Introduction to SCMs Dr. Rodolphe Cléracschnack/molmag/... · 2020. 7. 27. · Introduction to SCMs… by R. Clérac Florida, 2012 - 1 - Dr. Rodolphe Clérac CNRS - Researcher Centre

Introduction to SCMs… by R. Clérac Florida, 2012 - 1 -

Dr. Rodolphe CléracCNRS - Researcher

Centre de Recherche Paul Pascal, CNRS - UPR 8641

115, Avenue du Dr. A. Schweitzer 33600 Pessac – France

[email protected]

Introduction to SCMs


NN

OOX X

X = Br: 5-BrsalenX = Cl: 5-Clsalen

X = H: salen

NN

OO

salmen

A real system made by design: a SMM building-block [MnIII(salen)-FeIII(CN)6-MnIII(salen)] trinuclearcomplexes:

K[Mn2(5-Brsalen)2(H2O)2Fe(CN)6]•2H2O [1,4]K[Mn2(5-Clsalen)2(H2O)2Fe(CN)6]•2H2O [1](NEt4)[Mn2(5-Clsalen)2(H2O)2Fe(CN)6]•H2O [2](NEt4)[Mn2(salmen)2(MeOH)2Fe(CN)6] [3,5]

[1] H. Miyasaka, N. Matsumoto, H. Okawa, N. Re, E. Gallo, C. Floriani J. Am. Chem. Soc. 1996, 118, 981 [2] H. Miyasaka, N. Matsumoto, N. Re, E. Gallo, C. Floriani Inorg. Chem. 1997, 36, 670 [3] H. Miyasaka, H. Ieda, N. Matsumoto, N. Re, E. Crescenzi, C. Floriani Inorg. Chem. 1998, 37, 255 [4] H. J. Choi, J. J. Sokol, J. R. Long Inorg. Chem. 2004, 43, 1606 [5] M. Ferbinteanu, H. Miyasaka, W. Wernsdorfer, K. Nakata, K. Sugiura, M. Yamashita, C. Coulon, R. Clérac, J. Am. Chem. Soc. 2005, 127, 3090

S = 9/2D/kB = -1.25 K

An example of Single-Chain Magnets


The structural arrangement:(NEt4)2[Mn(5-MeOsalen)]2[Fe(CN)6]

Isolated chains from a magnetic point of view

M. Ferbinteanu, H. Miyasaka, W. Wernsdorfer, K. Nakata, K. Sugiura, M. Yamashita, C. Coulon, R. Clérac, J. Am. Chem. Soc. 2005, 127, 3090

Single-Chain Magnets


JF JF JF JF JF JF JF JF

J’ J’ J’

JFJ JFJ

J’ J

JF JF JFJ JFJ

The high temperature magnetic susceptibility:(NEt4)2[Mn(5-MeOsalen)]2[Fe(CN)6]

JF /kB = +6.5(1) K

J’/kB = +0.08(1) K

g = 2.03(2)

6

An Heisenberg trimer model with inter-trimer J’ interactions

treated in a mean field approximation

with H = −2JF

S Fe1

S Mn +

S Fe2

S Mn( )

An Heisenberg trimer model



JF JFJF JF

JF JFJF JF

J’J’ J’JJ

S = 2S = ½,S = 2,

« ST = 9/2 » because |JF | >> JMn-Mn and for |JF | >> kBT

J’ > 0J

F

J’ JJ’JJ

A physicist view:(NEt4)2[Mn(5-MeOsalen)]2[Fe(CN)6]

Chain of ferromagnetically coupled anisotropic S = 9/2 spins(it is fundamental to prove that the system is 1-D)


JF /kB = +6.5(1) K

J’/kB = +0.08(1) K

JMn-Mn/kB = +0.40(6) K


0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

M/M

s

H / T

Single crystal measurements: H in the hard plane(NEt4)2[Mn(5-MeOsalen)]2[Fe(CN)6]

D/kB = -0.94 K

D/kB ≈ -1.25 K

1.5 K

6.3 T

H = −2 ′ J

S T ,i

S T ,i+1

−∞

+∞

∑ + D

S T ,iz2

−∞

+∞

∑

Estimation of D

2DST2 ≈ gμBST Ha



Single crystal measurements: H along the easy axis(NEt4)2[Mn(5-MeOsalen)]2[Fe(CN)6]

