Introduction to SCMs Dr. Rodolphe Clérac CNRS - Researcher Centre de Recherche Paul Pascal, CNRS - UPR 8641 115, Avenue du Dr. A. Schweitzer 336 Pessac France clerac@crpp-bordeaux.cnrs.fr Introduction to SCMs by R. Clérac Florida, 1-1 -
An example of Single-Chain Magnets A real system made by design: a SMM building-block [Mn III (salen)-fe III (CN) 6 -Mn III (salen)] trinuclear complexes: K[Mn (5-Brsalen) (H O) Fe(CN) 6 ] H O [1,4] K[Mn (5-Clsalen) (H O) Fe(CN) 6 ] H O [1] (NEt 4 )[Mn (5-Clsalen) (H O) Fe(CN) 6 ] H O [] (NEt 4 )[Mn (salmen) (MeOH) Fe(CN) 6 ] [3,5] N N N N X O O X O O X = H: salen X = Br: 5-Brsalen X = Cl: 5-Clsalen salmen S = 9/ D/k B = -1.5 K [1] H. Miyasaka, N. Matsumoto, H. Okawa, N. Re, E. Gallo, C. Floriani J. Am. Chem. Soc. 1996, 118, 981 [] H. Miyasaka, N. Matsumoto, N. Re, E. Gallo, C. Floriani Inorg. Chem. 1997, 36, 67 [3] H. Miyasaka, H. Ieda, N. Matsumoto, N. Re, E. Crescenzi, C. Floriani Inorg. Chem. 1998, 37, 55 [4] H. J. Choi, J. J. Sokol, J. R. Long Inorg. Chem. 4, 43, 166 [5] M. Ferbinteanu, H. Miyasaka, W. Wernsdorfer, K. Nakata, K. Sugiura, M. Yamashita, C. Coulon, R. Clérac, J. Am. Chem. Soc. 5, 17, 39 Introduction to SCMs by R. Clérac Florida, 1 - -
Single-Chain Magnets The structural arrangement: (NEt 4 ) [Mn(5-MeOsalen)] [Fe(CN) 6 ] M. Ferbinteanu, H. Miyasaka, W. Wernsdorfer, K. Nakata, K. Sugiura, M. Yamashita, C. Coulon, R. Clérac, J. Am. Chem. Soc. 5, 17, 39 Isolated chains from a magnetic point of view Introduction to SCMs by R. Clérac Florida, 1-3 -
Single-Chain Magnets The high temperature magnetic susceptibility: (NEt 4 ) [Mn(5-MeOsalen)] [Fe(CN) 6 ] J J J J F J F J F J F J F J F J F J F J F J F J F J F with H = J F S Fe1 S Mn + ( S Fe S Mn ) An Heisenberg trimer model with inter-trimer J interactions treated in a mean field approximation J F /k B = +6.5(1) K J /k B = +.8(1) K g =.3() Introduction to SCMs by R. Clérac Florida, 1-4 -
Single-Chain Magnets A physicist view: (NEt 4 ) [Mn(5-MeOsalen)] [Fe(CN) 6 ] J F /k B = +6.5(1) K J /k B = +.8(1) K J Mn-Mn /k B = +.4(6) K «S T = 9/» S =, S = ½, S = because J F >> J Mn-Mn and for J F >> k B T J J> J J J J F J F J F J F J F J F J F J F Chain of ferromagnetically coupled anisotropic S = 9/ spins (it is fundamental to prove that the system is 1-D) Introduction to SCMs by R. Clérac Florida, 1-5 -
