View source for Magnetocaloric effect

{{short description|Phenomenon where a material changes temperature due to a magnetic field}}
[[File:Magnetocaloric1.01cr.png|thumb|[[Gadolinium]] alloy heats up inside the magnetic field and loses thermal energy to the environment, so it exits the field and becomes cooler than when it entered.]]

The '''magnetocaloric effect''' ('''MCE''', from ''[[magnet]]'' and ''[[calorie]]'') is a scientific phenomenon in which certain materials warm up when a magnetic field is applied. The warming is due to changes in the internal state of the material releasing heat. When the magnetic field is removed, the material returns to its original state, reabsorbing the heat, and returning to original temperature. This can be used to achieve refrigeration, by allowing the material to radiate away its heat while in the magnetized hot state. Removing the magnetism, the material then cools to below its original temperature.

The effect was first observed in 1881 by a German physicist [[Emil Warburg]], followed by French physicist [[Pierre Weiss|P. Weiss]] and Swiss physicist [[Auguste Piccard|A. Piccard]] in 1917.<ref name="Weiss 103–109">{{cite journal |last1=Weiss |first1=Pierre |last2=Piccard |first2=Auguste |title=Le phénomène magnétocalorique |journal=J. Phys. (Paris) |volume=5th Ser. |issue=7 |pages=103–109 |date=1917}}<br/>{{cite journal |last=Smith |first=Anders |title=Who discovered the magnetocaloric effect? |journal=The European Physical Journal H |volume=38 |issue=4 |pages=507–517 |date=2013 |doi=10.1140/epjh/e2013-40001-9|bibcode = 2013EPJH...38..507S |s2cid=18956148 }}</ref> The fundamental principle was suggested by [[Peter Debye|P. Debye]] (1926) and [[William Giauque|W. Giauque]] (1927).<ref>{{cite book | last = Zemansky | first = Mark W. | title = Temperatures very low and very high | publisher = Dover | date = 1981 | location = New York | page = 50 | isbn = 0-486-24072-X }}</ref> The first working magnetic refrigerators were constructed by several groups beginning in 1933.  Magnetic refrigeration was the first method developed for cooling below about 0.3 K (the lowest temperature attainable before magnetic refrigeration, by pumping on [[Helium-3|{{chem|3|He}}]] vapors).

The magnetocaloric effect can be used to attain extremely low [[temperature]]s, as well as the ranges used in common [[refrigerator]]s.<ref>{{cite journal | last1 = França | first1 = E.L.T. | last2 = dos Santos | first2 = A.O. | last3 = Coelho | first3 = A.A. | year = 2016 | title = Magnetocaloric effect of the ternary Dy, Ho and Er platinum gallides | journal = Journal of Magnetism and Magnetic Materials | volume = 401 | pages = 1088–1092 | doi = 10.1016/j.jmmm.2015.10.138 | bibcode = 2016JMMM..401.1088F }}</ref><ref name="doi10.1088/0022-327/38/23/R01">{{Cite journal | doi = 10.1088/0022-3727/38/23/R01| title = Developments in magnetocaloric refrigeration| journal = Journal of Physics D: Applied Physics| volume = 38| issue = 23| pages = R381–R391| year = 2005| last1 = Brück | first1 = E. |bibcode = 2005JPhD...38R.381B | s2cid = 122788079}}</ref><ref name="auto">{{Cite journal | doi = 10.1002/pssb.201451217| title = Magnetocaloric effect in "reduced" dimensions: Thin films, ribbons, and microwires of Heusler alloys and related compounds| journal = Physica Status Solidi B| volume = 251| issue = 10| pages = 2104| year = 2014| last1 = Khovaylo | first1 = V. V. | last2 = Rodionova | first2 = V. V. | last3 = Shevyrtalov | first3 = S. N. | last4 = Novosad | first4 = V. |bibcode = 2014PSSBR.251.2104K | s2cid = 196706851}}</ref><ref name="auto1">{{Cite journal | doi = 10.1016/j.ijrefrig.2008.01.004| title = Thirty years of near room temperature magnetic cooling: Where we are today and future prospects| journal = International Journal of Refrigeration| volume = 31| issue = 6| pages = 945| year = 2008| last1 = Gschneidner | first1 = K. A. | last2 = Pecharsky | first2 = V. K. | url = https://zenodo.org/record/1259069}}</ref>

== History ==

The effect was first observed by German physicist [[Emil Warburg]] in 1881<ref name="WARBURG, E. G p. 141-164">{{cite journal | last1 = Warburg | first1 = E. G. | year = 1881 | title = Magnetische Untersuchungen | url = https://zenodo.org/record/2170879| journal = Annalen der Physik | volume = 249 | issue = 5| pages = 141–164 | doi = 10.1002/andp.18812490510 | bibcode = 1881AnP...249..141W }}</ref> Subsequently by French physicist [[Pierre Weiss]] and Swiss physicist [[Auguste Piccard]] in 1917.<ref name="Weiss 103–109"/>

Major advances first appeared in the late 1920s when cooling via adiabatic demagnetization was independently proposed by chemistry [[Nobel Laureates]] [[Peter Debye]] in 1926 and   [[William F. Giauque]]  in 1927.

It was first demonstrated experimentally by Giauque and his colleague [[D. P. MacDougall]] in 1933 for cryogenic purposes when they reached 0.25&nbsp;K.<ref>{{cite journal |last1=Giauque |first1=W. F. |last2=MacDougall |first2=D. P. |date=1933 |title=Attainment of Temperatures Below 1° Absolute by Demagnetization of Gd<sub>2</sub>(SO<sub>4</sub>)<sub>3</sub>·8H<sub>2</sub>O |journal=Phys. Rev. |volume=43 |issue=9 |page=768 |doi=10.1103/PhysRev.43.768 |bibcode = 1933PhRv...43..768G }}</ref> Between 1933 and 1997, advances in MCE cooling occurred.<ref>{{cite book |last1=Gschneidner |first1=K. A. Jr. |last2=Pecharsky |first2=V. K. |date=1997 |title=Rare Earths: Science, Technology and Applications III |editor-first=R. G. |editor-last=Bautista |location=Warrendale, PA |publisher=The Minerals, Metals and Materials Society |page=209 |display-editors=etal}}<br/>{{cite journal |last1=Pecharsky |first1=V. K. |last2=Gschneidner |first2=K. A. Jr. |date=1999 |title=Magnetocaloric Effect and Magnetic Refrigeration |journal=J. Magn. Magn. Mater. |volume=200 |issue=1–3 |pages=44–56 |doi=10.1016/S0304-8853(99)00397-2 |bibcode = 1999JMMM..200...44P }}<br/>{{cite journal |last1=Gschneidner |first1=K. A. Jr. |last2=Pecharsky |first2=V. K. |date=2000 |title=Magnetocaloric Materials |journal=Annu. Rev. Mater. Sci. |volume=30 |issue=1 |pages=387–429 |doi=10.1146/annurev.matsci.30.1.387 |bibcode = 2000AnRMS..30..387G |url=https://zenodo.org/record/1235001 }}<br/>{{cite book |last1=Gschneidner |first1=K. A. Jr. |last2=Pecharsky |first2=V. K. |date=2002 |title=Fundamentals of Advanced Materials for Energy Conversion |editor1-first=D. |editor1-last=Chandra |editor2-first=R. G. |editor2-last=Bautista |location=Warrendale, PA |publisher=The Minerals, Metals and Materials Society |page=9 }}</ref>

