Known unknowns and unknown unknowns - Physics Department ...

Known unknowns and 

unknown unknowns: what can 

theory do for materials 

discovery? 

L e o n B a l e n t s , K I T P , 

UCSB 

It is easier to get into 

something than to get 

out of it 

MbD, UCSB, March 2011

There are known knowns; 

there are things we know we know. 

We also know there are known unknowns; 

that is to say we know there are some things we do not know. 

But there are also unknown unknowns – 

the ones we don't know we don't know. 

2002

There are known knowns; 

there are things we know we know. 

We also know there are known unknowns; 

that is to say we know there are some things we do not know. 

But there are also unknown unknowns – 

the ones we don't know we don't know. 

2002

The ground rules 

While this is perhaps narrow, I will consider 

only electronic materials for fundamental physics. 

I also want to focus on discovery research 

new phenomena, new materials and 

structures 

how can theory really help?

What this talk is not 

Advice on specific materials

Modes of Theory 

“pure” 

theory 

Quantum excitations and fluctuations in Yb2Ti2O7 

1, 2, 3, 4 

us 

1 Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106-9530, etc. 

2 DepartmentofPhysicsandAstronomy, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada 

3 CanadianInstituteforAdvancedResearch, 180 Dundas St. W.,Toronto, Ontario, M5G 1Z8, Canada 

4 BrockhouseInstituteforMaterialsResearch, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada 

(Dated: March 10, 2011) 

A flurry of recent theoretical and experimental work has highlightedexoticphysicsintheclas- 

sical dipolar spin ice compounds, Ho2Ti2O7 and Dy2Ti2O7, whichhavebeenshowntoexhibitan 

emergent “artificial magnetostatics”, manifesting as Coulombicdiffusespincorrelationsandparti- 

cles behaving as diffusive “magneticmonopoles”. Here we discussthe related material Yb2Ti2O7, 

and extract its full set of Hamiltonianparameters from high field inelasticneutron scattering experiments. 

These results show that Yb2Ti2O7 is in fact a highly analog of spin ice. 

Furthermore we show that the Hamiltonianmaysupport a Coulombicquantumspinliquidground 

state in low field, which could explainsomepuzzlingfeatures prior experiments. This is the first 

potentialsightingofaquantumspinliquidstateinamaterial which the spin Hamiltonianis 

quantitativelyknown, and opensthedoortoawiderange of fascinatingphenomenathatuptonow 

have been discussedonlytheoretically. 

Rare earth pyrochlores display a diverse set of fascinating 

physical phenomena. 1 One of the most interesting 

aspects of these materials from the point of view 

of fundamental physics is the strong frustration experiencedbycoupledmagnetic 

moments on this lattice. The 

best explored materials exhibitingthisfrustration are the 

“spin-ice” compounds, Ho2Ti2O7, Dy2Ti2O7, inwhich 

the moments can be regarded as classical spins with a 

strong easy-axis (Ising) anisotropy 2,3 . The frustration of 

these moments resultsinaremarkable classical spin liquid 

regime exhibitingCoulombic correlations and emergent 

“magnetic monopole” excitations that have now 

been studiedextensivelyintheory and experiment 4–6 . 

Strong quantum effectsare absent in the spin ice compounds, 

but can be significant in rare earth pyrochlores 

with easy-plane rather than easy-axis anisotropy. The 

materials Yb2Ti2O7 and Er2Ti2O7 have been identified 

as of this type, and it has recently been argued that 

the spins in these materials are controlled by exchange 

coupling rather than the long-range dipolar interactions 

which dominate in spin ice 11,17 . Because of the strong 

spin-orbit and crystal field effects, the spin dynamics at 

low temperature is dominated by a single Kramers doublet 

formed out of the underlyingJ =7/2 Yb 3+ spins in 

Yb2Ti2O7. This can be consideredas an effective spin 

S =1/2 moment, for which the strongest possible quantum 

effects are expected. This makes these materials 

nearly uniqueexamplesof strongly quantum magnets on 

the highly frustrated pyrochlore lattice. They are also 

nearly ideal subjects for detailed experimental investigation, 

existing as they do in large high purity single 

crystals, and with large magnetic moments amenable to 

neutron scatteringstudies. 

