**Magnetic dot arrays with multiple storage layers**

Magnetic dot arrays with multiple storage layers

(Parte **1** de 5)

Journal of Magnetism and Magnetic Materials 200 (1999) 4}56

Magnetocaloric e!ect and magnetic refrigeration

Vitalij K. Pecharsky, Karl A. Gschneidner Jr.*

Ames Laboratory and Department of Materials Science and Engineering, Iowa State University, 255 Spedding, Ames, IA 50011-3020, USA Received 21 January 1999; received in revised form 9 April 1999

Abstract

The phenomenon of the magnetocalorice!ect along with recent progress and the future needs in both the characterization and exploration of new magnetic refrigerant materials with respect to their magnetocaloric properties are discussed. Also the recent progress in magnetic refrigerator design is reviewed. ( 1999 Elsevier Science B.V. All rights reserved.

PACS: 65.40.#g; 65.50.#m; 75.30.Sg; 75.50.Cc

Keywords: Magnetocaloric e!ect; Magnetic refrigeration; Lanthanide materials; Ferromagnets; Paramagnets; Adiabatic demagnetization

1. Magnetocaloric e4ect 1.1. Discovery and fundamentals

Magnetocaloric e!ect (MCE), or adiabatic tem- perature change (*„!$ ), which is detected as the heating or the cooling of magnetic materials due to a varying magnetic "eld, was originally discovered in iron by Warburg [1]. The nature of the MCE was explained and its practical use to reach ultralow temperatures in a process known as adiabatic demagnetization was suggested independently by Debye [2] and by Giauque [3].

The MCE is intrinsic to all magnetic materials and is due to the coupling of the magnetic sublattice with the magnetic "eld, which changes the magnetic part of the entropy of a solid. Just as the

*Corresponding author. Tel.: #1-515-294-7931; fax: #1- 515-294-9579. E-mail address: cagey@ameslab.gov (K.A. Gschneidner Jr.) compressionof a gas, the isothermal magnetizing of a paramagnet or a soft ferromagnet reduces the entropy and, in a reversible process, demagnetizing (which is similar to the expansion of a gas) restores the zero-"eld magnetic entropy of a system. The thermodynamicsof the MCE in a ferromagnet near its magnetic ordering temperature (Curie temper- ature, „C ) is illustrated schematically in Fig. 1. At constant pressure the entropy of a magnetic solid, S(„, H), which is a function of both the magnetic "eld strength (H) and the absolute temperature („), is the combined total of the magnetic, SM , lattice,

S L!5 , and electronic, S E- contributions:

It is shown for a ferromagnetic material in two constant magnetic "elds (zero magnetic "eld, H0 , and a non-zero magnetic "eld, H1 ), together with the corresponding magnetic and non-magnetic terms. When the magnetic "eld is applied adiabatically (i.e. when the total entropy of the system

Fig. 1. The S}T diagram illustrating the existence of the magnetocaloric e!ect. The solid lines represent the total entropy in

’0. The horizon- tal arrow shows *„!$ and the vertical arrow shows *SM when the magnetic "eld is changed from H0 to H1

. The dotted line shows the combined lattice and electronic (non-magnetic) entropy, and dashed lines show the magnetic entropy in the two are zero "eld entropy and temperature, S

1and „1 are entropy and temperature at the elevated magnetic remains constant during the magnetic "eld change) in a reversible process, the magnetocaloric e!ect

(i.e. the adiabatic temperature rise, *„!$"

„1!„0 ) can be visualized as the isentropic di!er-

ence between the corresponding S(„)H functions as shown in Fig. 1 by the horizontal arrow. The MCE can be also expressed by means of the isothermal magnetic entropy change (or simply magnetic en-

, when the magnetic

"eld is applied isothermally. In the latter case it is equal to the isothermal di!erence between the cor- responding S(„)H functions as shown in Fig. 1 by repres- ent the two quantitative characteristics of the mag- netocaloric e!ect, and it is obvious that both *„ !$ and *SM are functions of the initial temperature,

„0 (i.e. the temperature before the magnetic "eld was altered), and the magnetic "eld change,

). It is easy to see (Fig. 1) that if raising the magnetic "eld increases magnetic order (i.e. reduces magnetic entropy, which is the case for simple paramagnetic and ferromagnetic materials), spondingly reversed when the magnetic "eld is reduced.

are correlated with the mag- netization (M), the magnetic "eld strength, the heat capacity at constant pressure (C), and the absolute temperature by one of the fundamental Maxwell’s relations [4] which for an isothermal}isobaric process after integration yields

