Magnetic cooling

The magnetic refrigeration ( cooling by adiabatic demagnetization) is a method of Low Temperature Physics , with the small quantities of materials to temperatures below 1 mK (Milli kelvin = 10 ^-3 K) can be cooled. It is based on the magnetocaloric effect and is primarily used for basic research .

theory

Magnetic cooling is based on the temperature dependence in the order ( entropy ) of the magnetic moments of the material used . Both the magnetic moments of the electrons (as in the adiabatic demagnetization of paramagnetic salts ) and the nuclear moments (see below: adiabatic nuclear demagnetization) can be used.

Principle of cooling through adiabatic demagnetization (details in the text)

At high temperatures, the thermal energy is greater than the interaction energy of the magnetic moments, which are therefore completely disordered. If the size of the moments involved corresponds to an angular momentum J , a constant ( molar ) entropy S results per mole :

{\ displaystyle {\ frac {S} {n}} = R \ cdot \ ln (2J + 1)}

in which

R denotes the general gas constant and
n is the amount of substance .

If at low temperatures (and without a magnetic field , i.e. at B = 0) the thermal energy falls below the interaction energy of the magnetic moments, these begin to organize; the entropy decreases along the dashed line in the schematic representation.

If a magnetic field is present, a preferred direction is determined and the order temperature is raised (point A to point B). Initially, the following heat is released per mole , which must be dissipated with suitable measures: ${\ displaystyle B_ {1}}$

{\ displaystyle {\ frac {\ Delta Q} {n}} = {\ frac {T_ {1} \ cdot [S (0, T_ {1}) - S (B_ {1}, T_ {1})] } {n}}}

This pre-cooling is generally done with the help of the ³ He- ⁴ He Entmischungskühlung .

If the magnetic field is then reduced to a value under thermal insulation (adiabatic) , the state of order causes a correspondingly lower temperature (point C in the diagram): ${\ displaystyle B_ {2} <B_ {1}}$ ${\ displaystyle T_ {2} <T_ {1}}$

{\ displaystyle {\ begin {aligned} T_ {2} & = T_ {1} \ cdot {\ sqrt {\ frac {B_ {2} ^ {2} + b ^ {2}} {B_ {1} ^ { 2} + b ^ {2}}}} \\ & \ approx T_ {1} \ cdot {\ frac {\ sqrt {B_ {2} ^ {2} + b ^ {2}}} {B_ {1} }} \ end {aligned}}}

The temperature that can be reached is limited by the internal field b , which is itself caused by the interactions between the magnetic moments. These can not be neglected for. The size of the internal field for paramagnetic salts (see below) can be determined from the Néel temperature . ${\ displaystyle T_ {2}}$ ${\ displaystyle B_ {2} \ rightarrow 0}$ ${\ displaystyle b}$

Applications

Adiabatic demagnetization of paramagnetic salts

The cooling by adiabatic demagnetization of paramagnetic salts (e.g. of cermagnesium nitrate / CMN) was the first method with which temperatures in the range of a few millikelvin could be reached. It was proposed in 1926 by Debye and in 1927 by Giauque and uses the magnetic moments of the electrons. The method was, however, largely on the ³ He- ⁴ He Entmischungskühlung replaced as these, in contrast to magnetic cooling continuously working.

It is also conceivable to use the adiabatic demagnetization of substances in the vicinity of the Curie point . In principle, it should be possible, through adiabatic demagnetization of gadolinium (Curie point: 16 ° C), to build cooling devices that do not contain environmentally harmful CFCs or mechanical parts. In the 1990s, cheaper suitable metal alloys without gadolinium were discovered.

In 2015, a refrigerator with a magnetocaloric metal salt (metamagnet) based on a manganese-iron-phosphorus-silicon alloy was presented at a consumer fair . Magnetocaloric heat pumps promise a largely silent operation and 25% lower energy consumption than conventional refrigeration compressor technology .

Adiabatic nuclear demagnetization

Cooling by adiabatic nuclear demagnetization, in which the magnetic moments of the atomic nuclei are used, is still the only method with which a solid can be cooled to well below 1 millikelvin - temperatures in the µKelvin range (10 ⁻⁶ K ). The small size of the nuclear moments (approx. 1/2000 of those of electrons) requires pre-cooling to a few millikelvin and high magnetic fields in the range of several Tesla .

literature

^ Frank Pobell: Matter and Methods at Low Temperatures . 2nd Edition. Springer, Berlin / Heidelberg 1996, ISBN 978-3-540-58572-5 , pp. 175 .

^ Christian Enss, Siegfried Hunklinger: Low-Temperature Physics . Springer, Heidelberg 2005, ISBN 978-3-540-23164-6 , pp. 486,487 .

↑ Volker Mrasek , April 14, 2015, 4:40 pm: Great idea, episode 14: Metamagnet instead of a compressor ( page no longer available , search in web archives ) Info: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice. (4.7 MiB), broadcast "Research Current" by Deutschlandfunk, transcript of the broadcast@1@ 2

[1] Frank Pobell: Matter and Methods at Low Temperatures . 2nd Edition. Springer, Berlin / Heidelberg 1996, ISBN 978-3-540-58572-5 , pp. 175 .

[2] Christian Enss, Siegfried Hunklinger: Low-Temperature Physics . Springer, Heidelberg 2005, ISBN 978-3-540-23164-6 , pp. 486,487 .