Magnetocaloric effect in Ni-Mn-Ga thin films - McMaster Department ...

Magnetocaloric effect in Ni-Mn-Ga thin films under concurrent 

magnetostructural and Curie transitions 

Yuepeng Zhang ( ), 1,a) R. A. Hughes, 2,5 J. F. Britten, 3 P. A. Dube, 2 J. S. Preston, 2,4 

G. A. Botton, 1,2 and M. Niewczas 1,2,b) 

1 

Department of Materials Science and Engineering, McMaster University, Hamilton, Ontario L8S 4L7, 

Canada 

2 

Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario L8S 4M1, Canada 

3 

McMaster Analytical X-ray Diffraction Facility, McMaster University, Hamilton, Ontario L8S 4L7, Canada 

4 

Department of Engineering Physics, McMaster University, Hamilton, Ontario L8S 4L7, Canada 

5 

Department of Mechanical Engineering, Temple University, 1947 N. 12th Street, Philadelphia, 

Pennsylvania, 19122, USA 

(Received 29 July 2010; accepted 19 May 2011; published online 7 July 2011) 

An investigation of the magnetocaloric effect for Ni-Mn-Ga films with a composition chosen to 

yield the highly advantageous magnetostructural phase transition between the paramagnetic 

austenitic and the ferromagnetic martensitic phases is presented. The observed effect is particularly 

strong at low magnetic fields, yielding a maximum negative entropy change of 1.4 J/kg K for a 

field change of only 0.5 T. It is also observed that the cooling process yields a 40% larger entropy 

change compared to the heating process. Temperature dependent magnetic, structural, and 

transport measurements indicate that the entropy peak difference between cooling and heating 

cycles is associated with a stronger overlap of the Curie transition of the austenitic phase with the 

magnetostructural phase transition upon cooling. The observed behavior is significant to microlength-scale 

spot cooling applications utilizing thin films and large-scale magnetic refrigeration 

applications where low magnetic fields are favorable. VC 2011 American Institute of Physics. 

[doi:10.1063/1.3602088] 

I. INTRODUCTION 

The magnetocaloric effect (MCE) is a phenomenon 

where a magnetic material exhibits a temperature or entropy 

change when subjected to a magnetic field variation. 1 The 

effect is often used in refrigeration cycles where low temperatures 

are achieved in a process of adiabatic demagnetization. 

As the material undergoes adiabatic demagnetization, the entropy 

of the spin system will increase whereby cooling occurs 

as the required entropy is extracted from the crystalline lattice. 

Compared to conventional gas compression technology, magnetic 

refrigeration technologies are more environmentally 

sound since they eliminate the need for energetically inefficient 

compressors and volatile liquid refrigerants. 1 Since the 

heat transfer during the refrigeration process is dependent 

upon the entropy change in the magnetic refrigerant element, 

a material system exhibiting a large entropy change is highly 

advantageous to magnetic refrigeration technologies. 

An entropy change can be induced in magnetic refrigerant 

materials by either magnetic or structural phase transitions 

provided that a difference in the magnetization exists 

between the initial and final phases. Numerous material 

systems, such as Gd 5(Si 1 xGe x) 4 (Ref. 2), Mn(As 1 xSb x) 

(Ref. 3), MnFe(P1 xAsx) (Ref. 4), Ni-Mn-In (Refs. 5 and 6), 

Ni-Mn-Ga (Refs. 7–10), and Ni-Mn-In-Co (Ref. 11), have 

demonstrated that the effect is far more pronounced when 

a) 

Present address: Institut Néel - CNRS, 25 rue des Martyrs, Grenoble 

38000, France. 

b) 

Electronic mail: niewczas@mcmaster.ca. 

JOURNAL OF APPLIED PHYSICS 110, 013910 (2011) 

the magnetic and structural phase transitions are coupled, 

i.e., when the materials exhibit a magnetostructural transition. 

For these systems, both the crystal and magnetic structures 

are different for the original and transformed phases. 

This gives rise to a larger MCE effect since, due to a strong 

magnetocrystalline coupling, the magnetostructural transition 

gives rise to a change in the distance between the magnetic 

atoms in the crystal lattice which, in turn, results in a 

significant change in the magnetization. 4 In addition, the 

total entropy change for the transition could be maximized 

through a sum of the contributions from both the crystallographic 

and the magnetic components. 12 

To date, the largest MCEs are observed almost exclusively 

for materials showing a magnetostructural transition. 

