Wassermann
Experimentalphysik, Universität Duisburg-Essen, D-47048 Duisburg, Germany
Xavier Moya, Llúıs Mañosa and Antoni Planes
Facultat de F́ısica, Departament dEstructura i Constituents de la Matèria,
Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia, Spain
Emmanuelle Suard and Bachir Ouladdiaf
Institut Laue-Langevin BP 156, 38042 Grenoble Cedex 9, France
(Dated: October 26, 2018)
Applying a magnetic field to a ferromagnetic Ni50Mn34In16 alloy in the martensitic state induces
a structural phase transition to the austenitic state. This is accompanied by a strain which re-
covers on removing the magnetic field giving the system a magnetically superelastic character. A
further property of this alloy is that it also shows the inverse magnetocaloric effect. The magnetic
superelasticity and the inverse magnetocaloric effect in Ni-Mn-In and their association with the first
order structural transition is studied by magnetization, strain, and neutron diffraction studies under
magnetic field.
PACS numbers: 75.80.+q , 61.12.-q
I. INTRODUCTION
Shape memory alloys exhibit unique thermomechanical
properties which originate from a martensitic transition
occurring between the austenite state with high crystallo-
graphic symmetry and a lower symmetry martensite state
[1]. These materials are superelastic and can remember
their original shape after severe deformation. Superelas-
ticity is related to the stress induced reversible structural
transition.
Research on shape memory alloys received significant
stimulus after the discovery of the magnetic shape mem-
ory (MSM) effect in Ni2MnGa [2]. This effect arises
from a magnetic field induced reorientation of twin-
related martensitic variants and relies on high magne-
tocrystalline anisotropy. The driving force is provided
by the difference between the Zeeman energies of neigh-
boring martensite variants [3, 4]. Giant strains up to
10% have been reported for off stoichiometric Ni-Mn-Ga
single variant crystals with the 14M modulated marten-
sitic structure [5]. Over the past decade, vast amount of
knowledge accumulated on the properties of Ni-Mn-Ga
Heusler alloys has enabled to foresee the possibility of
employing these alloys in device applications [6].
In applied magnetic fields, the martensitic start tem-
perature Ms of Ni-Mn-Ga shifts to higher temperatures
along with the other characteristic temperatures marten-
site finish Mf , austenite start As, and austenite finish Af
[7]. With this feature, it is possible to induce a reversible
structural phase transformation, whereby strain can be
fully recovered on removing the field without the neces-
sity of prestraining the specimen [8]. In such magnetic
field induced superelasticity, the maximum field induced
strain relies on the difference in the crystallographic di-
mensions in the martensitic and austenitic states. When
a field of sufficient strength is applied at a temperature
corresponding initially to the austenitic state, the shift
in all characteristic temperatures (therefore the shift in
the hysteresis associated with the transformation) can
be large enough so that the martensitic state is stabi-
lized. However, experiments performed in fields up to 10
T have shown that in the case of Ni54Mn21Ga25 the rate
of shift is only about ∼1 KT−1 [8]. Neutron diffraction
experiments under magnetic field on an alloy with similar
composition confirm these results [9].
Parallel to the development of the understanding of the
MSM effect in Ni-Mn-Ga and exploiting giant strains for
applications, search for other MSM material also took up
considerable place in the research agenda [10]. In Ni-Co-
Mn-In, it has recently been reported that when a mag-
netic field is applied to a pre-strained single crystal spec-
imen, the strain is recovered with a value that is nearly
equal to the size of the pre-strain [11]. Although this
is a considerable step in the search for magnetic supere-
lasticity, a system in which considerable length change
occurs reversibly by applying and removing a magnetic
field without requiring pre-strain is still to be found.
Recently, we have investigated a number of Ni-Mn
based Heusler systems other than Ni-Mn-Ga with the
aim of finding ferromagnetic alloys that undergo marten-
sitic transformations and understanding their properties
around the transformation point [12, 13]. In Ni-Mn-Sn
[14], we have come across an inverse magnetocaloric effect
at temperatures in the range of the first order martensitic
transition with size comparable to that of the archetype
Gd5(Si1−xGex)4 system, which exhibits the conventional
giant magnetocaloric effect [15].
Here, we demonstrate the presence of both magnetic
superelasticity and the inverse magnetocaloric effect in
Ni-Mn-In in the range of the martensitic transition.
Large field induced strains in polycrystalline Ni-Mn-In
of magnitude similar to that in polycrystalline Ni-Mn-
http://arxiv.org/abs/0704.1243v1
Ga are found. We show in Ni-Mn-In that instead of the
large field induced strain being due to twin boundary
motion in the martensitic phase, it relies essentially on
the reverse field induced martensite-to-austenite transi-
tion. Below, we present results of field dependent mag-
netization, calorimetry, neutron diffraction, strain, and
length change measurements in magnetic field on a Ni-
Mn-In alloy and discuss the field induced strain and the
inverse magnetocaloric effect in relation to the field in-
duced martensite-to-austenite transition.