In 1997, the first near room-temperature [[proof of concept]] magnetic refrigerator was demonstrated by [[Karl A. Gschneidner, Jr.]] by the [[Iowa State University]] at [[Ames Laboratory]]. This event attracted interest from scientists and companies worldwide who started developing new kinds of room temperature materials and magnetic refrigerator designs.<ref name="Ames"/>

A major breakthrough came 2002 when a group at the University of Amsterdam demonstrated the giant magnetocaloric effect in MnFe(P,As) alloys that are based on abundant materials.<ref>{{cite journal |last1=Tegus |first1=O. |last2=Brück |first2=E. |last3=de Boer |first3=F. R. |last4=Buschow |first4=K. H. J. |title=Transition-metal-based magnetic refrigerants for room-temperature applications |journal=[[Nature (journal)|Nature]] |volume=415 |issue=6868 |pages=150–152 |date=2002 |doi=10.1038/415150a |bibcode = 2002Natur.415..150T |pmid=11805828|s2cid=52855399 }}</ref>

Refrigerators based on the magnetocaloric effect have been demonstrated in laboratories, using magnetic fields starting at 0.6&nbsp;T up to 10&nbsp;T. Magnetic fields above 2&nbsp;T are difficult to produce with permanent magnets and are produced by a [[superconducting magnet]] (1&nbsp;T is about 20.000 times the [[Earth's magnetic field]]).

=== Room temperature devices ===

Recent research has focused on near room temperature. Constructed examples of room temperature magnetic refrigerators include:

