mce quantum using molecules - martes...
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![Page 1: MCE quantum using molecules - Martes Cuanticomartescuantico.weebly.com/uploads/2/3/9/7/23970537/... · Emil Gabriel Warburg (1846-1931) discovered the . Magneto-Caloric Effect (MCE)](https://reader034.vdocuments.mx/reader034/viewer/2022050408/5f84f67fdb292043a63fa6b6/html5/thumbnails/1.jpg)
magnetic cooling using molecules
Nearly-quantumless
Marco EvangelistiInstituto de Ciencia de Materiales de Aragón
CSIC and Universidad de Zaragoza 50009 Zaragoza, Spain
WWW: http://molchip.unizar.es/
Martes cuántico – Zaragoza – 26 de enero, 2016
magnetic coolingMCE
+quantum
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20002004200620072008200920102011
2012
2013
From “Molecule-basedmagnetic coolers”, M. Evangelisti, in “Molecular nanomagnets: physics and applications”, Eds. J. Bartolomé, J. F. Fernández and F. Luis, Springer-Verlag
As of December 2012
2
Ideal materialswith designer properties, defined at the molecular scale
and many, many, many more...
icmaMarcoEvangelisti
Cr
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• Definition and history
• Theoretical framework
• Experimental determination
• Suitable refrigerant materials
• Adiabatic demagnetization refrigerators
o Magnetically dense Gd-MOF
o Quantum signatures in {Gd7}
o Cooling by rotating {Dy2-ac}
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Magnetocaloric effect
&
Magnetic refrigeration
Molecular coolantswith examples
icmaMarcoEvangelisti
only if wehave time
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Magnetocaloric effect (MCE) is
heating produced in magnetic materials following an increaseof the applied magnetic field,
and cooling when the applied magnetic field is removed.
Or just the opposite in the “inverse MCE”.
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Emil Gabriel Warburg (1846-1931)
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
Misconception (it was irreversible, hysteresis heat)
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Nickel above room-T :observation of heating of 0.7 °C for 1.5 T.
J. Phys. (Paris), 5th Ser. 7, 103-109 (1917)6
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William Francis Giauque (1895-1982)Nobel laureate for his studies on the properties of matter at temperatures close to absolute zero
[at University of California, Berkeley]
Student!
Phys. Rev. 43, 768 (1933)
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61g of Gd2(SO4)38H2O for 0.8 T, 1.5 K 0.25 K
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Magnetic entropy Sm vstemperature for paramagnet under applied fields H1 and H2 > H1
The larger ∆Sm and ∆Tad, the “better” magnetic refrigerant
∆Tad = adiabatictemperature change
∆Sm = magneticentropy change
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mag
netic
ent
ropy
, Sm
temperature, T1 T2
AB
C
H1 H2
ln(2s + 1)
∆Tad
∆Sm
No. of degrees of freedom for a spin sicmaMarco
Evangelisti(véase martes cuántico)
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Differentialof entropy
Next, we considerthe Maxwell relation
where C is specific heat
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For adiabatic processat constant pressure
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Maxwell relation
Adiabatic temperature change:
Magnetic entropy change:
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Experimental determination of MCEindirectly from magnetization data:
indirectly from specific heat data:
both specific heat and magnetization can be “easily” measured11
mag
netic
ent
ropy
, Sm
temperature, Ti Tf
AB
C
Hi Hf
ln(2s + 1)
∆Tad
∆Sm
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≈ 90 %
≈ 9.9 % + 90 %
only
+ magnetization
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Experimental determination of MCEdirect method (home-made):
Unpublished – w/ E. Palacios
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Controlled non-adiabaticity, down to << 1 KKnown: thermal conductance (κ ) of wires
T0 = bath temperature
and
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“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; molecule-based magnetic materials (bad).
Near-room temperature:Gd and lanthanide-alloys(first-order phase transitions).
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Analogy between magnetic refrigeration and vapor cycle or conventional refrigeration. H = externally applied magnetic field; S = entropy; P = pressure.