II. EXPERIMENTAL
Arc melted samples were annealed at 1073 K under
argon atmosphere for two hours and quenched in ice wa-
ter. Magnetization measurements were carried out us-
ing a superconducting quantum interference device mag-
netometer, and calorimetric measurements in magnetic
field were performed using a high sensitivity differential
scanning calorimeter [16]. Neutron diffraction in mag-
netic fields up to 5 T was performed on the D2B powder
diffractometer at ILL, Grenoble. The strain measure-
ments were made using conventional strain-gage tech-
nique in magnetic fields up to 5T.
III. RESULTS
A. Calorimetry and magnetization
Ni50Mn50−xInx alloys undergo martensitic transitions
for about x < 16 [13, 17]. Here we concentrate on
the magneto-structural coupling in the ferromagnetic
Ni50.3Mn33.8In15.9 alloy, which has a Curie point TC =
305 K and transforms martensitically on cooling at Ms =
210 K. The other characteristic temperatures defining the
temperature limits of the transition are Mf = 175 K,
As = 200 K, and Af = 230 K. These temperatures are
determined from the calorimetry data in Fig. 1a.
In order to search for the presence of a coupling of the
structure with the magnetic degree of freedom within the
temperature range of the martensitic transition, we have
studied the field dependence of the magnetizationM(H).
The data shown in Fig. 1b are obtained in increasing field
and decreasing temperature. Here, the magnetizations in
the temperature interval 160 ≤ T ≤ 210 K initially show
a tendency to saturate, but, then, exhibit metamagnetic
transitions in higher fields. The characteristic field Hc
defining the transition point is determined as the crossing
point of the linear portions of the curves. The transition
shifts to higher fields with decreasing temperature, and
on removing the field, the magnetization returns to its
original value (see Fig. 7). As will be shown with neutron
diffraction in external field, the metamagnetic transition
is associated with the onset of a field induced reverse
martensitic transition.
0 1 2 3 4 5
160 180 200 220 240
220 K
160 K
H (T)
170 K
210 K
Temperature (K)
FIG. 1: Features in the martensitic transformation associated
with temperature and magnetic field dependence. a) Calori-
metric curves across the martensitic transition. The horizon-
tal arrows indicate the direction of temperature change. b)
Magnetization as a function of magnetic field measured on in-
creasing field in the vicinity of the martensitic transition. The
red lines drawn through the data points (shown only for the
200 K data) cross at a point corresponding to the characteris-
tic field around which the metamagnetic transition begins to
occur.
0 100 200 300
T (K)
M 5TS =150 K
M 2TS =185 K
M 0TS =205 K
FIG. 2: The relative length change in constant applied mag-
netic fields of 0 T, 2 T and 5 T. Arrows indicate the positions
of Ms.
In Fig. 2, we show the relative length change ∆l/l as
a function of temperature in different constant applied
magnetic fields. As the field increases, Ms (indicated
by arrows) decreases by an amount of about −10 KT−1.
The other characteristic temperatures are positioned in
the conventional manner around the temperature hys-
teresis loop, and all shift by nearly the same amount in
a given field. With increasing measuring field, the dif-
ference in ∆l/l between the austenitic and martensitic
states decreases. The cause of this decrease is associated
with the crystallographic orientation of the easy axis of
magnetization within the orthorhombic structure of the
martensitic phase. This property is discussed separately
in reference [18].
0 1 2 3 4 5
160 180 200 220
H (T)
T (K)
0 1 2 3 4 5 6
 [13]
H (T)
FIG. 3: Characteristic field dependent properties around
the martensitic transition. a) Shift in the martensitic
transition temperature as a function of magnetic field, for
Ni50.3Mn33.8In15.9, Ni2MnGa, and Ni53.5Mn19.5Ga27. b)
Temperature dependence of the magnetization obtained at
selected fields from Fig. 1b. The numbers refer to magnetic
field values in Tesla. c) The difference between the magneti-
zations in the cubic and martensite phases. ∆M saturates at
about 0.5 T. The lines drawn through the data are guides.
In Fig. 3a, we compare the magnitude of the shift of
the transition temperatures represented by ∆T as a func-
tion of the external magnetic field µ0H of the present
Ni-Mn-In alloy with those reported for Ni2MnGa and
Ni53.5Mn19.5Ga27; the latter exhibiting the strongest field
dependent transition temperature [19, 20]. Since the ap-
plied field shifts all characteristic temperatures by the
same amount, ∆T is the change in any one of the charac-
teristic transition temperatures in applied magnetic field
with respect to zero field. The shifts in Ms and As of
Ni-Mn-In determined from Fig. 2 are shown with up and
down triangles respectively. We have also included data
for µ0H ≤ 1 T obtained from calorimetric measurements
under constant magnetic field [13].
Two significant features show up from Fig. 3a:
(i) The rate of change of the transition temperature
in Ni50.3Mn33.8In15.9 (−10 KT
−1) is higher than in
Ni53.5Mn19.5Ga27 (6 KT
−1), and (ii) in Ni-Mn-In, ∆T is
negative, i.e., the transition temperature decreases with
increasing field. This is consistent with the fact that
the magnetization in the high temperature cubic phase
is larger than the magnetization in the martensitic phase
as seen in Fig. 3b, where the temperature dependence of
the magnetizations at constant fields obtained from Fig.
1b at selected fields are plotted. The difference in the
magnetization of the martensitic and austenitic states
around the transition temperature ∆M is plotted as a
function of applied field in Fig. 3c.
