Introduction to SCMs Dr. Rodolphe Cléracschnack/molmag/... · 2020. 7. 27. · Introduction to...
Transcript of Introduction to SCMs Dr. Rodolphe Cléracschnack/molmag/... · 2020. 7. 27. · Introduction to...
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
Introduction to SCMs
Introduction to SCMs… by R. Clérac Florida, 2012 - 2 -
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
Introduction to SCMs… by R. Clérac Florida, 2012 - 3 -
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
Introduction to SCMs… by R. Clérac Florida, 2012 - 4 -
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
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 5 -
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)
Single-Chain Magnets
JF /kB = +6.5(1) K
J’/kB = +0.08(1) K
JMn-Mn/kB = +0.40(6) K
Introduction to SCMs… by R. Clérac Florida, 2012 - 6 -
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-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 7 -
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-Chain Magnets
Single crystal measurements: H(NEt4)2[Mn(5-MeOsalen)]2[Fe(CN
Mag
magw
Introduction to SCMs… by R. Clérac Florida, 2012 - 8 -
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
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 9 -
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
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 10 -
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
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 11 -
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
Introduction to SCMs… by R. Clérac Florida, 2012 - 12 -
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
Introduction to SCMs… by R. Clérac Florida, 2012 - 13 -
• • • • • •
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
Introduction to SCMs… by R. Clérac Florida, 2012 - 14 -
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
Single-Chain Magnets
with ST = 9/2J’/kB ≈ 0.08 KD/kB = -0.94 K(|D /J’ | >> 4/3)
Introduction to SCMs… by R. Clérac Florida, 2012 - 15 -
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
τ T( ) =τ0exp2Δξ + ΔA
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
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 16 -
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
Single-Chain Magnets
with ST = 9/2J’/kB ≈ 0.08 KD/kB = -0.94 K(|D /J’ | >> 4/3)
Introduction to SCMs… by R. Clérac Florida, 2012 - 17 -
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
Introduction to SCMs… by R. Clérac Florida, 2012 - 18 -
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
τ T( ) =τ0exp2Δξ + ΔA
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
Introduction to SCMs… by R. Clérac Florida, 2012 - 19 -
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
Introduction to SCMs… by R. Clérac Florida, 2012 - 20 -
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
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 21 -
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
Single-Chain Magnets
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
Introduction to SCMs… by R. Clérac Florida, 2012 - 22 -
The Single-Chain Magnet:[Mn2(saltmen)2Ni(pao)2(py)2](ClO4)2
Single-Chain Magnets
Δ2/kB = 53 K
Δ1/kB = 74 K
ΔA/kB = 22 KΔξ/kB = 28 K
Δ1,theo/kB = 78 KΔ2,theo/kB = 50 K
Introduction to SCMs… by R. Clérac Florida, 2012 - 23 -
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
Introduction to SCMs… by R. Clérac Florida, 2012 - 24 -
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
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 25 -
Phys. Rev. Lett. 2009 102, 167204
Single-Chain Magnets
[Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2
Introduction to SCMs… by R. Clérac Florida, 2012 - 26 -
J. Am. Chem. Soc. 2002, 124, 43, 12837; Inorg. Chem. 2003, 42, 8203
[Mn2(saltmen)2Ni(pao)2(L)2](ClO4)2
1 mm
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 27 -
Marked changes in the chain packing induced by the 5-MeO groups…
i h
Phys. Rev. Lett. 2009 102, 167204
[Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 28 -
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( )
[Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2
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
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 29 -
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 »
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 30 -
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)
[Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 31 -
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
[Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 32 -
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…
[Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 33 -
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
τ T( ) =τ0exp2Δξ + ΔA
kBT
⎛
⎝ ⎜
⎞
⎠ ⎟
with
2Δξ + ΔA = 8 ′ J ST2 + D ST
2
Single-Chain Magnets
Relaxation time (ac susceptibility):[Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2
Introduction to SCMs… by R. Clérac Florida, 2012 - 34 -
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
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 35 -
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 »
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 36 -
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
[Mn2(5-MeOsaltmen)2Ni(pao)2(phen)2](ClO4)2
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…
Single-Chain Magnets
Introduction to SCMs… by R. Clérac Florida, 2012 - 37 -
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
Introduction to SCMs… by R. Clérac Florida, 2012 - 38 -
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
A Single-Chain Magnet behavior or not?
Introduction to SCMs… by R. Clérac Florida, 2012 - 39 -
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 Single-Chain Magnet behavior or not?
Introduction to SCMs… by R. Clérac Florida, 2012 - 40 -
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
A Single-Chain Magnet behavior or not?
Introduction to SCMs… by R. Clérac Florida, 2012 - 41 -
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
A Single-Chain Magnet behavior or not?
Introduction to SCMs… by R. Clérac Florida, 2012 - 42 -
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
A Single-Chain Magnet behavior or not?
Introduction to SCMs… by R. Clérac Florida, 2012 - 43 -
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
A Single-Chain Magnet behavior or not?
Introduction to SCMs… by R. Clérac Florida, 2012 - 44 -
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
Dynamics of the magnetization under applied dc field:
Phys. Rev. Lett. 2009 102, 167204
A maximum of the relaxation time is found at the critical field… maybe a second extremum…
A Single-Chain Magnet behavior or not?
Introduction to SCMs… by R. Clérac Florida, 2012 - 45 -
Linear response with the inter-chain interactions treated in the mean field approximation:
Dynamics of the magnetization under applied dc field:
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
A Single-Chain Magnet behavior or not?
Introduction to SCMs… by R. Clérac Florida, 2012 - 46 -
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:
Dynamics of the magnetization under applied dc field:
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
A Single-Chain Magnet behavior or not?
Introduction to SCMs… by R. Clérac Florida, 2012 - 47 -
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
A Single-Chain Magnet behavior or not?
Introduction to SCMs… by R. Clérac Florida, 2012 - 48 -
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.
A Single-Chain Magnet behavior or not?
Introduction to SCMs… by R. Clérac Florida, 2012 - 49 -
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.)
Introduction to SCMs… by R. Clérac Florida, 2012 - 50 -
• Kanazawa University, Japan Prof. Hitoshi Miyasaka and his group
• Institut Néel, Grenoble, France
Dr. Wolfgang Wernsdorfer
Acknowledgements:
Introduction to SCMs… by R. Clérac Florida, 2012 - 51 -
•
• University of Bordeaux
• MAGNETCAT and AC-MAGnets
• Conseil régional d’Aquitaine (Magnetometer, EPR, X-ray Diffractometer, PPMS) • The organizing committee
Acknowledgements:
Introduction to SCMs… by R. Clérac Florida, 2012 - 52 -
Thank you for Your attention!
The end…
Introduction to SCMs… by R. Clérac Florida, 2012 - 53 -