{| class="wikitable" style="font-size:90%;"
|+ Room temperature magnetic refrigerators
|-
! Sponsor !! Location !! Announcement date !! Type !! Max. cooling power (W)<sup>[1]</sup>!! Max Δ''T ''(K)<sup>[2]</sup> !! Magnetic field (T) !! Solid refrigerant !! Quantity (kg) !! COP (-)<sup>[3]</sup><!-- wtf is this? some refrigeration notation? or did someone copypaste over top of what used to be references? might be a question for the revision history -->
|-
! [[Ames Laboratory]]/Astronautics<ref>{{cite book |doi=10.1007/978-1-4757-9047-4_222 |chapter=Description and Performance of a Near-Room Temperature Magnetic Refrigerator |title=Advances in Cryogenic Engineering |date=1998 |last1=Zimm |first1=C. |last2=Jastrab |first2=A. |last3=Sternberg |first3=A. |last4=Pecharsky |first4=V. |last5=Gschneidner |first5=K. |last6=Osborne |first6=M. |last7=Anderson |first7=I. |pages=1759–1766 |isbn=978-1-4757-9049-8 }}</ref>
| Ames, Iowa/Madison, Wisconsin, US || February 20, 1997 || Reciprocating || 600 || 10 || 5 (S) || Gd spheres
|-
! Mater. Science Institute Barcelona<ref>{{Cite journal | doi =  10.1109/20.846216| title = Room-temperature magnetic refrigerator using permanent magnets| journal =  IEEE Transactions on Magnetics| volume = 36| issue = 3| pages = 538| year = 2000| last1 = Bohigas | first1 = X.| last2 = Molins | first2 = E.| last3 = Roig | first3 = A.| last4 = Tejada | first4 = J.| last5 = Zhang | first5 = X. X. | bibcode = 2000ITM....36..538B}}</ref><ref>{{Cite journal | doi = 10.1063/1.1451906| title = Permanent magnet array for the magnetic refrigerator| journal = Journal of Applied Physics| volume = 91| issue = 10| pages = 8894| year = 2002| last1 = Lee | first1 = S. J.| last2 = Kenkel | first2 = J. M.| last3 = Pecharsky | first3 = V. K.| last4 = Jiles | first4 = D. C.|bibcode = 2002JAP....91.8894L | url = https://dr.lib.iastate.edu/bitstreams/b32cc0f6-b890-4d1a-8089-8f78e84f6b0e/download}}</ref>
| Barcelona, Spain || May 2000 || Rotary || ? || 5 || 0.95 (P) || Gd foil
|-
! Chubu Electric/Toshiba<ref>{{Cite book | doi = 10.1063/1.1472125| chapter = Development of magnetic refrigerator for room temperature application| title = AIP Conference Proceedings| volume = 613| pages = 1027–1034| year = 2002| last1 = Hirano | first1 = N.}}</ref>
| Yokohama, Japan || Summer 2000 || Reciprocating || 100 || 21 || 4 (S) || Gd spheres
|-
! University of Victoria<ref>Rowe A.M. and Barclay J.A., Adv. Cryog. Eng. 47 995 (2002).</ref><ref>{{Cite journal | doi = 10.1063/1.1643200| title = Magnetic refrigeration: Single and multimaterial active magnetic regenerator experiments| journal = Journal of Applied Physics| volume = 95| issue = 4| pages = 2146–2150| year = 2004| last1 = Richard | first1 = M. -A. |bibcode = 2004JAP....95.2146R | s2cid = 122081896}}</ref>
| Victoria, British Columbia Canada || July 2001 || Reciprocating || 2 || 14 || 2 (S) || Gd & {{chem|Gd|1−x|Tb|x}} L.B.
|-
! Astronautics<ref>Zimm C, Paper No K7.003 Am. Phys. Soc. Meeting, March 4, Austin, Texas (2003) {{cite web |url=http://www.aps.org/meet/MAR03/baps/tocK.html |title=Archived copy |access-date=2006-06-12 |url-status=dead |archive-url=https://web.archive.org/web/20040229061413/http://www.aps.org/meet/MAR03/baps/tocK.html |archive-date=2004-02-29 }}</ref>
| Madison, Wisconsin, US || September 18, 2001 || Rotary || 95 || 25 || 1.5 (P) || Gd spheres
|-
! Sichuan Inst. Tech./Nanjing University<ref>Wu W., Paper No. K7.004 Am. Phys. Soc. Meeting, March 4, Austin, Texas (2003) {{cite web |url=http://www.aps.org/meet/MAR03/baps/tocK.html |title=Archived copy |access-date=2006-06-12 |url-status=dead |archive-url=https://web.archive.org/web/20040229061413/http://www.aps.org/meet/MAR03/baps/tocK.html |archive-date=2004-02-29 }}</ref>
| Nanjing, China || 23 April 2002 || Reciprocating || ? || 23 || 1.4 (P) || Gd spheres and Gd<sub>5</sub>Si<sub>1.985</sub>Ge<sub>1.985</sub>Ga<sub>0.03</sub> powder
|-
! Chubu Electric/Toshiba<ref name="aps.org">Hirano N., Paper No. K7.002 Am. Phys. Soc. Meeting March 4, Austin, Texas, {{cite web |url=http://www.aps.org/meet/MAR03/baps/tocK.html |title=Archived copy |access-date=2006-06-12 |url-status=dead |archive-url=https://web.archive.org/web/20040229061413/http://www.aps.org/meet/MAR03/baps/tocK.html |archive-date=2004-02-29 }}</ref>
| Yokohama, Japan || October 5, 2002 || Reciprocating || 40 || 27 || 0.6 (P) || {{chem|Gd|1−x|Dy|x}} L.B.
|-
! Chubu Electric/Toshiba<ref name="aps.org"/>
| Yokohama, Japan || March 4, 2003 || Rotary || 60 || 10 || 0.76 (P) || {{chem|Gd|1−x|Dy|x}} L.B. || 1
|-
! Lab. d’Electrotechnique Grenoble<ref>{{Cite journal | doi = 10.1109/TMAG.2003.816253| title = A magnet-based device for active magnetic regenerative refrigeration| journal = IEEE Transactions on Magnetics| volume = 39| issue = 5| pages = 3349| year = 2003| last1 = Clot | first1 = P.| last2 = Viallet | first2 = D.| last3 = Allab | first3 = F.| last4 = Kedous-Lebouc | first4 = A.| last5 = Fournier | first5 = J. M. | last6 = Yonnet | first6 = J. P. |bibcode = 2003ITM....39.3349C }}</ref>
| Grenoble, France || April 2003 || Reciprocating || 8.8 || 4 || 0.8 (P) || Gd foil
|-
! George Washington University<ref>{{Cite journal | doi = 10.1016/j.ijrefrig.2004.08.015| title = Analysis of room temperature magnetic regenerative refrigeration| journal = International Journal of Refrigeration| volume = 28| issue = 4| pages = 616| year = 2005| last1 = Shir | first1 = F. | last2 = Mavriplis | first2 = C. | last3 = Bennett | first3 = L. H. | last4 = Torre | first4 = E. D. }}</ref>
| US || July 2004 || Reciprocating || ? || 5 || 2 (P) || Gd foil
|-
! Astronautics<ref>Zimm C, Paper No. K7.003 Am. Phys. Soc. Meeting, March 4, Austin, Texas (2003) {{cite web |url=http://www.aps.org/meet/MAR03/baps/tocK.html |title=Archived copy |access-date=2006-06-12 |url-status=dead |archive-url=https://web.archive.org/web/20040229061413/http://www.aps.org/meet/MAR03/baps/tocK.html |archive-date=2004-02-29 }}</ref>
| Madison, Wisconsin, US || 2004 || Rotary || 95 || 25 || 1.5 (P) || Gd and GdEr spheres / {{chem|La(Fe|0.88|Si|0.12|13|H|1.0}}
|-
! University of Victoria<ref>{{Cite journal | doi = 10.1016/j.ijrefrig.2006.07.012| title = Experimental investigation of a three-material layered active magnetic regenerator| journal = International Journal of Refrigeration| volume = 29| issue = 8| pages = 1286| year = 2006| last1 = Rowe | first1 = A.| last2 = Tura | first2 = A.}}</ref>
| Victoria, British Columbia Canada || 2006 || Reciprocating || 15 || 50 || 2 (S) || Gd, {{chem|Gd|0.74|Tb|0.26}} and {{chem|Gd|0.85|Er|0.15}} pucks || 0.12
|-
! University of Salerno<ref>{{Cite journal | doi = 10.1016/j.ijrefrig.2015.09.005| title = The energy performances of a rotary permanent magnet magnetic refrigerator| journal = International Journal of Refrigeration| volume = 61| issue = 1| pages = 1–11| year = 2016| last1 = Aprea | first1 = C.| last2 = Greco | first2 = A.| last3 = Maiorino | first3 = A.| last4 = Masselli | first4 = C.}}</ref>
| Salerno, Italy || 2016 || Rotary || 250 || 12 || 1.2 (P) || Gd 0.600&nbsp;mm spherical particles|| 1.20|| 0.5 - 2.5
|-
! [[National University of Science and Technology MISiS|MISiS]]<ref>{{Cite web|url=https://3dnews.ru/986098|title=Российские инженеры создали высокоэффективный магнитный холодильник}}</ref>
| [[Tver]] and Moscow, Russia || 2019 || High speed rotary || ? || ? || ? || Gd bricks of two types, cascaded
|-
| colspan="8"| <sup>1</sup>maximum cooling power at zero temperature difference (Δ''T''=0); <sup>2</sup>maximum temperature span at zero cooling capacity (''W''=0); L.B. = layered bed; P = permanent magnet; S = superconducting magnet; <sup>3</sup> COP values under different operating conditions
|}

In one example, Prof. Karl A. Gschneidner, Jr. unveiled a [[proof of concept]] magnetic refrigerator near room temperature on February 20, 1997. He also announced the discovery of the GMCE in {{chem|Gd|5|Si|2|Ge|2}} on June 9, 1997.<ref name="auto2"/>  Since then, hundreds of peer-reviewed articles have been written describing materials exhibiting magnetocaloric effects.