Theoretical studies have pointed to the likelihoodof 

unusual ground states of quantum antiferromagnets on 

the pyrochlore lattice. Most excitingisthepossibilityof 

a quantum spin liquid (QSL) state, which avoids magnetic 

orderingand freezingevenat absolute zero temper- 

FIG. 1. (color online) The measured S(Q,ω) atT=30mK, 

sliced along various directions in the [HHL] plane, for both 

µ0H=5T (first row) and µ0H=2T (third row). The second 

and fourth row show the calculatedspectrum for these two 

field strengths, based on an anisotropic exchangemodelwith 

five free parameters (see text) that were extracted by fitting 

to the 5T data set. For a realisticcomparison to the data, the 

calculated S(Q,ω) is convolutedwithagaussianoffull-width 

0.09meV. Both the 2T and 5T data sets, comprised of spin 

wave dispersions along five different directions, are described 

extremely well by the same parameters. 

ature, and whose elementary excitations carry fractional 

quantum numbersand are decidedlydifferentfrom spin 

waves 7 . Intriguingly, neutron scattering measurements 

have reported a lack of magnetic ordering and the absence 

of spin waves in Yb2Ti2O7 at low fields 8,9 . In a 

recent study, sharp spin waves emerged whenamagnetic 

field of 0.5T or larger was applied, suggesting that the 

systemtransitioned into a conventional state 9 . The pos- 

phenomenology 

(~model theory) 

WIEN2k 

ab initio 

VASP


“pure” 

theory 


1, 2, 3, 4 

us 










































































phenomenology 


ab initio 

This tends to be 

heavily represented in 

materials efforts 

WIEN2k 

VASP


“pure” 

theory 


1, 2, 3, 4 

us 










































































phenomenology 


WIEN2k 

ab initio 

VASP 

Balance of all these modes is essential to materials discovery, 

and the proper balance is not weighted to the right!

major discoveries 

from theory? 

High Tc cuprates 

Fe-based SCs 

(F)QHE 

CMR 

graphene 

topological insulators

Topological 

Insulators 

300 

225 

papers in WOS 

150 

75 

0 

2005 2006 2007 2008 2009 2010 

publication year

Topological 

Insulators 

300 

225 

papers in WOS 

150 

2d 

Discovery 

3d 

75 

0 

2005 2006 2007 2008 2009 2010 

publication year

1, 2, 3, 4 us 

Topological 

Insulators 

300 

225 

papers in WOS 

150 

2d 

Discovery 

3d 

75 

0 

2005 2006 2007 2008 2009 2010 







A flu ry of recen theoretical and experimental work has highlightedexoticphysicsintheclas- 

sical dipolar spin ice compounds, Ho2Ti2O7 and Dy2Ti2O7, whic havebeenshowntoexhibitan 

emergent “artificial magnetostatics”, manifesting as Coulombicdiffusespincorelationsandparti- 

cles behaving as diffusive “magneticmonopoles”. Here we discu s the related material Yb2Ti2O7, 

and extract its fu l set of Hamiltonianparameters from high field inelasticneutron sca tering experiments. 


Furthermore we show tha the Hamiltonianmaysupport a Coulombicquantumspinliquidground 



quantitativelyknown, and opensthedoortoawiderange o fascinatingphenomenathatuptonow 

have been discu sed only theoretica ly. 











regim exhibitingCoulombi correlations and emergent 




but can be significant in rar earth pyrochlores 




the spins in these materials are contro led by exchange 









nearly uniqu examplesof strongly quantum magnets on 









a quantum spin liquid (QSL) state, which avoids magderingand 

freezingevenat absolute zero temper- 






five free parameters (see text) that wer extracted by fi ting 

to the 5T data set. For a realisti comparison to the data, the 

calculated S(Q,ω) is convolutedwithagausianoffu l-width 



extremely we l by the same parameters. 

