# SCIENTIFIC PROGRAMS AND ACTIVITIES

March 11, 2014
THE FIELDS INSTITUTE
FOR RESEARCH IN MATHEMATICAL SCIENCES

20th ANNIVERSARY YEAR
 September 24-26, 2012 Workshop on Frontiers in Quantum Materials Fields Institute Center for Quantum Materials Organizer:Center for Quantum Materials, Director, Yong-Baek Kim

Leon Balents (University of California, Santa Barbara)

Quantum spin liquid theory for quantum spin ice

Recent experiments show that strong quantum fluctuations may exist in some spin-ice-like materials. Theory shows that quantum spin liquid states are possible in this class of Hamiltonians. We will review the
microscopic theory for such quantum spin liquids, and then discuss the characteristics of the quantum spin liquid and nearby states, and report on the evolution of the ground states with increasing
temperature.

Collin Broholm (Johns Hopkins Univ)

Incommensurate correlations & mesoscopic spin resonance in YbRh2Si2

Andrea Damascelli (Univ of British Columbia)

From p-wave superconductors to relativistic-Mott insulators via spin-orbit interaction in solids

Spin-orbit coupling is essential to the quantum-mechanical description of atomic energy levels. Yet its most spectacular consequences are found in the low-energy electronic structure of solids, where this atomic-like interaction plays a key role in the emergence of some of the most unconventional quantum phenomena. In this talk I will show how spin and angle-resolved photoemission spectroscopy, in combination with in-situ doping techniques, can be used to unveil the role of spin-orbit interaction in the emergence of p-wave superconductivity in Sr2RuO4 [1,2] and relativistic Mott insulating behavior in Na2IrO3 [3].

[1] M.W. Haverkort et al., Phys. Rev. Lett. 101, 026406 (2008).
[2] C.N. Veenstra et al., in preparation (2012).
[3] R. Comin et al., arXiv:1204.4471 (2012).

Marcel Franz (University of British Columbia)

Lattice model for the surface states of a topological insulator

A surface of a strong topological insulator (STI) is characterized by an odd number of linearly dispersing gapless electronic surface states. It is well known that such a surface cannot be described by an effective two-dimensional lattice model (without breaking the time-reversal symmetry), which often hampers theoretical efforts to quantitatively understand some of the properties of such surfaces, including the effect of strong disorder, interactions and various symmetry-breaking instabilities. Here I describe a lattice model that can be used to describe a pair of STI surfaces and has an odd number of Dirac fermion states with wavefunctions localized on each surface. The Hamiltonian consists of two planar tight-binding models with spin-orbit coupling, representing the two surfaces, weakly coupled to each other by terms that remove the redundant Dirac points from the low-energy spectrum. The utility of this model is illustrated by studying the magnetic and exciton instabilities of the STI surface state driven by short-range repulsive interactions.

Bruce Gaulin (McMaster University)

Effective Spin 1/2 Hamiltonians in the Pyrochlore Magnets Er2Ti2O7 and Yb2Ti2O7

New neutron scattering instrumentation offers unprecedented opportunities for mapping out the full dispersion and dynamic susceptibility of magnetic materials. In turn, these measurements can be exploited to determine their microscopic spin Hamiltonians in great detail. We've used these techniques to examine two pyrochlore magnets with unusual and exotic ground states, Er2Ti2O7 and Yb2Ti2O7. These materials are both known to display anisotropic g-tensors with XY anisotropy, yet their ground state properties are very different. Collaborative work with Lucile Savary and Leon Balents has modelled our spin wave data in terms of an anisotropic exchange Hamiltonian on the pyrochlore lattice. As a result we can understand Er2Ti2O7's ordered ground state on the basis of selection by an order-by-quantum-disorder mechanism[1], while Yb2Ti2O7's ground state is shown to be in reasonably close proximity to spin liquid and other exotic ground states[2].

[1] K.A. Ross, L. Savary, B.D. Gaulin and L. Balents, Phys. Rev X, 1, 021022, 2011.
[2] L. Savary, K.A. Ross, B.D. Gaulin, J.P.C. Ruff, and L. Balents, arXiv:1204.1320 and to appear, Phys. Rev. Lett.

Michael Gingras (University of Waterloo)

The Tb2Ti2O7 Pyrochlore Antiferromagnet: the Platypus of Frustrated Magnetic Systems

The Tb2Ti2O7 pyrochlore antiferromagnet was first found to lack long range order down to 50 mK at about the same time as spin ice behavior was reported in the Ho2Ti2O7 compound. Thirteen years later, despite numerous experimental studies and theoretical attempts, we still do not have an understanding of what is the real nature of the low temperature state of this material. I will review in this talk the salients facts, some agreed upon by a most researchers and some not, regarding the nature of the low-temperature state of Tb2Ti2O7.

