MCE quantum using molecules - Martes...

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

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...

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Cr

• 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

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)

Differentialof entropy

Next, we considerthe Maxwell relation

where C is specific heat

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For adiabatic processat constant pressure

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

“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

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

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)

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

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

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

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 !

AF exchange interactions and MCE

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Potentially quantum !

Though hardly observable w/o direct MCE measurements

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

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

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

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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)

View along the c axis

P-1 triclinic

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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:

icmaMarcoEvangelisti

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

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:

icmaMarcoEvangelisti

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

icmaMarcoEvangelisti

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

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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)

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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 !!

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