ADRAdiabaticDemagnetizationRefrigerator
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Magnetic order MCE
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Magnetic phase transitions in >90% of publications on MCE
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0 1 2 3 4 5 6 7 80.0
0.2
0.4
0.6
0.8
1.0
C / R
T / TC
ISING - 3D ORDERspin 1/2
H = 0
Hap
0 1 2 3 4 5 6 7 80.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Hap
H = 0
Entro
py /
R
T / TC
Second-order phase transition
−∆Sm , ∆Tad and RCmaximized at TC
drawback:No more entropy left below TC
Not suitable for achieving very low T
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Magnetic order MCEicmaMarco
Evangelisti
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Gadolinium metal
ferromagnet at room-T
∆B = (9 – 0) T
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Magnetic order MCEicmaMarco
Evangelistine
ar-r
oom
tem
pera
ture
orthorhombic < TC monoclinic > TC
“Giant”MCE
PRL 78, 4494 (1997)
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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 FAAstage reaches a base temperature below 50 mK, and remains @ 100 mK for more than 200 hours. 18
ADRAdiabaticDemagnetizationRefrigerator
very
-low
tem
pera
ture
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very
-low
tem
pera
ture
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Valid alternative to the use of 3He and 4He
Mcf
ADRAdiabaticDemagnetizationRefrigerator
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ADR for outer-spaceapplications
absence of gravity
e.g.,high spectral resolutionobservation of the diffuseX-ray background in the60–1000 eV energy rangeusing an array of 361 mm2 microcalorimetersflown on a sounding rocket
D. McCammon et al., ApJ 576, 188 (2002)20
ADRAdiabaticDemagnetizationRefrigerator
very
-low
tem
pera
ture
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Ferric Ammonium Alum,as in commercial ADR
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High magnetic density for large MCE
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Mainstream, stiff competition and quantumless
For T between ca. 1 and 10 K
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Gd(OOCH)3 Rhombohedral lattice (R3m)
mw = 293 g/mol and ρ = 3.86 g/cm3
Very high metal:non-metal massratio among molecule-based materials
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Gadolinium formateMetal-Organic Framework (MOF)
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High magnetic density for large MCE
c
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Unpublished magnetic ordering – in progress
High magnetic density for large MCE
0.0 0.5 1.0 1.5 2.0 2.5 3.0
-1.5
-1.0
-0.5
0.0 0.5 1.0 1.5 2.0 2.5 3.00.0
0.5
1.0
1.5
2.0
ener
gy /
K
T / K
Experiment Monte Carlo
C / R
T / K
B0 = 0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.001234567
T = 0.4 K
experiment B0 parallel to c
Mm
ol /
NµB
B0 / T
Classical Monte Carlo for a pure dipolar system of isotropic spins arranged in a lattice analogous to Gd formate.
Ferrimagnetic order at TC1 = 0.9 K (solid line)made of alternating ferromagnetic 1D chainsalong c axis, i.e., two up and one down.
Agrees with experiments
TC1
TC2
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0
13
26
39
52
0
50
100
150
200
0 5 10 15 20 25 300
5
10
15
20
−∆S m
/ m
J cm
-3 K
-1
from: C M ∆B0= (7 − 0) T ∆B0= (3 − 0) T ∆B0= (1 − 0) T
−∆S m
/ J
kg-1 K
-1
∆B0 = (7 − 0) T ∆B0 = (3 − 0) T ∆B0 = (1 − 0) T
∆T /
K
T / K
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“A dense metal-organic framework for enhanced magnetic refrigeration”, G. Lorusso et al., Adv. Mater. 25, 4653 (2013)
High magnetic density for large MCE
0 500 1000 1500 2000
0.0
0.2
0.4
0.6
0.8
1.0 B T Tad
t−t0 / s
B / T
0.5
1.0
T / K
starting (Bi,Ti)
limited by TC2
Huge cryogenic MCE(ca. 0.5 K < T < 10 K)
even larger than GGG !
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AF exchange interactions and MCE
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Potentially quantum !
Though hardly observable w/o direct MCE measurements
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Simplest interacting case: let us consider a dimer of s1 = s2 = 1/2, i.e.,
AF exchange interactions and MCE
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Paramagnets have linear isentropes, giving a decrease in T as field is decreased.