ature, and whos elementary excitations carry fractional 








publication year

1, 2, 3, 4 us 

Topological 

Insulators 

300 

225 

papers in WOS 

150 

2d 

Discovery 

3d 

75 

0 

2005 2006 2007 2008 2009 2010 







A flu ry of recen theoretical and experimental work has highlightedexoticphysicsintheclas- 

sical dipolar spin ice compounds, Ho2Ti2O7 and Dy2Ti2O7, whic havebeenshowntoexhibitan 

emergent “artificial magnetostatics”, manifesting as Coulombicdiffusespincorelationsandparti- 

cles behaving as diffusive “magneticmonopoles”. Here we discu s the related material Yb2Ti2O7, 

and extract its fu l set of Hamiltonianparameters from high field inelasticneutron sca tering experiments. 


Furthermore we show tha the Hamiltonianmaysupport a Coulombicquantumspinliquidground 



quantitativelyknown, and opensthedoortoawiderange o fascinatingphenomenathatuptonow 

have been discu sed only theoretica ly. 











regim exhibitingCoulombi correlations and emergent 




but can be significant in rar earth pyrochlores 




the spins in these materials are contro led by exchange 









nearly uniqu examplesof strongly quantum magnets on 









a quantum spin liquid (QSL) state, which avoids magderingand 

freezingevenat absolute zero temper- 






five free parameters (see text) that wer extracted by fi ting 

to the 5T data set. For a realisti comparison to the data, the 

calculated S(Q,ω) is convolutedwithagausianoffu l-width 



extremely we l by the same parameters. 

ature, and whos elementary excitations carry fractional 








publication year

Why did it work? 

Very clear thinking by key theorists 

obviously correct and qualitatively new 

clear testable predictions made




clear testable predictions made 

Not correlated materials: traditional solid 

state physics methods apply

WIEN2k 

VASP 




clear testable predictions made 

Not correlated materials: traditional solid 

state physics methods apply 

theorists showed how to test for TIs in 

DFT calculation

TIs became the 

known unknowns

and now ab initio 

methods can be 

very productive

But the key step 

was the idea and 

the theory of how 

to search for TIs

What about the 

unknown 

unknowns?

Unknown unknowns 

We expect that the success of TIs in detailed 

prediction is an exception rather than the rule 

Better for theory to be more of a guide to 

materials classes than a detailed predictor 

In this case model-based theory is more 

informative because it gives direct intuition 

and dependence on essential parameters 

Some examples show how this can work

Ex. 1: Mott 

Interfaces 

Area has exploded since Hwang+Muller 

publicized it ~2002 

Vast majority of theory is ab initio 

H. Ohtomo et al, 2002

00.016404 PACS numbers: 71.27.+a, 74.78.Fk, 75.30.Et 

arch, cuprates remain 

the high-temperature 

ical grounds, the key 

that support high T c 

degeneracy, spin one- 

, and strong antiferrothese 

properties are 

ls (e.g., layered cobalhem. 

uprates is the presence 

& & 0:20 where the 

lane-wave–localizedand 

spin statistics may 

gy scales. The multiin 

an exotic ‘‘normal’’ 

quasiparticles, pseuthe 

superconducting 

of strongly correlated 

23d ions as Ti 3 and 

, Co 4 (a t 2g hole) and 

lectron) that possess a 

onment. These comhysical 

properties [1]; 

tal phase from which 

ng. 

bital degeneracy is ‘‘to 

igh symmetry of the 

ilding block of both 

s,—the orbital degend 

relaxes kinematical 

onsequently, a fermiing 

induced insulatorference 

to the pseudo- 

TiO 3 the formation of 

completes within just 

0:05 [2]. 

duces AF correlations 

ysics), as electrons are 

ng on the different orthat 

result in a rich variety of magnetic states in S 1=2 

oxides such as RTiO 3 , Na x CoO 2 , Sr 2 CoO 4 , RNiO 3 , 

NaNiO 2 . In contrast, spin correlations in single-band cuprates 

are of AF nature exclusively and hence strong. 