The transition is induced either solely by temperature or by 

the application of an external magnetic field while the sample 

temperature remains near the magnetostructural transition 

temperature. 2 The field induced magnetostructural transition 

results in a larger entropy change, but the process generates 

hysteresis losses, which reduces the efficiency of magnetic refrigeration 

cycles. 13,14 In addition, the magnetic field required 

for the activation of the magnetostructural transition is typically 

greater than 1 T. 2,8 From the perspective of micro-devices, 

such a large magnetic field is undesirable because it can 

interfere with the electronics of the device and significant 

power is required to generate the fields. The temperature 

driven magnetostructural transition is not heavily reliant on 

external magnetic fields and it is, therefore, advantageous to 

use this approach for micro-refrigeration applications. 

0021-8979/2011/110(1)/013910/8/$30.00 110, 013910-1 

VC 2011 American Institute of Physics 

Downloaded 07 Jul 2011 to 130.113.54.72. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions

013910-2 Zhang et al. J. Appl. Phys. 110, 013910 (2011) 

The Ni-Mn-Ga system exhibits a temperature driven 

magnetostructural transition. Both the Curie and martensitic 

transition temperatures can be tuned over a wide temperature 

range through the adjustment of the valence electron to atom 

ratio (e/a) associated with a particular alloy composition. 15,16 

For small e/a ratios (i.e., e/a < 7.7) the martensitic transition 

occurs in a temperature range far below the Curie temperature, 

while the reverse tendency occurs for larger ratios (i.e., 

e/a > 7.7) (Ref. 17). The intermediate range (i.e., e/a 7.7), 

where the two transitions overlap, 17,18 is therefore of the 

greatest interest to MCE applications. Various reports on the 

MCE in bulk Ni-Mn-Ga samples have recently been presented, 

8,9,19,20 however, the application of this effect to 

micro-scale applications using thin films has received little 

attention. 21 Here, we present a study of the magnetocaloric 

effect in Ni-Mn-Ga films with an e/a ratio of 7.73. The films 

exhibit a Curie transition of the austenitic phase which is 

coincident with the magnetostructural phase transition 

between the paramagnetic austenitic and ferromagnetic martensitic 

phases. The overlap, however, is stronger upon cooling 

than heating. The cooling transition results in an entropy 

change which is 40% larger than that obtained for gadolinium 

films. 22 These findings indicate that Ni-Mn-Ga films are 

excellent candidates for micro-length-scale magnetic refrigeration 

applications such as spot cooling in microelectromechanical 

systems (MEMS) 23 and micro-energy storage 

devices. 24 

II. EXPERIMENTAL 

In an earlier report 25 we detailed a procedure for the 

deposition of (101)-oriented Ni-Mn-Ga films on (100) YSZ 

(Y 2O 3 stabilized ZrO 2 with 8 Mole% Y 2O 3) substrates in a 

previously unexplored high deposition temperature regime 

using the pulsed laser deposition technique. For this method, 

high growth temperatures became accessible through the use 

of target materials enriched in both manganese and gallium, 

where the enrichment compensated for the high vapor pressures 

of these elements. The films produced by this procedure 

showed improved crystallinity with micrometer-sized 

grains and the desired highly-twinned microstructure for the 

martensitic phase. These properties gave rise to both a welldefined 

reversible martensitic transformation above room 

temperature and a reversible magnetically induced twin variant 

reorientation effect. 25,26 The thickness of the films is 250 

nm. The composition of the films, as determined by x-ray 

energy dispersive spectroscopy taken with the JEOL 2010 

FEG STEM, is Ni51Mn29Ga20ðat:%Þ. This composition corresponds 

to an electron to atom ratio (e/a) of 7.73; a value in 

the range where the martensitic and magnetic phase transitions 

overlap. 17,18 The three-dimensional x-ray diffraction 

(XRD3) measurements carried out at both 380 K and room 

temperature reveal an austenitic phase with a cubic crystal 

structure having lattice parameters of a ¼ b ¼ c ¼ 5.846(3) A ˚ 

and a martensitic phase having an orthorhombic structure 

with a ¼ 6.112(4) A ˚ , b¼ 5.885(3) A ˚ , and c ¼ 5.527(2) A ˚ 

(Ref. 26). 

The phase transformations and magnetic properties of 

Ni51Mn29Ga20 films were studied using different techniques. 