Cooling rate:
A – weakly dependent for small fieldsB – normal (paramagnet) for high fieldsC – drastically enhanced just above
level crossingD – heating just below level crossing
Enhanced MCE at field-induced level crossing
Isentropes
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The [Gd7]“snowflake”
Can be mapped onto2D frustrated triangular
AF lattice
AF exchange interactions and MCE
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Nat. Commun. 5, 12092 (2014)
The [Gd7]“snowflake”
AF exchange interactions and MCE
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The [Gd7]“snowflake”
Zeeman diagram calculated from spin Hamiltonian:
AF exchange interactions and MCE
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)
J1
J2
J1 = −0.09 K J2 = −0.08 K
= E i
–E 0
at B
Nat. Commun. 5, 12092 (2014)
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The [Gd7]“snowflake”
AF exchange interactions and MCE
Simulations
J1 = −0.09 K (as from experimental data)J2 = −0.09, −0.08, −0.07, −0.06 K
Expected experimentsfor J2 = −0.08 K
Frustration-enhanced MCE
Isentropes for S/R = 1
J1
J2
Nat. Commun. 5, 12092 (2014)
Low-energy states
Non-degenerate g.s. for J2 = 0
Competing AF exchanges for J1 ≠ 0 and J2 ≠ 0
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The [Gd7]“snowflake”
and
Home-made, sub-Kelvin direct MCE measurements
AF exchange interactions and MCE
Experimental T corrected for energy dissipated via wires (from addenda, C of sample and κ of wires)
Nat. Commun. 5, 12092 (2014)
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Simulations
The [Gd7]“snowflake”
Home-made, sub-Kelvin direct MCE measurements
AF exchange interactions and MCE
J1 = −0.09 K J2 = −0.08 K
J1
J2
Nat. Commun. 5, 12092 (2014)
o Experiments no longer blind to exchange couplings.o Sub-Kelvin cooling using magnetically-frustrated molecules.o Feasible because of high-density of low-energy excitations,
especially in certain T-B regions.
Experiments
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simulation
simulationIsotropic or anisotropic MCE ?
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MCE
Example: magnetic specific heat, CSch, of individual molecule with S = 10 and anisotropy D = −0.5 or −1.5 or −3.0 K
simulationIsotropic or anisotropic MCE ?
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“Recipes for enhanced molecular cooling”, M. Evangelisti and E. K. Brechin, Dalton Trans. 39, 4672 (2010)
Smaller anisotropy
Larger entropy change
Lower temperatures
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20002004200620072008200920102011
2012
2013
From “Molecule-basedmagnetic coolers”, M. Evangelisti, in “Molecular nanomagnets: physics and applications”, Eds. J. Bartolomé, J. F. Fernández and F. Luis, Springer-Verlag
As of December 2012
35and many, many, many Gd more...
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Cr
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T decreases upon rotating from an easier to a harder magnetization direction.
T increases upon rotating from a harder to a easier magnetization direction.
Ideal “rotocooler” or “rotoheater”
Magneticallyanisotropicsingle-crystal
Constantapplied field, B
![Page 38: MCE quantum using molecules - Martes Cuanticomartescuantico.weebly.com/uploads/2/3/9/7/23970537/... · Emil Gabriel Warburg (1846-1931) discovered the . Magneto-Caloric Effect (MCE)](https://reader034.vdocuments.mx/reader034/viewer/2022050408/5f84f67fdb292043a63fa6b6/html5/thumbnails/38.jpg)
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[{Gd(OAc)3(H2O)2}2]·4H2OIsotropic cooler:
Parent molecule
First time: use of light ligands (carboxylates)
Larger magnetic density (but low TC)
Good for cryogenic MCE
“Cryogenic magnetocaloric effect in a ferromagnetic molecular dimer”,M. Evangelisti et al., Angew. Chem. Int.-Ed. 50, 6606 (2011)
![Page 39: MCE quantum using molecules - Martes Cuanticomartescuantico.weebly.com/uploads/2/3/9/7/23970537/... · Emil Gabriel Warburg (1846-1931) discovered the . Magneto-Caloric Effect (MCE)](https://reader034.vdocuments.mx/reader034/viewer/2022050408/5f84f67fdb292043a63fa6b6/html5/thumbnails/39.jpg)
View along the c axis
P-1 triclinic
icmaMarcoEvangelisti
39“Cooling by rotating a magnetically anisotropic molecular dimer”,G. Lorusso, O. Roubeau and M. Evangelisti, Angew. Chem. Int.-Ed. (2016, in press)
As expected, significantly smaller MCE (ca. 1/3) w.r.t.