B. Neutron diffraction in magnetic field
To understand the properties of the transition observed
inM(T ) andM(H), we have undertaken powder neutron
0 1 2 3 4 5
200 K 
T=4 K 
140 K 
180 K
µ0H (T)
FIG. 4: The magnetic field dependence of the magnetization
for the sample used in the neutron diffraction experiments.
The crossing point of the red lines determine Hc.
diffraction experiments as a function of temperature and
magnetic field. The Ni49.7Mn34.3In16.0 sample used for
these experiments has a composition that differs slightly
from that used in the measurements presented above and,
therefore, the transition temperatures are slightly shifted.
Therefore, we plot in Fig. 4 the M(H) isotherms and will
compare these data to the neutron diffraction data.
Fig. 5a shows neutron diffraction patterns at 5 K and
317 K. The pattern at 317 K generates from an L21 struc-
ture with a lattice constant a = 0.6011 nm. At 5 K, the
pattern is that of a 10M modulated martensite struc-
ture having a monoclinic unit cell with β = 86.97 and
lattice constants a = 0.4398 nm, b = 0.5635 nm, and
c = 2.1720 nm. Other than this slight monoclinicity, the
structure is orthorhombic having a shuffle periodicity of
10 lattice planes in the [110] direction. In the pattern
at 317 K, some additional weak reflections can be iden-
tified around 36 and 47. These lie close to the positions
of the (1 0 −7) and (2 1 3) reflections of the martensitic
phase at 5 K, but at slightly smaller angles due to ther-
mal expansion, and their presence is attributed to small
amounts of mechanically induced martensite formed on
grinding the ingot for powder specimen preparation.
At 180 K, which is a temperature that falls well in the
range of the transformation (Fig. 4), we have studied the
evolution of the diffraction spectrum with applied mag-
netic field. Fig. 5b shows the spectrum in 2θ ranges
that encompass the vicinity of the positions of the (200)
and (220) reflections of the L21 phase. As the magnetic
field increases, the intensities of these reflections grow at
the expense of the intensities of the (1 0 −5) and (1 2
5) reflections, which lie nearly at the same positions as
20 30 40 50 60
24 30 40 50
2  (deg)
5) (0
317 K
H (T)
2 (deg)
180 K
FIG. 5: Neutron diffractograms. a) Patterns at 317 K (L21)
and 5 K (10M martensite). b) The field dependence of the
diffraction pattern at 180 K showing the field induced trans-
formation from the martensite to the austenite state.
the (200) and the (220) reflections of the L21 phase re-
spectively. This shows that a progressive magnetic field
induced structural transition from the martensitic to the
austenitic state is taking place with increasing magnetic
field. In cases where the positions of the reflections per-
tain only to the martensitic phase, e.g. (1 0 5), (1 2 −5),
etc., the intensity first increases with increasing mag-
netic field up to 2 T and, then, decreases. The initial
increase is related to the increase in the magnetization
in the martensitic state at 180 K up to around µ0Hc ≈ 2
T (Fig. 4). The subsequent decrease is associated with
the gradual decrease in the amount of martensite and
the stabilization of the L21 phase. However at 5 T, the
reflections associated with the martensitic phase do not
disappear, although their intensities are reduced. This
indicates that the transition is not complete in this field,
and larger magnetic fields are required to fully restore the
L21 state at 180 K. The neutron diffraction data indicate
clearly a magnetic field induced reverse transition and
give evidence that the observed metamagnetic transition
-5 -4 -3 -2 -1 0 1 2 3 4 5
T (K)
µ0H (T)
FIG. 6: Magnetic field dependence of strain at 195 K (T <
Ms) and 295 K (L21). The strain recovers on removing the
field indicating magnetically superelastic behavior. Arrows
show the direction of field change.
in M(H) is related to the reverse martensitic transition.
C. Magnetic field induced strain
The magnetic field induced structural phase transition
in the present alloy can have important consequences on
macroscopic strains occurring during the application of
the field. Fig. 6 shows the results of magnetic field depen-
dent strain measurements, where the strain is defined as
∆l/l = [l(H)−l0]/l0. Here, l0 is the length in the absence
of field and l(H) the length in field. The sample is well
within the austenitic temperature range at 295 K (filled
circles) and is within the structural transition region at
195 K (open circles). The small field induced strain at
295 K increasing negatively with increasing field corre-
sponds to the intrinsic magnetostriction of the austenite,
while at 195 K, a strain of about 0.14% is reached in the
initial curve. After the first field cycle is completed, the
strain reduces to about 0.12 % and remains constant at
this value, which is roughly the same as that attained
in polycrystalline Ni-Mn-Ga. However, the effect here is
due to the crystallographic transformation from marten-
site to austenite with increasing field instead of a field
induced twin boundary motion that occurs within the
martensitic state as in Ni-Mn-Ga. Although hysteresis is
observed in Fig. 6, the sample returns to its zero-field
length on removing the field.
The features in the field dependence of the strain is
reflected in the field dependence of the magnetization at
the same temperature as seen in Fig. 7. The M(H)
curves show metamagnetic transitions around 2 T and 1
T for the increasing and decreasing field branches respec-
tively. These points correspond to the fields where ∆l/l
also changes rapidly. As in the case of ∆l/l, M(H) also
shows essentially no remanence and recovers its zero-field
value.