Eq. (3) indicates that the magnetic entropy change is proportional to the derivative of magnetization with respect to temperature at constant "eld and to the magnetic "eld change. By combining Eq. (2) with the corresponding „ dS equation it easy to show [4] that the in"nitesimal adiabatic temperature rise for the reversible adiabatic}isobaric process is equal to

Hence, the adiabatic temperature rise is directly proportional to the absolute temperature, to the derivative of magnetization with respect to temperature at constant "eld and to the magnetic "eld change; and it is inversely proportional to the heat capacity. After integrating Eq. (4) one gets the value of the magnetocaloric e!ect as

Eqs. (2)}(5) have a fundamental importance on the understanding of the behavior of the MCE in solids, and serve as a guide for the search of new materials with a large magnetocaloric e!ect. First, since the magnetization at constant "eld of paramagnets and simple ferromagnets decreases with

V.K. Pecharsky, K.A. Gschneidner Jr. / Journal of Magnetism and Magnetic Materials 200 (1999) 4}56 45

should be negative (Eqs. (2) and (3)),

should be positive (Eqs. (4) and

(5)), which agrees with Fig. 1. Second, in ferromag- nets D(RM/R„)H D is the largest at the „C

, and there-

(Eqs. (2) and (3)).

Third, although it is not straightforward from Eqs. (4) and (5) because the heat capacity at constant

"eld is also anomalous near the „C , it has been in ferromagnets peaks at the Curie temperature when *HP0. The behavior should be similar to the behavior of

D, i.e. it will be gradually reduced both below and above the „C . Fourth, for the same will be larger at a higher absolute temperature, and also when the total heat capacity of the solid is lower (Eq. (5)). The latter point is critical in understanding the fact that para- temperatures close to absolute zero, where the lim- ited value of D(RM/R„)H D is easily o!set by the negli- gible lattice heat capacity. Furthermore, at high temperatures the measurable adiabatic heating (or cooling) is expected only if the solid orders spon- taneously, i.e. when value of D(RM/R„)H D becomes signi"cant.

1.2. Measurement of the magnetocaloric ewect

The magnetocaloric e!ect can be measured directly or it can be calculated indirectly from the measured magnetization or "eld dependence of the heat capacity. Direct techniques always involve measurements of the sample temperatures („0 and

„F ) in magnetic "elds H0 and HF

, where subscripts

0 and F designate initial and "nal magnetic "eld, is then determined as the di!erence between „F and „0 for a given

Direct MCE measurements can be carried out using contact (i.e. when the temperature sensor is in direct thermal contact with the sample) and noncontact techniques (i.e. when the sample temperature is measured without the sensor being directly connected to the sample) [6}14]. Since during the direct MCE measurements a rapid change of the magnetic "eld is required, the measurements can be carried out on immobilized samples when the mag- netic "eld change is provided either by charging/discharging the magnet, or by moving the sample in and out of a uniform magnetic "eld volume. Using immobilized samples and pulse magnetic "elds direct MCE measurements in magnetic "elds from 1 to 40 T have been reported. The use of electromagnets usually limits the magnetic "eld strength to less than 2 T. Experimental apparati, where the sample or the magnet are moved to provide the varying magnetic "eld environment usually employ superconducting or permanent magnets, which limit the magnetic "eld range to 0.1}10 T. The accuracy of the direct experimental techniques depends on the errors in thermometry, errors in "eld setting, the quality of thermal insulation of the sample (this becomes a critical source of error when the MCE is large and thus disrupts the adiabatic conditions), the quality of the compensation scheme to eliminate the e!ect of the changing magnetic "eld on the temperature sensor reading. Considering all these e!ects the accuracy is claimed to be in the 5}10% range [6}14].

Unlike the direct MCE measurements, which only yield the adiabatic temperature change, the indirect experiments allow the calculation of both

* heat capacitymeasure-

* magnetization measure- ments. Magnetization measured experimentally as a function of temperature and magnetic "eld pro- after numerical integration of

Eq. (3), and has been rightfully suggested as a useful technique for the rapid screening of prospective magnetic refrigerant materials [15]. The accuracy calculated from magnetization data depends on the accuracy of the magnetic moment, temperature, and magnetic "eld measurements. Because numerical integration is involved, and because the exact di!erentials (dM,d „, and dH) are substituted, respectively, by the measured *M, *„, from magnetization measurements is reported to be in the range of 3}10% [15]. The relative error may become signi"cantly larger particularly for small

D values.

The heat capacity measured as a function of provides the most complete characterization of magnetic materials with respect to their magnetocaloric

(Parte **1** de 5)