1. Quantum phase transitions
G. Aeppli (LCN)
Y-A. Soh (Dartmouth)
A. Yeh (NEC)
T. F. Rosenbaum (UChicago)
S.M. Hayden (Bristol)
T.G. Perring (RAL)
T.E. Mason (ORNL)
H.A. Mook (ORNL)
P. Evans (Wisconsin)
E. Isaacs (ANL)
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.
2/22/2019

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

3. put atoms together to make a ferromagnet-

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

5. Hysteresis

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

7. 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

8. + classical dynamics

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

10. 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

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

12. 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

13. Need look no further than Heisenberg antiferromagnet
H=SJSiSj with J>0
classical ground state

16. outermost zone m m

17. Evans et al, Science 02
100 m

18. QCP

19. Electrical properties

20. Yeh et al, Nature ‘02

22. Lee et al, PRL 04

23. T (K)
300
200
100
Cr1-x Vx
% V 2 4 6
QCP
DISORDER
ORDER

26. 576 detectors
147,456 total pixels
36,864 spectra
0.5Gb
Typically collect 100 million data points

27. Large magnetic fluctuations on the PM side of QCP…

29. Hayden et al
PRL ‘00

31. Quantum criticality in car bumper New physics easy to see near
CrV
Quantum criticality in car bumper
New physics easy to see near
room T using 19th century
technique!
Small science/big science
Major puzzle
T (K)
300
200
100
Cr1-x Vx
% V 2 4 6
QCP
DISORDER
ORDER

32. Wider implications…

34. High-Tc superconductivity
Quantum
critical
point

35. Aeppli et al. Science 97

36. Lake et al, Science 01 & Nature 02

37. summary
Quantum fluctuations in magnets generally neglected because ferromagnets in most
Practical circumstances don’t have them
QF important in AFM and can now be seen & do matter
QPT in AFM very common and pose unresolved issues about Fermi surface integrity,
relation to SC
Marriage of big & little science is key