Temperature dependent XRD3 measurements were used to 

monitor the crystallographic phase transformation. The 

measurements were performed with a Rigaku RU-200 rotating 

anode Cu Ka x-ray generator, on a Bruker 3-circle D8 

goniometer with a parallel-focusing mirror optic, and a 

Smart 6000 CCD detector. Electrical resistivity measurements 

were carried out using an in-house developed four-point Van 

der Pauw resistivity apparatus, capable of operating between 

4 and 410 K. The isothermal and temperature dependent magnetization 

was obtained with a Quantum Design magnetic 

property measurement system associated with the superconducting 

quantum interference device. Other experimental 

details are available elsewhere. 25,26 

III. RESULTS 

A. Phase transformations 

The temperature dependence of the structural phase 

transition for the Ni51Mn29Ga20 films was directly observed 

using a three-dimensional XRD technique. The analysis of 

the intensities of the (400) and (004) martensite and (400) 

austenite reflections during the heating and cooling sequences 

allows for the characterization of the structural phase 

transformation based on the relative intensities of these diffraction 

peaks. Figure 1 shows the progression of the peak 

intensities as the film is heated from 233 to 371 K and then 

cooled back down to 233 K. A response dominated by the 

cubic austenitic and orthorhombic martensitic phases, 

respectively, is observed at the high and low temperature 

extremes of the sequence. Between 299 and 371 K there 

exists a mixed response of varying degree which characterizes 

the phase coexistence, which is a feature typical for a 

first-order phase transition. The back and forth 

FIG. 1. (Color online) Three-dimensional x-ray diffraction data showing the 

structural phase transition for a Ni51Mn29Ga20 film as the temperature is 

cycled back and forth through the martensite-austenite phase transition. The 

data at 371 K shows only a single (400) peak for the cubic austenitic phase 

while the 233 K data shows the (400)/(004) peak splitting expected for the 

orthorhombic martensitic phase. A first-order martensitic phase transformation 

occurs between 299 and 371 K where one phase gradually transforms 

into the other. In this temperature regime, all three peaks are visible due to 

the austenite-martensite phase coexistence. Note that the phase transition is 

completely reversible and exhibits a hysteresis. Also noteworthy is the 

existence of an extremely weak peak between the two martensite peaks at 

233 K, which is a feature consistent with residual levels of the austenitic 

phase. 



FIG. 2. (Color online) Temperature dependence of the volume fractions for 

the martensitic (circles) and austenitic (triangles) phases during the heating 

(top) and cooling (bottom) processes. The dashed lines denote the temperatures 

corresponding to Theat 50 ¼ 358 K and Tcool 50 ¼ 355 K (i.e., where the volume 

fractions for the two phases are equal). The fact that these values are 

offset by about 3 K is a clear indication of the temperature hysteresis in the 

phase transformation. The line connecting the data points is a guide for the 

eye. 

transformations between the martensitic and austenitic 

phases, and the associated hysteresis, are quite apparent. The 

fact that even at the lowest temperature (i.e., 233 K) residual 

amounts of the austenitic phase exist is noteworthy. This observation 

is consistent with the room-temperature transmission 

electron microscopy images which show a 2–3 nm thick 

austenite layer at the film-substrate interface. 26 The complete 

reversibility of the martensitic transformation is also evident 

from the data. 

The volume fractions for the austenitic and martensitic 

phases over the entire heating-cooling cycle were extracted 

form the data in Fig. 1. The values were determined by comparing 

the integrated peak intensities in the two-phase 

regions to those obtained at the high and low temperatures 

where a single phase dominates (i.e., 371 and 299 K). This 

methodology yields temperature dependent volume fractions 

for the austenitic (fA) and martensitic (fM) phases which are 

given by, 

fAðTÞ ¼ IAðTÞ 

IAð371 KÞ ; fMðTÞ ¼ IMðTÞ 

; (1) 

IMð299 KÞ 

where IA and IM are the integrated intensities of the (400) 

pole from the austenitic phase and the (040) pole from the 

martensitic phase, respectively. Figure 2 shows the temperature 

dependence of the austenite and martensite volume fractions 

as obtained from the XRD measurements for both the 

heating and cooling sequences. The data reveal a hysteresis 

in the first-order phase transformation and allows for the 

extraction of the values Tcool 50 ¼ 355 K and Theat 50 ¼ 358 K, 

which define the temperatures where the film is comprised of 

equal amounts of the austenitic and martensitic phases during 

the cooling and heating sequences, respectively. 

The temperature dependence of the resistivity for the 

Ni51Mn29Ga20 films was measured for temperatures between 

7 and 400 K. The results shown in Fig. 3 reveal a welldefined 

hysteretic feature extending from 307 to 370 K, 

which is consistent with the martensitic phase transformation 

FIG. 3. Temperature dependent dc resistivity measured using the Van der 

Pauw technique. The characteristics show a reversible martensitic transformation 

in the temperature range of 307 to 370 K. All values were normalized 

to the resistivity (q 0) of the films at 7 K. 

observed with three-dimensional XRD. Using the deviation 

from linearity in the slope of the resistivity-temperature characteristics 

as a criterion for the beginning and ending of the 

phase transformation, the austenite to martensite phase transformation 

start (Ms) and finish (Mf) temperatures, and the 

martensite to austenite transformation start (As) andfinish 

(Af) temperatures, were determined to be Ms ¼ 361 K, 

Mf ¼ 307 K, As ¼ 312 K, and Af ¼ 370 K. With no other 

resistivity anomaly present in the data down to 7 K it is likely 

that the films have no inter-martensitic transformations. 

