Cooling and heating by adiabatic magnetization in the
  Ni$_{50}$Mn$_{34}$In$_{16}$ magnetic shape memory alloy
Cooling and heating by adiabatic magnetization in the Ni50Mn34In16 magnetic shape
memory alloy
Xavier Moya, Llúıs Mañosa∗ and Antoni Planes
Departament d’Estructura i Constituents de la Matèria, Facultat de F́ısica,
Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia, Spain
Seda Aksoy, Mehmet Acet, Eberhard F. Wassermann and Thorsten Krenke†
Fachbereich Physik, Experimentalphysik, Universität Duisburg-Essen, D-47048 Duisburg, Germany
(Dated: November 22, 2021)
We report on measurements of the adiabatic temperature change in the inverse magnetocaloric
Ni50Mn34In16 alloy. It is shown that this alloy heats up with the application of a magnetic field
around the Curie point due to the conventional magnetocaloric effect. In contrast, the inverse
magnetocaloric effect associated with the martensitic transition results in the unusual decrease of
temperature by adiabatic magnetization. We also provide magnetization and specific heat data
which enable to compare the measured temperature changes to the values indirectly computed from
thermodynamic relationships. Good agreement is obtained for the conventional effect at the second-
order paramagnetic-ferromagnetic phase transition. However, at the first order structural transition
the measured values at high fields are lower than the computed ones. Irreversible thermodynamics
arguments are given to show that such a discrepancy is due to the irreversibility of the first-order
martensitic transition.
PACS numbers: 75.30.Sg,64.70.Kb,81.30Kf
I. INTRODUCTION
When the magnetization of any magnetic material is
changed isothermally under the application of a mag-
netic field, heat is exchanged with the surroundings. If
the change is performed adiabatically, the temperature
changes. This is the magnetocaloric effect (MCE), which
provides the basis of the adiabatic demagnetization cool-
ing technique [1]. This technique was developed to reach
mK temperatures soon after the pioneering work by De-
bye [2] and Giauque [3], who independently suggested
such a possibility. The discovery in the nineties of the gi-
ant magnetocaloric effect associated with first-order mag-
netostructural transitions in a number of intermetallic
alloy families [4] opened up the possibility of using this
technique in room temperature refrigeration applications
and, thus, yielded renewed interest in the subject [5].
It has been known for a long time that the isother-
mal reduction of a magnetic field gives rise to a de-
crease in entropy in some antiferromagnetic and ferri-
magnetic systems, [6, 7]. This inverse magnetocaloric
phenomenon was supposed to produce small effects and
has been largely ignored. Recently, however, it has been
shown that in some ferromagnetic [8] and metamagnetic
[9] systems, inverse MCE can have an amplitude com-
parable to the conventional effect detected in giant mag-
netocaloric intermetallic materials. The inverse effect is
related to the existence of regions in phase space where
∗Electronic address: lluis@ecm.ub.es
†Present address: ThyssenKrupp Electrical Steel GmbH, D-45881
Gelsenkirchen, Germany
ζ = (∂M/∂T )H is positive. In a paramagnetic system,
ζ is always negative, and thus, the origin of a positive ζ
must be ascribed to coupling between magnetic moments.
The inverse MCE can occur in the vicinity of magne-
tostructural and metamagnetic phase transitions due to
changes in the magnetic coupling driven by the interplay
between magnetic and structural degrees of freedom [10].
In the present paper, we study the MCE in a
Ni50Mn34In16 alloy. This is a magnetic shape-memory
alloy which undergoes a martensitic transition from a
cubic (L21) to a monoclinic (10M) structure below its
Curie temperature [11]. Interestingly, the sample shows
both inverse and conventional MCE in rather close tem-
perature intervals. While the conventional effect arises
from the continuous transition from paramagnetic to fer-
romagnetic states, the inverse effect is associated with the
martensitic transition at which the magnetic moment of
the system decreases. This decrease originates from the
tendency of the excess of Mn atoms (with respect to 2-1-
1 stoichiometry) to introduce antiferromagnetic coupling.
The antiferromagnetic coupling is caused by the change
in the Mn-Mn distance as the martensitic phase of lower
symmetry gains stability [12].
