Known unknowns and unknown unknowns - Physics Department ...
Known unknowns and unknown unknowns - Physics Department ... 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
- Page 2 and 3: There are known knowns; there are t
- Page 4 and 5: The ground rules While this is perh
- Page 6 and 7: Modes of Theory “pure” theory Q
- Page 8 and 9: Modes of Theory “pure” theory Q
- Page 10 and 11: Topological Insulators 300 225 pape
- Page 12 and 13: 1, 2, 3, 4 us Topological Insulator
- Page 14 and 15: Why did it work? Very clear thinkin
- Page 16 and 17: WIEN2k VASP Why did it work? Very c
- Page 18 and 19: and now ab initio methods can be ve
- Page 20 and 21: What about the unknown unknowns?
- Page 22 and 23: Ex. 1: Mott Interfaces Area has exp
- Page 24 and 25: 00.016404 PACS numbers: 71.27.+a, 7
- Page 26 and 27: Ex.2: Quantum Spin Liquids But...th
- Page 28 and 29: Yb2Ti2O7 ature, and whose elementar
- Page 30 and 31: Ex. 3: SOC +Interactions Schematic
- Page 32 and 33: What and Where? Iridates: λ ~ U ~
- Page 34: Recommendations Pure theory and phe
<strong>Known</strong> <strong><strong>unknown</strong>s</strong> <strong>and</strong><br />
<strong>unknown</strong> <strong><strong>unknown</strong>s</strong>: what can<br />
theory do for materials<br />
discovery?<br />
L e o n B a l e n t s , K I T P ,<br />
UCSB<br />
It is easier to get into<br />
something than to get<br />
out of it<br />
MbD, UCSB, March 2011
There are known knowns;<br />
there are things we know we know.<br />
We also know there are known <strong><strong>unknown</strong>s</strong>;<br />
that is to say we know there are some things we do not know.<br />
But there are also <strong>unknown</strong> <strong><strong>unknown</strong>s</strong> –<br />
the ones we don't know we don't know.<br />
2002
There are known knowns;<br />
there are things we know we know.<br />
We also know there are known <strong><strong>unknown</strong>s</strong>;<br />
that is to say we know there are some things we do not know.<br />
But there are also <strong>unknown</strong> <strong><strong>unknown</strong>s</strong> –<br />
the ones we don't know we don't know.<br />
2002
The ground rules<br />
While this is perhaps narrow, I will consider<br />
only electronic materials for fundamental physics.<br />
I also want to focus on discovery research<br />
new phenomena, new materials <strong>and</strong><br />
structures<br />
how can theory really help?
What this talk is not<br />
Advice on specific materials
Modes of Theory<br />
“pure”<br />
theory<br />
Quantum excitations <strong>and</strong> fluctuations in Yb2Ti2O7<br />
1, 2, 3, 4<br />
us<br />
1 Kavli Institute for Theoretical <strong>Physics</strong>, University of California, Santa Barbara, CA, 93106-9530, etc.<br />
2 <strong>Department</strong>of<strong>Physics</strong><strong>and</strong>Astronomy, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada<br />
3 CanadianInstituteforAdvancedResearch, 180 Dundas St. W.,Toronto, Ontario, M5G 1Z8, Canada<br />
4 BrockhouseInstituteforMaterialsResearch, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada<br />
(Dated: March 10, 2011)<br />
A flurry of recent theoretical <strong>and</strong> experimental work has highlightedexoticphysicsintheclas-<br />
sical dipolar spin ice compounds, Ho2Ti2O7 <strong>and</strong> Dy2Ti2O7, whichhavebeenshowntoexhibitan<br />
emergent “artificial magnetostatics”, manifesting as Coulombicdiffusespincorrelations<strong>and</strong>parti-<br />
cles behaving as diffusive “magneticmonopoles”. Here we discussthe related material Yb2Ti2O7,<br />
<strong>and</strong> extract its full set of Hamiltonianparameters from high field inelasticneutron scattering experiments.<br />
These results show that Yb2Ti2O7 is in fact a highly analog of spin ice.<br />
Furthermore we show that the Hamiltonianmaysupport a Coulombicquantumspinliquidground<br />
state in low field, which could explainsomepuzzlingfeatures prior experiments. This is the first<br />
potentialsightingofaquantumspinliquidstateinamaterial which the spin Hamiltonianis<br />
quantitativelyknown, <strong>and</strong> opensthedoortoawiderange of fascinatingphenomenathatuptonow<br />
