S.Ghorai et al. Instrument A setup for direct measurement of the adiabatic temperature change in magnetocaloric materials

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S.Ghorai et al./Instrument

A setup for direct measurement of the adiabatic temperature change in

magnetocaloric materials

Sagar Ghorai,1, ∗Daniel Hedlund,1Martin Kapuscinski,1and Peter Svedlindh1

1Department of Materials Science and Engineering,Uppsala University, Box 35, SE-751 03,Uppsala, Sweden

(Dated: October 24, 2022)

In order to ﬁnd a highly eﬃcient, environment-friendly magnetic refrigerant, direct measurements

of the adiabatic temperature change ∆Tadb is required. Here, in this work a simple setup for the

∆Tadb measurement is presented. Using a permanent magnet Halbach array with a maximum

magnetic ﬁeld of 1.8 T and a rate of magnetic ﬁeld change of 5 T/s, accurate determination of

∆Tadb is possible in this system. The operating temperature range of the system is from 100 K to

400 K, designed for the characterization of materials with potential for room temperature magnetic

refrigeration applications. Using the setup, the ∆Tadb of a ﬁrst-order and a second-order compound

have been studied. Results from the direct measurement for the ﬁrst-order compound have been

compared with ∆Tadb calculated from the temperature and magnetic ﬁeld dependent speciﬁc heat

data. By comparing results from direct and indirect measurements, it is concluded that for a reliable

characterization of the magnetocaloric eﬀect, direct measurement of ∆Tadb should be adopted.

I. INTRODUCTION

Since 1997, after the observation of the giant magne-

tocaloric eﬀect near room temperature in Gd5(Si2Ge2),[1]

several thousands of research papers have been published

in search of a suitable magnetic refrigerant which can be

applied in room temperature magnetic refrigerators. Un-

fortunately, till today no material has been found that is

both commercially viable and environmentally friendly.

The magnetocaloric eﬀect (MCE) is an intrinsic property

of a material originating from the spin-phonon interac-

tion of the material. In case of adiabatic conditions the

total entropy of a system, being the sum of its phonon

and spin (or magnetic) entropies, is conserved. There-

fore, changing the magnetic entropy by the application

or removal of an magnetic ﬁeld will change the phonon

entropy and the temperature of the system. This change

of temperature is known as the adiabatic temperature

change (∆Tadb) and the measurement of ∆Tadb is known

as the direct measurement of the MCE. Isothermal mag-

netization measurements yielding information about the

isothermal entropy change (∆SM) upon application or

removal of a magnetic ﬁeld can also be used to estimate

∆Tadb if combined with temperature and magnetic ﬁeld

dependent heat capacity measurements (CH). The mea-

surement of ∆SMand CHis known as the indirect mea-

surement of the MCE. Owing to the widespread avail-

ability of systems used for magnetization and speciﬁc

heat measurements often indirect measurements of the

MCE have been reported. A keyword search on 19th

October 2022, in the “Web of Science” yields around

8929 publications where the keyword “magnetocaloric”

is mentioned and among them only around 179 publica-

tions mention “magnetocaloric” and“direct” “adiabatic

temperature”. These numbers are approximate but give

evidence of that reports of direct measurements of ∆Tadb

∗e-mail: sagar.ghorai@angstrom.uu.se

are scarce. Moreover, several publications [2–6] report

that ∆Tadb estimated from indirect measurements diﬀers

largely from that of direct measurements owing to non-

adiabatic conditions and approximations involved in in-

direct measurements. Pecharsky et al.[7] have estimated

the error involved in the indirect measurement process

and found that it can be as large as ∼15% for elemen-

tal Gd. Furthermore, the values are highly sensitive to

any approximation used in the calculation. By compar-

ing direct and indirect MCE measurements, Pecharsky

et al. have also concluded that, in the indirect measure-

ment, there will be around 1 K to 1.5 K uncertainty in

the determination of ∆Tadb near room temperature[8]. It

can therefore be argued that reliable estimattion of the

∆Tadb require direct measurements.

Here, in this work we demonstrate a simple setup for

the direct measurement of ∆Tadb. Using this setup, we

have compared the direct and indirect measurements of

the MCE of the ﬁrst-order material La0.7Ca0.3MnO3.

Also, we have reported the direct MCE results for the

second-order material La0.8Sr0.2MnO3.

II. INSTRUMENTATION

A ∆Tadb measurement process consists of three im-

portant steps; ﬁrst adiabatic conditions should be estab-

lished, second the magnetic ﬁeld should be changed and

measured, and third the temporal variation of the sam-

ple temperature should be monitored. These three steps

have been incorporated in our setup. To create adiabatic

conditions for the measurements, a high vacuum cham-

ber (∼10−6hPa) is used. Along with the high vacuum

chamber, the sample is wrapped with a layer (∼2 mm)

of Pyrogel®(cf. Fig. 1(a)) to reduce the heat transfer

rate from the sample, which provide suﬃcient time for

the measurement of ∆Tadb upon a change of the mag-

netic ﬁeld. A schematic of the sample rod is shown in

Fig. 1(a). The sample rod is placed inside the vacuum

arXiv:2210.11509v1 [cond-mat.mtrl-sci] 20 Oct 2022

chamber, which is kept inside a liquid N2ﬁlled cryostat.

Therefore, the system can operate at temperatures above

the boiling point of liquid N2.