While most of the reported data on giant MCE ma-
terials refer to the isothermal entropy change, the most
relevant parameter for actual applications of this effect
is the adiabatic temperature change [13]. This value is
usually computed from entropy data by means of equilib-
rium thermodynamic relationships. However, irreversible
effects are expected to take place at first-order phase
transitions which can yield discrepancies between the
computed temperature change and the directly measured
one. Actually, direct measurements of the temperature
change in giant MCE compounds are scarce, and the re-
http://arxiv.org/abs/0704.1241v1
mailto:lluis@ecm.ub.es
ported values in many cases do not seem to be consistent
with those indirectly computed [14, 15, 16]. Here, we
report on adiabatic temperature measurements, which
provide direct evidence of cooling by adiabatic magne-
tization in an inverse magnetocaloric material. It is
also shown that heating is achieved at the paramagnetic-
ferromagnetic phase transition. We focus on moderate
magnetic fields which are readily available for applica-
tions of giant MCE materials [13]. Furthermore, data
obtained from magnetization and heat capacity experi-
ments have enabled us to compare the measured tem-
perature change with that computed from entropy data.
Irreversible thermodynamics arguments are provided to
account for the discrepancies observed at the first-order
structural phase transition.
II. EXPERIMENTAL DETAILS
A polycrystalline Ni50Mn34In16 ingot was prepared by
arc melting the pure metals under argon atmosphere in
a water-cooled Cu crucible and subsequently re-melted
in order to ensure homogeneity. The ingot was sealed
under argon in a quartz recipient and annealed at 1073
K for 2 hours. Finally, it was quenched in ice-water.
The composition of the alloy was determined by energy
dispersive X-ray photoluminescence analysis (EDX). For
calorimetric and magnetization measurements, a small
sample (61.5 mg) was cut using a low-speed diamond
saw. The remaining button (13 mm in diameter, 6 mm
thickness and 4.6 g) was used for the adiabatic tempera-
ture change measurements.
Magnetization was measured by means of a SQUID
magnetometer, and differential scanning calorimetric
(DSC) measurements were conducted using a high-
sensitivity calorimeter. Specific heat measurements
were performed using a modulated differential scanning
calorimeter (MDSC), and data were taken with the con-
stant temperature method [17] starting from the lowest
temperature (190 K).
Adiabatic temperature changes were measured at at-
mospheric pressure using a specially designed set-up. A
thin (0.75 mm diameter) Ni-Cr/Ni-Al thermocouple was
used to measure the temperature. The output of this
thermocouple was continuously monitored by means of a
multimeter that also electronically compensates for the
reference junction. Measurements without any specimen
confirmed that the recorded values were not affected by
magnetic fields up to 1.3 T. The thermocouple was em-
bedded within the sample and good thermal contact be-
tween the sample and the thermocouple was ensured by
Ariston conductive paste. The sample is situated inside a
copper container (sample holder), which is placed on the
top face of a Peltier element. The bottom surface sits on
a copper cylinder, which acts as a heat sink. The bottom
end of the cylinder is in contact with a nitrogen bath.
By controlling the current input into the Peltier element,
it is possible to achieve fine tuning of the temperature
0 5 10 15 20 25
150 200 250 300 350
x (at. %)
Cooling
T (K)
Heating
FIG. 1: (Color online) Phase diagram of Ni50Mn50−xInx, ob-
tained using the data in ref. [11]. MS indicates the marten-
sitic transition line and TC indicates the Curie point line.The
inset shows DSC curves for heating and cooling runs for the
x = 16 sample.
in the 200-320 K interval. Temperature oscillations were
less than 0.05 K. Thermal insulation (adiabaticity) be-
tween the sample and sample holder was ensured by a
polystyrene layer. The sample holder was placed in be-
tween the poles of an electromagnet (28 mm gap), which
enabled fields up to 1.3 T to be applied. A major advan-
tage of using an electromagnet is the short rising time in
the application of the field (the field rises from 0 to 1 T
in about 0.5 s). Such a field rise time is several orders
of magnitude shorter than the thermal relaxation time
of the sample-holder system (∼ 100 s), thus ensuring the
adiabaticity of the process.
In order to check the reliability of the device, we mea-
sured the MCE of commercial pure (99.9 wt %) Gd.
The measured temperature changes obtained around the
Curie point for a magnetic field of 1T agree with those
reported in the literature [18].