M/M s 1.8.6.4. Single-Chain Magnets Single crystal measurements: H in the hard plane (NEt 4 ) [Mn(5-MeOsalen)] [Fe(CN) 6 ] 1.5 K 6.3 T + + H = J S T,i S T,i +1 + D Estimation of D DS T gμ B S T H a S T,iz 4 6 8 1 H / T D/k B = -.94 K D/k B -1.5 K Introduction to SCMs by R. Clérac Florida, 1-6 -
Single-Chain Magnets Single crystal measurements: H along the easy axis (NEt 4 ) [Mn(5-MeOsalen)] [Fe(CN) 6 ] M vs H hysteresis loops Magnet behavior, i.e. slow relaxation of the magnetization compatible with SCM behavior Introduction to SCMs by R. Clérac Florida, 1-7 -
Single-Chain Magnets Relaxation time measurements (ac susceptibility): (NEt 4 ) [Mn(5-MeOsalen)] n)] [Fe(CN) 6 ] A single relaxation mode compatible with SCM behavior Introduction to SCMs by R. Clérac Florida, 1-8 -
Single-Chain Magnets Relaxation time measurements (M vs time): (NEt 4 ) [Mn(5-MeOsalen)] [Fe(CN) 6 ] 1.8.8 K.86 K M/M s.6.4 1.5 K 1.34 K 1.5 K.9 K.98 K 1.16 K 1.3 K 1.1 K e -1. 1.6 K 1.7 K 1.1-11 1-9 11-7 1-5 1 1-3 1-1 1 1 1 t t/ / s Determination of the relaxation time down to.8 K Introduction to SCMs by R. Clérac Florida, 1-9 -
Single-Chain Magnets Relaxation time: (NEt 4 ) [Mn(5-MeOsalen)] [Fe(CN) 6 ] τ T k B T ( ) =τ exp Δ eff Δ 1 /k B 31.1 K Δ /k B 5 K Crossover between two activated relaxation regimes Introduction to SCMs by R. Clérac Florida, 1-1 -
Single-Molecule vs. Single-Chain Magnets Relaxation time SMM vs SCM: (NEt 4 ) [Mn(5-MeOsalen)] [Fe(CN) 6 ] / s 1 6 1 4 1 1 1-1 -4.4.6.8 1 1. T -1 / K -1 SCM 1 4 (NEt 4 ) [Mn(salmen)(MeOH)] [Fe(CN) 6 ] SMM In a given temperature range the correlations enhance the relaxation time Introduction to SCMs by R. Clérac Florida, 1-11 -
Chain of Ising spins T (a) Glauber, R. J. J. Math. Phys. 1963, 4, 94; (b) Coulon, C.; Miyasaka, H.; Clérac, R. Struct. Bond. 6, 1, 163 M / M S = exp t τ H = + H = JS σ iσ i+1 τ T ( )=τ i T ( ) ξ a ξ =τ i T ( )exp Δ ξ k B T a with Δ ξ = 4 JS Introduction to SCMs by R. Clérac Florida, 1-1 -
Real Single-Chain Magnets The relaxation time of a Single-Chain Magnet: Chain of ferromagnetically coupled Ising spins (Glauber) τ T ( ) =τ i T ( )exp Δ ξ with Δ ξ = 4 J S k B T (a) Glauber, R. J. J. Math. Phys. 1963, 4, 94; (b) Coulon, C.; Miyasaka, H.; Clérac, R. Struct. Bond. 6, 1, 163 1) For a chain of anisotropic spins (D < and D/J > 4/3: Ising limit) : τ i T ( ) =τ exp Δ A + + H = J' S T,i S T,i +1 + D S T,iz with Δ A = D S T τ T k B T ( ) =τ exp Δ + Δ ξ A k B T ξ Coulon, C.; Clérac, R.; Lecren, L.; Wernsdorfer, W.; Miyasaka, H.Phys. Rev. B 4, 69, 1348 Introduction to SCMs by R. Clérac Florida, 1-13 -
