Report

1 Molecular nanomagnets as milestones for the study of low-dimensional magnetism: fundamental physics and applications Wide-band solid-state NMR at a glance Molecular spin dynamics vs temperature Low temperature quantum level crossing 2 3 Possible applications of MNMs : High density magnetic memory Magneto- optical recording Quantum computing Spintronics Magnetic sensors… 4 As all molecular clusters, studying bulk means studying single molecule as Jinter-mol << Jintra-mol As all molecular clusters, finite number of ions : accurate spin Hamiltonian and exact calculation of energy levels and eigenfunctions = . +1 + + . + > Highly symmetric geometry 5 Ideal physical framework for low dimensional magnetism ( 0-D and/or 1-D) + S=0 Finite size system Reduced number of spins Discrete energy levels structure Quantum phenomena + , S=3/2 Spin topology of a Quasi-Zero-Dimensional magnetic system...... “Open” molecular ring : peculiar spin dynamics Interesting quantum behaviors due to “real” or anti- level crossing 6 By NMR we are measuring the response of nuclei but, through it, we are studying the physical properties of the whole system (electrons, nuclei & phonons) How is it possible Nuclei ? Nuclei are a local probe But in interaction with the whole system 7 electron phonon Advanced tools for molecular spin dynamics investigation 1H NMR 53Cr NMR F NMR 19 53Cr NMR 1H NMR F NMR 19 8 Abundance proton (High sensitivity ) Study of NMR relaxation rates and spectra 5000 NMR Spectrum 4000 I(a.u.) 3000 Full width at half maximum (FWHM) From 1H NMR spectrum it is possible to extract the Full Width at Half Maximum – FWHM, given by : 2000 < ∆ 2 > +< ∆ 2 > ∝ 1000 0 -1.5 -1.0 -0.5 0.0 w(MHz) 0.5 1.0 120 1.5 300 H=1.5T H=0.5T H=0.3T 80 FWHM(kHz) 200 FWHM(kHz) H C 250 Cr8Zn 150 Cr8 60 40 20 0 100 50 0 1 0.47 T 1.23 T 100 10 100 1 10 T(k) 100 Paramagnetic behaviour of 8 in the high temperature region (T>20K) T(k) The temperature and magnetic field dependence of 1H FWHM is similar to 9 other antiferromagnetic molecular rings, but ……. 300 H C Dramatic Increase!!! 250 H=1.5T H=0.5T H=0.3T FWHM(kHz) 200 Cr8Zn 150 At relatively high fields, the gap is reduced and =0 and = 1 states are populated equally 100 50 ; = = = −∆/ 8 0 1 10 100 6 Energy(cm)-1 T(k) 2 For T<20K, condensation in the G.S. 0 ∝ 10 = 4 First excited state First state M ST=1=+1 ST=1, s 2 > 1 1.5T < ∆ 2 > +< ∆ 0 Ground state ST=0 2 3 4 Magnetic field (T) 5 6 Cr8 0.47 T Cr8 0.73 T Cr8 1.23 T Fe6(Na) 0.5 T Fe6(Na) 1 T Fe6(Li) 1.5 T Fe10 1.28 T Fe10 2.5 T 1.0 9 8 R/Rmax , , … Cr8Zn ( HC) H=1.5T H=0.5T H=0.3T 7 0.8 0.6 0.4 0.2 0.0 0.1 1 10 T/T0(H) Homometallic rings (previous studies): 5 -1 T1 (ms) 6 4 , = 3 = + 2 Two alternatives; 0 25 50 75 T(k) Current case (heterometallic Cr8Zn): , = 11 ∝ = = , = ′ + Theoretical calculation in progress… ∝ −∆/ At low T (much less than the gap among =0 and =1, e.g. T=1.7K) molecular rings populate the ground state The local (at 1 sites) magnetic field due to the contribution of electronic (molecular) magnetic moments, becomes: = + ∝ < ∆ 2 > +< ∆ 2 > approx. M < ∆ 2 > = 1 2 = 12 ( ∈ A(, ) [ 2 < , − 0 >∆ ) ∈ ∈ , 3 < , >∆ ]2 NMR spectral broadening due to the increase of the electronic magnetization value Cr8Zn M(H) a 2K 6 parall perpen 4 2 [emu/g] non-magnetic Ground State ST = 0 0 -2 -4 -6 -5 -4 -3 -2 -1 0 0H [Oe] magnetic Ground State ST = 1 13 Calculated energy levels in external magnetic field 1 2 3 4 5 4 x 10 M(H) curve at T=2K magnetic Ground State ST = 2 12000 Cr8Zn NMR Spectrum H=1.8T Larmor Frequency=76.576 MHz 10000 Proton NMR spectra versus magnetic field on based on energy levels structure by using frequency sweep technique at the fixed temperature (T=1.7 K) 6000 4000 2000 0 -0.5 0.0 z) − () 0.5 NMR spectra before the first level crossing ( = 0 ↔ Non-magnetized system) NMR spectra broadening by passing of crossing level H=3T 1.0 Larmor Frequency=127.688MHz 15000 10000 5000 5000 Cr8Zn NMR Spectrum H=7.5T 4000 Larmor Frequency=319.214MHz 0 -1.0 -0.5 0.0 z) − () 0.5 1.0 3000 1H NMR spectra after the first level crossing ( = 0 → = 1) ( Non-magnetized »»» Magnetized system) I(a.u.) 1H Cr8Zn NMR Spectrum 20000 -1.0 I(a.u.) I(a.u.) 8000 2000 1000 0 -1.0 Calculated energy levels in an external magnetic field 14 -0.5 0.0 0.5 1.0 − z) () 1H NMR spectra after the second level crossing (ST = 1 ST = 2) Future investigation: spin-lattice relaxation rate study of spin dynamics (also level crossing problem details and mix of eigenfunctions) Anti level crossing; Mixed functions 15 Real level crossing; Unmixed functions Conclusions: Temperature spin dynamics of detected by “ 1H NMR 1/ ” is qualitatively similar to homometallic rings; an exact calculation of correlation function is needed. At low temperature 1H NMR spectra broadening reflects the effects of M increase when Quantum level crossing occur Future issues : 16 Theoretical investigation of spin dynamics vs temperature Quantum effects due to “Real ”/ Anti level crossing studied by means of low-T 1H NMR spin-lattice relaxation rate January 15th 2013 Italy 17 T2 relaxation curve T1 relaxation curve 18 NMR spectrum