III. RESULTS AND DISCUSSION
For the present study we selected a composition with
the para-ferromagnetic and martensitic transition tem-
peratures close to each other. This is illustrated in fig-
ure 1, which shows the Curie and martensitic transi-
tion start temperatures as a function of In content for
Ni50Mn50−xInx alloys. Continuous lines are polynomial
fits to the data given in ref. [11]. The arrows indi-
cate the composition of the studied sample. The in-
set presents DSC curves (heating and cooling) for the
present Ni50Mn34In16 alloy [19]. The peaks at higher
temperature correspond to the Curie point and those at
lower temperatures correspond to the martensitic tran-
sition (which occurs with 15 K thermal hysteresis). In-
tegration of the peaks associated with the martensitic
transition renders latent heats of -1750 ± 100 J/kg for
210 220 230 240
200 240 280 320
T (K)
 0.5 T
 0.7 T
 1 T 
 1.3 T
T (K)
FIG. 2: (Color online) (a) Measured adiabatic temperature
change and (b) computed isothermal entropy change, as a
function of temperature at selected values of the magnetic
field. The inset shows an enlarged view for the 0.5 and 1.3
T fields which illustrates the shift in the inverse MCE with
magnetic field.
the cooling run (forward transition) and 1850 ± 100 J/kg
for the heating run (reverse transition).
The adiabatic temperature changes measured over the
200-320 K temperature range for selected values of the
magnetic field are shown in figure 2(a). Data points were
obtained according to the following procedure, which en-
sures the suppression of any history dependent effect:
first, the sample is heated up to 320 K (above the Curie
point) and then cooled down to the fully martensitic state
at 170 K. Subsequently, it is heated up to the desired tem-
perature and the magnetic field is switched on for 20 s.
After switching off the field, the sample is heated again
above the Curie point and the protocol is repeated for
the next data point. The measured adiabatic tempera-
ture changes shown in fig. 2(a) prove unambiguously that
the sample cools down upon adiabatic application of the
field in the temperature range 200-245 K, while it heats
up in the temperature range 245-320K. The positive tem-
perature change has its maximum value (∆T ≃1.5 K for
1.3 T) at the Curie point. The maximum temperature
decrease (∆T ≃ – 0.6 K for 1.3 T) occurs at a tem-
perature that shifts with magnetic field [see inset in fig-
ure 2(a)], in agreement with the decrease in the marten-
sitic transition temperature reported for Ni-Mn-In alloys
[11]. The values found for ∆T at their corresponding
peak temperatures are comparable to those reported for
other giant MCE materials. However, a novel feature for
200 240 280 320
T (K)
 0.5 T
 0.7 T
 1.3 T
) (a)
FIG. 3: (Color online) (a) Temperature dependence of the
magnetization for selected values of the magnetic field. (b)
Specific heat as a function of temperature. Arrows indicate
the region of the reverse martensitic transition.
Ni50Mn34In16 is that these relatively large temperature
changes can be either positive or negative.
In order to correlate the measured temperature
changes with those indirectly computed from entropy
data, we measured the magnetization of the sample as
a function of temperature and magnetic field. Results at
selected fields are shown in fig 3(a). In the temperature
range 245-320 K, ζ is negative, while a positive ζ is ob-
tained in the range 200-245 K. From these data, we com-
puted the magnetic field-induced entropy change by using
the Maxwell relation ∆S = µ0
ζdH . Results are shown
in Fig. 2(b). Excellent qualitative agreement is observed
between the two quantities (∆T and ∆S) characterizing
giant MCE. Conventional MCE is observed within the
245-320 K temperature range, i.e. a negative entropy
change with the associated positive temperature change,
while in the 200-245 K interval, the sample exhibits in-
verse MCE: an increase in entropy with the associated
negative temperature change.
It is customary to compute the adiabatic temperature
change from isothermal entropy data by means of the
following relationship,
∆Trev = −
∆S, (1)
which is expected to be valid in equilibrium. C is the spe-
cific heat at constant magnetic field and is assumed to be
independent of the magnetic field. In order to check the
200 240 280 320
(a) µ
H=0.5 T
H=0.7 T
H=1 T
H=1.3 T
T (K)
FIG. 4: (Color online) Adiabatic temperature change, as a
function of temperature, for different magnetic fields. Black
symbols stand for measured data and red symbols correspond
to data indirectly computed using equilibrium thermodynam-
ics relationships.
validity of this approach, we measured the specific heat
of our Ni50Mn34In16 sample. Results are shown in figure
3(b). The large lambda-type peak at 302 K corresponds
to the second-order para-ferromagnetic phase transition.