Temperature dependent dc magnetization measurements, 

carried out in a magnetic field of l 0H ¼ 0:005 T 

between 2 and 400 K, were used to probe the ferromagnetic 

phase transition. The results are shown in Fig. 4. The rapid 

increase of magnetization in the temperature range between 

352 and 360 K reveals the existence of a ferromagnetic transition. 

It is noteworthy that the M(T) curve shows a hysteresis 

between the cooling and heating sequences along with a 

FIG. 4. (Color online) Temperature dependent dc magnetization for a 

Ni51Mn29Ga20 film in an external magnetic field of 0.005 T, for both the 

cooling (backward arrow) and heating (forward arrow) sequences. The magnetization 

curves show a peak near 352 K and a hysteresis between the cooling 

and heating sequences due to the concurrent magnetostructural and 

Curie transitions. The inset shows an expanded view for the temperature 

range of 335–375 K, which reveals a cross-over in the magnetization curves 

at 356 K. 



peak. This peak, which is centered around 352 K, has a lower 

maximum value in the heating sequence than it does in the 

cooling sequence. There does exist, however, a cross-over 

point at 356 K, demarcating a 7 K temperature interval 

where the observed magnetization during the heating 

sequence is somewhat higher. Of the utmost importance is 

the fact that the magnetic transition overlaps with the structural 

transition observed in the three-dimensional XRD and 

resistivity measurements (Figs. 1 and 3). This scenario, while 

only rarely reported for Ni-Mn-Ga films, has been attributed 

to the composition of the alloy 27 and is responsible for the 

observed hysteresis and cross-over in the temperature interval 

of the magnetic transition. 

While the overlap in the structural and magnetic phase 

transitions complicates the magnetization data considerably, 

it is still possible to extract the Curie temperature,Tc, through 

suitable processing of the dataset. This temperature is typically 

obtained from the inflection point in the magnetization’s 

temperature dependence, but such a procedure is 

ineffective here due to the complex shape of the magnetization 

curve (Fig. 4). An alternative method relies on an Arrott 

plot 28 which determines the Curie temperature from the 

measured magnetization isotherms. The method requires that 

the magnetization is plotted in the form of M2 versus H=M, 

where a linear extrapolation of the high field data to the zero 

magnetic field yields the square of the spontaneous magnetization, 

M2 0 . In the ferromagnetic region (i.e., T < Tc), M2 0 is 

positive 29 while in the paramagnetic region (i.e., Tc) itis 

negative (i.e., where the M2 versus H=M curve intercepts 

the H/M-axis). 29 At T ¼ Tc, the spontaneous magnetization 

is zero and, thus, the M2 versus H=M curve passes through 

the origin. The low field data is excluded from the extrapolation 

because it represents an averaged response over differently 

oriented magnetic domains. 29 

In this study, the magnetization isotherms used to generate 

the Arrott plots were measured in a cooling sequence 

(Fig. 5) since the onset of ferromagnetism is more accurately 

determined than its disappearance. 28 It is also noted that the 

Curie temperature of the martensitic phase, TM c , significantly 

differs from that of the austenitic phase due to the different 

crystal structures of the two phases. 30,31 This is not surprising 

since the Mn-Mn interatomic distances within the unit 

FIG. 5. The isothermal magnetization curves for a Ni51Mn29Ga20 film 

measured at different temperatures, which extend through the magnetostructural 

phase transformation. 

cell are different for the austenitic and martensitic lattices, 

and it is these distances which, to a large degree, determine 

the spin exchange interactions responsible for the magnetic 

ordering. 30 The Tc temperature determined here through the 

Arrott plots is the Curie temperature of the austenitic phase, 

TA c , since the magnetization isotherms used are measured at 

the temperatures where austenite is the predominant phase 

(i.e., those measured at temperatures above Tcool 50 ¼ 355 K). 

In fact, for the films studied here, the Curie temperature of 

the martensitic phase, TM c , is a virtual temperature since it is 

well above the temperatures where the martensitic phase persists 

(i.e., TM c > Ms). This is apparent from the temperature 

dependent dc magnetization (Fig. 4) which does not show 

any anomalies below the martensitic transformation finish 

temperature of 307 K. Such a virtual transition temperature 

can still be estimated through the orthodox Landau theory, 30 

but this aspect is beyond the scope of this paper. The important 

point being made here is that the two phases spontaneously 

magnetize at different temperatures and it is the Curie 

transition of the austenitic phase that overlaps with the martensitic 

transformation. It should also be noted that at the 

martensitic transformation start temperature, Ms, the two 

structural phases have a different magnetic characteristic 

where the austenitic phase is paramagnetic (i.e., the magnetization 

is zero for temperatures above Ms ¼ 361 K; see Fig. 4) 

while the martensitic phase is ferromagnetic (TM c > Ms). 