Mott Interfaces 

How to suppress the orbital degeneracy and promote 

cupratelike physics in other S 1=2 oxides? In this 

Letter, we suggest and argue theoretically that this goal 

can be achieved in oxide superlattices. Specifically, we 

focus on Ni-based superlattices (see Fig. 1) which can be 

fabricated using recent advances in oxide heterostructure 

But technology the ([3–5] most and references influential therein). While the proposed 

compound has a pseudocubic ABO 3 structure, its 

theory paper - which 

low-energy electronic states are confined to the NiO 

really galvanized experiment 2 

- is 

planes and, hence, are of a quasi-2D nature. A substrate 

induced compression of the NiO 

phenomenological 

6 octahedra further stabilizes 

the x 2 -y 2 orbital. Net effect is a strong enhancement of 

(a) 

MO 2 

LaO 

NiO 2 

LaO 

MO 2 

a 

c 

b 

(b) 

(c) 

(d) 

substrate 

FIG. 1. (a) Superlattice La 2 NiMO 6 with alternating NiO 2 and 

MO 2 planes. MO 2 layers suppress the c-axis hopping resulting in 

2D electronic structure. Chaloupka Arrows indicate+ 

the c-axis compression 

of the NiO 6 octahedron imposed by tensile epitaxial strain and 

supported by Jahn-Teller Khaliullin, coupling. (b) 2008 ,(c), (d) Strain-induced 

stretching of the NiO 2 planes occurs when superlattices with 

M Al, Ga, Ti are grown on SrTiO 3 or LaGaO 3 substrates 

having large lattice parameter compared to that of LaNiO 3 . 

Al 

Ni 

Ga 

Ni 

Ti 

Ni 


1, 2, 3, 4 

us 























































Keimer 












Khaliullin 








systemtransitioned into a conventional state 9 . The pos-

00.016404 PACS numbers: 71.27.+a, 74.78.Fk, 75.30.Et 

arch, cuprates remain 

the high-temperature 

ical grounds, the key 

that support high T c 

degeneracy, spin one- 

, and strong antiferrothese 

properties are 

ls (e.g., layered cobalhem. 

uprates is the presence 

& & 0:20 where the 

lane-wave–localizedand 

spin statistics may 

gy scales. The multiin 

an exotic ‘‘normal’’ 

quasiparticles, pseuthe 

superconducting 

of strongly correlated 

23d ions as Ti 3 and 

, Co 4 (a t 2g hole) and 

lectron) that possess a 

onment. These comhysical 

properties [1]; 

tal phase from which 

ng. 

bital degeneracy is ‘‘to 

igh symmetry of the 

ilding block of both 

s,—the orbital degend 

relaxes kinematical 

onsequently, a fermiing 

induced insulatorference 

to the pseudo- 

TiO 3 the formation of 

completes within just 

0:05 [2]. 

duces AF correlations 

ysics), as electrons are 

ng on the different orthat 

result in a rich variety of magnetic states in S 1=2 

oxides such as RTiO 3 , Na x CoO 2 , Sr 2 CoO 4 , RNiO 3 , 

NaNiO 2 . In contrast, spin correlations in single-band cuprates 

are of AF nature exclusively and hence strong. 

Mott Interfaces 

How to suppress the orbital degeneracy and promote 

cupratelike physics in other S 1=2 oxides? In this 

Letter, we suggest and argue theoretically that this goal 

can be achieved in oxide superlattices. Specifically, we 

focus on Ni-based superlattices (see Fig. 1) which can be 

fabricated using recent advances in oxide heterostructure 

But technology the ([3–5] most and references influential therein). While the proposed 

compound has a pseudocubic ABO 3 structure, its 

theory paper - which 

low-energy electronic states are confined to the NiO 

really galvanized experiment 2 

- is 

planes and, hence, are of a quasi-2D nature. A substrate 

induced compression of the NiO 

phenomenological 

6 octahedra further stabilizes 

the x 2 -y 2 orbital. Net effect is a strong enhancement of 

(a) 