have been discussedonlytheoretically.<br />
Rare earth pyrochlores display a diverse set of fascinating<br />
physical phenomena. 1 One of the most interesting<br />
aspects of these materials from the point of view<br />
of fundamental physics is the strong frustration experiencedbycoupledmagnetic<br />
moments on this lattice. The<br />
best explored materials exhibitingthisfrustration are the<br />
“spin-ice” compounds, Ho2Ti2O7, Dy2Ti2O7, inwhich<br />
the moments can be regarded as classical spins with a<br />
strong easy-axis (Ising) anisotropy 2,3 . The frustration of<br />
these moments resultsinaremarkable classical spin liquid<br />
regime exhibitingCoulombic correlations <strong>and</strong> emergent<br />
“magnetic monopole” excitations that have now<br />
been studiedextensivelyintheory <strong>and</strong> experiment 4–6 .<br />
Strong quantum effectsare absent in the spin ice compounds,<br />
but can be significant in rare earth pyrochlores<br />
with easy-plane rather than easy-axis anisotropy. The<br />
materials Yb2Ti2O7 <strong>and</strong> Er2Ti2O7 have been identified<br />
as of this type, <strong>and</strong> it has recently been argued that<br />
the spins in these materials are controlled by exchange<br />
coupling rather than the long-range dipolar interactions<br />
which dominate in spin ice 11,17 . Because of the strong<br />
spin-orbit <strong>and</strong> crystal field effects, the spin dynamics at<br />
low temperature is dominated by a single Kramers doublet<br />
formed out of the underlyingJ =7/2 Yb 3+ spins in<br />
Yb2Ti2O7. This can be consideredas an effective spin<br />
S =1/2 moment, for which the strongest possible quantum<br />
effects are expected. This makes these materials<br />
nearly uniqueexamplesof strongly quantum magnets on<br />
the highly frustrated pyrochlore lattice. They are also<br />
nearly ideal subjects for detailed experimental investigation,<br />
existing as they do in large high purity single<br />
crystals, <strong>and</strong> with large magnetic moments amenable to<br />
neutron scatteringstudies.<br />
Theoretical studies have pointed to the likelihoodof<br />
unusual ground states of quantum antiferromagnets on<br />
the pyrochlore lattice. Most excitingisthepossibilityof<br />
a quantum spin liquid (QSL) state, which avoids magnetic<br />
ordering<strong>and</strong> freezingevenat absolute zero temper-<br />
FIG. 1. (color online) The measured S(Q,ω) atT=30mK,<br />
sliced along various directions in the [HHL] plane, for both<br />
µ0H=5T (first row) <strong>and</strong> µ0H=2T (third row). The second<br />
<strong>and</strong> fourth row show the calculatedspectrum for these two<br />
field strengths, based on an anisotropic exchangemodelwith<br />
five free parameters (see text) that were extracted by fitting<br />
to the 5T data set. For a realisticcomparison to the data, the<br />
calculated S(Q,ω) is convolutedwithagaussianoffull-width<br />
0.09meV. Both the 2T <strong>and</strong> 5T data sets, comprised of spin<br />
wave dispersions along five different directions, are described<br />
extremely well by the same parameters.<br />
ature, <strong>and</strong> whose elementary excitations carry fractional<br />
quantum numbers<strong>and</strong> are decidedlydifferentfrom spin<br />
waves 7 . Intriguingly, neutron scattering measurements<br />
have reported a lack of magnetic ordering <strong>and</strong> the absence<br />
of spin waves in Yb2Ti2O7 at low fields 8,9 . In a<br />
recent study, sharp spin waves emerged whenamagnetic<br />
field of 0.5T or larger was applied, suggesting that the<br />
systemtransitioned into a conventional state 9 . The pos-<br />
phenomenology<br />
(~model theory)<br />
WIEN2k<br />
ab initio<br />
VASP
Modes of Theory<br />
“pure”<br />
theory<br />
Quantum excitations <strong>and</strong> fluctuations in Yb2Ti2O7<br />
1, 2, 3, 4<br />
us<br />
1 Kavli Institute for Theoretical <strong>Physics</strong>, University of California, Santa Barbara, CA, 93106-9530, etc.<br />
2 <strong>Department</strong>of<strong>Physics</strong><strong>and</strong>Astronomy, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada<br />