Harold Hwang (Stanford)

Magnetism between nonmagnetic insulators

One of the aspirations of the study of complex oxide heterostructures is the creation of interface states without a bulk analog. An interesting example is the ferromagnetism which emerges at the LaAlO3/SrTiO3 interface. We will report our studies of the magnetism found here in terms of spatial variations in the plane, stability, and spectroscopy.

Takashi Imai (Department of Physics and Astronomy, McMaster University, Hamilton, and Canadian Institute for Advanced Research)

NMR Search for the Spin Nematic State in LaFeAsO

The mechanism of high Tc superconductivity in iron-pnictides remains controversial. While earlier NMR measurements provide ample evidence for the enhancement of spin fluctuations near the optimized superconducting transition [1], the softening of spins is accompanied by that of the lattice [2]. A theoretical analysis of the magnetic properties of the FeAs planes based on the frustrated J1-J2 model suggests that the SDW (spin density wave) transition may be highly unconventional due to the strong magneto-elastic coupling between spins and the lattice [3]. Moreover, the intermediate temperature range between the tetragonal-orthorhombic structural phase transition at TTO and the SDW transition at TSDW may be a realization of the spin nematic state [4].

NMR is an ideal probe to investigate these effects, thanks to its sensitivity to both the spin and lattice degrees of freedom. Moreover, the angle-dependent measurements of the spin-lattice relaxation rate 1/T1 has been proposed to be an effective probe of the spin nematic phase [5]. In this talk, we report a 75As single crystal NMR investigation of LaFeAsO, the parent phase of a pnictide high Tc superconductor [6]. We demonstrate that spin dynamics develop a strong two-fold anisotropy within each orthorhombic domain in the orthorhombic phase below TTO~156 K, prior to the SDW transition at TSDW ~ 142K. This intermediate state with a dynamical breaking of the rotational symmetry freezes progressively into a SDW state below TSDW ~ 142 K. Our findings are consistent with the presence of a spin nematic state below TTO with an incipient magnetic order.

The work at McMaster was supported by NSERC and CIFAR.

[1] F. L. Ning, T.I. et al., Phys. Rev. Lett. 104, 037001 (2010).
[2] R. M. Fernandes et al., Phys. Rev. Lett. 105, 157003 (2010).
[3] C. Xu, M. Müller, and S. Sachdev, Phys. Rev. B 78, 020501R, (2008).
[4] C. Fang, W. F. Tsao, J. P. Hu, and S. A. Kivelson, Phys. Rev. B 77, 224509 (2008).
[5] A. Smerald and N. Shannon, Phys. Rev. B 84, 184437 (2011).
[6] M. Fu, D. A. Torchetti, T. Imai, F. L. Ning, J.-Q. Yan, and A. S. Sefat, arXiv:1208.5652.

Catherine Kallin (McMaster University)

Anomalous Hall effect in chiral superconductors and density wave states

The polar Kerr effect is a sensitive and direct probe of broken time-reversal symmetry. A non-zero Kerr effect, which implies an anomalous Hall effect, has been observed in the superconducting
state of Sr2RuO4 (SRO) as well as in the pseudogap phase of several cuprate materials. Here, we discuss recent theoretical work on the anomalous Hall effect in clean chiral superconductors, which suggests new experiments that might identify the nature of the superconductivity, as well as which bands are primarily active, in SRO. The anomalous Hall conductivity of non-superconducting chiral density wave states, e.g., chiral d-density wave order, will also be discussed and contrasted to the superconducting case.

Sung-Sik Lee (Perimeter Institute/McMaster)

Chiral non-Fermi liquids in two dimensions

We propose a renormalization group scheme which is suitable for theories with Fermi surface. Low energy modes near the Fermi surface are viewed as a collection of one dimensional fermions with a
continuous flavour labelling the momentum along the Fermi surface. Based on this approach, we provide a non-perturbative argument for the stability of the chiral non-Fermi Liquid states where one patch of
Fermi surface is coupled with a gapless boson in two dimensions. We point out that the validity (or breakdown) of local patch description in momentum space is closely related to a phenomenon known as the
UV/IR mixing where infrared singularity is controlled by a UV cut-off scale. Finally, we will suggest a possible experimental realization ofa chiral non-Fermi liquid state.