Magnet behavior, i.e. slow relaxation of the

magnetization compatible with SCM behavior

M vs H hysteresis loops


Single crystal measurements: H(NEt4)2[Mn(5-MeOsalen)]2[Fe(CN

Mag

magw


Relaxation time measurements (ac susceptibility):(NEt4)2[Mn(5-MeOsalen)]2[Fe(CN)6] Relaxation time measuremen(NEt4)2[Mn(5-MeOsalen

nts (ac susceptibility):(CN)6]

uremenn)]2[Fe(

A single relaxation mode compatible with SCM behavior



0

0.2

0.4

0.6

0.8

1

0.1 1 10 100 1000t / s

1.7 K

1.6 K

1.5 K

1.34 K1.25 K

1.16 K 1.03 K1.1 K

0.98 K

0.86 K

0.92 K

0.8 KM

/Ms

Relaxation time measurements (M vs time):(NEt4)2[Mn(5-MeOsalen)]2[Fe(CN)6]

0

0.2

0.4

0.6

0.8

1

10-11 10-9 10-7 10-5 10-3 10-1 101

M/M

s

t/

e-1

Determination of the relaxation time down to 0.8 K



Relaxation time:(NEt4)2[Mn(5-MeOsalen)]2[Fe(CN)6]

τ T( ) =τ0expΔ eff

kBT

⎛

⎝ ⎜

⎞

⎠ ⎟

Δ1/kB ≈ 31.1 K Δ2/kB ≈ 25 K

Crossover between two activated relaxation regimes



10-4

10-2

100

102

104

106

0.4 0.6 0.8 1 1.2

/ s

T-1 / K-1

Relaxation time SMM vs SCM:

(NEt4)2[Mn(5-MeOsalen)]2[Fe(CN)6]

104

SCM

SMM

In a given temperature range the correlations

enhance the relaxation time

(NEt4)[Mn(salmen)(MeOH)]2[Fe(CN)6]

Single-Molecule vs. Single-Chain Magnets


H = 0 H ≠ 0

T

M / MS = exp − t

τ⎛⎝⎜

⎞⎠⎟

2ξ

τ T( ) =τ i T( ) ξa

⎛⎝⎜

⎞⎠⎟

2

=τ i T( )exp2Δξ

kBT

⎛⎝⎜

⎞⎠⎟

H = −2 ′J S2 σ iσ i+1−∞

+∞

∑ a

with Δξ = 4 ′J S2

(a) Glauber, R. J. J. Math. Phys. 1963, 4, 294; (b) Coulon, C. ; Miyasaka, H. ; Clérac, R. Struct. Bond. 2006, 122, 163

Chain of Ising spins


• • • • • •

The relaxation time of a Single-Chain Magnet:Chain of ferromagnetically coupled Ising spins (Glauber)

2ξ

τ T( ) =τ i T( )exp2Δξ

kBT

⎛

⎝ ⎜

⎞

⎠ ⎟ with Δξ = 4 ′ J S2

1) For a chain of anisotropic spins (D < 0 and |D/J | > 4/3: Ising limit) :

τ i T( ) =τ0expΔA

kBT

⎛

⎝ ⎜

⎞

⎠ ⎟ with ΔA = D ST

2 τ T( ) =τ0exp2Δξ + ΔA

kBT

⎛

⎝ ⎜

⎞

⎠ ⎟

H = −2J'

S T ,i

S T ,i+1

−∞

+∞

∑ + D

S T ,iz2

−∞

+∞

∑

(a) Glauber, R. J. J. Math. Phys. 1963, 4, 294; (b) Coulon, C. ; Miyasaka, H. ; Clérac, R. Struct. Bond. 2006, 122, 163

Fl id 2012 13Fl id 2012

Coulon, C. ; Clérac, R.; Lecren, L.; Wernsdorfer, W.; Miyasaka, H. Phys. Rev. B 2004, 69, 132408

Real Single-Chain Magnets


Δ1/kB = (8J’+ |D|)ST2/kB

= 32 KΔ

Relaxation time: the Glauber’s regime(NEt4)2[Mn(5-MeOsalen)]2[Fe(CN)6]

Δ1/kB ≈ 31.1 K Δ2/kB ≈ 25 K

τ T( ) =τ0exp2Δξ + ΔA

kBT

⎛

⎝ ⎜

⎞

⎠ ⎟

with

2Δξ + ΔA = 8 ′ J ST2 + D ST

2


with ST = 9/2J’/kB ≈ 0.08 KD/kB = -0.94 K(|D /J’ | >> 4/3)