== Process ==

The MCE is a magneto-[[thermodynamic]] phenomenon in which a temperature change of a suitable material is caused by exposing the material to a changing magnetic field. This is also known by low temperature physicists as ''[[Adiabatic process|adiabatic]] demagnetization''. In that part of the refrigeration process, a decrease in the strength of an externally applied magnetic field allows the magnetic domains of a magnetocaloric material to become disoriented from the magnetic field by the agitating action of the thermal energy ([[phonon]]s) present in the material.  If the material is isolated so that no energy is allowed to (re)migrate into the material during this time, (i.e., an adiabatic process) the temperature drops as the domains absorb the thermal energy to perform their reorientation.  The randomization of the domains occurs in a similar fashion to the randomization at the [[Curie temperature]] of a [[ferromagnetic]] material, except that [[magnetic dipole]]s overcome a decreasing external magnetic field while energy remains constant, instead of magnetic domains being disrupted from internal [[ferromagnetism]] as energy is added.

One of the most notable examples of the magnetocaloric effect is in the chemical element [[gadolinium]] and some of its [[alloys]]. Gadolinium's temperature increases when it enters certain magnetic fields. When it leaves the magnetic field, the temperature drops. The effect is considerably stronger for the gadolinium [[alloy]] {{chem|Gd|5|(Si|2|Ge|2|)}}.<ref name="Ames">{{cite web|author=Karl Gschneidner Jr. |author2=Kerry Gibson |name-list-style=amp |title=Magnetic Refrigerator Successfully Tested |work=Ames Laboratory News Release |publisher=Ames Laboratory |date=December 7, 2001 |url=http://www.external.ameslab.gov/news/release/01magneticrefrig.htm |access-date=2006-12-17 |url-status=dead |archive-url=https://web.archive.org/web/20100323011159/http://www.external.ameslab.gov/news/release/01magneticrefrig.htm |archive-date=March 23, 2010 }}</ref> [[Praseodymium]] alloyed with [[nickel]] ({{chem|Pr|Ni|5}}) has such a strong magnetocaloric effect that it has allowed scientists to approach to within one millikelvin, one thousandth of a degree of [[absolute zero]].<ref>{{cite book | last = Emsley | first = John| title = Nature's Building Blocks | publisher = [[Oxford University Press]] |date= 2001 | page = 342 | isbn = 0-19-850341-5 }}</ref>

=== Equation ===

The magnetocaloric effect can be quantified with the following equation:

<math display="block">\Delta T_{ad}=-\int_{H_0}^{H_1}\left(\frac {T}{C(T,H)}\right)_H{\left(\frac {\partial M(T,H)}{\partial T}\right)}_H dH</math>

where <math>\Delta T_{ad}</math> is the adiabatic change in temperature of the magnetic system around temperature T, H is the applied external magnetic field, C is the heat capacity of the working magnet (refrigerant) and M is the [[magnetization]] of the refrigerant.

From the equation we can see that the magnetocaloric effect can be enhanced by:

* a large field variation
* a magnet material with a small heat capacity
* a magnet with large changes in net magnetization vs. temperature, at constant magnetic field

The adiabatic change in temperature, <math>\Delta T_{ad}</math>, can be seen to be related to the magnet's change in magnetic [[entropy]] (<math>\Delta S </math>) since<ref>{{Cite journal| last1=Balli|first1=M.|last2=Jandl|first2=S.|last3=Fournier|first3=P.|last4=Kedous-Lebouc|first4=A.|date=2017-05-24| title=Advanced materials for magnetic cooling: Fundamentals and practical aspects| journal=Applied Physics Reviews| volume=4|issue=2|pages=021305| doi=10.1063/1.4983612| bibcode=2017ApPRv...4b1305B|arxiv=2012.08176|s2cid=136263783}}</ref>

<math display=block> \Delta S(T) = \int_{H_0}^{H_1}\left(\frac{\partial M(T,H')}{\partial T} \right)dH'</math>

This implies that the absolute change in the magnet's entropy determines the possible magnitude of the adiabatic temperature change under a thermodynamic cycle of magnetic field variation. T

=== Thermodynamic cycle ===

[[Image:MCE_vectorized.svg|right|thumb|400px|Analogy between magnetic refrigeration and vapor cycle or conventional refrigeration. ''H'' = externally applied magnetic field; ''Q'' = heat quantity; ''P'' = pressure; Δ''T''<sub>ad</sub> = adiabatic temperature variation]]

The cycle is performed as a [[refrigeration cycle]] that is analogous to the [[Carnot cycle|Carnot refrigeration cycle]], but with increases and decreases in magnetic field strength instead of increases and decreases in pressure.  It can be described at a starting point whereby the chosen working substance is introduced into a [[magnetic field]], i.e., the magnetic flux density is increased.  The working material is the refrigerant, and starts in thermal equilibrium with the refrigerated environment.

* ''Adiabatic magnetization:''  A magnetocaloric substance is placed in an insulated environment.  The increasing external magnetic field (+''H'') causes the magnetic dipoles of the atoms to align, thereby decreasing the material's magnetic [[entropy]] and [[heat capacity]]. Since overall energy is not lost (yet) and therefore total entropy is not reduced (according to thermodynamic laws), the net result is that the substance is heated (''T'' + Δ''T''<sub>ad</sub>).
* ''Isomagnetic enthalpic transfer:'' This added heat can then be removed (-''Q'') by a fluid or gas&nbsp;— gaseous or liquid [[helium]], for example.  The magnetic field is held constant to prevent the dipoles from reabsorbing the heat.  Once sufficiently cooled, the magnetocaloric substance and the coolant are separated (''H''=0).
* ''{{Visible anchor|Adiabatic demagnetization}}:''  The substance is returned to another adiabatic (insulated) condition so the total entropy remains constant.  However, this time the magnetic field is decreased, the thermal energy causes the magnetic moments to overcome the field, and thus the sample cools, i.e., an adiabatic temperature change.  Energy (and entropy) transfers from thermal entropy to magnetic entropy, measuring the disorder of the magnetic dipoles.<ref>{{cite book |title=Introduction to Statistical Physics |edition=illustrated |first1=João Paulo |last1=Casquilho |first2=Paulo Ivo Cortez |last2=Teixeira |publisher=Cambridge University Press |year=2014 |isbn=978-1-107-05378-6 |page=99 |url=https://books.google.com/books?id=Hp-TBQAAQBAJ}} [https://books.google.com/books?id=Hp-TBQAAQBAJ&pg=PA99 Extract of page 99]</ref>
* ''Isomagnetic entropic transfer:''  The magnetic field is held constant to prevent the material from reheating. The material is placed in thermal contact with the environment to be refrigerated. Because the working material is cooler than the refrigerated environment (by design), heat energy migrates into the working material (+''Q'').