3 CanadianInstituteforAdvancedResearch, 180 Dundas St. W.,Toronto, Ontario, M5G 1Z8, Canada<br />
4 BrockhouseInstituteforMaterialsResearch, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada<br />
(Dated: March 10, 2011)<br />
A flurry of recent theoretical <strong>and</strong> experimental work has highlightedexoticphysicsintheclas-<br />
sical dipolar spin ice compounds, Ho2Ti2O7 <strong>and</strong> Dy2Ti2O7, whichhavebeenshowntoexhibitan<br />
emergent “artificial magnetostatics”, manifesting as Coulombicdiffusespincorrelations<strong>and</strong>parti-<br />
cles behaving as diffusive “magneticmonopoles”. Here we discussthe related material Yb2Ti2O7,<br />
<strong>and</strong> extract its full set of Hamiltonianparameters from high field inelasticneutron scattering experiments.<br />
These results show that Yb2Ti2O7 is in fact a highly analog of spin ice.<br />
Furthermore we show that the Hamiltonianmaysupport a Coulombicquantumspinliquidground<br />
state in low field, which could explainsomepuzzlingfeatures prior experiments. This is the first<br />
potentialsightingofaquantumspinliquidstateinamaterial which the spin Hamiltonianis<br />
quantitativelyknown, <strong>and</strong> opensthedoortoawiderange of fascinatingphenomenathatuptonow<br />
have been discussedonlytheoretically.<br />
Rare earth pyrochlores display a diverse set of fascinating<br />
physical phenomena. 1 One of the most interesting<br />
aspects of these materials from the point of view<br />
of fundamental physics is the strong frustration experiencedbycoupledmagnetic<br />
moments on this lattice. The<br />
best explored materials exhibitingthisfrustration are the<br />
“spin-ice” compounds, Ho2Ti2O7, Dy2Ti2O7, inwhich<br />
the moments can be regarded as classical spins with a<br />
strong easy-axis (Ising) anisotropy 2,3 . The frustration of<br />
these moments resultsinaremarkable classical spin liquid<br />
regime exhibitingCoulombic correlations <strong>and</strong> emergent<br />
“magnetic monopole” excitations that have now<br />
been studiedextensivelyintheory <strong>and</strong> experiment 4–6 .<br />
Strong quantum effectsare absent in the spin ice compounds,<br />
but can be significant in rare earth pyrochlores<br />
with easy-plane rather than easy-axis anisotropy. The<br />
materials Yb2Ti2O7 <strong>and</strong> Er2Ti2O7 have been identified<br />
as of this type, <strong>and</strong> it has recently been argued that<br />
the spins in these materials are controlled by exchange<br />
coupling rather than the long-range dipolar interactions<br />
which dominate in spin ice 11,17 . Because of the strong<br />
spin-orbit <strong>and</strong> crystal field effects, the spin dynamics at<br />
low temperature is dominated by a single Kramers doublet<br />
formed out of the underlyingJ =7/2 Yb 3+ spins in<br />
Yb2Ti2O7. This can be consideredas an effective spin<br />
S =1/2 moment, for which the strongest possible quantum<br />
effects are expected. This makes these materials<br />
nearly uniqueexamplesof strongly quantum magnets on<br />
the highly frustrated pyrochlore lattice. They are also<br />
nearly ideal subjects for detailed experimental investigation,<br />
existing as they do in large high purity single<br />
crystals, <strong>and</strong> with large magnetic moments amenable to<br />
neutron scatteringstudies.<br />
Theoretical studies have pointed to the likelihoodof<br />
unusual ground states of quantum antiferromagnets on<br />
the pyrochlore lattice. Most excitingisthepossibilityof<br />
a quantum spin liquid (QSL) state, which avoids magnetic<br />
ordering<strong>and</strong> freezingevenat absolute zero temper-<br />
FIG. 1. (color online) The measured S(Q,ω) atT=30mK,<br />
sliced along various directions in the [HHL] plane, for both<br />
µ0H=5T (first row) <strong>and</strong> µ0H=2T (third row). The second<br />
<strong>and</strong> fourth row show the calculatedspectrum for these two<br />
field strengths, based on an anisotropic exchangemodelwith<br />
five free parameters (see text) that were extracted by fitting<br />