In the temperature range 216-257 K a small bump is
observed, which coincides with the reverse martensitic
transition. No latent heat contributions are expected for
the isothermal-modulated method we have used.
In Fig. 4, we compare the measured adiabatic temper-
ature changes (black symbols) with those computed from
the entropy [Fig. 2(b)] and specific heat data [Fig. 3(b)]
(red symbols) for different values of the applied field.
Good agreement between measured and computed values
over the complete temperature range is obtained at low
magnetic fields. As the magnetic field is increased, there
is still good agreement between the data corresponding
to conventional MCE [20], but the absolute value of the
measured temperature change becomes smaller than the
computed one in the inverse MCE region. Such a dif-
ference is due to the irreversibility associated with the
first-order phase transition.
In order to consider the effect of dissipation, we start
from the Clausius inequality
≤ 0, which can be ex-
pressed as δq
= dS − δSi, where dS is a reversible dif-
ferential change of entropy and δSi is the entropy pro-
duction (δSi ≥ 0). When the magnetic field is adiabat-
ically changed, δq = 0, and under the assumption of a
quasistatic, continuous process with hysteresis [21], the
adiabatic temperature change is expressed as
[−∆S + Si] = ∆Trev +
, (2)
where TSi is the dissipated energy (Ediss). For an in-
verse magnetocaloric effect, there is an increase of en-
tropy by the application of the field, i.e. ∆S > 0. On
the other hand, Si is always positive. Hence, for an out-
of-equilibrium process, the two terms within brackets in
equation 2 will partially cancel each other when the field
is swept from zero to a given value, and therefore, the
measured temperature change will always be less than
the value computed using equilibrium thermodynamics
(see equation 1). Such a difference is expected to be small
at low fields (close to equilibrium conditions), but it be-
comes larger at higher fields. Note that for conventional
MCE, when the field changes from 0 to H, ∆T ≥ ∆Trev,
which is consistent with the data around the Curie point.
At each temperature, the dissipated energy is given by
Ediss = T∆S + C∆T . A value of 158 J/kg is found at
225 K for a field of 1.3 T. This value amounts to about
10 % of the latent heat of the martensitic transition in
this alloy.
In giant magnetocaloric materials for which the MCE
is associated with a first-order transition, the giant effect
relies on the possibility of inducing the phase transition
by application of a magnetic field. The martensitic tran-
sition is driven by phonon instabilities in the transverse
TA2 phonon branch ([110] propagation and [11̄0] polar-
ization) [22, 23]. Recent ab-initio calculations for cubic
Ni2MnIn have shown that increasing the magnetization
due to an external field favors the cubic structure and
leads to a gradual vanishing of the phonon instability
[24] due to the coupling between vibrational and mag-
netic degrees of freedom. This effect results in a marked
decrease of the martensitic transition temperature with
increasing field that enables to induce the transition by
the application of a field at a temperature close to the
zero field transition temperature. Hence, the microscopic
origin of the inverse MCE in Ni50Mn34In16 must be as-
cribed to such magnetoelastic coupling responsible for
the change in the relative stability of the martensitic and
cubic phases.
IV. CONCLUSION
By directly measuring the adiabatic temperature
change in the Ni50Mn34In16 alloy, we provide experi-
mental evidences of both cooling and heating in a giant
inverse magnetocaloric compound. It has been shown
that the irreversibility associated with the first-order
structural transition gives rise to measured temperature
changes which are lower than those indirectly computed
using equilibrium thermodynamics. The existence of a
temperature region where the magnetocaloric effect re-
verses sign under weakly applied magnetic fields opens
up the possibility of new applications of this fascinating
property.
Acknowledgments
This work received financial support from the CICyT
(Spain), Project No. MAT2004–01291, DURSI (Catalo-
nia), Project No. 2005SGR00969, and from the Deutsche
Forschungsgemeinschaft (GK277). XM acknowledges
support from DGICyT (Spain). We thank Peter Hinkel
for technical support.
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