Once the refrigerant and refrigerated environment are in thermal equilibrium, the cycle can restart.

=== Applied technique ===

The basic operating principle of an adiabatic demagnetization refrigerator (ADR) is the use of a strong magnetic field to control the entropy of a sample of material, often called the "refrigerant". Magnetic field constrains the orientation of magnetic dipoles in the refrigerant. The stronger the magnetic field, the more aligned the dipoles are,  corresponding to lower entropy and [[specific heat capacity|heat capacity]] because the material has (effectively) lost some of its internal [[degrees of freedom (physics and chemistry)|degrees of freedom]]. If the refrigerant is kept at a constant temperature through thermal contact with a [[heat]] sink (usually liquid [[helium]]) while the magnetic field is switched on, the refrigerant must lose some energy because it is [[thermodynamic equilibrium|equilibrated]] with the heat sink. When the magnetic field is subsequently switched off, the heat capacity of the refrigerant rises again because the degrees of freedom associated with orientation of the dipoles are once again liberated, pulling their share of [[equipartition of energy|equipartitioned]] energy from the [[kinetic energy|motion]] of the [[molecule]]s, thereby lowering the overall temperature of a [[system]] with decreased energy. Since the system is now [[Thermal insulation|insulated]] when the magnetic field is switched off, the process is adiabatic, i.e., the system can no longer exchange energy with its surroundings (the heat sink), and its temperature decreases below its initial value, that of the heat sink.

The operation of a standard ADR proceeds roughly as follows.  First, a strong magnetic field is applied to the refrigerant, forcing its various magnetic dipoles to align and putting these degrees of freedom of the refrigerant into a state of lowered entropy. The heat sink then absorbs the heat released by the refrigerant due to its loss of entropy. Thermal contact with the heat sink is then broken so that the system is insulated, and the magnetic field is switched off, increasing the heat capacity of the refrigerant, thus decreasing its temperature below the temperature of the heat sink. In practice, the magnetic field is decreased slowly in order to provide continuous cooling and keep the sample at an approximately constant low temperature. Once the field falls to zero or to some low limiting value determined by the properties of the refrigerant, the cooling power of the ADR vanishes, and heat leaks will cause the refrigerant to warm up.

== Working materials ==

The MCE is an intrinsic property of a magnetic solid. This thermal response of a solid to the application or removal of magnetic fields is maximized when the solid is near its magnetic ordering temperature. Thus, the materials considered for magnetic refrigeration devices should be magnetic materials with a magnetic phase transition temperature near the temperature region of interest.<ref name="doi10.1002/aenm.201200167">{{Cite journal | doi = 10.1002/aenm.201200167| title = Materials Challenges for High Performance Magnetocaloric Refrigeration Devices| journal = Advanced Energy Materials| volume = 2| issue = 11| pages = 1288| year = 2012| last1 = Smith | first1 = A. | last2 = Bahl | first2 = C. R. H. | last3 = Bjørk | first3 = R. | last4 = Engelbrecht | first4 = K. | last5 = Nielsen | first5 = K. K. | last6 = Pryds | first6 = N. | bibcode = 2012AdEnM...2.1288S| s2cid = 98040294}}</ref> For refrigerators that could be used in the home, this temperature is room temperature. The temperature change can be further increased when the [[Phase transition#Order parameters|order-parameter]] of the phase transition changes strongly within the temperature range of interest.<ref name="doi10.1088/0022-327/38/23/R01"/>

The magnitudes of the magnetic entropy and the adiabatic temperature changes are strongly dependent upon the magnetic ordering process. The magnitude is generally small in [[antiferromagnet]]s, [[ferrimagnet]]s and [[spin glass]] systems but can be much larger for ferromagnets that undergo a magnetic phase transition. First order phase transitions are characterized by a discontinuity in the magnetization changes with temperature, resulting in a latent heat.<ref name="doi10.1002/aenm.201200167"/> Second order phase transitions do not have this latent heat associated with the phase transition.<ref name="doi10.1002/aenm.201200167"/>

In the late 1990s Pecharksy and Gschneidner reported a magnetic entropy change in {{chem|Gd|5|(Si|2|Ge|2|)}} that was about 50% larger than that reported for Gd metal, which had the largest known magnetic entropy change at the time.<ref name="auto2">{{Cite journal | doi = 10.1103/PhysRevLett.78.4494| title = Giant Magnetocaloric Effect in Gd_{5}(Si_{2}Ge_{2})| journal = Physical Review Letters| volume = 78| issue = 23| pages = 4494| year = 1997| last1 = Pecharsky | first1 = V. K.| last2 = Gschneidner, Jr. | first2 = K. A.|bibcode = 1997PhRvL..78.4494P }}</ref> This giant magnetocaloric effect (GMCE) occurred at 270 K, which is lower than that of Gd (294 K).<ref name="auto1"/> Since the MCE occurs below room temperature these materials would not be suitable for refrigerators operating at room temperature.<ref name="doi10.1038/NMAT3951">{{Cite journal | doi = 10.1038/NMAT3951| title = Caloric materials near ferroic phase transitions| journal = Nature Materials| volume = 13| issue = 5| pages = 439–50| year = 2014| last1 = Moya | first1 = X.| last2 = Kar-Narayan | first2 = S.| last3 = Mathur | first3 = N. D.|bibcode = 2014NatMa..13..439M | pmid=24751772| url = https://www.repository.cam.ac.uk/bitstream/1810/267195/1/Caloric%20review_open%20access%20version.pdf}}</ref> Since then other alloys have also demonstrated the giant magnetocaloric effect. These include {{chem|Gd|5|(Si|''x''|Ge|1−''x''|)|4}}, {{chem|La(Fe|''x''|Si|1−''x''|)|13|H|''x''}} and {{chem|MnFeP|1−''x''|As|''x''}} alloys.<ref name="doi10.1002/aenm.201200167"/><ref name="doi10.1038/NMAT3951"/> Gadolinium and its alloys undergo second-order phase transitions that have no magnetic or thermal [[hysteresis]].<ref>{{Cite journal | doi = 10.1038/srep02291| title = Integrating giant microwave absorption with magnetic refrigeration in one multifunctional intermetallic compound of LaFe11.6Si1.4C0.2H1.7| journal = Scientific Reports| volume = 3| pages = 2291| year = 2013| last1 = Song | first1 = N. N. | last2 = Ke | first2 = Y. J. | last3 = Yang | first3 = H. T. | last4 = Zhang | first4 = H. | last5 = Zhang | first5 = X. Q. | last6 = Shen | first6 = B. G. | last7 = Cheng | first7 = Z. H. |bibcode = 2013NatSR...3.2291S | pmid=23887357 | pmc=3724178}}</ref> However, the use of rare earth elements makes these materials very expensive.