Therefore, the transition between the two structural phases 

is, in fact, a magnetostructural phase transition. To determine 

the Curie temperature of the austenitic phase, TA c , the 

M2 versus H=M curves were measured in the temperature 

range of 356–362 K, where the austenitic phase predominates 

(Tcool 50 ¼ 355 K), as is shown in Fig. 6. At 360 and 

362 K, the linear extrapolation of the high field data 

ðl0H > 0:4 TÞintercepts the H/M-axis while at 356 and 358 

K it intercepts the M2 axis. This indicates that the TA c temperature 

is around 359 K. This value is consistent with that 

observed for bulk Ni-Mn-Ga samples of similar composition. 

32 For the purpose of comparison, the 352 and 354 K 

FIG. 6. (Color online) M 2 vs H/M plots for a Ni51Mn29Ga20 film derived 

from the isothermal magnetization data for temperatures between 352 and 

362 K. A linear extrapolation of the high field data (l0H > 0:4 T) for the 

356–362 K curves was used to estimate the Curie temperature of the austenitic 

phase. The fact that M2 0 is positive at 358 K but negative at 360 K indicates 

the onset of the ferromagnetic transition of the austenitic phase near 359 K. 



isotherms, where the response is dominated by the martensitic 

phase, are also presented in Fig. 6. The fact that these 

two curves exhibit very different curvatures at high fields as 

compared to the 356–362 K data is consistent with the argument 

that the martensitic and austenitic phase each has different 

magnetic response and Curie temperature. 

It should be noted that the Arrott plot is based on the 

equation of state: 33 ðH=MÞ 1=c ¼ðT TcÞ=T1 þðM=M1Þ 1=b . 

By plotting M2 versus H=M, it is assumed that the critical 

exponents, c and b, follow the mean field theory (i.e., c ¼ 1, 

b ¼ 1/2). However, the 356, 358, 360, and 362 K plots, 

shown in Fig. 6, all display curvature even at high fields, 

indicating that the actual critical exponents for the austenitic 

phase of the Ni-Mn-Ga system deviate from the mean field 

values. The degree of deviation is not significant since these 

plots are still parallel at higher fields ðl0H > 0:4 TÞ. To estimate 

the deviation between the actual Curie temperature and 

the one derived from the mean field model, various critical 

exponents have been examined in the range defined by the 

mean field (c ¼ 1, b ¼ 1/2) and the Heisenberg model 

(c ¼ 1.386, b ¼ 0.365) (Ref. 34). These two models, for the 

most part, define the range of c and b values for crystalline 

ferromagnets. From this examination it is found that the Tc values obtained always fall within the temperature range of 

357–359 K. This indicates that the mean field theory does 

not significantly overestimate the Curie temperature and validates 

the 359 K onset for the ferromagnetic ordering of the 

austenitic phase. It is noted that this trial-and-error process is 

not the standard method used for determining the critical 

exponents. The correct method requires a fit of the experimental 

data to the equation of state 33 and power-law dependence 

35 using the iterative approach described by Pramanik 

and Banerjee. 34 Unfortunately, such an iterative process is 

not possible here due to the coexistence of the martensitic 

transformation. As a result of the overlap between the structural 

and magnetic transition, nearly all of the magnetization 

isotherms measured below 356 K (Tcool 50 ¼ 355 K) contain a 

strong signal from the martensitic phase and, thus, cannot be 

used in the fitting procedure for the estimation of the Curie 

temperature of the austenitic phase. While it is not customary 

to use the trial-and-error process described above, it does 

provide a means by which to evaluate the mean field value. 

The measurements and procedures outlined in this section 

have allowed for the determination of all of the critical 

temperature parameters associated with Ni51Mn29Ga20 films 

under study. From these parameters, which are summarized 

in Table I, it is possible to construct the sequence by which 

the structural and magnetic phase transitions unfold upon 

transitioning from the paramagnetic austenite (PA) to the ferromagnetic 

martensite (FM) phase or vice versa. These two 

sequences, given by 

TABLE I. The critical temperatures associated with the structural and magnetic 

phase transitions for a Ni51Mn29Ga20 film. 