Single-Chain Magnets Relaxation time: the Glauber s regime (NEt 4 ) [Mn(5-MeOsalen)] [Fe(CN) 6 ] Δ 1 /k B 31.1 K Δ /k B 5 K τ T with S T = 9/ J /k B.8 K D/k B = -.94 K ( D /J >> 4/3) ( ) =τ exp Δ ξ + Δ A with k B T Δ ξ + Δ A = 8 J S T + D S T Δ 1 /k B = (8J + D )S T /k B = 3 K Introduction to SCMs by R. Clérac Florida, 1-14 -
Single-Chain Magnets The relaxation time in a Single-Chain Magnet: ) For a chain of anisotropic spins with a length L (D < and D/J > 4/3 Ising limit): + + H = J' S T,i S T,i +1 + D for ξ < L for ξ > L Luscombe, J. H. et al., Phys. Rev. E 1996, 53, 585 Leal da Silva, J. K. et al., Phys. Rev. E 1995, 5, 457 τ T S T,iz ( ) =τ exp Δ + Δ ξ A τ T (a) Coulon, C. ; Miyasaka, H. ; Clérac, R. Struct. Bond. 6, 1, 163 (b) Coulon, C. ; Clérac, R.; Lecren, L.; Wernsdorfer, W.; Miyasaka, H. Phys. Rev. B 4, 69, 1348 k B T ( ) =τ exp Δ ξ + Δ A k B T ξ Introduction to SCMs by R. Clérac Florida, 1-15 -
Single-Chain Magnets Relaxation time: the finite-size chain regime (NEt 4 ) [Mn(5-MeOsalen)] [Fe(CN) 6 ] with S T = 9/ J /k B.8 K D/k B = -.94 K ( D /J >> 4/3) Δ 1 /k B 31.1 K Δ /k B 5 K τ T with ( )=τ exp Δ ξ + Δ A k B T Δ ξ + Δ A = 4 JS T + D S T Δ /k B = (4J + D )S T /k B = 5.5 K Introduction to SCMs by R. Clérac Florida, 1-16 -
Final proof of a Single-Chain Magnets Another evidence of the finite-size chain regime: (NEt 4 ) [Mn(5-MeOsalen)] [Fe(CN) 6 ] Ising Chain Model χ = C eff T exp Δ ξ k B T with Δ ξ = 4 J S T H = J'S T + σ i σ i +1 Finite chain regime χ = n C eff ξ > L T n 44 L 6 nm Infinite chain regime ξ < L S T = 9/ J /k B = +.8(1) K Introduction to SCMs by R. Clérac Florida, 1-17 -
Single-Chain Magnets (Take home message) + + H = J' S T,i S T,i +1 + D S T,iz Always correct: χ = C eff T exp Static properties Dynamic properties for ξ < L for ξ > L (a) Coulon, C.; Miyasaka, H. ; Clérac, R. Struct. Bond. 6, 1, 163 (b) Coulon, C.; Clérac, R.; Lecren, L.; Wernsdorfer, W.; Miyasaka, H. Phys. Rev. B 4, 69, 1348 Introduction to SCMs by R. Clérac Florida, 1-18 - Δ ξ k B T τ T ( ) =τ exp Δ + Δ ξ A τ T k B T ( ) =τ exp Δ ξ + Δ A k B T In the Ising limit D < and D/J > 4/3: Δ ξ = 4 JS T and Δ A = D S T In the Heisenberg limit D <, and small and D/J << 4/3: Δ ξ = S T D J and Δ A =?? Between the Ising and the Heisenberg limits (D <, D/J < 4/3): Billoni, O. V.; Pianet, V.; Pescia, D.; Vindigni, A. Phys. Rev. B 11, 84, 64415 Δ ξ =?? and Δ A =??