MO 2 

LaO 

NiO 2 

LaO 

MO 2 

a 

c 

b 

(b) 

(c) 

(d) 

substrate 

FIG. 1. (a) Superlattice La 2 NiMO 6 with alternating NiO 2 and 

MO 2 planes. MO 2 layers suppress the c-axis hopping resulting in 

2D electronic structure. Chaloupka Arrows indicate+ 

the c-axis compression 

of the NiO 6 octahedron imposed by tensile epitaxial strain and 

supported by Jahn-Teller Khaliullin, coupling. (b) 2008 ,(c), (d) Strain-induced 

stretching of the NiO 2 planes occurs when superlattices with 

M Al, Ga, Ti are grown on SrTiO 3 or LaGaO 3 substrates 

having large lattice parameter compared to that of LaNiO 3 . 

Al 

Ni 

Ga 

Ni 

Ti 

Ni 

c.f. S. Stemmer 

6pm today

Ex.2: Quantum Spin 

Liquids 

Ψ = 

Anderson 1973: a material with localized 

electrons where the spins never order but 

instead form “resonating valence bonds” 

Expected to have many exotic properties 

(spin-charge separation, etc) and may be a 

good platform for quantum computing 

c.f. L.B., Nature 464,199 (2010)

Ex.2: Quantum Spin 

Liquids 

But...the candidate materials are hard to 

model, and DFT (even DMFT) fails to 

describe ground state properties 

These local moment systems usually have 

some exchange model description (and it is 

useful!) 

but: this is not known and really hard to 

calculate from first principles 

c.f. L.B., Nature 464,199 (2010)

Be precise. A lack of 

precision is dangerous 

when the margin of error 

is small 

J

Yb2Ti2O7 








systemtransitioned into a conventional state 9 . The possingle 

crystals 

crucial! 

Complete phenomenological Hamiltonian can 

be quantitatively extracted from INS with 

B=5T 


The first QSL candidate where H is known! 

K. Ross, L. Savary, B. Gaulin, and LB, in preparation 

1, 2, 3, 4 us 

































































extremely well by the same parameters.

Ex. 3: SOC 

+Interactions 

Schematic phase diagram from Pesin 

+Balents, 2010 

heavily influenced by experiments and 

materials grown and studied by Y. Maeno, 

Y. Matsuhira, H. Takagi, Y. Tokura, B.-J. 

Kim, G. Cao

Ex. 3: SOC 

+Interactions 

Schematic phase diagram from Pesin 

+Balents, 2010 

U/t 

“traditional” Mott 

insulators 

strong SO Mott 

insulators 

“simple” 

materials 

TIs, SO-semimetals 

λ/t

What and where? 

Most important thing is intuition 

correlations: d electrons 

strong SOC: 4d or 5d and orbital 

degeneracy 

U/W is crucial parameter 

Must choose carefully because for 4d+5d’s, 

U/W is usually smallish

What and Where? 

Iridates: λ ~ U ~ t and favorable (t2g) 5 

configuration: Ln2Ir2O7, Sr2IrO4, Na2IrO3,... 

Topological Mott insulator, topological 3d 

Dirac semimetal, magnetic topological 

insulator, high T c superconductor, Kitaev spin 

liquid... 

Double perovskites: anomalously low bandwidth: 

Ba2YMoO6, Ba2LiOsO6, Sr2MgReO6, ... 

Multipolar order, quantum spin liquid...

Recommendations 

Pure theory and phenomenology are at least 

as important in materials discovery as ab initio 

Really works best when theory and growth/ 

measurement work closely together 

Theorists need to be trained in how to 

develop models for new materials

Recommendations 

Pure theory and phenomenology are at least 

as important in materials discovery as ab initio 

Really works best when theory and growth/ 

measurement work closely together 

Theorists need to be trained in how to 

develop models for new materials 

If you are not criticized, 

you may not be doing 

much

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