An insulating salt as a laboratory for ‘emergent’ quantum phenomena G. Aeppli (LCN) J. Brooke (NEC/UChicago) T. F. Rosenbaum (UChicago) D. Bitko (UChicago) H. Ronnow (PSI/NEC) D. McMorrow (LCN) R. Parthasarathy (UChicago/Berkeley) S. Ghosh (UCSB) S. Coppersmith (Wisconsin) 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. 11/14/2018

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 11/14/2018

Realizing the transverse field Ising model, where can vary G – LiHoF4 b Ho Li F g=14 doublet 9K gap to next state dipolar coupled 5 micron domains 11/14/2018

Realizing the transverse field Ising model, where can vary G – LiHoF4 b Ho Li F g=14 doublet 9K gap to next state dipolar coupled 11/14/2018

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Susceptibility Real component diverges at FM ordering Imaginary component shows dissipation 11/14/2018

c vs T for Ht=0 Gamma = 1.00 pm 0.09 11/14/2018 D. Bitko, T. F. Rosenbaum, G. Aeppli, Phys. Rev. Lett.77(5), pp. 940-943, (1996)

Now impose transverse field … 11/14/2018

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=0.013 +/- 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) 11/14/2018

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=0.013 +/- 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) 11/14/2018

165Ho3+ J=8 and I=7/2 A=3.36meV 11/14/2018

W=A<J>I ~ 140meV 11/14/2018

Diverging c 11/14/2018

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. 11/14/2018

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. 11/14/2018

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. 11/14/2018

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. 11/14/2018

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. 11/14/2018

Spin Wave excitations in the FM LiHoF4 Energy Transfer (meV) 1 1.5 2 11/14/2018

Spin Wave excitations in the FM LiHoF4 Energy Transfer (meV) 1 1.5 2 11/14/2018

What happens near QPT? 11/14/2018

H. Ronnow et al. Science (2005) 11/14/2018

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W=A<J>I ~ 140meV 11/14/2018

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d2s/dWdw=Sf|<f|S(Q)+|0>|2d(w-E0+Ef) where S(Q)+ =SmSm+expiq.rm 11/14/2018

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 11/14/2018

wider significance ‘best’ Electronic- TFI Connection to single molecule dynamics ‘best’ Electronic- TFI 11/14/2018

conclusion ‘slaved’ degrees of freedom which are classically irrelevant can have qualitative quantum impact 11/14/2018