Magnetic properties of a frustrated nickel cluster with a butterfly structure Introduction Crystal structure Magnetic susceptibility High field magnetization Evaluation of the exchange constants ESR Evaluation of the single ion anisotropy constants Temperature evolution of magnetization process in a pulsed field Summary RIKEN Masayuki HAGIWARA Outline

Molecular magnet Mn 12 O 12 (CH 3 COO) 16 (H 2 O) 4 Discrete double well structure Magnetization curves Mn 3+ (S=2) 8 ions Mn 4+ (S=3/2) 4 ions S=10 Quantum tunneling Mn12-Acetate

Frustration Geometrical frustration ？ Triangle lattice Tetrahedron Kagome lattice Railroad trestle Antiferromagnetic exchange interactions

Frustrated molecular magnet Molecular magnet Frustrated system Mn12, Fe8, V15 etc.Triangle lattice etc. Frustrated molecular magnet Butterfly structure (Diamond structure)

Sample preparation & Apparatus

Unit structure of Ni tetramer c-axis a-axis [1,1,0] a-axis Tetragonal A. Escuer et al., J. Chem. Soc., Dalton Trans., 1998, 3473.

Crystal structure (packing) a-axis c-axis

Magnetic susceptibility (H // c ） Similar results for H // a

High field magnetization H // c-axis ½ and ¾ magnetization plateaus are observed with large hysteresis. The transition field from the ½ plateau to the ¾ plateau for H // a is nearly identical to that for H // c. H // a-axis

Spin Hamiltonian Assumption because of the similarity of the magnetizations for H // a and H //c.

Evaluation of J 1 and J 2 The transition fields are independent of J 3. The exchange constants are evaluated from the analyses of magnetization curve. Evaluated values from susceptibility H 1 =40.7 T, H 2 =69 T g=2.2 J 1 /k B =41.9 K (29.1 cm -1 ), J 2 /k B =9.2 K (6.4 cm -1 ) A. Escuer et al., J. Chem. Soc., Dalton Trans., 1998, E ~J 1 -3J 2 14 K 0 J 3 2J 3 J 3 <0 J 3 >0 Energy diagram Expanded (Ferromagnetic) (Antiferromagnetic) J 3 plus or minus?

Determination of J 3 by fitting Magnetic susceptibilityMagnetization (static) J 3 /k B =-0.6 ∼ 0.7 K (Ferromagnetic) Magnetization is calculated from the lowest singlet, triplet and quintet states.

ESR spectra (H // c) Static field Pulsed field

Frequency-field diagram (H // c)

Determination of D value D/k B = -4.0K, -3.4K

Magnetic parameter values g=2.2±0.02 J 1 /k B =41.9±0.5 K J 2 /k B =9.2±0.3 K J 3 /k B =-0.65±0.05 K D= -4.0±0.1 K, -3.4±0.1 K High field magnetization ESR (static & pulse) Magnetization & susceptibility ESR (static & pulse) We can determine the magnetic parameter values by making a comparison between calculations and various kinds of experiments. A fine tuning of the parameters is needed.

ESR spectra (H // a) low frequency H // a T=1.6 K

Frequency-field diagram (H // a) H // a

Temperature dependence of the spectra H // c-axis H // a-axis

Origins of hysteresis & magnetization Magnetization behavior depends on the field sweep rate and the magnitude of the energy gap. The magnetization at T=>0 K due to a thermal origin differs from that due to a quantum one.

Temperature evolution of M curves Field increasing Field decreasing Nearly identical behavior below 1.3 K with decreasing temperature

Hysteresis around 40 T Magnetization in ascending process nearly coincides with that in descending process at 900 mK around 40 T.

Energy branches vs magnetic field 100 GHz ≈4.8 K H1H1 H2H2

Magnetization process in field ascending process E H ~20 T~41 T This step is probably caused by “magnetic föhn effect.

Magnetization process in field descending process E H ~20 T~41 T Quantum origin

Summary 1.We performed high field magnetization and ESR experiments on single crystals of the Ni tetramer cluster compound [Ni 4 (  -CO 3 ) 2 (aetpy) 8 ][ClO 4 ]. 2. We observed step wise magnetizations with ½ and ¾ magnetization plateaux in a magnetic field up to 70 T. 3. We observed several ESR lines with g~2.2 and All the magnetic parameters including exchange constants as shown in the figure are evaluated: J 1 /k B =41.9 K (29.1 cm -1 ), J 2 /k B =9.2 K (6.4 cm -1 ) J 3 /k B = -0.6~0.7 K, D/k B =-3.3 K, D’/k B =-4.0 K 5. We observed interesting temperature dependence of magnetization hysteresis near the second step.

Acknowledgements RIKEN Haruhiko Yashiro (HF ESR static) KYKUGEN, Osaka University Akira Matsuo (HF magnetization) Shojiro Kimura (HF ESR pulse) Yasuo Narumi (HF magnetization static magnetization) Koichi Kindo (Pulse experiments) Collaborators