Ms Mf As Af T A c T M c T cool 

50 

T heat 

50 

361 K 307 K 312 K 370 K 359 K > 361 K 355 K 358 K 

FM Mf T cool 

50 T A c Ms PA ðcoolingÞ; 

FM ! As ! T heat 

50 ! TA c ! Af ! PA ðheatingÞ; 

allow for an understanding of the temperature dependent 

magnetization characteristics shown in Fig. 4. With T A c and 

Ms being extremely close to one another, the magnetization 

of the film is influenced by both structural and magnetic 

phase transitions. The temperature hysteresis observed in the 

M(T) curves between the heating and cooling sequences is a 

reflection of the hysteresis associated with the first-order 

martensitic phase transition. Due to this hysteresis, the temperature 

dependence of the volume fraction for each of the 

two phases is different for the heating and cooling sequences. 

The film, therefore, contains more martensitic phase on heating 

than on cooling for each temperature in the phase transition 

regime. With the magnetization of each phase being 

proportional to its volume fraction and the overall magnetization 

being the sum of the individual magnetizations of the 

two phases, the hysteresis will give rise to a difference in the 

temperature dependent magnetization for the heating and 

cooling sequences. It should be noted that due to its high 

magnetocrystalline anisotropy 36 the magnetization of the 

martensitic phase is smaller than that of the austenitic phase 

under the small magnetic field applied here (l 0H ¼ 0:005 T). 

Hence, the lower magnetization in the heating sequence is 

due to the film containing more volume fraction of the martensite 

phase. It follows that the 352 K magnetization peak 

has a lower magnitude upon heating than upon cooling. It is 

noted, however, that the origin of this magnetization peak is 

more complex than a simple combination of the temperature 

dependences of the two phases. It is also influenced by the 

thermal variation of the austenite susceptibility which has a 

maximum near Tc. Such a peak is reminiscent of the Hopkinson 

peak which characterizes anisotropic materials. For the 

present case, we tentatively attribute this phenomenon to the 

fact that the martensitic and austenitic phases are made of 

exchange–coupled nanograins. Upon heating, the magnetic 

moment of the austenitic phase tends to align along the already 

established magnetization of the martensitic phase, 

while upon cooling the austenite moment is likely to orient 

along the applied magnetic field since the martensitic phase 

is nearly absent. Finally, the occurrence of the crossover 

between the heating and cooling magnetization curves at 

356 K (see the inset to Fig. 4) is a manifestation of the low 

austenite magnetization in the proximity of its Curie temperature 

(Tc ¼ 359 K), combined with the presence of the higher 

volume fraction of the ferromagnetic martensitic phase in 

the film at these temperatures upon heating rather than 

cooling. 

B. Magnetocaloric effect 

The overlapping magnetic and structural phase transitions 

provide the prerequisite condition for the occurrence of 

a large entropy change which depends upon both the magnitude 

of the applied magnetic field (H) and the temperature 

(T). This entropy change, DSðT; HÞ DH , produced under isobaric 

conditions, can be estimated from the magnetization 

isotherms using the Maxwell relation: 37 



which upon integration yields: 38 

@S 

¼ 

@H T 

@M 

; (2) 

@T H 

ð H 

@MðT; HÞ 

DSðT; HÞDH ¼ 

dH: (3) 

0 @T H 

For the case of a first-order phase transition, the use of this 

Maxwell relation has been controversial because the magnetization 

is expected to undergo a discontinuous change at a 

constant temperature, 39,40 and, as a consequence, @MðT; HÞ= 

@T, is infinite. Actual first-order transitions, however, occur 

over a non-negligible temperature range. In this case, the 

Maxwell relation is still applicable, and Eq. (3) is modified 

to (Ref. 41): 

DSðT; DHÞ ¼ 

ð Hcrit: 

0 

ðHmax þ 

1 

2 

@MðT; HÞ 

@T 

dH 

H 

@MðT; HÞ 

@T 

dH 

H 

Hcrit:þdH 

dHcrit: 

dTcrit: 

dMðT; Hcrit:Þ: (4) 

where Hmax is the maximum applied magnetic field, Hcrit. is 

the critical field that induces the first-order phase transition 

(Hcrit. < Hmax), dH is an infinitesimal increase of the magnetic 

field (i.e., dH ! 0), dM is the difference in magnetization 

between the initial and product phases, and T crit. is the 

transition temperature. The first and the second terms in 

Eq. (4) are the entropy change in the magnetic field intervals 

[0, H crit.] and [H crit. þ dH, H max]. The third term is the work 

done (under the variation of the magnetic field) to generate 

the magnetization change (dM) at the first-order transition 

and is only applied to the transition region, i.e., the field 

interval [Hcrit., Hcrit. þ dH]. A comparison of Eqs. (3) and (4) 

reveals that there is no difference between the two equations 

if the applied magnetic fields are smaller than the critical 

field. It is also evident that, in this case, the calculated entropy 

change is underestimated when compared to the values 

obtained using a larger field span which includes the critical 

field. For applied fields larger than the critical field, Eq. (4) 

is more applicable, since Eq. (3) overestimates the value of 

the entropy change. Both of the previously discussed cases 

have been experimentally demonstrated by Casanova et al. 