0 1 2 3 4 5
195 K
µ0H (T)
FIG. 7: The magnetic field dependence of the magnetization
at 195 K.
140 160 180 200
T (K)
0H (T)
FIG. 8: Temperature dependence of ∆S.
D. Magnetocaloric effect
Due to the first order magnetic field induced transition
and considerable difference in the magnetization of the
martensitic and L21 states at the transition temperature,
substantial magnetocaloric effects can be expected. The
field induced entropy change ∆S around the martensitic
transition temperature can be estimated from magneti-
zation measurements by employing the Maxwell equation
∆S(T,H) = µ0
dH, (1)
from which the magnetocaloric effect can be evaluated by
numerical integration using the data in Fig. 1b. The re-
sulting ∆S in the temperature range 170 K ≤ T ≤ 225 K
is plotted in Fig. 8. The sign of ∆S is positive for all tem-
peratures indicating that an inverse magnetocaloric effect
is present, i.e. the sample cools on applying a magnetic
field adiabatically as in Ni-Mn-Sn [14]. The maximum
value of ∆S = 12 JK−1kg−1 is reached in a magnetic
field of 4 T at about 205 K. Since there is no substantial
change in the magnetization above 4 T at this tempera-
ture, increasing the magnetic field any further does not
lead to any further increase in ∆S. As expected for mag-
netostructural transitions [22], this value is larger than
the transition entropy change [13] since it also includes
the effect of magnetization changes with temperature be-
yond the transition region.
IV. DISCUSSION
The origins of both distinct properties of the studied
alloy, namely, the field induced martensite to austen-
ite transition and the inverse magnetocaloric effect, are
related to the lower value of the magnetization in the
martensitic phase with respect to that in the austenitic
phase. The difference in the magnetization can be as-
cribed to the fact that in Mn based Heusler alloys,
the magnetic moments are localized mainly on the Mn
atoms and the exchange interaction strongly depends on
the Mn-Mn distance. Hence, any change in the dis-
tance caused by a change in the crystallographic con-
figuration can modify the strength of the interactions
leading to different magnetic exchange in each of the
phases. Indeed, it has been shown that in the case of a
Ni0.50Mn0.36Sn0.14 alloy that short range antiferromag-
netism is present between Mn atoms located at the 4(b)
positions of the austenite phase which is then strength-
ened in the martensitic state [23]. The present Ni-Mn-
In alloy transforms to the same martensitic structure as
in Ni0.50Mn0.36Sn0.14. Therefore, the strong reduction of
the magnetization belowMs in Ni-Mn-In can be expected
to be due to a similar cause. The presence of short range
antiferromagnetism in the ferromagnetic matrix leads to
frustration in the temperature range of the martensitic
transition. In such a frustrated system, the application
of a magnetic field can lead to the degeneracy of the spin
states giving rise to an increase in the configurational
entropy that is required for the observed positive ∆S.
However, the quantitative details of the frustrated state
and the microscopic process leading to a positive ∆S re-
main to be described.
In Ni-Mn-Ga, giant strains are due to the reorientation
of twin-related variants in the martensitic state and re-
covery of this strain is, in general, not achieved by simply
removing the field. By contrast, the magnetic supere-
lastic effect and the associated strain reported here for
Ni-Mn-In is related to the field induced structural tran-
sition. This enables to reversibly induce and recover the
strain by simply applying and removing the field.
V. CONCLUSION
Ni0.50Mn0.34In0.16 exhibits a magnetic field induced
structural transition from the martensitic state to the
austenitic state. The transition is directly evidenced by
neutron diffraction measurements under magnetic field.
Here, other than in Ni-Mn-Ga alloys, where the magneti-
zation of the martensitic state is higher than that in the
cubic phase, the austenite is stabilized by the application
of a magnetic field. The shift of the transition temper-
atures was found to be large and negative with values
up to about -50 K in 5 Tesla. Due to the reversible
magnetic field induced transition, magnetic superelastic-
ity with 0.12% strains occur. Other than in magnetic
shape memory alloys, where strain is mainly created
by twin boundary motion, strain in Ni0.50Mn0.34In0.16
is caused by changes in lattice parameters during the
transition. Additionally, an inverse magnetocaloric ef-
fect with a maximum value in the entropy change of
about 12 Jkg−1K−1 at 190 K and a minimum entropy
change of 8 Jkg−1K−1 in a broad temperature range
170K ≤ T ≤ 190K is also found in this alloy.
Acknowledgments
We thank Peter Hinkel and Sabine Schremmer for tech-
nical support. This work was supported by Deutsche
Forschungsgemeinschaft (GK277) and CICyT (Spain),
project MAT2004-1291. XM acknowledges support from
DGICyT (Spain).
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  Applying a magnetic field to a ferromagnetic Ni$_{50}$Mn$_{34}$In$_{16}$
alloy in the martensitic state induces a structural phase transition to the
austenitic state. This is accompanied by a strain which recovers on removing
the magnetic field giving the system a magnetically superelastic character. A
further property of this alloy is that it also shows the inverse magnetocaloric
effect. The magnetic superelasticity and the inverse magnetocaloric effect in
Ni-Mn-In and their association with the first order structural transition is
studied by magnetization, strain, and neutron diffraction studies under
magnetic field.