Young S. Lee (MIT)

Experimental signatures of spin liquid physics on the S=1/2 kagome lattice

Materials based on the kagome lattice appear to be ideal hosts for the possibility of a quantum spin liquid ground state in two-dimensions. I will discuss our work which includes single crystal growth, bulk characterization, and neutron scattering measurements of the S=1/2 kagome lattice material ZnCu3(OH)6Cl2 (also known as herbertsmithite). Recent susceptibility measurements yield valuable information on the additional terms in the spin Hamiltonian beyond nearest neighbor Heisenberg exchange, and anomalous x-ray diffraction yields detailed information on the presence of a small amount of atomic impurities. Most interestingly, inelastic neutron scattering measurements of the spin correlations in a single crystal sample reveal a continuum of spinon excitations in this two-dimensional insulating magnet. Such fractionalized excitations are a long-sought hallmark of the quantum spin liquid.

Graeme Luke (McMaster University)

Ground State and Excitations in Spin Ice and Quantum Spin Ice

Magnetic rare earth pyrochlore systems exhibit a rich variety of phenomena arising from geometrical frustration of their magnetic interactions. Dy2Ti2O7 and Ho2Ti2O7 have been identified as dipolar spin ices, where the combination of ferromagnetic interactions and crystal field scheme leads to a ground state consisting of two spins pointing in and two spins pointing out of each tetrahedral unit in the crystal structure, in analogy to water ice where each oxygen has two closely bound and two weakly bound hydrogen neighbours. Yb2Ti2O7 has been proposed to be an example of a related quantum spin ice state, though the precise determination of the ground state remains controversial.

I will present muon spin relaxation measurements of Dy2Ti2O7 where we find that the ground state exhibits a form of persistent spin dynamics to low temperature which exist in addition to any proposed emergent magnetic monopoles. In the case of Yb2Ti2O7, we find that the spins remain dynamic to the lowest temperature, though there is a distinct change in the local spin susceptibility in both single crystal and polycrystalline samples at the temperature where specific heat measurements identify a phase transition. Our results show that there are no static magnetic moments in Yb2Ti2O7.

Tae Won Noh (IBS Center for Functional Interfaces of Correlated Electron System, & Dept of Physics and Astronomy, Seoul National University)

Electronic band structures of LaNiO3 ultrathin films in-situ studied by angle resolved photoemission spectroscopy

Bulk LaNiO3 (R: rare earth) is metal and has d7 electronic configuration with fully occupied t2g and partially filled eg electrons, similar to the cuprates. Recent theoretical calculations predicted the cuprate-like eg orbital reconstruction and a gap opening in LaNiO3/LaAlO3 heterostructure.[1,2] To confirm these theoretical predictions, the orbital characters in LaNiO3/LaAlO3 heterostructure have been studied by using synchrotron-based x-ray measurements.[3-5] However, fundamental understandings on the eg orbital reconstruction are still elusive due to the absence of direct band structure measurements.
Recently, we performed in-situ angle-resolved photoemission spectroscopy (ARPES) studies on LaNiO3 ultrathin films. (1) By using LaAlO3, NdGaO3, and SrTiO3 substrates, we could obtain LaNiO3 films which were under compressive, nearly free, and tensile strains, respectively. The measured electronic band structure of the LaNiO3 film on NdGaO3 substrate can be explained by the DMFT calculations (not by the LDA calculations), indicating the importance of the correlation effects. In addition, the electronic band structure of the LaNiO3 film under compressive strain can be explained in terms of octahedral elongation. On the other hand, under tensile stress, we found that the octahedral elongation is not enough to explain the electronic structure. (2) We also deposited LaNiO3 ultrathin films on SrTiO3 substrates with thickness between 1 and 5 unit cells (u.c.) We observed that the dimensional crossover of the band structure occurs between 4 u.c. to 3 u.c. of LaNiO3 film. Contrary to earlier theoretical works, our LaNiO3 ultrathin film has a Fermi surface down to 1 u.c.. Compared to 3 dimensional LaNiO3 thick films, we found that the electronic correlation effect was getting weaker in 2 dimensional LaNiO3 ultrathin films. Further details will be discussed more in presentation.

1. Jir?i´ Chaloupka et al., Phys. Rev. Lett. 100, 016404 (2008).
2. P. Hansmann et al., Phys. Rev. Lett. 103, 016401 (2009).
3. Eva Benckiser et al., Nature Mater. 10, 189 (2011).
4. Jian Liu et al., Phys. Rev. B 83, 161102(R) (2011).
5. J. Chakhalian et al., Phys. Rev. Lett. 107, 116805 (2011).