The relaxation time in a Single-Chain Magnet:

2) For a chain of anisotropic spins with a length L (D < 0 and |D/J | > 4/3 Ising limit):

H = −2J'

S T ,i

S T ,i+1

−∞

+∞

∑ + D

S T ,iz2

−∞

+∞

∑

(a) Coulon, C. ; Miyasaka, H. ; Clérac, R. Struct. Bond. 2006, 122, 163 (b) Coulon, C. ; Clérac, R.; Lecren, L.; Wernsdorfer, W.; Miyasaka, H. Phys. Rev. B 2004, 69, 132408


kBT

⎛

⎝ ⎜

⎞

⎠ ⎟ for 2ξ < L

2ξ

τ T( ) =τ0expΔξ + ΔA

kBT

⎛

⎝ ⎜

⎞

⎠ ⎟ for 2ξ > L

Luscombe, J. H. et al., Phys. Rev. E 1996, 53, 5852 Leal da Silva, J. K. et al., Phys. Rev. E 1995, 52, 4527



Δ2/kB = (4J’+ |D|)ST2/kB

= 25.5 KΔ

Relaxation time: the finite-size chain regime(NEt4)2[Mn(5-MeOsalen)]2[Fe(CN)6]

Δ1/kB ≈ 31.1 K Δ2/kB ≈ 25 K

τ T( ) =τ 0expΔξ + ΔA

kBT

⎛⎝⎜

⎞⎠⎟

with

Δξ + ΔA = 4 ′J ST2 + D ST

2


with ST = 9/2J’/kB ≈ 0.08 KD/kB = -0.94 K(|D /J’ | >> 4/3)


Another evidence of the finite-size chain regime:(NEt4)2[Mn(5-MeOsalen)]2[Fe(CN)6]

H = −2J'ST

2 σ i σ i+1

−∞

+∞

∑Ising Chain Model

χ =Ceff

Texp

Δξ

kBT

⎛

⎝ ⎜

⎞

⎠ ⎟

with Δξ = 4 ′ J ST2

Infinite chain regime 2ξξ < L

ST = 9/2J’/kB = +0.08(1) K

Finite chain regime

2ξ > Lχ = n

Ceff

Tn ≈ 44

L ≈ 60 nm

J

Final proof of a Single-Chain Magnets


H = −2J'

S T ,i

S T ,i+1

−∞

+∞

∑ + D

S T ,iz2

−∞

+∞

∑ (a) Coulon, C.; Miyasaka, H. ; Clérac, R. Struct. Bond. 2006, 122, 163 (b) Coulon, C.; Clérac, R.; Lecren, L.; Wernsdorfer, W.; Miyasaka, H. Phys. Rev. B 2004, 69, 132408

Single-Chain Magnets (Take home message)

Always correct:

χ =Ceff

Texp

Δξ

kBT

⎛⎝⎜

⎞⎠⎟

Static properties


kBT

⎛

⎝ ⎜

⎞

⎠ ⎟ for 2ξ < L

τ T( ) =τ0expΔξ + ΔA

kBT

⎛

⎝ ⎜

⎞

⎠ ⎟ for 2ξ > L

Dynamic properties

In the Ising limit D < 0 and |D/J | > 4/3: Δξ = 4 ′J ST2 and ΔA = D ST

2

In the Heisenberg limit D < 0, and small and |D/J | << 4/3:

Δξ = 2ST2 2 D ′J and ΔA = ??

Between the Ising and the Heisenberg limits (D < 0, |D/J | < 4/3):

Δξ = ?? and ΔA = ??Billoni, O. V.; Pianet, V.; Pescia, D.; Vindigni, A. Phys. Rev. B 2011, 84, 064415


The ingredients in order to obtain a SCM:• chain architecture• high-spin chain units with uniaxial anisotropy• large intra-chain magnetic interaction• as small as possible inter-chain interactions

There are a few SCM examples in the literature since 2001

Transition metals organized by ligands:• 3d: Mn(III), Fe(III), Ni(II), Co(II), V(II)• Lanthanides: Tb(III), Dy(III), Ho(III)• Mixed metals 3d/3d or 4f/4f or 3d/4f• Mixed spins: 3d/radical and 4f/radical