Magnetic superelasticity and inverse magnetocaloric effect in Ni-Mn-In
Thorsten Krenke, Eyüp Duman, Mehmet Acet, and Eberhard F. Wassermann
Experimentalphysik, Universität Duisburg-Essen, D-47048 Duisburg, Germany
Xavier Moya, Llúıs Mañosa and Antoni Planes
Facultat de F́ısica, Departament dEstructura i Constituents de la Matèria,
Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia, Spain
Emmanuelle Suard and Bachir Ouladdiaf
Institut Laue-Langevin BP 156, 38042 Grenoble Cedex 9, France
(Dated: October 26, 2018)
Applying a magnetic field to a ferromagnetic Ni50Mn34In16 alloy in the martensitic state induces
a structural phase transition to the austenitic state. This is accompanied by a strain which re-
covers on removing the magnetic field giving the system a magnetically superelastic character. A
further property of this alloy is that it also shows the inverse magnetocaloric effect. The magnetic
superelasticity and the inverse magnetocaloric effect in Ni-Mn-In and their association with the first
order structural transition is studied by magnetization, strain, and neutron diffraction studies under
magnetic field.
PACS numbers: 75.80.+q , 61.12.-q
I. INTRODUCTION
Shape memory alloys exhibit unique thermomechanical
properties which originate from a martensitic transition
occurring between the austenite state with high crystallo-
graphic symmetry and a lower symmetry martensite state
[1]. These materials are superelastic and can remember
their original shape after severe deformation. Superelas-
ticity is related to the stress induced reversible structural
transition.
Research on shape memory alloys received significant
stimulus after the discovery of the magnetic shape mem-
ory (MSM) effect in Ni2MnGa [2]. This effect arises
from a magnetic field induced reorientation of twin-
related martensitic variants and relies on high magne-
tocrystalline anisotropy. The driving force is provided
by the difference between the Zeeman energies of neigh-
boring martensite variants [3, 4]. Giant strains up to
10% have been reported for off stoichiometric Ni-Mn-Ga
single variant crystals with the 14M modulated marten-
sitic structure [5]. Over the past decade, vast amount of
knowledge accumulated on the properties of Ni-Mn-Ga
Heusler alloys has enabled to foresee the possibility of
employing these alloys in device applications [6].
In applied magnetic fields, the martensitic start tem-
perature Ms of Ni-Mn-Ga shifts to higher temperatures
along with the other characteristic temperatures marten-
site finish Mf , austenite start As, and austenite finish Af
[7]. With this feature, it is possible to induce a reversible
structural phase transformation, whereby strain can be
fully recovered on removing the field without the neces-
sity of prestraining the specimen [8]. In such magnetic
field induced superelasticity, the maximum field induced
strain relies on the difference in the crystallographic di-
mensions in the martensitic and austenitic states. When
a field of sufficient strength is applied at a temperature
corresponding initially to the austenitic state, the shift
in all characteristic temperatures (therefore the shift in
the hysteresis associated with the transformation) can
be large enough so that the martensitic state is stabi-
lized. However, experiments performed in fields up to 10
T have shown that in the case of Ni54Mn21Ga25 the rate
of shift is only about ∼1 KT−1 [8]. Neutron diffraction
experiments under magnetic field on an alloy with similar
composition confirm these results [9].
Parallel to the development of the understanding of the
MSM effect in Ni-Mn-Ga and exploiting giant strains for
applications, search for other MSM material also took up
considerable place in the research agenda [10]. In Ni-Co-
Mn-In, it has recently been reported that when a mag-
netic field is applied to a pre-strained single crystal spec-
imen, the strain is recovered with a value that is nearly
equal to the size of the pre-strain [11]. Although this
is a considerable step in the search for magnetic supere-
lasticity, a system in which considerable length change
occurs reversibly by applying and removing a magnetic
field without requiring pre-strain is still to be found.
Recently, we have investigated a number of Ni-Mn
based Heusler systems other than Ni-Mn-Ga with the
aim of finding ferromagnetic alloys that undergo marten-
sitic transformations and understanding their properties
around the transformation point [12, 13]. In Ni-Mn-Sn
[14], we have come across an inverse magnetocaloric effect
at temperatures in the range of the first order martensitic
transition with size comparable to that of the archetype
Gd5(Si1−xGex)4 system, which exhibits the conventional
giant magnetocaloric effect [15].
Here, we demonstrate the presence of both magnetic
superelasticity and the inverse magnetocaloric effect in
Ni-Mn-In in the range of the martensitic transition.
Large field induced strains in polycrystalline Ni-Mn-In
of magnitude similar to that in polycrystalline Ni-Mn-
http://arxiv.org/abs/0704.1243v1
Ga are found. We show in Ni-Mn-In that instead of the
large field induced strain being due to twin boundary
motion in the martensitic phase, it relies essentially on
the reverse field induced martensite-to-austenite transi-
tion. Below, we present results of field dependent mag-
netization, calorimetry, neutron diffraction, strain, and
length change measurements in magnetic field on a Ni-
Mn-In alloy and discuss the field induced strain and the
inverse magnetocaloric effect in relation to the field in-
duced martensite-to-austenite transition.