(Ref. 42) for the Gd5(SixGe1-x)4 system. The current study 

corresponds to the first scenario where the magnetic fields 

used in both the cooling and heating sequences are smaller 

than the critical field, a fact which is discernible by the absence 

of a metamagnetic character 40 for the magnetization 

isotherms measured in the magnetostructural transition temperature 

range. As a result, the entropy changes derived from 

the present results are most likely underestimated for both 

the heating and cooling processes when compared to the values 

reported in the literature. 19,20 Low magnetic fields were 

used in the present work despite these difficulties in order to 

demonstrate the applicability of the films to MEMS devices 

where low fields are favorable for avoiding interference 

between electronic circuits. 

For magnetization measurements made at discrete fields 

and temperature intervals, Eq. (3) can be numerically solved 

using the approximate equation, 43 

DSðT0; HÞ DH 

1 

DT 

ð H 

0 

MðT2; HÞ H dH 

ð H 

0 

MðT1; HÞ H dHŠ ; 

where the temperature interval (DT) and the average midpoint 

temperature (T0) of the interval are given by 

DT ¼ T2 T1; T0 ¼ T1 þ T2 

: (6) 

2 

From Eq. (5) it is known that the entropy change occurring 

over the DT temperature interval is assigned to the average 

temperature, T0. Figure 7(a) shows a plot of the temperature 

dependent entropy change, calculated in this manner, as the 

sample is cooled through the phase transitions for magnetic 

field intervals ranging from 0.1 to 0.5 T. For each interval, 

the negative of the entropy change shows a narrow peak with 

a maximum at 355 K and a peak width characterized by a 

full width at half maximum (FWHM) of approximately 6 K. 

Figure 7(b) shows the corresponding plot for the case where 

the sample is heated through the transition instead of being 

FIG. 7. The negative magnetic entropy change as a function of temperature 

for a Ni51Mn29Ga20 film derived from the magnetization data using magnetic 

field intervals ranging from 0.1 to 0.5 T upon (a) cooling and (b) heating 

through the phase transitions. Note that upon cooling, the peaks in DS 

are significantly larger and are shifted to a lower temperature. The dataset is 

also given in units of [mJ/(cm 3 K)] to facilitate comparisons with data 

obtained for other magnetic refrigerant materials reported in the literature. 

Downloaded 07 Jul 2011 to 130.113.54.72. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 

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cooled. For this case, the negative of the magnetic entropy 

change shows a similar response except that the peak position 

is shifted to 358 K and the height of the maximum is significantly 

reduced for each value of the magnetic field. 

A second important criterion for magnetocaloric materials 

is the refrigerant capacity (RC). The RC value is a direct 

measure of the heat transferred from the cooled volume to 

the hot reservoir in a refrigeration cycle. 44 It is defined as, 38 

RC ¼ 

ð Th 

Tc 

DSðT; HÞdT; (7) 

where Tc and Th are the temperatures of the cold and hot volumes 

in the refrigeration cycle. The graphical solution of 

Eq. (7) is the area under the DS versus T peak for the temperature 

interval extending from Tc to Th. By convention, the 

temperatures associated with the FWHM of the peak is typically 

taken as T c and T h. In the present work, we use a wider 

temperature interval (325–365 K) to compare the RC values 

for the two thermal processes to account for the asymmetric 

shape of the entropy peaks. The RC values derived for the 

cooling and heating processes are 15.4 and 15.9 J/kg, respectively. 

These RC values are quite large for the low magnetic 

fields applied (m 0H ¼ 0.5 T), a result which is promising for 

micro-scale magnetic refrigeration applications. 

IV. DISCUSSION 

The Ni51Mn29Ga20 films show a magnetostructural 

phase transformation between the paramagnetic austenitic 

and ferromagnetic martensitic phases for both the cooling 

and the heating sequences. Overlapped with the magnetostructural 

transition is the Curie transition of the austenitic 

phase itself. However, the overlap occurs to a smaller extent 

for the heating sequence than it does for the cooling 

sequence. In order to appreciate this point, one must bear 

in mind that the Curie temperature of the martensitic phase 

is well above the martensitic transition temperature 

(T M c 

> 361 K) for both the heating and cooling sequences. 