Je-Geun Park (Seoul National University)

Spin dynamics of multiferroic BiFeO3 and unusual low energy features

1 IBS Center for Functional Interfaces of Correlated Electron Systems, Seoul National University, Seoul 151-742, Korea
2 Department of Physics & Astronomy, Seoul National University, Seoul 151-742, Korea
3 Center for Strongly Correlated Materials Research, Seoul National University, Seoul, 151-742, Korea

Multiferroic materials having a coexistence of otherwise seemingly incompatible phases of magnetic and ferroelectric ground states have been the focus of intensive materials researches recently. BiFeO$_3$ is arguably one of the most interesting multiferroic materials with both magnetic and ferroelectric transitions occurring above room temperature: T$\rm{_N}$=650 K and T$\rm{_C}$=1050 K. Moreover, it has an unusual incommensurate magnetic transition with an extremely long period of 650 $\stackrel{\circ}{\text{A}}$.

By using 10 single crystals co-aligned within $3^{\circ}$ of one another, we have recently measured the spin waves of the antiferromagnetic phase at two state-of-the-art inelastic neutron scattering instruments: one is AMATERA of J-PARC and another MERLIN of ISIS. These two experiments allowed us to map out the full dispersion curve, for the first time, over the entire Brillouin zones and succeeded in determining the essential magnetic exchange interactions: two antiferromagnetic interactions and one Dzyaloshinskii-Moriya term.

We have further investigated the low energy spin waves using a cold TAS of LLB to find that there exists unusual spin dynamics near the zone center. We will also discuss our latest experimental studies using high-resolution neutron and synchrotron diffraction studies as well as high field studies to find that there are clear anomalies in the temperature dependence of lattice constants. We will put our findings in a broader context of this interesting material.

George A. Sawatzky (Physics Dept and Max Planck-UBC Centre for Quantum Materials, University of British Columbia)

New Magnetic Materials Based on Defects, Interfaces and Doping

This is a joint work with Ilya Elfimov, Bayo Lau, Mirko Moeller and Mona Berciu

Ideas based on theory and some experiments will be presented regarding possible new magnetic materials based on extended and point defects (1), interface engineering (2), anion substitution in oxides and hole and electron doping of oxides. The concentration will be on rather ionic oxides mostly not involving conventional magnetic elements. Special attention will also be placed on surface and interface effects involving polar surfaces as well as on the role of doped holes in O 2p in charge transfer gap oxides. O 2p holes play an extremely important role in the magnetism and superconductivity of oxides and new results will be presented regarding the ferromagnetic exchange coupling they introduce in transition metal oxides(3). They are also important in describing the interplay between transport properties, magnetic order and the general phase diagrams of materials involving O2p holes either in the so called self doped case of stochiometric oxides like CrO2, in chemically substituted systems, and for cation or anion vacancies. We also present exact results on the spin polaron formation(4,5) and charge propagation of doped Fermions in Ferromagnetic lattices and the pairing interaction due to the magnetic background.

Some relevant publications:

1. I. S. Elfimov, S. Yunoki, and G. A. Sawatzky PRL 89, 216403, (2002)
2. N. Pavlenko, T. Kopp, E.Y. Tsymbal, G.A. Sawatzky, and J. Mannhart PRB 85, 020407, (2012)
3. Bayo Lau, Mona Berciu and George A. Sawatzky, PRL 106, 036401 (2011)
4. Mona Berciu and George A Sawatzky, PRB 79, 195116 (2009)
5. Mirko Moeller, George A. Sawatzky and Mona Berciu PRL 108,216403 (2012) and PRB 86, 075128 (2012)

Quantum melting of stripes

Abstract: We describe a theory of continuous stripe melting quantum phase transitions in two-dimensional metals and the associated Fermi surface reconstruction. Such phase transitions are strongly coupled
but yet theoretically tractable in situations where the stripe ordering is destroyed by proliferating doubled dislocations of the charge stripe order. The resulting non-Landau quantum critical point
has strong stripe fluctuations which we show decouple dynamically from the Fermi surface even though static stripe ordering reconstructs the Fermi surface. We discuss connections to various stripe phenomena in the cuprates. We point out several puzzling aspects of old experimental results [G. Aeppli et al., Science 278 1432 (1997)] on singular stripe fluctuations in the cuprates, and provide a possible
explanation within our theory. These results may thus have been the first observation of non-Landau quantum criticality in an experiment.

Xiao-Gang Wen (Perimeter/MIT)

Symmetry protected topological/trivial (SPT) phases

SPT phases are a new kind of phases at zero-temperature that have a symmetry and a finite energy gap. The SPT phases have the following defining properties: (a) distinct SPT phases with a given symmetry cannot smoothly deform into each other without phase transition, if the deformation preserve the symmetry. (b) however, they all can smoothly deform into the same trivial product state without
phase transition, if we break the symmetry during deformation.

Using the notion of quantum entanglement, we can say that SPT states are short-range entangled states with a symmetry. Haldane phase of spin-1 chain and topological insulators are examples of SPT phases. We will discuss a classification, as well as some examples of the SPT phases in frustrated magnets.