II. EXPERIMENTAL
Arc melted samples were annealed at 1073 K under
argon atmosphere for two hours and quenched in ice wa-
ter. Magnetization measurements were carried out us-
ing a superconducting quantum interference device mag-
netometer, and calorimetric measurements in magnetic
field were performed using a high sensitivity differential
scanning calorimeter [16]. Neutron diffraction in mag-
netic fields up to 5 T was performed on the D2B powder
diffractometer at ILL, Grenoble. The strain measure-
ments were made using conventional strain-gage tech-
nique in magnetic fields up to 5T.
III. RESULTS
A. Calorimetry and magnetization
Ni50Mn50−xInx alloys undergo martensitic transitions
for about x < 16 [13, 17]. Here we concentrate on
the magneto-structural coupling in the ferromagnetic
Ni50.3Mn33.8In15.9 alloy, which has a Curie point TC =
305 K and transforms martensitically on cooling at Ms =
210 K. The other characteristic temperatures defining the
temperature limits of the transition are Mf = 175 K,
As = 200 K, and Af = 230 K. These temperatures are
determined from the calorimetry data in Fig. 1a.
In order to search for the presence of a coupling of the
structure with the magnetic degree of freedom within the
temperature range of the martensitic transition, we have
studied the field dependence of the magnetizationM(H).
The data shown in Fig. 1b are obtained in increasing field
and decreasing temperature. Here, the magnetizations in
the temperature interval 160 ≤ T ≤ 210 K initially show
a tendency to saturate, but, then, exhibit metamagnetic
transitions in higher fields. The characteristic field Hc
defining the transition point is determined as the crossing
point of the linear portions of the curves. The transition
shifts to higher fields with decreasing temperature, and
on removing the field, the magnetization returns to its
original value (see Fig. 7). As will be shown with neutron
diffraction in external field, the metamagnetic transition
is associated with the onset of a field induced reverse
martensitic transition.
0 1 2 3 4 5
160 180 200 220 240
220 K
160 K
H (T)
170 K
210 K
Temperature (K)
FIG. 1: Features in the martensitic transformation associated
with temperature and magnetic field dependence. a) Calori-
metric curves across the martensitic transition. The horizon-
tal arrows indicate the direction of temperature change. b)
Magnetization as a function of magnetic field measured on in-
creasing field in the vicinity of the martensitic transition. The
red lines drawn through the data points (shown only for the
200 K data) cross at a point corresponding to the characteris-
tic field around which the metamagnetic transition begins to
occur.
0 100 200 300
T (K)
M 5TS =150 K
M 2TS =185 K
M 0TS =205 K
FIG. 2: The relative length change in constant applied mag-
netic fields of 0 T, 2 T and 5 T. Arrows indicate the positions
of Ms.
In Fig. 2, we show the relative length change ∆l/l as
a function of temperature in different constant applied
magnetic fields. As the field increases, Ms (indicated
by arrows) decreases by an amount of about −10 KT−1.
The other characteristic temperatures are positioned in
the conventional manner around the temperature hys-
teresis loop, and all shift by nearly the same amount in
a given field. With increasing measuring field, the dif-
ference in ∆l/l between the austenitic and martensitic
states decreases. The cause of this decrease is associated
with the crystallographic orientation of the easy axis of
magnetization within the orthorhombic structure of the
martensitic phase. This property is discussed separately
in reference [18].
0 1 2 3 4 5
160 180 200 220
H (T)
T (K)
0 1 2 3 4 5 6
 [13]
H (T)
FIG. 3: Characteristic field dependent properties around
the martensitic transition. a) Shift in the martensitic
transition temperature as a function of magnetic field, for
Ni50.3Mn33.8In15.9, Ni2MnGa, and Ni53.5Mn19.5Ga27. b)
Temperature dependence of the magnetization obtained at
selected fields from Fig. 1b. The numbers refer to magnetic
field values in Tesla. c) The difference between the magneti-
zations in the cubic and martensite phases. ∆M saturates at
about 0.5 T. The lines drawn through the data are guides.
In Fig. 3a, we compare the magnitude of the shift of
the transition temperatures represented by ∆T as a func-
tion of the external magnetic field µ0H of the present
Ni-Mn-In alloy with those reported for Ni2MnGa and
Ni53.5Mn19.5Ga27; the latter exhibiting the strongest field
dependent transition temperature [19, 20]. Since the ap-
plied field shifts all characteristic temperatures by the
same amount, ∆T is the change in any one of the charac-
teristic transition temperatures in applied magnetic field
with respect to zero field. The shifts in Ms and As of
Ni-Mn-In determined from Fig. 2 are shown with up and
down triangles respectively. We have also included data
for µ0H ≤ 1 T obtained from calorimetric measurements
under constant magnetic field [13].
Two significant features show up from Fig. 3a:
(i) The rate of change of the transition temperature
in Ni50.3Mn33.8In15.9 (−10 KT
−1) is higher than in
Ni53.5Mn19.5Ga27 (6 KT
−1), and (ii) in Ni-Mn-In, ∆T is
negative, i.e., the transition temperature decreases with
increasing field. This is consistent with the fact that
the magnetization in the high temperature cubic phase
is larger than the magnetization in the martensitic phase
as seen in Fig. 3b, where the temperature dependence of
the magnetizations at constant fields obtained from Fig.
