Magnetization Hysteresis in Triangular Ring -Quantum and Classical cases Hiroyuki Nojiri, Department of Physics, Okayama University Introduction Hysteresis in regular triangle V15 distorted triangle V3 Mn3 and other Summary

Collaborators Okayama University T. Taniguchi, K . Aikawa Kyushu University Y. Ajiro Laboratory de Magnetisme Loise Néel, B. Barbara University of Bielefeld A. Müeller Tokyo Institute of Technology T. Yamase, E. Ishikawa Acknowledgement S. Miyashita

Molecular magnets Ensemble of Independent molecules Study of 1-molecule property by bulk measurement Study of Quantum Dynamics Discrete energy spectrum Coherence, phase of wave function Control of Hamiltonian　 Magnetic field with time structure Decoupling from thermal bath S=75 S=10 S=3/2 1023 1015 104 101 SQUID Molecule Atom

Quantum Dynamics of Spin H Quantum Dynamics of Spin Thermal assisted tunneling Non-Adiabatic process Cross relaxation Tunneling Thermal process Adiabatic(=equilibrium) process

Low spin molecular magnet Rectangular, Four spin ring S=0, 1, 2, equally spaced steps with no hysteresis What about triangle? (1)Effect of frustration (2)Double degeneracy of the ground state (3)Mixing and symmetry V12 S=2

Quantum? hysteresis in V15 for Hidden double degeneracy K6[V15As6O42(H2O)] • 8H2O Fifteen S=1/2 spins Hexagon sites 　AF Interaction ~800 K Singlet state Triangular site 　AF interaction S=1/2 ground state 　 S=3/2 Excited state 　 D=3.7 K Y. Ajiro et al.

Hysteresis at zero field Magnetization in S=1/2 system Tunneling gap ~0.1 K Kramers doublet Time reversal symmetry Hidden Double Degeneracy Two-sets of doubles separated by Dzyaloshinskii Moriya interaction S. Miyashita and N. Nagaosa Prog. Theor. Phys. 106(2001)533 S=1/2ー3/2 level crossing? Chiorescu et al. PRL 84(2000)3454

Magnetization process at low temperature In steady field Jump to 3 mB at level crossing In pulsed field Hysteresis and half jump T=0.5 K 　 M (μb） up sweep down sweep I. Chiorescu et al. J.Magn.Magn.Mater.221(2000)103.

Half jump at level crossing Up sweep DS=1/2 S=1/2 to S=1 Half jump Down sweep DS=1 S=3/2 to S=1/2 Full jump Saturate in a certain time

Quenching of thermal effect Comparison of width of dM/dH Width is narrower in pulsed fields Quench of thermal fluctuations Observation of pure quantum phenomenon

Double degeneracy and quantum hysteresis Transition only from the blue level Thermalize of the red level in 1 ms Reach saturation Populate only in the blue level Thermalize S=3/2 D S=1/2 DM interaction causes asymmetric splitting S. Miyashita and K. Saito at LT23, 2002

Relaxation time among different levels t1/2: Relaxation in Kramers doublets t3/2:Relaxation between 1/2 and 3/2 Dt2> t1/2>Dt1 Fast Slow

Distorted triangle V3-Sb, Bi K11H[(VO)3(SbW9O33)2]･27H2O. Slightly Distorted triangle :V :O A spin triangle consists of three S=1/2 spins

Magnetization process of V3-Bi V3-Bi powder 　 T=0.5 K Double peak Hc=4 T Hc=5T　 down M(μB） dM/dH(arb.units) up down up B (T) B (T)

Magnetization at finite temperature Population P1(red) ＞P2(blue) P1+P2＝１ 1μB E S=3/2 Hc1 Hc2 H 5.5 K Red+Blue M 1.1 K 2μb S=1/2 1μB Hc1 Hc2 H Hc1 Hc2 H

Summary Hysteresis in triangles,caused by mixing structure Suppress of Thermal fluctuation Magnetization is sensitive to double degeneracy Adiabatic transition Large spin system with Fragile ground state Anisotropy of MH with single crystal of V3 D M interaction vs HF coupling Non adiabatic regime in ultra-fast sweeping fields Quantum Oscillation