Polynuclear complexes organized by linkers:• SMMs• anisotropic complexes

Synthesis methods:• serendipitous!• by design

Single-Chain Magnets recipe


Angew. Chem. Int. Ed. 2001, 40, 1760

The first chain exhibiting slow relaxation:CoII(hfac)2(NITPhOMe)

Δeff/kB = 153 K

hfac: hexafluoroacetylacetonate NITPhOMe: 4’-methoxy-phenyl-4,4,5,5-tetramethyl imidazoline-1-oxyl-3-oxide

O

CoII

O

O O

O NN O

MeO

F3C CF3

F3C CF3



The first Single-Chain Magnet:[Mn2(saltmen)2Ni(pao)2(py)2](ClO4)2 saltmen2-: N,N’–(1,1,2,2-tetramethylethylene) bis(salicylideneiminate)pao-: pyridine-2-aldoximate; py: pyridine


Mn(III)S = 2

Ni(II)S = 1

« ST = 3 »

S = 3D/kB = -2.5 KΔA/kB = 22 K

J. Am. Chem. Soc. 2002, 124, 43, 12837


The Single-Chain Magnet:[Mn2(saltmen)2Ni(pao)2(py)2](ClO4)2


Δ2/kB = 53 K

Δ1/kB = 74 K

ΔA/kB = 22 KΔξ/kB = 28 K

Δ1,theo/kB = 78 KΔ2,theo/kB = 50 K


The ingredients in order to obtain a SCM:• chain architecture• high-spin chain units with uniaxial anisotropy• large intra-chain magnetic interaction• as small as possible inter-chain interactions

There are a few SCM examples in the literature since 2001

Transition metals organized by ligands:• 3d: Mn(III), Fe(III), Ni(II), Co(II), V(II)• Lanthanides: Tb(III), Dy(III), Ho(III)• Mixed metals 3d/3d or 4f/4f or 3d/4f• Mixed spins: 3d/radical and 4f/radical

Polynuclear complexes organized by linkers:• SMMs• anisotropic complexes

Synthesis methods:• serendipitous• by design

Single-Chain Magnets recipe


Phys. Rev. Lett. 2009 102, 167204

The synthesis: [Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2

saltmen2-: N,N’–(1,1,2,2-tetramethylethylene) bis(salicylideneiminate)

pao-: pyridine-2-aldoximate



Phys. Rev. Lett. 2009 102, 167204


[Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2


J. Am. Chem. Soc. 2002, 124, 43, 12837; Inorg. Chem. 2003, 42, 8203

[Mn2(saltmen)2Ni(pao)2(L)2](ClO4)2

1 mm



Marked changes in the chain packing induced by the 5-MeO groups…

i h

Phys. Rev. Lett. 2009 102, 167204




JAF /kB = -21.9(1) K

J’/kB = +0.46(5) K

g = 1.95(2)

21

An Heisenberg trimer model with inter-trimer J’ interactions

treated in a mean field approximation

with H = −2JAF SNiSMn1 + SNiSMn2( )


JAF JAF

JAF JAF

JAF JAF

JAF JAF JAF JAF

J’ J’ J’

5

5.5

6

6.5

7

7.5

8

8.5

9

0 50 100 150 200 250 300

T /

cm3

K m

ol-1

T /K



JAF JAF

JAF JAF

JAF JAF JAF JAF

J’ J’ J’

JJAFJJAFJ

J’ J

S = 2S = 1,S = 2,

because |JAF | >> J’ and for |JAF | >> kBT

J’ > 0

JAF /kB = -21.9(1) K and J’/kB = +0.46(5) K

Chain of ferromagnetically coupled S = 3 spins

A physicist view:[Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2

« ST = 3 »



0

1

2

3

4

5

6

0 20 40 60 80 100 120

M /

μB

H / Oe

1.8 K

D/kB = -2.2 K

Single Crystal Measurements:H applied in the hard magnetic plane

1.5 K

9.7 T

H = −2 ′ J

S T ,i

S T ,i+1

−∞

+∞

∑ + D

S T ,iz2

−∞

+∞

∑

Estimation of D

2DST2 ≈ gμBST Ha

Ising type anisotropy (easy axis and hard plane)