Single-Chain Magnets recipe 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 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 There are a few SCM examples in the literature since 1 Introduction to SCMs by R. Clérac Florida, 1-19 -
Single-Chain Magnets The first chain exhibiting slow relaxation: Co II (hfac) (NITPhOMe) hfac: hexafluoroacetylacetonate NITPhOMe: 4 -methoxy-phenyl-4,4,5,5-tetramethyl MeO imidazoline-1-oxyl-3-oxide F 3C CF 3 O Co II O O N N O O O F 3C CF 3 Angew. Chem. Int. Ed. 1, 4, 176 Δ eff /k B = 153 K Introduction to SCMs by R. Clérac Florida, 1 - -
Single-Chain Magnets The first Single-Chain Magnet: [Mn (saltmen) Ni(pao) (py) ](ClO 4 ) saltmen - : N,N (1,1,,-tetramethylethylene) bis(salicylideneiminate) pao - : pyridine--aldoximate; py: pyridine Mn(III) S = Ni(II) S = 1 J. Am. Chem. Soc., 14, 43, 1837 «S T = 3» S = 3 D/k B = -.5 K Δ A /k B = K Introduction to SCMs by R. Clérac Florida, 1-1 -
Single-Chain Magnets The Single-Chain Magnet: [Mn (saltmen) Ni(pao) (py) ](ClO 4 ) Δ A /k B = K Δ ξ /k B = 8 K Δ 1 /k B = 74 K Δ 1,theo /k B = 78 K Δ,theo /k B = 5 K Δ /k B = 53 K Introduction to SCMs by R. Clérac Florida, 1 - -
Single-Chain Magnets recipe 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 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 There are a few SCM examples in the literature since 1 Introduction to SCMs by R. Clérac Florida, 1-3 -
Single-Chain Magnets The synthesis: [Mn (5-MeOsaltmen) Ni(pao) (phen) ](ClO 4 ) saltmen - : N,N (1,1,,- tetramethylethylene) bis(salicylideneiminate) pao - : pyridine--aldoximate Phys. Rev. Lett. 9 1, 1674 Introduction to SCMs by R. Clérac Florida, 1-4 -
Single-Chain Magnets [Mn (5-MeOsaltmen) Ni(pao) (phen) ](ClO 4 ) Phys. Rev. Lett. 9 1, 1674 Introduction to SCMs by R. Clérac Florida, 1-5 -
Single-Chain Magnets [Mn (saltmen) Ni(pao) (L) ](ClO 4 ) 1 mm J. Am. Chem. Soc., 14, 43, 1837; Inorg. Chem. 3, 4, 83 Introduction to SCMs by R. Clérac Florida, 1-6 -
Single-Chain Magnets Phys. Rev. Lett. 9 1, 1674 [Mn (5-MeOsaltmen) Ni(pao) (phen) ](ClO 4 ) Marked changes in the chain packing induced by the 5-MeO groups Introduction to SCMs by R. Clérac Florida, 1-7 -
Single-Chain Magnets [Mn (5-MeOsaltmen) Ni(pao) (phen) ](ClO 4 ) J J J J AF J AF J AF J AF J AF J AF J AF J AF T / cm 3 K mol -1 9 8.5 8 7.5 7 J AF J AF 6.5 6 5.5 5 5 1 15 5 3 T /K with H = J AF SNiSMn1 + ( S NiSMn ) An Heisenberg trimer model with inter-trimer J interactions treated in a mean field approximation J AF /k B = -1.9(1) K J /k B = +.46(5) K g = 1.95() Introduction to SCMs by R. Clérac Florida, 1-8 -
Single-Chain Magnets A physicist view: [Mn (5-MeOsaltmen) Ni(pao) (phen) ](ClO 4 ) J AF /k B = -1.9(1) K and J /k B = +.46(5) K «S T = 3» S =, S = 1, S = because J AF >> J and for J AF >> k B T J J > J J J AF J AF J AF J AF J AF J AF J AF J AF Chain of ferromagnetically coupled S = 3 spins Introduction to SCMs by R. Clérac Florida, 1-9 -