Thus, it is expected that the ferromagnetic ordering is firmly 

established for the martensitic phase for both sequences over 

the entire experimental temperature range. This, however, is 

not the case for the austenitic phase since its Curie transition 

is within the temperature range of the magnetostructural 

phase transition which occurs between 307 and 370 K. With 

the austenite Curie transition occurring in a narrow temperature 

range below 359 K (Fig. 4), but where the austenite 

phase exists in significant quantities only for temperatures 

above Theat 50 ð¼ 358 KÞ and Tcool 50 ð¼ 355 KÞ for the heating 

and cooling sequences, the influence of the ferromagnetism 

is expected to be highly sequence dependent. For the heating 

sequence, only a small amount of the austenitic phase participates 

in the ferromagnetic ordering since the austenite has 

lost nearly all of its ferromagnetism when its volume fraction 

becomes larger than 50%. In contrast, the cooling sequence 

is characterized by a significant volume fraction of the austenite 

which transforms from the paramagnetic to the ferromagnetic 

state. It is also noted that the observed phase 

transformation behavior is consistent with the phenomeno- 

logical Ni-Mn-Ga phase diagram proposed by Albertini 

et al. (Ref. 40) for both the nickel-rich (Ni2.16Mn0.84Ga) and 

manganese-rich (Ni2Mn1.2Ga0.8) compositions (TAM and 

TMA in Ref. 40 correspond to Tcool 50 and Theat 50 in the present 

work, respectively). 

Accompanying the magnetostructural phase transition is 

an MCE which is characterized by a maximum negative entropy 

change of 1.4 and 1.0 J/kg K for a magnetic field interval 

of 0.5 T upon cooling and heating, respectively. While it 

is difficult to directly compare these values to other results in 

the literature due to the widely varying field intervals used, it 

is noted that the values obtained compare quite favorably to 

gadolinium films measured at similar magnetic fields. The 

entropy change obtained at 0.5 T for the cooling sequence is 

about 40% larger than that of gadolinium at 0.6 T (Ref. 22). 

Thus, the film shows potential to be used in fabricating 

micro-length-scale refrigerant devices which could operate 

at significantly lower fields. 

There are two distinctive features associated with the entropy 

peaks observed for the films: (i) the temperature dependent 

hysteresis between the heating and cooling 

sequences, and (ii) the peak height differences between these 

two thermal pathways. Since the Curie transition is a secondorder 

phase transition which normally does not exhibit any 

hysteresis, the difference in peak position is related to the 

temperature hysteresis in the forward and reverse martensitic 

phase transitions. With regard to the entropy change peak 

height, a nearly 40% larger value is observed for the cooling 

sequence over that of the heating sequence. The source of 

this enhanced peak height is most likely the contribution 

from the ferromagnetic ordering of the austenitic phase since 

it overlaps to a greater extent with the magnetostructural 

transformation between the martensitic and austenitic phases 

upon cooling. The much steeper M(T) curve and the significant 

asymmetry associated with the DS peak during the 

cooling sequence, as shown in Figs. 4 and 7, respectively, is 

consistent with a rapid development of magnetic ordering in 

the system through both the Curie and magnetostructural 

transitions. As a final comment on the use of the Maxwell 

relation as a means of determining the amount of the entropy 

change, it should be noted that the values obtained here 

underestimate the entropy change for both the cooling and 

heating sequences due to the application of magnetic fields 

which are smaller than the critical field required for the fieldinduced 

magnetostructural phase transition, as explained in 

Sec. III B. This, however, does not alter the conclusions 

drawn from the analysis of the two thermal processes regarding 

the relative effect of the entropy change between the 

cooling and heating sequences, since the first-order magnetostructural 

transition is equally involved and is temperature 

driven for both cases. It also remains true that the higher entropy 

change observed in the cooling process is a result of 

the additional contribution from the second-order Curie transition 

in the austenitic phase. 

V. SUMMARY AND CONCLUSIONS 

The phase transformations and magnetocaloric effect 

have been studied for Ni-Mn-Ga thin films using electrical 



resistivity, magnetometry, and three-dimensional XRD 

measurements. A maximum entropy change of 1.4 J/kg K 

has been observed at 355 K for a low magnetic field change 

of 0.5 T. The effect is induced mainly by a magnetostructural 

martensitic transformation, but is further augmented by the 

concurrent ferromagnetic ordering of the austenitic phase. 

The results are promising for micro-length-scale spot cooling 

applications utilizing films and pave the way for the development 

of bulk materials with improved properties for largescale 

magnetic refrigeration operating under low magnetic 

fields. 

ACKNOWLEDGMENTS 

The authors sincerely thank Dr. Dominique Givord for 

his constructive discussion on dc magnetization results and 

acknowledge the Natural Sciences and Engineering Research 

Council of Canada (NSERC), the Ontario Centres of Excellence, 

and the Canadian Institute for Advanced Research 

(CIFAR) for funding. 

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