Magnet behavior, i.e. slow relaxation of the

magnetization compatible with SCM behavior

M vs H hysteresis loops

Phys. Rev. Lett. 2009 102, 167204

-1

-0.5

0

0.5

1

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

1.5 K

1.6 K

1.7 K

1.8 K

1.9 K

2 K

2.2 K

2.4 K

2.9 K

M/M

s

μ0H (T)

Single Crystal Measurements:H applied along the easy magnetic axis




0

0.5

1

1.5

2

2.5

3

2 3 4 5 6 7

1 Hz3 Hz5 Hz10 Hz30 Hz50 Hz100 Hz200 Hz400 Hz600 Hz1000 Hz1200 Hz

" / c

m3

mol

-1

T / K

0

2

4

6

8

10

2 3 4 5 6 7

' / c

m3

mol

-1

T / K

0

0.5

1

1.5

2

2.5

1 10 100 1000

2.3 K2.5 K2.8 K3.0 K3.2 K3.5 K3.7 K4.0 K4.5 K

" / c

m3

mol

-1

/ Hz

0

2

4

6

8

1 10 100 1000

' / c

m3

mol

-1

/ Hz

Relaxation time measurements (ac susceptibility):

A single relaxation mode compatible with SCM behavior but…




10-4

10-3

10-2

10-1

100

101

0.2 0.25 0.3 0.35 0.4 0.45

/ s

T-1 / K-1

τ T( ) =τ0expΔ eff

kBT

⎛

⎝ ⎜

⎞

⎠ ⎟

Δ1/kB ≈ 52 K

A dynamics of the magnetization compatible with a SCM…

Arrhenius behavior

Δ1/kB = (8J’+ |D|)ST2/kB

= 52.9 K

with ST = 3J’/kB ≈ +0.46 KD/kB = -2.2 K


kBT

⎛

⎝ ⎜

⎞

⎠ ⎟

with

2Δξ + ΔA = 8 ′ J ST2 + D ST

2


Relaxation time (ac susceptibility):[Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2


0

0.5

1

1.5

2

2.5

3

2 3 4 5 6 7

1 Hz3 Hz5 Hz10 Hz30 Hz50 Hz100 Hz200 Hz400 Hz600 Hz1000 Hz1200 Hz

" / c

m3

mol

-1

T / K

0

2

4

6

8

10

2 3 4 5 6 7

' / c

m3

mol

-1

T / K

Relaxation time measurements (ac susceptibility):

[Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2 [Mn2(saltmen)2Ni(pao)2(py)2](ClO4)2

0

5

10

15

20

2 3 4 5 6 7 8

1 Hz10 Hz50 Hz100 Hz200 Hz400 Hz600 Hz1000 Hz1500 Hz

" / c

m3

mol

-1

T / K

0

10

20

30

40

50

2 3 4 5 6 7 8

' / c

m3

mol

-1

T / K

J. Am. Chem. Soc. 2002, 124, 12837; Inorg. Chem. 2003, 42, 8203



Two selected examples of “SCM” systems:

{[Fe(bpy)(CN)4]2Co(4,4′-bipyridine)}•4H2O

T. Liu et al. J. Am. Chem. Soc. 2010, 132, 8250

[Mn6O2(4-MeOsalox)6(N3)2(MeOH)4]

C.-I. Yang et al. Chem. Commun. 2010, 46, 5716

Photo-induced « SCM »



4

6

810

30

50

0 0.05 0.1 0.15 0.2 0.25 0.3

T (

cm3 .

K.m

ol-1

)

T-1 (K-1)

0 Oe

500 Oe

1000 Oe


10

100

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35T

(cm

3 .K

.mol

-1)

T-1 (K-1)

0 Oe

1000 Oe

[Mn2(saltmen)2Ni(pao)2(py)2](ClO4)2

H = −2J'ST

2 σ i σ i+1

−∞

+∞

∑Ising Chain Model

One-dimensional correlation length:

χ =Ceff

Texp

Δξ

kBT

⎛⎝⎜

⎞⎠⎟

with Δξ = 4 ′J ST2

Infinite chain regime ξξ < L

Δξ/kB = 28 KJ’/kB = +0.77 K

Δξ/kB = 18 KJ’/kB = +0.5 K

One dimensional properties: Single-Chain Magnet, but…



0

100

200

300

400

500

2 2.5 3 3.5 4 4.5 5 5.5

H (

Oe)

T (K)

0

100

200

300

400

500

2 2.5 3 3.5 4 4.5 5 5.5

Single crystal

Powder data

T (K)

H (

Oe)

0

20

40

60

80

0 0.5 1 1.5 2 2.5 3

2.0 K2.5 K3.0 K3.5 K4.0 K4.5 K5.0 K

dM/d

H /

cm3

K m

ol-1

H / kOe

A Single-Chain Magnet behavior or not?