The magnetic ﬁeld variation was controlled by a

Halbach-type permanent magnet array,[9, 10] which can

produce a maximum magnetic ﬁeld of 1.8 T. To measure

the magnetic ﬁeld accurately at the position of the sam-

ple, a calibrated Hall-sensor is mounted on the sample

rod, in a way that the magnetic ﬁeld is perpendicular to

the Hall-sensor (cf. Fig. 1(a)). Although the heat radia-

tion and convection are much reduced, the heat conduc-

tion from sample cannot be completely eliminated. This

limits the overall measurement time. The measurement

time is highly inﬂuenced by the magnetic ﬁeld sweep rate,

i.e. if the magnetic ﬁeld sweep rate is low compared to

the heat conduction rate from the sample, some amount

of heat will be lost during the measurement. Khovaylo et

al. showed [2] that approximately a minimum magnetic

ﬁeld rate of 3 T/s is required for a correct determina-

tion of ∆Tadb. Using our system, the temporal variation

of the sample temperature, ∆TS(t) have been measured

for diﬀerent magnetic ﬁeld sweep rates for a ﬁrst-order

material, La0.7Ca0.3MnO3. The measurements were per-

formed at a temperature near to the magnetic ordering

temperature TC(251 K) of the material with the highest

available magnetic ﬁeld change (1.79 T). The recorded

data are presented in Fig. 1(b). To describe the eﬀect of

magnetic ﬁeld sweep rate, the temporal variation of the

sample temperature has been normalized with the value

of ∆Tadb (2.12(±0.01) K) deﬁned as the largest change

of the sample temperature induced by a magnetic ﬁeld

change. From Fig. 1(b), it is clear that a minimum mag-

netic ﬁeld sweep rate of 3 T/s is required to achieve a

value of ∆TS(t)/∆Tadb greater than 98%. Noticeably, a

higher magnetic ﬁeld sweep rate allows a longer time pe-

riod for the ∆Tadb measurement. Therefore, all results

presented in the following discussion have been obtained

using a magnetic ﬁeld sweep rate of 5 T/s. This rate is

high enough to neglect the heat dissipation during the

magnetization or demagnetization process.

The temperature of the sample is monitored and con-

trolled by a commercially available temperature con-

troller (LakeShore 335). As temperature sensors, T-type

thermocouples (accuracy of ∼0.01 K) are used and as

heat source a resistive Manganin®heater providing a

maximum power of 50 W is used. Both in thermocouples

and in heater, twisted types of wires have been used in

order to reduce any noise produced by the induced stray

magnetic ﬁeld in the wires[11]. To understand the heat

transfer process in the system, a block diagram and its

equivalent electrical circuit are presented in Figs. 1(c)

and (d), respectively. The sample with heat capacity CS

and temperature TSis attached to a thermocouple via a

thermal link (Ag-paint with thermal conductivity KAg).

Therefore, the temperature of the thermocouple Ttdiﬀer

slightly from the sample temperature TSand this dif-

ference depends upon the heat capacity of the thermo-

couple Ct. In the equivalent circuit, the inverse of the

thermal conductivity represents a resistance, the heat ca-

pacitiy corresponds to a capacitance and the ﬂow of heat

is described by an electrical current. Thus, the heat ﬂow

across the sample due to the change of magnetic ﬁeld

has been replaced by a current source. Moreover, there

is heat ﬂow from the sample to the liquid N2chamber

through the Pyrogel®(with thermal conductivity KP),

and this heat ﬂow is being controlled by the resistive

heater; all these heat ﬂows are collectively replaced by

another current source in the equivalent electric circuit

diagram. When the sample is subjected to a magnetic

ﬁeld change, either applied or removed, the tempera-

ture change of the sample is represented as ∆Tr

adb, i.e.

the real value of the adiabatic temperature change, while

the measured temperature change across the thermocou-

ple is represented as ∆Tm

adb. These two quantities cor-

respond to voltages across the capacitances CSand Ct

in the equivalent circuit and are related by the following

equation,

∆Tm

adb = ∆Tr

adb

CS+Ct

.(1)

Therefore, for an ideal measurement of ∆Tadb, the

value of CSshould be much larger than the value of Ct.

One way to satisfy this condition is to use larger mass

of the sample compared to the mass of the thermocou-

ple. Porcari et al.[12] has demonstrated experimentally

the eﬀect of sample mass on the ∆Tadb measurement, ac-

cording to which around 50 mg of sample is required for

a measurement with better than 98% accuracy. Apart

from the sample mass, the thermal conductivity of the

thermal link (Ag-paint) plays a crucial role in determin-

ing the time response of the ∆Tadb measurement. The

time(t) response from the RC-circuit can be expressed

as,

∆Tm

adb = ∆Tr

adb(1 −e−t/τt),(2)

where τtis the time constant of the thermocouple. τt

determines the rate at which thermocouple temperature

Ttwill reach the sample temperature TS. From the equiv-

alent RC-circuit, τtcan be expressed as,

τt=Ct

KAg

.(3)

Near room temperature, considering a T-type thermo-

couple and the thermal conductivity of silver paint, the

value of τtis <10−3s. From Fig. 1(b) it is clear that

the value of ∆Tadb is stable over a time period of a few

seconds, which proves that our measurement process is

reliable.

Although Pyrogel®is required to establish adiabatic

conditions, it creates a time lag between the thermocou-

ple attached to the sample and the heat source (resistive

heater) which aﬀects the process of temperature control.

To overcome this problem, a second thermocouple has

been introduced outside the Pyrogel®attached to the

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S.Ghoraietal./InstrumentAsetupfordirectmeasurementoftheadiabatictemperaturechangeinmagnetocaloricmaterialsSagarGhorai,1,DanielHedlund,1MartinKapuscinski,1andPeterSvedlindh11DepartmentofMaterialsScienceandEngineering,UppsalaUniversity,Box35,SE-75103,Uppsala,Sweden(Dated:October24,2022)Inordertondah...

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S.Ghorai et al. Instrument A setup for direct measurement of the adiabatic temperature change in magnetocaloric materials

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