1. Quantum effects in Magnetic Salts
G. Aeppli (LCN)
J. Brooke (NEC/UChicago/Lincoln Labs)
T. F. Rosenbaum (UChicago)
D. Bitko (UChicago)
H. Ronnow (PSI/NEC)
D. McMorrow (LCN)
R. Parthasarathy (UChicago/Berkeley)
Outline:
Q. Fluctuations: Variations (e.g., oscillations between) from the classical states of the true state.
Q. Tunneling: transition between two classical states that is classically forbidden.
So to know Tun, it helps to understand Fluct. So, e.g., if there’s a barrier, the true quantum eigenstate overlaps with the classically inaccessible state beyond the barrier. Tunneling is just the “classically outrageous” subset of the quantum fluctuations.
We see that tunneling requires small w, Delta, net mass, or large hbar.
But, when compared to tunneling, what is the magnetic mass? It’s the prefactor to the k^2 term.
Furthermore, the GS and Ess of the Hamiltonian are Eigenstates (by definition). Qtunn occurs when the system is metastable, I.e., not in a proper eigenstate. Therefore, when constructing such a system, it helps to have a driven system, either physically driven, or with built-in quenched inequilibrium.
What about N? What sets the size limit to a quantum quasiparticle? Is it merely the above constraint, or is there more?
Intro to quantum fluctuations (ala Premi’s 1D AFM?)
What does it mean to be “dynamically unstable to Q. Fluctuations”?
The true GS has a lower energy than the classically-expected in 1d, and has fluctuations so
hence no long-range order in 1d (solving for dm to get stability).
Do these persist to higher dimensions?
What’s it take? Requires overlap. ~Exp(-sqrt(2MDelta/hbar)),  small N, m, D, x, large hbar. Dimension?
Dynamics: introduce spin-waves
sigma_x  raising, lowering ops  fermionic operators, annihilation and creation 
(see no definite fermion number n=c^dag c)  fermion op momentum eigenstates 
Bogoliubov transformation to fermion numbers that ARE conserved via unitary transformation
 demand no terms like alpha^dagger alpha^dagger that violate number conservation
 solve for energy  the “mass” is the prefactor to the k^2 term.
Picture of dispersion? Showing k^2 behavior.
The GS and Ess of the Hamiltonian are Eigenstates (by definition). Qtunn occurs when the system is metastable, I.e., not in a proper eigenstate. Therefore it helps to have a driven system, either physically driven, or with built-in quenched inequilibrium.
Intro to Ising system?
Simplest spin system.
Can arise do to broken symmetry of surrounding crystal matrix.
(f electrons  L=3, and LiHoF4 has I=5/8, Ho has 4f11 6s2, so Ho3+ has 4f8, 1 doubly-occupied level?)
LiHoF4
Intro
marginal, (LiErF4 orders AFM-ly, so expect disorder could really hit this sucker).
QCP data
Interlude: Effects of disorder
Griffiths-McCoy singularities (divergence of local susceptibility due to disorder)
as dimensionality increases, so does validity of MF, so expect disorder to play smaller role.
Spin Glass intro
LiHo0.44Y0.56F4
Phase diagram
Nature of suscptibility
enhanced effective disorder as Hc grows
Spectroscopy
QC is more efficient than CC!!
Quantitative tunneling analysis: looking more closely at the spectroscopy
Simplest model is debye relaxation. We will determine the relaxation distribution from data.
Choose a simple distribution: delta function (high freq) + 1/tau falloff, fit to chi(f).
Plot the fo’s that come from this fit.
Fit this to a Classical + Quantum form!
From fit, extract Delta(Gamma) at high temps to isolate mw^2 from WKB part.
see that Gamma primarily reduces effective mass, not Delta.
Get tunneling mass corresponding to 10 theoretical spin masses.
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2. outline Introduction – saltsquantum mechanicsclassical magnetism
RE fluoride magnet LiHoF4 – model quantum phase transition
1d model magnets
2d model magnets – Heisenberg & Hubbard models

4. Not magnetic, so need to look for a salt containing a simple magnetic ion… consult periodic table on Google

8. 4f76s2

9. EuO O Eu

10. From quantum mechanics
Electrons carry spin
Spin uncompensated for many ions in solids
e.g. Eu2+(f7,S=7/2),
but also Cu2+(d9,S=1/2), Ni2+ (d8,S=1), Fe2+ (d6,S=2)

11. put atoms together to make a ferromagnet-

12. Classical onset of magnetization in a conventional transition metal alloy(PdCo)

13. Hysteresis

14. Hysteresis comes from magnetic domain walls
300K
Perpendicular
recording medium

15. conventional paradigm for magnetism
Curie(FM) point Tc so that
for T<Tc, finite <Mo>=(1/N)S<Sj>
<Mo>=(Tc-T)b , x~|Tc-T|-n , c~|Tc-T|-g
for T<Tc, there are static magnetic domains,
from which most applications of magnetism are derived

16. + classical dynamics

17. Perring et al, Phys. Rev. Lett. 81 217201(2001)

18. What is special about ordinary ferromagnets?
[H,M]=0  order parameter is a conserved quantity 
classical FM eigenstates (Curie state | ½ ½ ½ … ½ >,| -½ -½ -½ … -½ >
& spin waves) are also quantum eigenstates
 no need to worry about quantum mechanics once spins exist

19. Do we ever need to worry about quantum mechanics for real magnets?
need to examine cases where
commutator does not vanish

20. Why should we ask?
Search for useable - scaleable, easily measurable - quantum
degrees of freedom,
e.g. for quantum computing
many hard problems (e.g. high-temperature superconductivity)
in condensed matter physics involve strongly fluctuating
quantum spins