Single-Chain Magnets Single Crystal Measurements: H applied in the hard magnetic plane [Mn (5-MeOsaltmen) Ni(pao) (phen) ](ClO 4 ) 6 5 1.5 K + + H = J S T,i S T,i +1 + D S T,iz M / μ B 4 3 9.7 T 1 1.8 K 4 6 8 1 1 H / Oe Estimation of D DS T gμ B S T H a D/k B = -. K Ising type anisotropy (easy axis and hard plane) Introduction to SCMs by R. Clérac Florida, 1-3 -
Single-Chain Magnets Single Crystal Measurements: H applied along the easy magnetic axis [Mn (5-MeOsaltmen) Ni(pao) (phen) ](ClO 4 ) 1 1.5 K 1.6 K 1.7 K 1.8 K 1.9 K K. K.4 K.9 K M vs H hysteresis loops.5 M/M s -.5-1 -1. -.8 -.4.4.8 1. μ H (T) Magnet behavior, i.e. slow relaxation of the magnetization compatible with SCM behavior Phys. Rev. Lett. 9 1, 1674 Introduction to SCMs by R. Clérac Florida, 1-31 -
Single-Chain Magnets ' / cm 3 mol -1 1 8 6 4 Relaxation time measurements (ac susceptibility): [Mn (5-MeOsaltmen) Ni(pao) (phen) ](ClO 4 ) ' / cm 3 mol -1 8 6 4 " / cm 3 mol -1 3 4 5 6 7 T / K 3 1 Hz.5 3 Hz 5 Hz 1 Hz 3 Hz 1.5 5 Hz 1 Hz Hz 1 4 Hz 6 Hz.5 1 Hz 1 Hz 3 4 5 6 7 T / K 1 1 1 1 / Hz Introduction to SCMs by R. Clérac Florida, 1-3 - " / cm 3 mol -1 1 1 1 1 / Hz.5 A single relaxation mode compatible with SCM behavior but 1.5 1.5.3 K.5 K.8 K 3. K 3. K 3.5 K 3.7 K 4. K 4.5 K
/ s 1 1 1 1-1 1-1 -3 Single-Chain Magnets Relaxation time (ac susceptibility): [Mn (5-MeOsaltmen) Ni(pao) (phen) ](ClO 4 ) Arrhenius behavior τ T k B T ( ) =τ exp Δ eff Δ 1 /k B 5 K τ T with S T = 3 J /k B +.46 K D/k B = -. K ( ) =τ exp Δ ξ + Δ A with k B T Δ ξ + Δ A = 8 J S T + D S T 1-4 Δ..5.3.35.4.45 1 /k B = (8J + D )S T /k B = 5.9 K T -1 / K -1 A dynamics of the magnetization compatible with a SCM Introduction to SCMs by R. Clérac Florida, 1-33 -
Single-Chain Magnets Relaxation time measurements (ac susceptibility): 1 5 J. Am. Chem. Soc., 14, 1837; Inorg. Chem. 3, 4, 83 8 4 ' / cm 3 mol -1 6 4 ' / cm 3 mol -1 3 1 " / cm 3 mol -1 3 4 5 6 7 T / K 3 1 Hz.5 3 Hz 5 Hz 1 Hz 3 Hz 1.5 5 Hz 1 Hz Hz 1 4 Hz 6 Hz.5 1 Hz 1 Hz 3 4 5 6 7 T / K " / cm 3 mol -1 3 4 5 T / K 6 7 8 15 1 5 3 4 5 6 7 8 T / K 1 Hz 1 Hz 5 Hz 1 Hz Hz 4 Hz 6 Hz 1 Hz 15 Hz [Mn (5-MeOsaltmen) Ni(pao) (phen) ](ClO 4 ) [Mn (saltmen) Ni(pao) (py) ](ClO 4 ) Introduction to SCMs by R. Clérac Florida, 1-34 -
Single-Chain Magnets Two selected examples of SCM systems: Photo-induced «SCM» [Mn 6 O (4-MeOsalox) 6 (N 3 ) (MeOH) 4 ] C.-I. Yang et al. Chem. Commun. 1, 46, 5716 {[Fe(bpy)(CN) 4 ] Co(4,4 -bipyridine)} 4H O T. Liu et al. J. Am. Chem. Soc. 1, 13, 85 Introduction to SCMs by R. Clérac Florida, 1-35 -
Single-Chain Magnets One-dimensional correlation length: Ising Chain Model χ = C eff T exp Δ ξ k B T H = J'S T JS T with Δ ξ = 4 + σ i σ i +1 Infinite chain regime ξ < L T (cm 3.K.mol -1 ) 5 3 1 8 6 4.5.1.15..5.3 T -1 (K -1 ) Oe Δ ξ /k B = 18 K J /k B = +.5 K 1 Oe 5 Oe T (cm 3.K.mol -1 ) 1 1 Δ ξ /k B = 8 K J /k B = +.77 K.5.1.15..5.3.35 T -1 (K -1 ) Oe 1 Oe [Mn (5-MeOsaltmen) Ni(pao) (phen) ](ClO 4 ) [Mn (saltmen) Ni(pao) (py) ](ClO 4 ) One dimensional properties: Single-Chain Magnet, but Introduction to SCMs by R. Clérac Florida, 1-36 -
