Nearly-quantumless magnetic cooling. using molecules. Marco Evangelisti

Transcription

1 Martes cuántico Zaragoza 26 de enero, 2016 Instituto de Ciencia de Materiales de Aragón CSIC and Universidad de Zaragoza Zaragoza, Spain WWW: Nearly-quantumless magnetic cooling MCE magnetic cooling + quantum using molecules

2 Cr As of December 2012 Ideal materials with designer properties, defined at the molecular scale and many, many, many more From Molecule-based magnetic coolers, M., in Molecular nanomagnets: physics and applications, Eds. J. Bartolomé, J. F. Fernández and F. Luis, Springer-Verlag 2

3 Definition and history Theoretical framework Experimental determination Suitable refrigerant materials Magnetocaloric effect & Magnetic refrigeration Adiabatic demagnetization refrigerators o Magnetically dense Gd-MOF o Quantum signatures in {Gd 7 } o Cooling by rotating {Dy 2 -ac} only if we have time Molecular coolants with examples 3

4 Magnetocaloric effect (MCE) is heating produced in magnetic materials following an increase of the applied magnetic field, and cooling when the applied magnetic field is removed. Or just the opposite in the inverse MCE. 4

5 Misconception (it was irreversible, hysteresis heat) Emil Gabriel Warburg ( ) discovered the Magneto-Caloric Effect (MCE) in an iron sample, which heated a few millikelvin when moved into a magnetic field and cooled back when removed out of it. [at Freiburg in 1881] 5

6 Nickel above room-t : observation of heating of 0.7 C for 1.5 T. J. Phys. (Paris), 5 th Ser. 7, (1917) 6

7 William Francis Giauque ( ) Nobel laureate for his studies on the properties of matter at temperatures close to absolute zero [at University of California, Berkeley] 61g of Gd 2 (SO 4 ) 3 8H 2 O for 0.8 T, 1.5 K 0.25 K Phys. Rev. 43, 768 (1933) Student! 7

8 No. of degrees of freedom for a spin s (véase martes cuántico) ln(2s + 1) magnetic entropy, S m A C T ad S m H 1 H 2 temperature, T 1 T 2 B T ad = adiabatic temperature change S m = magnetic entropy change Magnetic entropy S m vs temperature for paramagnet under applied fields H 1 and H 2 > H 1 The larger S m and T ad, the better magnetic refrigerant 8

9 Differential of entropy where C is specific heat For adiabatic process at constant pressure Next, we consider the Maxwell relation 9

10 Maxwell relation Adiabatic temperature change: Magnetic entropy change: 10

11 Experimental determination of MCE indirectly from magnetization data: only 90 % ln(2s + 1) indirectly from specific heat data: + magnetization A T ad H i S m H f 9.9 % + 90 % C magnetic entropy, S m B temperature, T i T f both specific heat and magnetization can be easily measured 11

12 Experimental determination of MCE direct method (home-made): Controlled non-adiabaticity, down to << 1 K Known: thermal conductance (κ ) of wires T 0 = bath temperature and Unpublished w/ E. Palacios 12

13 Suitability of refrigerants depends on target temperatures Very-low temperatures (10 mk < T < 1 K): paramagnetic salts (e.g., cerium magnesium nitrate, CMN); molecular nanomagnets (so-so). Low temperatures (1 K < T < 10 K): magnetic nanoparticles; lanthanide alloys; molecule-based magnetic materials (good). Intermediate temperatures: intermetallic and lanthanide alloys (second-order phase transitions), magnetic nanoparticles; moleculebased magnetic materials (bad). Near-room temperature: Gd and lanthanide-alloys (first-order phase transitions). 13

14 ADR Adiabatic Demagnetization Refrigerator Analogy between magnetic refrigeration and vapor cycle or conventional refrigeration. H = externally applied magnetic field; S = entropy; P = pressure. 14

15 Magnetic order MCE Magnetic phase transitions in >90% of publications on MCE 15

16 Magnetic order MCE Second-order phase transition H = 0 ISING - 3D ORDER spin 1/2 C / R H ap T / T C S m, T ad and RC maximized at T C drawback: No more entropy left below T C Entropy / R H = 0 H ap 0.1 Not suitable for achieving very low T T / T C 16

17 Magnetic order MCE Gadolinium metal PRL 78, 4494 (1997) near-room temperature ferromagnet at room-t B = (9 0) T Giant MCE orthorhombic < T C monoclinic > T C 17