21. Simplest quantum magnet
Ising model in a
transverse field:
Quantum
fluctuations
matter for G  0:
Spins constrained along “easy” axis
Simple Hamiltonian:
Classical, thermally-driven paramagnet-ferromagnet transition at TC.
A transverse magnetic field, G, induces a quantum transition at T=0.
Disorder introduced via spin deletion, random coupling
Frustration introduced via geometry or coupling strength PM 1
Gc~kTc~J
0.5 FM
0.5 1
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22. Plan of talk
Experimental realization of Ising model in transverse field
The simplest quantum critical point
Nuclear spin bath
Quantum mechanics with tunable mass
Possible applications

23. Realizing the transverse field Ising model, where can vary G – LiHoF4b Ho Li F
g=14 doublet
9K gap to next state
dipolar coupled
5 micron domains
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24. Realizing the transverse field Ising model, where can vary G – LiHoF4b
Ho 3+
Li+ F-
g=14 doublet (J=8)
9K gap to next state
dipolar coupled
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27. Susceptibility Real component diverges at FM ordering
Imaginary component shows dissipation
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28. c vs T for Ht=0
Gamma = 1.00 pm 0.09
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D. Bitko, T. F. Rosenbaum, G. Aeppli, Phys. Rev. Lett.77(5), pp , (1996)

29. Now impose transverse field …
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30. MFT works great for this limit, as you can see
Critical scaling of T,Gamma also give beta=1/2, the mean-field value for both T and Ht.
Two free parameters, the coupling energy J and g_perp, which is close (but not exactly) to zero.
(d=3 short-range Ising system beta=0.31, v=0.64, delta=5, gamma=1.25, alpha= /- 0.01)
(mean-field Ising system beta=0.5, v=0.5, delta=3, gamma=1)
Chi ~ (T-TC)-gamma
M ~ (T-TC)-beta
M ~ h1/delta
C ~ (T-TC)-alpha
Mean-field, 2 parameters
3+1 dimensions.
Phase diagram with quantum critical point at T=0,H=5T
mean field theory using single-ion(Ho3+ with J=8 and I=7/2) x-tal field and hyperfine coupling parameters describes phase diagram as well as absolute magnetic susceptibilities and critical exponents (c~|D-Dc|-1, T-1 at QCP)
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31. MFT works great for this limit, as you can see
Critical scaling of T,Gamma also give beta=1/2, the mean-field value for both T and Ht.
Two free parameters, the coupling energy J and g_perp, which is close (but not exactly) to zero.
(d=3 short-range Ising system beta=0.31, v=0.64, delta=5, gamma=1.25, alpha= /- 0.01)
(mean-field Ising system beta=0.5, v=0.5, delta=3, gamma=1)
Chi ~ (T-TC)-gamma
M ~ (T-TC)-beta
M ~ h1/delta
C ~ (T-TC)-alpha
Mean-field, 2 parameters
3+1 dimensions.
Phase diagram with quantum critical point at T=0,H=5T
mean field theory using single-ion(Ho3+ with J=8 and I=7/2) x-tal field and hyperfine coupling parameters describes phase diagram as well as absolute magnetic susceptibilities and critical exponents (c~|D-Dc|-1, T-1 at QCP)
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32. 165Ho J=8 and I=7/2
A=3.36meV
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33. W=A<J>I
~ 140meV
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34. Diverging c
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35. Magnetic Mass = The Ising term  energy gap 2J
The G term does not commute with
Need traveling wave solution:
Total energy of flip
Quantize ito spin-wave momentum states
Softer magnets have smaller masses  more spins can get involved.
for RT magnets, m~10me.
9/22/2018

36. Magnetic Mass = The Ising term  energy gap 2J
The G term does not commute with
Need traveling wave solution:
Total energy of flip
Quantize ito spin-wave momentum states
Softer magnets have smaller masses  more spins can get involved.
for RT magnets, m~10me.
9/22/2018

37. Magnetic Mass = The Ising term  energy gap 2J
The G term does not commute with
Need traveling wave solution:
Total energy of flip
Quantize ito spin-wave momentum states
Softer magnets have smaller masses  more spins can get involved.
for RT magnets, m~10me.
9/22/2018

38. Magnetic Mass = The Ising term  energy gap 2J
The G term does not commute with
Need traveling wave solution:
Total energy of flip
Quantize ito spin-wave momentum states
Softer magnets have smaller masses  more spins can get involved.
for RT magnets, m~10me.
9/22/2018

39. Magnetic Mass = The Ising term  energy gap 2J
The G term does not commute with
Need traveling wave solution:
Total energy of flip
Quantize ito spin-wave momentum states
Softer magnets have smaller masses  more spins can get involved.
for RT magnets, m~10me.
9/22/2018

40. Spin Wave excitations in the FM LiHoF4
Energy Transfer (meV) 1
1.5 2
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41. Spin Wave excitations in the FM LiHoF4
Energy Transfer (meV) 1
1.5 2
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42. What happens near QPT?
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43. H. Ronnow et al. Science 308, 392-395 (2005)
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44. W=A<J>I
~ 140meV
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46. d2s/dWdw=Sf|<f|S(Q)+|0>|2d(w-E0+Ef) where S(Q)+ =SmSm+expiq.rm
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47. Where does spectral weight go & diverging correlation length appear?
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Ronnow et al, unpub (2006)

48. summary Electronic coherence limited by nuclear spins
QCP dynamics radically altered by simple ‘spectator’ degree of freedom
Nuclear spin bath ‘pulls back’ quantum system into classical regime
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49. wider significance ‘best’ Electronic- TFI
Connection to ‘decoherence’ problem in mesoscopic systems
‘best’
Electronic-
TFI
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