A Single-Chain Magnet behavior or not? Field dependence of the magnetization: [Mn (5-MeOsaltmen) Ni(pao) (phen) ](ClO 4 ) 6 Phys. Rev. Lett. 9 1, 1674 (T, H ) Phase diagram dm/dh / cm 3 K mol -1 5 5 8. K. K 4.5 K.5 K 4 6 3. K 3. K 3 3.5 K 3 3.5 K 4. K 4 4. K 4.5 K 1 4.5 K 5. K 5. K 1.5 1 1.5.5 3 H / koe.5 1 1.5.5 3 M / μ B H / koe Single crystal (easy axis) H (Oe) Single crystal Powder data.5 3 3.5 4 4.5 5 5.5 T (K) Introduction to SCMs by R. Clérac Florida, 1-37 -
A Single-Chain Magnet behavior or not? Temperature dependence of the susceptibility: [Mn (5-MeOsaltmen) Ni(pao) (phen) ](ClO 4 ) Phys. Rev. Lett. 9 1, 1674 (H, T) Phase diagram / cm 3 mol -1 16 1 8 4 4 6 8 1 1 14 T / K 5 Oe 1 Oe 5 Oe 1 Oe 3 Oe 5 Oe 6 Oe 7 Oe Powder measurements H (Oe) 5 4 3 1 Single Single crystal crystal (M vs H) Powder data ( vs T) Powder data data(m vs H).5 3 3.5 4 4.5 5 5.5 T (K) Introduction to SCMs by R. Clérac Florida, 1-38 -
H (Oe) A Single-Chain Magnet behavior or not? Metamagnetic behavior: [Mn (5-MeOsaltmen) Ni(pao) (phen) ](ClO 4 ) 5 4 3 1 (H, T) Phase diagram AF Phase Paramagnetic Phase.5 3 3.5 4 4.5 5 5.5 T (K) T N = 4.95 K An antiferromagnetic phase BUT also a MAGNET!!! Introduction to SCMs by R. Clérac Florida, 1-39 - M/M s 1.5 -.5-1 1.5 K 1.6 K 1.7 K 1.8 K 1.9 K K. K.4 K.9 K -1. -.8 -.4.4.8 1. μ H (T)
A Single-Chain Magnet behavior or not? Two-sublattices model in the Ising limit treating the interchain interactions in the mean field approximation: A possible magnetic structure: ( J = J + J 1 ) J = with J i J 1 + ( ) J < J i Phys. Rev. Lett. 9 1, 1674 Introduction to SCMs by R. Clérac Florida, 1-4 -
m 1 A Single-Chain Magnet behavior or not? Two-sublattices model in the Ising limit treating the interchain interactions in the mean field approximation: H = J // S T σ n+1, p σ n, p J S T 1 n, p T n, p, p σ n, p σ n, p m i.5 -.5 m b C b inv -1..4.6.8 1 1. 1.4 b J k B = J k B =+.5 K r = z J =.3 zj b = μ BH zj S T Phys. Rev. Lett. 9 1, 1674 Introduction to SCMs by R. Clérac Florida, 1-41 -
A Single-Chain Magnet behavior or not? Two-sublattices model in the Ising limit treating the interchain magnetic interactions in the mean field approximation: 5 4 Paramagnetic Phase J k B = J k B =+.5 K H (Oe) 3 1 AF Phase r = z J =.3 zj J J k B.5 K k B.15 K.5 3 3.5 4 4.5 5 5.5 T (K) An antiferromagnetic phase of Chains Phys. Rev. Lett. 9 1, 1674 Introduction to SCMs by R. Clérac Florida, 1-4 -
A Single-Chain Magnet behavior or not? Dynamics of the magnetization under applied dc field: T =.9 K 1.8 M/M.6.4. 546 Oe 448 Oe 378 Oe 38 Oe 168 Oe.1.1.1 1 1 1 Time (s) Phys. Rev. Lett. 9 1, 1674 Introduction to SCMs by R. Clérac Florida, 1-43 -
A Single-Chain Magnet behavior or not? Dynamics of the magnetization under applied dc field: /H = 8 7 T =.9 K 6 5 4 3 1 1 3 4 5 6 H / Oe / H = 8 7 6 5 4 3 1 T = 3.3 K 1 3 4 5 6 H / Oe A maximum of the relaxation time is found at the critical field maybe a second extremum Phys. Rev. Lett. 9 1, 1674 Introduction to SCMs by R. Clérac Florida, 1-44 -