Gd-analogue
but…
[{Dy(OAc)3(H2O)2}2]·4H2OAnisotropic cooler:
![Page 40: MCE quantum using molecules - Martes Cuanticomartescuantico.weebly.com/uploads/2/3/9/7/23970537/... · Emil Gabriel Warburg (1846-1931) discovered the . Magneto-Caloric Effect (MCE)](https://reader034.vdocuments.mx/reader034/viewer/2022050408/5f84f67fdb292043a63fa6b6/html5/thumbnails/40.jpg)
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40“Cooling by rotating a magnetically anisotropic molecular dimer”,G. Lorusso, O. Roubeau and M. Evangelisti, Angew. Chem. Int.-Ed. (2016, in press)
Magnetic anisotropyeasier to harder
B ⊥ bc
B // b
B // c
Single-crystal photograph
a forms 300 w.r.t.cristal plane
View along the c axis
P-1 triclinic
[{Dy(OAc)3(H2O)2}2]·4H2OAnisotropic cooler:
No ordering
![Page 41: MCE quantum using molecules - Martes Cuanticomartescuantico.weebly.com/uploads/2/3/9/7/23970537/... · Emil Gabriel Warburg (1846-1931) discovered the . Magneto-Caloric Effect (MCE)](https://reader034.vdocuments.mx/reader034/viewer/2022050408/5f84f67fdb292043a63fa6b6/html5/thumbnails/41.jpg)
1 104
6
8
10
12
14
1 10
1
10
100
Sm /
J kg
-1 K
-1
T / K
B = 0
C /
J kg
-1 K
-1
T / K
B = 0
T 3 T −2
Dy3+ ion has ground state 6H15/2 (4f9)
Zero-field specific heat, C, from which: entropy
Relatively high-T magnetic entropy, Sm, to 2Rln(2) effective spin s = 1/2
icmaMarcoEvangelisti
41“Cooling by rotating a magnetically anisotropic molecular dimer”,G. Lorusso, O. Roubeau and M. Evangelisti, Angew. Chem. Int.-Ed. (2016, in press)
[{Dy(OAc)3(H2O)2}2]·4H2OAnisotropic cooler:
![Page 42: MCE quantum using molecules - Martes Cuanticomartescuantico.weebly.com/uploads/2/3/9/7/23970537/... · Emil Gabriel Warburg (1846-1931) discovered the . Magneto-Caloric Effect (MCE)](https://reader034.vdocuments.mx/reader034/viewer/2022050408/5f84f67fdb292043a63fa6b6/html5/thumbnails/42.jpg)
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42“Cooling by rotating a magnetically anisotropic molecular dimer”,G. Lorusso, O. Roubeau and M. Evangelisti, Angew. Chem. Int.-Ed. (2016, in press)
[{Dy(OAc)3(H2O)2}2]·4H2OAnisotropic cooler:
From
and zero-fieldentropy, S(T,0)
field-dependentS(T,B)
Magnetization measurements on single-crystal
![Page 43: MCE quantum using molecules - Martes Cuanticomartescuantico.weebly.com/uploads/2/3/9/7/23970537/... · Emil Gabriel Warburg (1846-1931) discovered the . Magneto-Caloric Effect (MCE)](https://reader034.vdocuments.mx/reader034/viewer/2022050408/5f84f67fdb292043a63fa6b6/html5/thumbnails/43.jpg)
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43“Cooling by rotating a magnetically anisotropic molecular dimer”,G. Lorusso, O. Roubeau and M. Evangelisti, Angew. Chem. Int.-Ed. (2016, in press)
[{Dy(OAc)3(H2O)2}2]·4H2OAnisotropic cooler:
Anisotropic MCE
∆TR = ∆Tad(easier) – ∆Tad(harder)
e a s i e r h a r d e r
![Page 44: MCE quantum using molecules - Martes Cuanticomartescuantico.weebly.com/uploads/2/3/9/7/23970537/... · Emil Gabriel Warburg (1846-1931) discovered the . Magneto-Caloric Effect (MCE)](https://reader034.vdocuments.mx/reader034/viewer/2022050408/5f84f67fdb292043a63fa6b6/html5/thumbnails/44.jpg)
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[{Dy(OAc)3(H2O)2}2]·4H2OAnisotropic cooler:
From ca. 4 to 1.5 K, by 900 in 5 T
“Cooling by rotating a magnetically anisotropic molecular dimer”,G. Lorusso, O. Roubeau and M. Evangelisti, Angew. Chem. Int.-Ed. (2016, in press)
![Page 45: MCE quantum using molecules - Martes Cuanticomartescuantico.weebly.com/uploads/2/3/9/7/23970537/... · Emil Gabriel Warburg (1846-1931) discovered the . Magneto-Caloric Effect (MCE)](https://reader034.vdocuments.mx/reader034/viewer/2022050408/5f84f67fdb292043a63fa6b6/html5/thumbnails/45.jpg)
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Experimental “rotocooler” or “rotoheater”
Right now (!) implementing itby recycling anold rotator…
Will allow directmeasurements of the rotating MCE
Hoy a las 13hr !!
![Page 46: MCE quantum using molecules - Martes Cuanticomartescuantico.weebly.com/uploads/2/3/9/7/23970537/... · Emil Gabriel Warburg (1846-1931) discovered the . Magneto-Caloric Effect (MCE)](https://reader034.vdocuments.mx/reader034/viewer/2022050408/5f84f67fdb292043a63fa6b6/html5/thumbnails/46.jpg)
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