{{chem|Ni|2|Mn-X}} (X = Ga, Co, In, Al, Sb) Heusler alloys are also promising candidates for magnetic cooling applications because they have Curie temperatures near room temperature and, depending on composition, can have martensitic phase transformations near room temperature.<ref name="auto"/> These materials exhibit the [[magnetic shape memory]] effect and can also be used as actuators, energy harvesting devices, and sensors.<ref>{{Cite journal | doi = 10.1002/adma.201002753| pmid = 20957766| title = Size Effects on Magnetic Actuation in Ni-Mn-Ga Shape-Memory Alloys| journal = Advanced Materials| volume = 23| issue = 2| pages = 216–32| year = 2011| last1 = Dunand | first1 = D. C. | last2 = Müllner | first2 = P. | bibcode = 2011AdM....23..216D| s2cid = 4646639}}</ref> When the martensitic transformation temperature and the Curie temperature are the same (based on composition) the magnitude of the magnetic entropy change is the largest.<ref name="doi10.1088/0022-327/38/23/R01"/> In February 2014, GE announced the development of a functional Ni-Mn-based magnetic refrigerator.<ref>{{cite web|url= http://www.ge.com/research/live/magnetic_refrigeration/|title= GE Global Research Live|access-date= 2015-02-18|archive-date= 2015-02-18|archive-url= https://web.archive.org/web/20150218202913/http://www.ge.com/research/live/magnetic_refrigeration/|url-status= dead}}</ref><ref>{{cite web|url=http://www.gizmag.com/ge-magnetocaloric-refrigerator/30835/|title=Your next fridge could keep cold more efficiently using magnets|work=gizmag.com|date=2014-02-14}}</ref>

The development of this technology is very material-dependent and will likely not replace vapor-compression refrigeration without significantly improved materials that are cheap, abundant, and exhibit much larger magnetocaloric effects over a larger range of temperatures. Such materials need to show significant temperature changes under a field of two tesla or less, so that permanent magnets can be used for the production of the magnetic field.<ref name="ReferenceA">{{Cite journal | doi = 10.1088/0034-4885/68/6/R04| title = Recent developments in magnetocaloric materials| journal = Reports on Progress in Physics| volume = 68| issue = 6| pages = 1479| year = 2005| last1 = Gschneidnerjr | first1 = K. A. | last2 = Pecharsky | first2 = V. K. | last3 = Tsokol | first3 = A. O. |bibcode = 2005RPPh...68.1479G | s2cid = 56381721| url = https://zenodo.org/record/1235742}}</ref><ref>{{Cite journal | doi = 10.1016/S0304-8853(99)00397-2| title = Magnetocaloric effect and magnetic refrigeration| journal = Journal of Magnetism and Magnetic Materials| volume = 200| issue = 1–3| pages = 44–56| year = 1999| last1 = Pecharsky | first1 = V. K. | last2 = Gschneidner Jr | first2 = K. A. |bibcode = 1999JMMM..200...44P }}</ref>

=== Paramagnetic salts ===

The original proposed refrigerant was a [[paramagnetism|paramagnetic]] [[salt (chemistry)|salt]], such as [[cerium]] [[magnesium]] [[nitrate]].  The active magnetic dipoles in this case are those of the [[electron shell]]s of the paramagnetic atoms.

In a paramagnetic salt ADR, the heat sink is usually provided by a pumped {{chem|4|He}} (about 1.2&nbsp;K) or {{chem|3|He}} (about 0.3&nbsp;K) [[cryostat]].  An easily attainable 1&nbsp;T magnetic field is generally required for initial magnetization. The minimum temperature attainable is determined by the self-magnetization tendencies of the refrigerant salt, but temperatures from 1 to 100 mK are accessible. [[Dilution refrigerator]]s had for many years supplanted paramagnetic salt ADRs, but interest in space-based and simple to use lab-ADRs has remained, due to the complexity and unreliability of the dilution refrigerator.

At a low enough temperature, paramagnetic salts become either [[diamagnetism|diamagnetic]] or ferromagnetic, limiting the lowest temperature that can be reached using this method.{{Citation needed|reason=What is this transition temperature called?|date=June 2023}}

=== Nuclear demagnetization ===

One variant of adiabatic demagnetization that continues to find substantial research application is nuclear demagnetization refrigeration (NDR).  NDR follows the same principles, but in this case the cooling power arises from the [[Spin (physics)#Magnetic moments|magnetic dipoles of the nuclei]] of the refrigerant atoms, rather than their electron configurations.  Since these dipoles are of much smaller magnitude, they are less prone to self-alignment and have lower intrinsic minimum fields.  This allows NDR to cool the nuclear spin system to very low temperatures, often 1 μK or below. Unfortunately, the small magnitudes of nuclear magnetic dipoles also makes them less inclined to align to external fields.  Magnetic fields of 3 teslas or greater are often needed for the initial magnetization step of NDR.

In NDR systems, the initial heat sink must sit at very low temperatures (10–100 mK).  This precooling is often provided by the mixing chamber of a dilution refrigerator<ref>{{Cite journal | doi = 10.1016/j.cryogenics.2021.103390| issn=0011-2275| title = Development of Dilution refrigerators – A review | journal = Cryogenics| volume = 121| year = 2022| last1 = Zu | first1 = H.| last2 = Dai | first2 = W.| last3 = de Waele | first3 = A.T.A.M.| s2cid=244005391}}</ref> or a paramagnetic salt.

