slides - Graduate Studies in Physics at UniMI

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
𝐻=𝐽
𝑆𝑖 . 𝑆𝑖+1 +
𝑖
𝑈 𝑆𝑖 +
𝑖
𝑈𝑖𝑗 𝑆𝑖 . 𝑆𝑗 + 𝑔𝜇𝐵 𝐵
𝑖>𝑗
𝑆𝑖
𝑖
Highly symmetric geometry
5
Ideal physical framework for low dimensional
magnetism ( 0-D and/or 1-D)
𝒁𝒏𝟐+ S=0
Finite size system
Reduced number of spins
Discrete energy levels structure
Quantum phenomena
𝑪𝒓𝟑+ , 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 ?
𝑻𝟐𝒏
Nuclei are a local probe
But
in interaction with the whole system
7
electron
𝑻𝟐𝒆
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
< ∆𝜗 2 >𝑑 +< ∆𝜗 2 >𝑚
𝐹𝑊𝐻𝑀 ∝
1000
0
-1.5
-1.0
-0.5
0.0
w(MHz)
0.5
1.0
120
1.5
300
H C
FWHM(kHz)
200
H=1.5T
H=0.5T
H=0.3T
80
FWHM(kHz)
𝑪𝒓𝟖 𝒁𝒏
250
Cr8Zn
150
0.47 T
1.23 T
𝑪𝒓𝟖
100
Cr8
60
40
20
0
100
1
10
T(k)
100
50
0
1
10
100
Paramagnetic behaviour of 𝐶𝑟8 𝑍𝑛
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 𝑺𝑻 =0 and 𝑺𝑻 = 1 states
are populated equally
100
50
8
𝐵𝑜𝑙𝑡𝑧𝑚𝑎𝑛𝑛 𝑟𝑢𝑙𝑒 ;
𝑵𝑺𝑻=𝟏 = 𝑵𝑺𝑻=𝟎 𝒆−∆𝑬/𝒌𝑩𝑻
0
1
10
100
6
Energy(cm)-1
T(k)
4
2
For T<20K, condensation in the G.S.
0
𝐹𝑊𝐻𝑀 ∝
10
𝑯𝒍𝒐𝒄𝒂𝒍 = 𝑯𝟎
First excited state
First
state M
ST=1=+1
ST=1,
s

2 > 1 1.5T
< ∆𝜗 2 >𝑑 +< ∆𝜗
0
𝑚
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
R/Rmax
𝑪𝒓𝟖 , 𝑭𝒆𝟔 , 𝑭𝒆𝟏𝟎 …
9
𝑪𝒓𝟖 𝒁𝒏
8
Cr8Zn ( HC)
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
𝑹 𝑯, 𝑻 =
3
𝟏
𝝎𝒄 𝑻
=𝑨 𝟐
𝑻𝟏 𝒙𝑻
𝝎𝒄 𝑻 + 𝝎𝟐
2
Two alternatives;
0
25
50
75
T(k)
Current case (heterometallic Cr8Zn):
𝟏
𝑹 𝑯, 𝑻 =
𝑻𝟏 𝒙𝑻
11
𝟏
𝝎𝒄 𝑻 ∝ = 𝑪𝑻𝜶
𝝉𝒄
𝝎𝒄 𝑻 =
𝝎𝒄𝒊 ,
𝒊
𝟏
𝝎𝒄 𝑻
= 𝑨′ 𝟐
𝑻𝟏
𝝎𝒄 𝑻 + 𝝎𝟐 Theoretical calculation in progress…
𝝎𝒄𝒊 ∝ 𝒆−∆/𝑻
 At low T (much less than the gap among 𝑆𝑇 =0 and 𝑆𝑇 =1, e.g. T=1.7K)
molecular rings populate the ground state
 The local (at 1𝐻 sites) magnetic field due to the contribution of electronic
(molecular) magnetic moments, becomes:
𝑯𝒍𝒐𝒄𝒂𝒍 = 𝑯𝟎 + 𝑯𝒆𝒇𝒇𝒆𝒄𝒕
𝐹𝑊𝐻𝑀 ∝
< ∆𝜗 2 >𝑑 +< ∆𝜗 2 >𝑚
approx.  M
< ∆𝜗 2 >𝑚 =
1
𝑁
𝛾2
=
𝑁
12
𝑅 ( 𝑖∈𝑅
A(𝜗𝑖,𝑗 )
[
𝑅
2
< 𝜗𝑅,𝑖 − 𝜗0 >∆𝑡 )
𝑖∈𝑅 𝑗∈𝑅
𝑟𝑖,𝑗 3
< 𝑚𝑧,𝑗 >∆𝑡 ]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 𝑪𝒓𝟖𝒁𝒏 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)
𝝎−𝝎
𝟎 (𝑴𝑯𝒛)
0.5
NMR spectra before the first level crossing
(𝑆𝑇 = 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)
𝝎 − 𝝎𝟎 (𝑴𝑯𝒛)
0.5
1.0
3000
1H
NMR spectra after the first level crossing
(𝑆𝑇 = 0 → 𝑆𝑇 = 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
𝝎
− 𝝎z)𝟎 (𝑴𝑯𝒛)
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 𝑪𝒓𝟖 𝒁𝒏 detected by “ 1H NMR 1/𝑻𝟏 ” 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
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T2 relaxation curve
T1 relaxation curve
18
NMR spectrum