Below 1 Kelvin

Cooling with Magnetic Molecules

  • Fig. 1a: The structure of [Gd7(OH)6(thmeH2)5(thmeH)(tpa)6(MeCN)2](NO3)2 ["Gd7"; H3thme=tris(hydroxymethyl)ethane;Htpa = triphenylacetic acid].Fig. 1a: The structure of [Gd7(OH)6(thmeH2)5(thmeH)(tpa)6(MeCN)2](NO3)2 ["Gd7"; H3thme=tris(hydroxymethyl)ethane;Htpa = triphenylacetic acid].
  • Fig. 1a: The structure of [Gd7(OH)6(thmeH2)5(thmeH)(tpa)6(MeCN)2](NO3)2 ["Gd7"; H3thme=tris(hydroxymethyl)ethane;Htpa = triphenylacetic acid].
  • Fig. 1b:The structure of a finite size cutout of a triangular lattice.
  • Fig. 2: Theoretical curves of constant entropy, i.e. isentropes of Gd7 (coloured) compared to those of a paramagnet (straight black lines).

The first sub-Kelvin cooling with magnetic molecules was achieved by an international team from Bielefeld, Manchester and Zaragoza. The results demonstrate that it is indeed possible to use magnetic molecules for magnetic refrigeration at such low temperatures, but moreover it also shows that the respective thermodynamic processes are very different from those using paramagnets. Magnetic molecules offer the opportunity to design the important curves of constant entropy (isentropes) through the design of appropriate magnetic molecules.

The Magnetocaloric Effect

That magnetic materials can change their temperature is known since the pioneering work of Emil Warburg in 1881. He discovered that plain iron changes its temperature when an applied magnetic field is removed. This magnetocaloric effect (MCE) can be used for a variety of cooling applications, for instance in special room-temperature refrigerators that work without refrigerant fluids. The magnetocaloric effect is also employed in order to achieve the lowest possible temperatures in thermodynamic cycles such as the Carnot or Ericsson cycles, which work with paramagnetic substances. Sub-Kelvin temperatures were experimentally obtained already in 1933 by W.F. Giauque who received the Nobel prize for his achievement in 1949. In contrast to paramagnets, magnetic molecules should offer more flexibility concerning the cooling process, but until now this remained a hypothetical option.

Cooling Below 1 K

The authors of [1] achieved a cooling down to approximately 0.2 Kelvin using a substance that consists of magnetic molecules, i.e. tiny nanomagnets. For their experiment they employed the molecular cluster [Gd7(OH)6(thmeH2)5(thmeH)(tpa)6(MeCN)2](NO3)2 ["Gd7"; H3thme = tris(hydroxymethyl)ethane; Htpa = triphenylacetic acid] which consists of a planar centered hexagon of weakly AF coupled Gd(III) ions, each of which has an electronic spin s = 7/2. Figure 1 shows the molecular structure which is related to the well-known triangular lattice antiferromagnet.

Besides the fact that this investigation constitutes the first sub-Kelvin cooling experiment with magnetic molecules it also exemplifies the richness of adiabatic processes in interacting magnetic quantum systems.

For a paramagnet the curves of constant entropy, on which the important adiabatic processes run up or down, are straight lines heading towards the origin of the T-B plane (compare black lines in Fig. 2). Their slope, which is the cooling rate, is always T/B for each pair of temperature T and field B, from where one wants to cool down, for instance. Magnetic molecules allow one to achieve very different cooling rates in certain parts of the T-B plane, especially close to the B axis. Such a behavior could be theoretically predicted for Gd7 and successfully measured. The bumpy structure of the isentropes of Gd7 shown in Figure 2 as colored curves reflects the unusual structure of magnetic energy levels present in Gd7 and simultaneously demonstrates that an interacting quantum magnet may produce cooling rates that are much larger in certain T-B regions compared to a paramagnet, a phenomenon that is termed enhanced magnetocaloric effect. In addition, processes such as heating upon decreasing the field are possible, too, which never happen with paramagnets.

Frustrated States

The unusual and pronounced bumpy structure of the isentropes of Gd7 (Fig. 2), which could be followed in the cooling experiments, is an outcome of the frustrated nature of the antiferromagnetic interactions in Gd7. Since the centered hexagon consists of triangles, the antiferromagnetic interaction is unable to constitute a magnetic ground state of pairwise "happy" combinations of up and down spins. Such a situation is termed "frustrated" [2]. Frustration often leads to an unusual bunching of low-lying energy levels, which as a function of applied magnetic field may vary strongly. It is this strong variation of the density of low-lying energy levels that produces the beautiful bumpy entropy landscape. The hope is thus that in the future we would be able to design isentropes according to our needs by means of rational design of magnetic molecules.

References
[1] Sharples J. W. et al.: Nature Communications 5, 5321 (2014)
[2] Schnack J.: Dalton Trans. 39, 4677-4686 (2010)

 

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Universität Bielefeld - Physikalische Chemie I

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