18 ADR Adiabatic Demagnetization Refrigerator very-low temperature A cryogen-free two-stage ADR using Gadolinium Gallium Garnet (GGG) and Ferric Ammonium Alum (FAA) paramagnetic pills for the first and second stage, with Kevlar string supports for each stage. The FAA stage reaches a base temperature below 50 mk, and 100 mk for more than 200 hours. 18

19 ADR Adiabatic Demagnetization Refrigerator Valid alternative to the use of 3 He and 4 He very-low temperature Mcf 19

20 ADR Adiabatic Demagnetization Refrigerator very-low temperature ADR for outer-space applications absence of gravity e.g., high spectral resolution observation of the diffuse X-ray background in the ev energy range using an array of 36 1 mm 2 microcalorimeters flown on a sounding rocket D. McCammon et al., ApJ 576, 188 (2002) 20

21 High magnetic density for large MCE Ferric Ammonium Alum, as in commercial ADR Mainstream, stiff competition and quantumless For T between ca. 1 and 10 K 21

22 High magnetic density for large MCE c Gadolinium formate Metal-Organic Framework (MOF) Gd(OOCH) 3 Rhombohedral lattice (R3m) m w = 293 g/mol and ρ = 3.86 g/cm 3 Very high metal:non-metal mass ratio among molecule-based materials 22

23 High magnetic density for large MCE 2.0 T C1-0.5 C / R T C2 energy / K T / K 0.5 B 0 = 0 Experiment Monte Carlo T / K Classical Monte Carlo for a pure dipolar system of isotropic spins arranged in a lattice analogous to Gd formate. Ferrimagnetic order at T C1 = 0.9 K (solid line) made of alternating ferromagnetic 1D chains along c axis, i.e., two up and one down. Agrees with experiments M mol / Nµ B T = 0.4 K experiment B 0 parallel to c Unpublished magnetic ordering in progress B 0 / T 23

24 High magnetic density for large MCE S m / J kg -1 K from: C M B 0 = (7 0) T B 0 = (3 0) T B 0 = (1 0) T S m / mj cm -3 K -1 Huge cryogenic MCE (ca. 0.5 K < T < 10 K) even larger than GGG! T / K B 0 = (7 0) T B 0 = (3 0) T B 0 = (1 0) T 0 B / T starting (B i,t i ) B T Tad T / K T / K t t 0 / s limited by T C2 A dense metal-organic framework for enhanced magnetic refrigeration, G. Lorusso et al., Adv. Mater. 25, 4653 (2013) 24

25 AF exchange interactions and MCE Potentially quantum! Though hardly observable w/o direct MCE measurements 25

26 AF exchange interactions and MCE Paramagnets have linear isentropes, giving a decrease in T as field is decreased. Simplest interacting case: let us consider a dimer of s 1 = s 2 = 1/2, i.e., Cooling rate: A weakly dependent for small fields B normal (paramagnet) for high fields C drastically enhanced just above level crossing D heating just below level crossing Isentropes Enhanced MCE at fieldinduced level crossing 26

27 AF exchange interactions and MCE Can be mapped onto 2D frustrated triangular AF lattice The [Gd 7 ] snowflake 27

28 AF exchange interactions and MCE The [Gd 7 ] snowflake Nat. Commun. 5, (2014) 28

29 AF exchange interactions and MCE = E i E 0 at B J 1 = 0.09 K J 2 = 0.08 K J 1 J 2 Zeeman diagram calculated from spin Hamiltonian: The [Gd 7 ] snowflake See also: Application of the finite-temperature Lanczos method for the evaluation of magnetocaloric properties of large magnetic molecules, J. Schnack and C. Heesing, Eur. Phys. J. B 86, 46 (2013) Nat. Commun. 5, (2014) 29

30 AF exchange interactions and MCE Frustration-enhanced MCE Competing AF exchanges for J 1 0 and J 2 0 J 1 = 0.09 K (as from experimental data) J 2 = 0.09, 0.08, 0.07, 0.06 K J 1 Isentropes for S/R = 1 J 2 Non-degenerate g.s. for J 2 = 0 Expected experiments for J 2 = 0.08 K The [Gd 7 ] snowflake Low-energy states Simulations Nat. Commun. 5, (2014) 30

31 AF exchange interactions and MCE The [Gd 7 ] snowflake Home-made, sub-kelvin direct MCE measurements Experimental T corrected for energy dissipated via wires (from addenda, C of sample and κ of wires) and Nat. Commun. 5, (2014) 31