A Single-Chain Magnet behavior or not? Dynamics of the magnetization under applied dc field: Linear response with the inter-chain interactions treated in the mean field approximation: 1 τ = 1 + 1 A τ 1 1 1 A 1 τ A 1 A 1 1 τ 1 τ + 4 A 1A τ 1 τ τ i are the relaxation times of the isolated chain in their effective magnetic field A i = (1 m i ) 3/ 4zJ S T k B T exp( 4J // S T / k B T ) Phys. Rev. Lett. 9 1, 1674 4 z J A i = (1 m i ) 3/ S T k B T exp( 4J // S T / k B T ) Introduction to SCMs by R. Clérac Florida, 1-45 -
/H = 8 7 6 5 4 3 1 Dynamics of the magnetization under applied dc field: Linear response with the inter-chain interactions treated in the mean field approximation: 1 τ = 1 T =.9 K 1 3 4 5 6 T N = 5 K r = z J A Single-Chain Magnet behavior or not? H / Oe + 1 A τ 1 1 1 A 1 τ 1 3 4 5 6 Introduction to SCMs by R. Clérac Florida, 1-46 - /H = zj =.3 J k B =+.5 K 8 7 6 5 4 3 1 A 1 A 1 1 τ 1 τ H / Oe + 4 A 1 A τ 1 τ T = 3.3 K Phys. Rev. Lett. 9 1, 1674
A Single-Chain Magnet behavior or not? Two-sublattices model in the Ising limit treating the interchain magnetic interactions in the mean field approximation: A perfect agreement between static and dynamic properties 5 4 Paramagnetic Phase H (Oe) 3 1 AF Phase.5 3 3.5 4 4.5 5 5.5 T (K) Phys. Rev. Lett. 9 1, 1674 An antiferromagnetic ordered phase of Single-Chain Magnets Introduction to SCMs by R. Clérac Florida, 1-47 -
A Single-Chain Magnet behavior or not? Strictly speaking: NO Phys. Rev. Lett. 9 1, 1674; Chem. Eur. J. 1 16, 3656 An 3D antiferromagnetic ordered phase of Single-Chain Magnets Completely described (static and dynamics properties) by a simple two-sublattices Ising model with the interchain magnetic interactions treated in the mean field approximation The existence of an AF order does not prevent slow dynamics of the magnetization induced by the presence of Single-Chain Magnet Slowing down of the relaxation is even observed close to the AF- Paramagnetic transition line. Introduction of large intrachain interactions between anisotropic spins could promote high-blocking SCM-based materials independently of the presence of an ordered AF phase. Introduction to SCMs by R. Clérac Florida, 1-48 -
Acknowledgements: The «Molecular Magnetic Material» team: C. Coulon (Prof.) P. Dechambenoit (A. Prof.) E. Hillard (CNRS Res.) M. Rouzières (A. Eng.) Postdocs: Dr. Céline Pichon, Dr. Dalice Pinero Ph-D Students: 3rd year: Ie-Rang Jeon Indrani Bhowmick nd year: Dmitri Mitcov 1st year: Vivien Pianet, Mihail Secu, Kasper Steen Pedersen Introduction to SCMs by R. Clérac Florida, 1-49 -
Acknowledgements: Kanazawa University, Japan Prof. Hitoshi Miyasaka and his group Institut Néel, Grenoble, France Dr. Wolfgang Wernsdorfer Introduction to SCMs by R. Clérac Florida, 1-5 -
Acknowledgements: University of Bordeaux MAGNETCAT and AC-MAGnets Conseil régional d Aquitaine (Magnetometer, EPR, X-ray Diffractometer, PPMS) The organizing committee Introduction to SCMs by R. Clérac Florida, 1-51 -
The end Thank you for Your attention! Introduction to SCMs by R. Clérac Florida, 1-5 -
Introduction to SCMs by R. Clérac Florida, 1-53 -