1b at selected fields are plotted. The difference in the
magnetization of the martensitic and austenitic states
around the transition temperature ∆M is plotted as a
function of applied field in Fig. 3c.
B. Neutron diffraction in magnetic field
To understand the properties of the transition observed
inM(T ) andM(H), we have undertaken powder neutron
0 1 2 3 4 5
200 K 
T=4 K 
140 K 
180 K
µ0H (T)
FIG. 4: The magnetic field dependence of the magnetization
for the sample used in the neutron diffraction experiments.
The crossing point of the red lines determine Hc.
diffraction experiments as a function of temperature and
magnetic field. The Ni49.7Mn34.3In16.0 sample used for
these experiments has a composition that differs slightly
from that used in the measurements presented above and,
therefore, the transition temperatures are slightly shifted.
Therefore, we plot in Fig. 4 the M(H) isotherms and will
compare these data to the neutron diffraction data.
Fig. 5a shows neutron diffraction patterns at 5 K and
317 K. The pattern at 317 K generates from an L21 struc-
ture with a lattice constant a = 0.6011 nm. At 5 K, the
pattern is that of a 10M modulated martensite struc-
ture having a monoclinic unit cell with β = 86.97 and
lattice constants a = 0.4398 nm, b = 0.5635 nm, and
c = 2.1720 nm. Other than this slight monoclinicity, the
structure is orthorhombic having a shuffle periodicity of
10 lattice planes in the [110] direction. In the pattern
at 317 K, some additional weak reflections can be iden-
tified around 36 and 47. These lie close to the positions
of the (1 0 −7) and (2 1 3) reflections of the martensitic
phase at 5 K, but at slightly smaller angles due to ther-
mal expansion, and their presence is attributed to small
amounts of mechanically induced martensite formed on
grinding the ingot for powder specimen preparation.
At 180 K, which is a temperature that falls well in the
range of the transformation (Fig. 4), we have studied the
evolution of the diffraction spectrum with applied mag-
netic field. Fig. 5b shows the spectrum in 2θ ranges
that encompass the vicinity of the positions of the (200)
and (220) reflections of the L21 phase. As the magnetic
field increases, the intensities of these reflections grow at
the expense of the intensities of the (1 0 −5) and (1 2
5) reflections, which lie nearly at the same positions as
20 30 40 50 60
24 30 40 50
2  (deg)
5) (0
317 K
H (T)
2 (deg)
180 K
FIG. 5: Neutron diffractograms. a) Patterns at 317 K (L21)
and 5 K (10M martensite). b) The field dependence of the
diffraction pattern at 180 K showing the field induced trans-
formation from the martensite to the austenite state.
the (200) and the (220) reflections of the L21 phase re-
spectively. This shows that a progressive magnetic field
induced structural transition from the martensitic to the
austenitic state is taking place with increasing magnetic
field. In cases where the positions of the reflections per-
tain only to the martensitic phase, e.g. (1 0 5), (1 2 −5),
etc., the intensity first increases with increasing mag-
netic field up to 2 T and, then, decreases. The initial
increase is related to the increase in the magnetization
in the martensitic state at 180 K up to around µ0Hc ≈ 2
T (Fig. 4). The subsequent decrease is associated with
the gradual decrease in the amount of martensite and
the stabilization of the L21 phase. However at 5 T, the
reflections associated with the martensitic phase do not
disappear, although their intensities are reduced. This
indicates that the transition is not complete in this field,
and larger magnetic fields are required to fully restore the
L21 state at 180 K. The neutron diffraction data indicate
clearly a magnetic field induced reverse transition and
give evidence that the observed metamagnetic transition
-5 -4 -3 -2 -1 0 1 2 3 4 5
T (K)
µ0H (T)
FIG. 6: Magnetic field dependence of strain at 195 K (T <
Ms) and 295 K (L21). The strain recovers on removing the
field indicating magnetically superelastic behavior. Arrows
show the direction of field change.
in M(H) is related to the reverse martensitic transition.
C. Magnetic field induced strain
The magnetic field induced structural phase transition
in the present alloy can have important consequences on
macroscopic strains occurring during the application of
the field. Fig. 6 shows the results of magnetic field depen-
dent strain measurements, where the strain is defined as
∆l/l = [l(H)−l0]/l0. Here, l0 is the length in the absence
of field and l(H) the length in field. The sample is well
within the austenitic temperature range at 295 K (filled
circles) and is within the structural transition region at
195 K (open circles). The small field induced strain at
295 K increasing negatively with increasing field corre-
sponds to the intrinsic magnetostriction of the austenite,
while at 195 K, a strain of about 0.14% is reached in the
initial curve. After the first field cycle is completed, the
strain reduces to about 0.12 % and remains constant at
this value, which is roughly the same as that attained
in polycrystalline Ni-Mn-Ga. However, the effect here is
due to the crystallographic transformation from marten-
site to austenite with increasing field instead of a field
induced twin boundary motion that occurs within the
martensitic state as in Ni-Mn-Ga. Although hysteresis is
observed in Fig. 6, the sample returns to its zero-field
length on removing the field.