32 AF exchange interactions and MCE J 1 J 2 Experiments The [Gd 7 ] snowflake o Experiments no longer blind to exchange couplings. J Home-made, o Sub-Kelvin sub-kelvin cooling using magnetically-frustrated 1 molecules. = 0.09 K J 2 = 0.08 K direct MCE o Feasible because of high-density of low-energy excitations, measurements especially in certain T-B regions. Simulations Nat. Commun. 5, (2014) 32

33 simulation Isotropic or anisotropic MCE? simulation 33

34 Isotropic or anisotropic MCE? Example: magnetic specific heat, C Sch, of individual molecule with S = 10 and anisotropy D = 0.5 or 1.5 or 3.0 K simulation MCE Smaller anisotropy Larger entropy change Lower temperatures Recipes for enhanced molecular cooling, M. and E. K. Brechin, Dalton Trans. 39, 4672 (2010) 34

35 Cr As of December and many, many, many Gd more From Molecule-based magnetic coolers, M., in Molecular nanomagnets: physics and applications, Eds. J. Bartolomé, J. F. Fernández and F. Luis, Springer-Verlag 35

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37 Ideal rotocooler or rotoheater Constant applied field, B Magnetically anisotropic single-crystal T decreases upon rotating from an easier to a harder magnetization direction. T increases upon rotating from a harder to a easier magnetization direction. 37

38 Isotropic cooler: [{Gd(OAc) 3 (H 2 O) 2 } 2 ] 4H 2 O Parent molecule First time: use of light ligands (carboxylates) Larger magnetic density (but low T C ) Good for cryogenic MCE Cryogenic magnetocaloric effect in a ferromagnetic molecular dimer, M. et al., Angew. Chem. Int.-Ed. 50, 6606 (2011) 38

39 Anisotropic cooler: [{Dy(OAc) 3 (H 2 O) 2 } 2 ] 4H 2 O P-1 triclinic View along the c axis As expected, significantly smaller MCE (ca. 1/3) w.r.t. Gd-analogue but Cooling by rotating a magnetically anisotropic molecular dimer, G. Lorusso, O. Roubeau and M., Angew. Chem. Int.-Ed. (2016, in press) 39

40 Anisotropic cooler: [{Dy(OAc) 3 (H 2 O) 2 } 2 ] 4H 2 O P-1 triclinic View along the c axis Single-crystal photograph Magnetic anisotropy easier to harder B bc No ordering B // b B // c Cooling by rotating a magnetically anisotropic molecular dimer, G. Lorusso, O. Roubeau and M., Angew. Chem. Int.-Ed. (2016, in press) a forms 30 0 w.r.t. cristal plane 40

41 Anisotropic cooler: [{Dy(OAc) 3 (H 2 O) 2 } 2 ] 4H 2 O Dy 3+ ion has ground state 6 H 15/2 (4f 9 ) Zero-field specific heat, C, from which: entropy C / J kg -1 K S m / J kg -1 K T / K B = 0 B = 0 1 T 3 T T / K Relatively high-t magnetic entropy, S m, to 2Rln(2) effective spin s = 1/2 Cooling by rotating a magnetically anisotropic molecular dimer, G. Lorusso, O. Roubeau and M., Angew. Chem. Int.-Ed. (2016, in press) 41

42 Anisotropic cooler: [{Dy(OAc) 3 (H 2 O) 2 } 2 ] 4H 2 O From and zero-field entropy, S(T,0) field-dependent S(T,B) Magnetization measurements on single-crystal Cooling by rotating a magnetically anisotropic molecular dimer, G. Lorusso, O. Roubeau and M., Angew. Chem. Int.-Ed. (2016, in press) 42

43 Anisotropic cooler: [{Dy(OAc) 3 (H 2 O) 2 } 2 ] 4H 2 O Anisotropic MCE e a s i e r h a r d e r T R = T ad (easier) T ad (harder) Cooling by rotating a magnetically anisotropic molecular dimer, G. Lorusso, O. Roubeau and M., Angew. Chem. Int.-Ed. (2016, in press) 43

44 Anisotropic cooler: [{Dy(OAc) 3 (H 2 O) 2 } 2 ] 4H 2 O From ca. 4 to 1.5 K, by 90 0 in 5 T Cooling by rotating a magnetically anisotropic molecular dimer, G. Lorusso, O. Roubeau and M., Angew. Chem. Int.-Ed. (2016, in press) 44

45 Experimental rotocooler or rotoheater Right now (!) implementing it by recycling an old rotator Will allow direct measurements of the rotating MCE Hoy a las 13hr!! 45

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