Unlocking the Potential: Deep dive into ocean of Ceramic Magnets.pptx
Frustration and Low Dimenionality
1. Search for novel quantum phases in
copper minerals
Hiroi Lab. M1 Ryutaro Okuma
27/10/2014
2. Contents
• Basic notions of magnetism
• Frustration, spin liquid, exotic phases
• Experimental
• Newly synthesized copper compounds with interesting
geometry
• Summary and future plans
3. What is quantum spin systems?
• In 3d transition metal compounds called Mott insulator,
each 3d electron is confined to the neighborhood of an
atom
• With degrees of freedom of electron spin survived, we
can think there exists spin operator in the position of an
atom
• Interaction between spin is described by Heisenberg
Hamiltonian
1 hole behaves
as S=1/2 spin
Cu2+: (Ar)3d9
4. Ferromagnets and anitiferromagnets
At high temperature, spins point arbitrary direction(paramagnetic).
Lowering temperature, spins in magnets tends to favor certain
ordered states.
Ferromagnetic order Neel order
easy
axis
If the Hamiltonian is “round” there is no special axis.
But in real material magnetically easy axis exists.
The picture of spontaneous symmetry breaking
doesn’t hold true.
J<0 J>0
In this ‘classical’ picture, spin is supposed to be
a kind of unit vector. Is it always the case?
6. Electron spin. A kind of angular momentum?
An electron can be seen as a magnet where only two states
exist: up and down. From what does it originate?
Classically, circular current creates
magnetic moment (how strong magnet is)
At least an electron has angular momentum
e.g. Einstein de Haas effect
Is electron autorotating?
7. Description of electron spin in Bloch sphere
1. Electron has intrinsic “angular momentum” called spin
2. Components of take discrete values: ℏ /2 or -ℏ /2
3. State of spin is described by linear combination of up and down
Spin coherent state
After projection onto z-axis, the probability
of “up” or “down” is given by
Electron’s spin can be regarded as a vector ℏ /2 in length
if it is not entangled(like spin singlet).
!
! S
S
8. Geometrical frustration
Resonating Valence Bond state
Arbitrary combination of spins
form singlet pairs. Ground state
is linear combination of such states
Typical lattices
with frustration
a. triangular
b. kagome
c. pyrochlore
Magnetic orders
realized in real
material are
described
Triangular lattice with
AF interaction can’t be
arranged in Neel order.
Singlet pair+1up/down
spin is the ground state
spin singlet state
Spin liquid material can be
compared to liquid Helium. No
inorganic material is evident
enough for every one to believe it
spin liquid so far. However,
interesting magnetism still exists
in frustrated system.
9. Novel phases in kagome lattice
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3287 Calculated M-H plot for S=1/2 kagome lattice
Msat
1
0.5
Q=3
Kagome
7/9
5/9
4
3
2
1
–1
1/Lx Ly=Periodic
Ly=4
8
Ly=6
Open
M/1/3
1/9
0
0 1 2 3
H/J
translational symmetry are quasi-degenerate Fig. S2 and Supplementary Note 3), and their to the shape and size of the cluster. We consider good reason that the symmetry-breaking long Therefore, we perform the conventional DMRG entanglement entropy of the 1/9-plateau manner as refs 2 and 9, as shown in Fig. magnetization, we need to keep the system size nine, and thus the choice of the clusters are with the calculation on the M/N¼0 topological dimension obtained in the Lygives the value D¼3. Thus, the spin-gapped magnetization is possibly a Z3 spin liquid, example of a spin-liquid plateau induced by Even a Z3 spin liquid itself has so far been specified bosonic model24, and the present Figure 1 | Magnetization curve of the spin-1/2 kagome Heisenberg
antiferromagnet in a uniform magnetic field. The saturation value of the
magnetization density per site is Msat/N¼1/2. The inset shows the
geometry of the kagome lattice. The shaded hexagon is the original lattice
unit cell including three sites (Q¼3). Data points are obtained by the grand
canonical analysis on a hexagonal cluster with N¼114 and 132, which
directly gives the curve of the thermodynamic limit without any size scaling.
The range of each plateau is highlighted.
By contrast, in our grand canonical calculation the size
dependence becomes negligible (less than 10!3 in two dimen-sions,
see Methods) once we enter a cluster size of the proper
system length. Therefore, one could evaluate the spin gap by the
onset value of H/J in the magnetization curve near zero field. In
Fig. 1, we find D¼0.05±0.02 (see the red shaded region), which
is obtained on a hexagonal cluster.
We briefly mention that our results are fully consistent with the
a b
Ly Lx
4
3
2
1
0
–2
0 0.05 0.1 0.15
0 S(Lx, Ly)
S(∞, Ly)
0
Figure 2 | Entanglement entropy of a 1/9 magnetization results here are calculated on a long cylinder by the (a) S(Lx, Ly) as a function of 1/Lx is given for Ly¼denote the number of sites along the leg and the cylinder, respectively. (b) The value extrapolated for Lx¼N, is given as a function of circumference Ly. Ly!g gives g¼1.18±0.3. We estimate the error in Lx-N, which gives the uncertainty of linear scaling displayed by grey shading in b.
Typical M-H curve for Antiferromagnets
Magnetic Field
hexagram magnetization patterns appear at plateaus
M
H
All spins point in the direction of magnetic field
Features
1. 4 plateaus & 1 jump
2. spin liquid state
at M/Ms=0, 1/9
3. hexagram patterns at
M/Ms=1/3, 5/9, 7/9
We want to
discover unusual
magnetism in
frustrated system
not limited to
spin liquid
easy axis
Nishimoto, Satoshi et al.,
Nature communications 4 (2013).
T=0K
12. Synthesis: Hydrothermal method
1. Ingredient is sealed with solvent in a teflon(or Au) tube
2. Heated up to 150~250℃(Au can bear over 600℃)
3. At high temperature, water becomes highly reactive
13. Features of hydrothermal method
Compared with solid state reaction, hydrothermal synthesis
Pros
• Can make material contains H
• Likely to get new substance
• And single crystals with way less time
Cons
• Must tune more parameters (pH, density, Temp, time…)
• Often neglects molar ratio of chemical formula
• Tends to produce many byproducts
17. Spin flop transition around M/Ms=1/2
Features
• Very low saturation field~7T
• FM interaction nearly cancels AFM.
• Hysteresis around M/Ms=1/2
• usually AFmagnets have no
hysteresis
• spin flop transition is 1st order,
but hysteresis is usually
T=2K
Spin flop transition small(ΔB<<1T)
Phase transition at just
M/Ms = 1/2 may be
related to interesting
magnetism
B
When the magnetic order is
perpendicular to B, spins
can’t change their direction
easily. If they do, that will be
a sudden transition.
21. Future Plans
• Uncovering the magnetic state of As-vesignieite at M/
Ms=1/2
• Synthesis of a large crystal of perfect kagome mineral
Vesignieite
• Making more and more new material with interesting
properties!