The features in the field dependence of the strain is
reflected in the field dependence of the magnetization at
the same temperature as seen in Fig. 7. The M(H)
curves show metamagnetic transitions around 2 T and 1
T for the increasing and decreasing field branches respec-
tively. These points correspond to the fields where ∆l/l
also changes rapidly. As in the case of ∆l/l, M(H) also
shows essentially no remanence and recovers its zero-field
value.
0 1 2 3 4 5
195 K
µ0H (T)
FIG. 7: The magnetic field dependence of the magnetization
at 195 K.
140 160 180 200
T (K)
0H (T)
FIG. 8: Temperature dependence of ∆S.
D. Magnetocaloric effect
Due to the first order magnetic field induced transition
and considerable difference in the magnetization of the
martensitic and L21 states at the transition temperature,
substantial magnetocaloric effects can be expected. The
field induced entropy change ∆S around the martensitic
transition temperature can be estimated from magneti-
zation measurements by employing the Maxwell equation
∆S(T,H) = µ0
dH, (1)
from which the magnetocaloric effect can be evaluated by
numerical integration using the data in Fig. 1b. The re-
sulting ∆S in the temperature range 170 K ≤ T ≤ 225 K
is plotted in Fig. 8. The sign of ∆S is positive for all tem-
peratures indicating that an inverse magnetocaloric effect
is present, i.e. the sample cools on applying a magnetic
field adiabatically as in Ni-Mn-Sn [14]. The maximum
value of ∆S = 12 JK−1kg−1 is reached in a magnetic
field of 4 T at about 205 K. Since there is no substantial
change in the magnetization above 4 T at this tempera-
ture, increasing the magnetic field any further does not
lead to any further increase in ∆S. As expected for mag-
netostructural transitions [22], this value is larger than
the transition entropy change [13] since it also includes
the effect of magnetization changes with temperature be-
yond the transition region.
IV. DISCUSSION
The origins of both distinct properties of the studied
alloy, namely, the field induced martensite to austen-
ite transition and the inverse magnetocaloric effect, are
related to the lower value of the magnetization in the
martensitic phase with respect to that in the austenitic
phase. The difference in the magnetization can be as-
cribed to the fact that in Mn based Heusler alloys,
the magnetic moments are localized mainly on the Mn
atoms and the exchange interaction strongly depends on
the Mn-Mn distance. Hence, any change in the dis-
tance caused by a change in the crystallographic con-
figuration can modify the strength of the interactions
leading to different magnetic exchange in each of the
phases. Indeed, it has been shown that in the case of a
Ni0.50Mn0.36Sn0.14 alloy that short range antiferromag-
netism is present between Mn atoms located at the 4(b)
positions of the austenite phase which is then strength-
ened in the martensitic state [23]. The present Ni-Mn-
In alloy transforms to the same martensitic structure as
in Ni0.50Mn0.36Sn0.14. Therefore, the strong reduction of
the magnetization belowMs in Ni-Mn-In can be expected
to be due to a similar cause. The presence of short range
antiferromagnetism in the ferromagnetic matrix leads to
frustration in the temperature range of the martensitic
transition. In such a frustrated system, the application
of a magnetic field can lead to the degeneracy of the spin
states giving rise to an increase in the configurational
entropy that is required for the observed positive ∆S.
However, the quantitative details of the frustrated state
and the microscopic process leading to a positive ∆S re-
main to be described.
In Ni-Mn-Ga, giant strains are due to the reorientation
of twin-related variants in the martensitic state and re-
covery of this strain is, in general, not achieved by simply
removing the field. By contrast, the magnetic supere-
lastic effect and the associated strain reported here for
Ni-Mn-In is related to the field induced structural tran-
sition. This enables to reversibly induce and recover the
strain by simply applying and removing the field.
V. CONCLUSION
Ni0.50Mn0.34In0.16 exhibits a magnetic field induced
structural transition from the martensitic state to the
austenitic state. The transition is directly evidenced by
neutron diffraction measurements under magnetic field.
Here, other than in Ni-Mn-Ga alloys, where the magneti-
zation of the martensitic state is higher than that in the
cubic phase, the austenite is stabilized by the application
of a magnetic field. The shift of the transition temper-
atures was found to be large and negative with values
up to about -50 K in 5 Tesla. Due to the reversible
magnetic field induced transition, magnetic superelastic-
ity with 0.12% strains occur. Other than in magnetic
shape memory alloys, where strain is mainly created
by twin boundary motion, strain in Ni0.50Mn0.34In0.16
is caused by changes in lattice parameters during the
transition. Additionally, an inverse magnetocaloric ef-
fect with a maximum value in the entropy change of
about 12 Jkg−1K−1 at 190 K and a minimum entropy
change of 8 Jkg−1K−1 in a broad temperature range
170K ≤ T ≤ 190K is also found in this alloy.
Acknowledgments
We thank Peter Hinkel and Sabine Schremmer for tech-
nical support. This work was supported by Deutsche
Forschungsgemeinschaft (GK277) and CICyT (Spain),
project MAT2004-1291. XM acknowledges support from
DGICyT (Spain).
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