== Commercial development ==

Research and a demonstration proof of concept device in 2001 succeeded in applying commercial-grade materials and permanent magnets at room temperatures to construct a magnetocaloric refrigerator.<ref name="Ames Lab-2001">{{cite news | url = http://www.ameslab.gov/news/ins01-11Magnetic.htm | last = Gibson | first = Kerry | work = INSIDER Newsletter for employees of Ames Laboratory | title = Magnetic Refrigerator Successfully Tested: Ames Laboratory developments help push boundaries of new refrigeration technology | date = November 2001 | url-status = dead | archive-url = https://web.archive.org/web/20100527140630/http://www.ameslab.gov/news/ins01-11Magnetic.htm | archive-date = 2010-05-27 }}(Vol. 112, No.10 )</ref>

On August 20, 2007, the [[Risø National Laboratory]] (Denmark) at the [[Technical University of Denmark]], claimed to have reached a milestone in their magnetic cooling research when they reported a temperature span of 8.7&nbsp;K.<ref>[http://www.risoe.dk/News_archives/News/2007/0820_magnetisk_koeling.aspx Milestone in magnetic cooling, Risø News, August 20, 2007] {{webarchive|url=https://web.archive.org/web/20070905023927/http://www.risoe.dk/News_archives/News/2007/0820_magnetisk_koeling.aspx |date=September 5, 2007 }}. Retrieved August 28, 2007.</ref> They hoped to introduce the first commercial applications of the technology by 2010.

As of 2013 this technology had proven commercially viable only for ultra-low temperature [[cryogenic]] applications available for decades. Magnetocaloric refrigeration systems are composed of pumps, motors, secondary fluids, heat exchangers of different types, magnets and magnetic materials. These processes are greatly affected by irreversibilities and should be adequately considered.
At year-end, Cooltech Applications announced that its first commercial refrigeration equipment would enter the market in 2014. Cooltech Applications launched their first commercially available magnetic refrigeration system on 20 June 2016.
At the 2015 [[Consumer Electronics Show]] in Las Vegas, a consortium of [[Haier]], [[Astronautics Corporation of America]] and [[BASF]] presented the first cooling appliance.<ref>{{cite web|title=Premiere of cutting-edge magnetocaloric cooling appliance|url=https://www.youtube.com/watch?v=jnl9m0rSE7U| archive-url=https://web.archive.org/web/20150106071051/https://www.youtube.com/watch?v=jnl9m0rSE7U&gl=US&hl=en| archive-date=2015-01-06 | url-status=dead|publisher=BASF|access-date=16 July 2015}}</ref> BASF claim of their technology a 35% improvement over using compressors.<ref>{{cite web|url=http://www.basf-new-business.com/en/projects/e-power-management/solid-state-cooling/|title=Solid state cooling|work=BASF New Business GmbH|access-date=23 March 2018}}</ref>

In November 2015, at the Medica 2015 fair, Cooltech Applications presented, in collaboration with Kirsch medical GmbH, the world's first magnetocaloric medical cabinet.<ref>[https://www.kirsch-medical.com/products/magnetocool.html first magnetocaloric medical cabinet]</ref> One year later, in September 2016, at the 7th International Conference on Magnetic Refrigeration at Room Temperature (Thermag VII)] held in Torino, Italy, Cooltech Applications presented the world's first magnetocaloric frozen heat exchanger.<ref>{{cite web | url=https://iifiir.org/fr/fridoc/7-lt-sup-gt-e-lt-sup-gt-conference-internationale-sur-le-froid-magnetique-a-6052 | title=7th International Conference on Magnetic Refrigeration at Room Temperature (Thermag VII). Proceedings: Turin, Italy, September 11-14, 2016 | date=11 September 2016 }}</ref>

In 2017, Cooltech Applications presented a fully functional 500 liters' magnetocaloric cooled cabinet with a {{cvt|30|kg|lb}} load and an air temperature inside the cabinet of +2{{nbsp}}°C. That proved that magnetic refrigeration is a mature technology, capable of replacing the classic refrigeration solutions.

One year later, in September 2018, at the 8th International Conference on Magnetic Refrigeration at Room Temperature (Thermag VIII]), Cooltech Applications presented a paper on a magnetocaloric prototype designed as a 15&nbsp;kW proof-of-concept unit.<ref>{{cite journal |last1=Lionte |first1=Sergiu |last2=Risser |first2=Michel |last3=Muller |first3=Christian |title=A 15kW magnetocaloric proof-of-concept unit: Initial development and first experimental results |journal=International Journal of Refrigeration |date=February 2021 |volume=122 |pages=256–265 |doi=10.1016/j.ijrefrig.2020.09.019 }}</ref> This has been considered by the community as the largest magnetocaloric prototype ever created.<ref>{{cite journal |last1=Kitanovski |first1=Andrej |title=Energy Applications of Magnetocaloric Materials |journal=Advanced Energy Materials |date=March 2020 |volume=10 |issue=10 |doi=10.1002/aenm.201903741 |bibcode=2020AdEnM..1003741K }}</ref>

At the same conference, Dr. Sergiu Lionte announced that, due to financial issues, Cooltech Applications declared bankruptcy.<ref>[http://thermag2018.de/frontend/folder_id=1511.html Dr. Sergiu Lionte's speech at Thermag VIII conference as invited speaker]</ref> Later on, in 2019 Ubiblue company, today named Magnoric, is formed by some of the old Cooltech Application's team members. The entire patent portfolio form Cooltech Applications was taken over by Magnoric since then, while publishing additional patents at the same time.

In 2019, at the 5th Delft Days Conference on Magnetocalorics, Dr. Sergiu Lionte presented Ubiblue's (former Cooltech Application) last prototype.<ref>{{Cite web|title=DDMC 2019|url=https://www.tudelft.nl/tnw/over-faculteit/afdelingen/radiation-science-technology/research/research-groups/fundamental-aspects-of-materials-and-energy/workshopsconferences/delft-days-magnetocalorics/ddmc-2019|access-date=2021-11-07|website=TU Delft|language=nl-NL}}</ref> Later, the magnetocaloric community acknowledged that Ubiblue had the most developed magnetocalorics prototypes.<ref>{{cite journal | doi=10.1002/aenm.201903741 | title=Energy Applications of Magnetocaloric Materials | date=2020 | last1=Kitanovski | first1=Andrej | journal=Advanced Energy Materials | volume=10 | issue=10 | s2cid=213786208 | doi-access=free | bibcode=2020AdEnM..1003741K }}</ref>

Thermal and magnetic [[hysteresis]] problems remain to be solved for first-order phase transition materials that exhibit the GMCE.<ref name="ReferenceA"/>