Field dependence of the magnetization:[Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2

(T, H ) Phase diagram

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3

2.0 K2.5 K3.0 K3.5 K4.0 K4.5 K5.0 K

M / μ

B

H / kOe

Single crystal(easy axis)

Phys. Rev. Lett. 2009 102, 167204


0

100

200

300

400

500

2 2.5 3 3.5 4 4.5 5 5.5

Single crystal (M vs H)Powder data ( vs T)Powder data (M vs H)

T (K)

H (

Oe)

0

100

200

300

400

500

2 2.5 3 3.5 4 4.5 5 5.5

Single crystal

Powder data

T (K)

H (

Oe)

Temperature dependence of the susceptibility:[Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2

(H, T) Phase diagram

Powder measurements

0

4

8

12

16

2 4 6 8 10 12 14

5 Oe10 Oe50 Oe100 Oe300 Oe500 Oe600 Oe700 Oe

/ cm

3 m

ol-1

T / K

Phys. Rev. Lett. 2009 102, 167204



Metamagnetic behavior:[Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2

0

100

200

300

400

500

2 2.5 3 3.5 4 4.5 5 5.5

T (K)

H (

Oe)

AFPhase

ParamagneticPhase

(H, T) Phase diagram

An antiferromagnetic phase… BUT also a MAGNET !!!

-1

-0.5

0

0.5

1

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

1.5 K

1.6 K

1.7 K

1.8 K

1.9 K

2 K

2.2 K

2.4 K

2.9 K

M/M

s

μ0H (T)TN = 4.95 K



A possible magnetic structure:

Two-sublattices model in the Ising limit treating the interchain interactions in the mean field approximation:

Phys. Rev. Lett. 2009 102, 167204

J⊥ =J⊥1 + J⊥2( )

2

′J⊥ =′J⊥1 + ′J⊥2( )

2with ′J⊥ i < J⊥ i



Phys. Rev. Lett. 2009 102, 167204

Two-sublattices model in the Ising limit treating the interchain interactions in the mean field approximation:

b = −μBH

2zJ⊥ST

-1

-0.5

0

0.5

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4

mi

b

m1

m2

binv

bC

T

H = −2J / /ST2 σ n+1, pσ n, p

n, p∑ − 2J⊥ST

2 σ n, pσ n, ′pn, p, ′p∑

J kB = ′J kB = +0.5 K

r = ′z ′J⊥

zJ⊥

= 0.3



0

100

200

300

400

500

2 2.5 3 3.5 4 4.5 5 5.5

T (K)

H (

Oe)

AFPhase

ParamagneticPhase

0

100

200

300

400

500

2 2.5 3 3.5 4 4.5 5 5.5

T (K)

H (

Oe)

AFPhase

ParamagneticPhase

Two-sublattices model in the Ising limit treating the interchain magnetic interactions in the mean field approximation:

Phys. Rev. Lett. 2009 102, 167204

J kB = ′J kB = +0.5 K

r = ′z ′J⊥

zJ⊥

= 0.3

J⊥ kB ≈ −0.005 K

′J⊥ kB ≈ −0.0015 K

An antiferromagnetic phase of Chains



0

0.2

0.4

0.6

0.8

1

0.001 0.01 0.1 1 10 100

448 Oe546 Oe

M/M

0

Time (s)

0

0.2

0.4

0.6

0.8

1

0.001 0.01 0.1 1 10 100

378 Oe238 Oe168 Oe

M/M

0

Time (s)

Dynamics of the magnetization under applied dc field:

Phys. Rev. Lett. 2009 102, 167204

T = 2.9 K



0

1

2

3

4

5

6

7

8

0 100 200 300 400 500 600

H / Oe

T = 3.3 K

/H

= 0

0

1

2

3

4

5

6

7

8

0 100 200 300 400 500 600

T = 2.9 K

H / Oe

/H

= 0


Phys. Rev. Lett. 2009 102, 167204

A maximum of the relaxation time is found at the critical field… maybe a second extremum…



Linear response with the inter-chain interactions treated in the mean field approximation:


Phys. Rev. Lett. 2009 102, 167204

1

τ=

1

2

1− ′A1

τ1

+1− ′A2

τ 2

⎛⎝⎜

⎞⎠⎟−

1

2

1− ′A1

τ1

−1− ′A2

τ 2

⎛⎝⎜

⎞⎠⎟

2

+ 4A1A2

τ1τ 2

Ai = −(1− mi2 )3/2 4z J⊥ ST

2

kBT exp(−4J / /ST2 / kBT )

′Ai = −(1− mi2 )3/2 4 ′z ′J⊥ ST

2

kBT exp(−4J / /ST2 / kBT )

τi are the relaxation times of the isolated chain in their effective magnetic field



0

1

2

3

4

5

6

7

8

0 100 200 300 400 500 600

T = 2.9 K

H / Oe

/H

= 0

0

1

2

3

4

5

6

7

8

0 100 200 300 400 500 600

H / Oe

T = 3.3 K

/H

= 0

0

1

2

3

4

5

6

7

8

0 100 200 300 400 500 600

H / Oe

T = 3.3 K

/H

= 0

0

1

2

3

4

5

6

7

8

0 100 200 300 400 500 600

T = 2.9 K

H / Oe

/H

= 0

Linear response with the inter-chain interactions treated in the mean field approximation:


Phys. Rev. Lett. 2009 102, 167204

1

τ=

1

2

1− ′A1

τ1

+1− ′A2

τ 2

⎛⎝⎜

⎞⎠⎟−

1

2

1− ′A1

τ1

−1− ′A2

τ 2

⎛⎝⎜

⎞⎠⎟

2

+ 4A1A2

τ1τ 2

TN = 5 K r = ′z ′J⊥

zJ⊥

= 0.3 J kB = +0.5 K



0

100

200

300

400

500

2 2.5 3 3.5 4 4.5 5 5.5

T (K)

H (

Oe)

AFPhase

ParamagneticPhase

0

100

200

300

400

500

2 2.5 3 3.5 4 4.5 5 5.5

T (K)

H (

Oe)

AFPhase

ParamagneticPhase

Two-sublattices model in the Ising limit treating the interchain magnetic interactions in the mean field approximation:

Phys. Rev. Lett. 2009 102, 167204

An antiferromagnetic ordered phase of Single-Chain Magnets

A perfect agreement between static and dynamic properties



Completely described (static and dynamics properties) by a simple two-sublattices Ising model with the interchain

magnetic interactions treated in the mean field approximation

Phys. Rev. Lett. 2009 102, 167204; Chem. Eur. J. 2010 16, 3656

Strictly speaking: NO

An 3D antiferromagnetic ordered phase of Single-Chain Magnets…

• Slowing down of the relaxation is even observed close to the AF-Paramagnetic transition line.

• The existence of an AF order does not prevent slow dynamics of the magnetization induced by the presence of Single-Chain Magnet

• Introduction of large intrachain interactions between anisotropic spins could promote high-blocking SCM-based materials independently of the presence of an ordered AF phase.



Postdocs: Dr. Céline Pichon, Dr. Dalice Pinero

Ph-D Students: • 3rd year: Ie-Rang Jeon

Indrani Bhowmick • 2nd year:

Dmitri Mitcov • 1st year:

Vivien Pianet, Mihail Secu, Kasper Steen Pedersen

Acknowledgements:

DD

MMMPP dd

1 t

III

VVK

aiill SSeeecccuuun

uuu,

The « Molecular Magnetic Material » team: C. Coulon (Prof.) P. Dechambenoit (A. Prof.) E. Hillard (CNRS Res.) M. Rouzières (A. Eng.)


• Kanazawa University, Japan Prof. Hitoshi Miyasaka and his group

• Institut Néel, Grenoble, France

Dr. Wolfgang Wernsdorfer

Acknowledgements:


•

• University of Bordeaux

• MAGNETCAT and AC-MAGnets

• Conseil régional d’Aquitaine (Magnetometer, EPR, X-ray Diffractometer, PPMS) • The organizing committee

Acknowledgements:


Thank you for Your attention!

The end…


Documents

Introduction to SCMs Dr. Rodolphe Cléracschnack/molmag/... · 2020. 7. 27. · Introduction to SCMs… by R. Clérac Florida, 2012 - 1 - Dr. Rodolphe Clérac CNRS - Researcher Centre