[[Vapor-compression refrigeration]] units typically achieve performance coefficients of 60% of that of a theoretical ideal [[Carnot cycle]], much higher than current MR technology. Small domestic refrigerators are however much less efficient.<ref>{{cite conference |osti=40784 |title=Improving the energy efficiency of refrigerators in India|publisher= US Department of Energy, Office of Scientific and Technical Information | conference= Annual meeting of the American Society of Heating, Refrigeration and Air-Conditioning Engineers, Inc. (ASHRAE), San Diego, CA (United States), 24-28 Jun 1995  |date=2012-08-31 |orig-date=1995 |last1=Sand |first1=J. R. |last2=Vineyard |first2=E. A. |last3=Bohman |first3=R. H. }}</ref>

In 2014 giant anisotropic behavior of the magnetocaloric effect was found in {{chem|HoMn|2|O|5}} at 10 K. The anisotropy of the magnetic entropy change gives rise to a large rotating MCE offering the possibility to build simplified, compact, and efficient magnetic cooling systems by rotating it in a constant magnetic field.<ref>{{cite journal |last1=Balli |first1=M. |last2=Jandl |first2=S. |last3=Fournier |first3=P. |last4=Gospodinov |first4=M. M. |title=Anisotropy-enhanced giant reversible rotating magnetocaloric effect in HoMn2O5 single crystals |journal=Applied Physics Letters |date=9 June 2014 |volume=104 |issue=23 |doi=10.1063/1.4880818 }}</ref>

In 2015 Aprea ''et al.''<ref>{{cite journal |last1=Aprea |first1=Ciro |last2=Greco |first2=Adriana |last3=Maiorino |first3=Angelo |title=GeoThermag: A geothermal magnetic refrigerator |journal=International Journal of Refrigeration |date=November 2015 |volume=59 |pages=75–83 |doi=10.1016/j.ijrefrig.2015.07.014 }}</ref> presented a new refrigeration concept, GeoThermag, which is a combination of magnetic refrigeration technology with that of low-temperature geothermal energy. To demonstrate the applicability of the GeoThermag technology, they developed a pilot system that consists of a 100-m deep geothermal probe; inside the probe, water flows and is used directly as a regenerating fluid for a magnetic refrigerator operating with gadolinium. The GeoThermag system showed the ability to produce cold water even at 281.8 K in the presence of a heat load of 60 W. In addition, the system has shown the existence of an optimal frequency f AMR, 0.26&nbsp;Hz, for which it was possible to produce cold water at 287.9 K with a thermal load equal to 190 W with a COP of 2.20. Observing the temperature of the cold water that was obtained in the tests, the GeoThermag system showed a good ability to feed the cooling radiant floors and a reduced capacity for feeding the fan coil systems.

== See also ==

* {{anl|Coefficient of performance}}
* {{anl|Cryostat}}
* {{anl|Curie's law}}
* {{anl|Dilution refrigerator}}
* {{anl|Elastocaloric  effect}}
* {{anl|Electrocaloric effect}}
* {{anl|Thermoacoustic refrigeration}}

== References ==

{{refs}}

== Further reading ==

* Lounasmaa, ''Experimental Principles and Methods Below 1&nbsp;K'', Academic Press (1974).
* Richardson and Smith, ''Experimental Techniques in Condensed Matter Physics at Low Temperatures'', Addison Wesley (1988).
* {{cite journal | last1 = Lucia | first1 = U | year = 2008 | title = General approach to obtain the magnetic refrigeration ideal Coefficient of Performance COP | journal = Physica A: Statistical Mechanics and Its Applications | volume = 387 | issue = 14| pages = 3477–3479 | doi = 10.1016/j.physa.2008.02.026 | arxiv = 1011.1684 | bibcode = 2008PhyA..387.3477L }}
* {{cite journal | last1 = Bouhani | first1 = H | year = 2020 | title = Engineering the magnetocaloric properties of PrVO3 epitaxial oxide thin films by strain effects | journal = Applied Physics Letters | volume = 117 | issue = 7| page = 072402 | doi =10.1063/5.0021031 | arxiv = 2008.09193 | bibcode = 2020ApPhL.117g2402B | s2cid = 225378969 }}
* {{cite journal | last1 = de Souza | first1 = M. | year = 2021 | title = Elastocaloric-effect-induced adiabatic magnetization in paramagnetic salts due to the mutual interactions | journal = Scientific Reports | volume = 11 | issue = 9461| page = 9431 | doi =10.1038/s41598-021-88778-4| pmid = 33941810 | pmc = 8093207 | bibcode = 2021NatSR..11.9431S }}

== External links ==

* [https://www.feynmanlectures.caltech.edu/II_35.html#Ch35-S5 Cooling by adiabatic demagnetization - The Feynman Lectures on Physics]
* [https://www.physlink.com/Education/AskExperts/ae488.cfm What is magnetocaloric effect and what materials exhibit this effect the most?]
* [https://web.archive.org/web/20030504003504/http://www.ameslab.gov/News/release/crada.html Ames Laboratory news release, May 25, 1999, Work begins on prototype magnetic-refrigeration unit].
* {{cite journal |last1=Liu |first1=Danmin |last2=Yue |first2=Ming |last3=Zhang |first3=Jiuxing |last4=McQueen |first4=T. M. |last5=Lynn |first5=Jeffrey W. |last6=Wang |first6=Xiaolu |last7=Chen |first7=Ying |last8=Li |first8=Jiying |last9=Cava |first9=R. J. |last10=Liu |first10=Xubo |last11=Altounian |first11=Zaven |last12=Huang |first12=Q. |title=Origin and tuning of the magnetocaloric effect in the magnetic refrigerant Mn<sub>1.1</sub> Fe<sub>0.9</sub> (P<sub>0.8</sub> Ge<sub>0.2</sub> ) |journal=Physical Review B |date=26 January 2009 |volume=79 |issue=1 |page=014435 |doi=10.1103/PhysRevB.79.014435 |arxiv=0807.3707 |bibcode=2009PhRvB..79a4435L }}
* [https://archive.today/20130117170121/http://www.basf.com/group/pressrelease/P-09-348] Magnetic technology revolutionizes refrigeration]
* {{cite report |type=Preprint |last1=Lucia |first1=Umberto |title=Exergy analysis of magnetic refrigeration |date=2010 |arxiv=1011.1684 }}

{{Emerging technologies|other=yes}}

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[[Category:Thermodynamic cycles]]
[[Category:Cooling technology]]
[[Category:Statistical mechanics]]
[[Category:Condensed matter physics]]
[[Category:Magnetism]]