to the 5T data set. For a realisticcomparison to the data, the<br />
calculated S(Q,ω) is convolutedwithagaussianoffull-width<br />
0.09meV. Both the 2T <strong>and</strong> 5T data sets, comprised of spin<br />
wave dispersions along five different directions, are described<br />
extremely well by the same parameters.<br />
ature, <strong>and</strong> whose elementary excitations carry fractional<br />
quantum numbers<strong>and</strong> are decidedlydifferentfrom spin<br />
waves 7 . Intriguingly, neutron scattering measurements<br />
have reported a lack of magnetic ordering <strong>and</strong> the absence<br />
of spin waves in Yb2Ti2O7 at low fields 8,9 . In a<br />
recent study, sharp spin waves emerged whenamagnetic<br />
field of 0.5T or larger was applied, suggesting that the<br />
systemtransitioned into a conventional state 9 . The pos-<br />
phenomenology<br />
(~model theory)<br />
ab initio<br />
This tends to be<br />
heavily represented in<br />
materials efforts<br />
WIEN2k<br />
VASP
Modes of Theory<br />
“pure”<br />
theory<br />
Quantum excitations <strong>and</strong> fluctuations in Yb2Ti2O7<br />
1, 2, 3, 4<br />
us<br />
1 Kavli Institute for Theoretical <strong>Physics</strong>, University of California, Santa Barbara, CA, 93106-9530, etc.<br />
2 <strong>Department</strong>of<strong>Physics</strong><strong>and</strong>Astronomy, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada<br />
3 CanadianInstituteforAdvancedResearch, 180 Dundas St. W.,Toronto, Ontario, M5G 1Z8, Canada<br />
4 BrockhouseInstituteforMaterialsResearch, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada<br />
(Dated: March 10, 2011)<br />
A flurry of recent theoretical <strong>and</strong> experimental work has highlightedexoticphysicsintheclas-<br />
sical dipolar spin ice compounds, Ho2Ti2O7 <strong>and</strong> Dy2Ti2O7, whichhavebeenshowntoexhibitan<br />
emergent “artificial magnetostatics”, manifesting as Coulombicdiffusespincorrelations<strong>and</strong>parti-<br />
cles behaving as diffusive “magneticmonopoles”. Here we discussthe related material Yb2Ti2O7,<br />
<strong>and</strong> extract its full set of Hamiltonianparameters from high field inelasticneutron scattering experiments.<br />
These results show that Yb2Ti2O7 is in fact a highly analog of spin ice.<br />
Furthermore we show that the Hamiltonianmaysupport a Coulombicquantumspinliquidground<br />
state in low field, which could explainsomepuzzlingfeatures prior experiments. This is the first<br />
potentialsightingofaquantumspinliquidstateinamaterial which the spin Hamiltonianis<br />
quantitativelyknown, <strong>and</strong> opensthedoortoawiderange of fascinatingphenomenathatuptonow<br />
have been discussedonlytheoretically.<br />
Rare earth pyrochlores display a diverse set of fascinating<br />
physical phenomena. 1 One of the most interesting<br />
aspects of these materials from the point of view<br />
of fundamental physics is the strong frustration experiencedbycoupledmagnetic<br />
moments on this lattice. The<br />
best explored materials exhibitingthisfrustration are the<br />
“spin-ice” compounds, Ho2Ti2O7, Dy2Ti2O7, inwhich<br />
the moments can be regarded as classical spins with a<br />
strong easy-axis (Ising) anisotropy 2,3 . The frustration of<br />
these moments resultsinaremarkable classical spin liquid<br />
regime exhibitingCoulombic correlations <strong>and</strong> emergent<br />
“magnetic monopole” excitations that have now<br />
been studiedextensivelyintheory <strong>and</strong> experiment 4–6 .<br />
Strong quantum effectsare absent in the spin ice compounds,<br />
but can be significant in rare earth pyrochlores<br />
with easy-plane rather than easy-axis anisotropy. The<br />
materials Yb2Ti2O7 <strong>and</strong> Er2Ti2O7 have been identified<br />
as of this type, <strong>and</strong> it has recently been argued that<br />
the spins in these materials are controlled by exchange<br />
coupling rather than the long-range dipolar interactions<br />
which dominate in spin ice 11,17 . Because of the strong<br />
spin-orbit <strong>and</strong> crystal field effects, the spin dynamics at<br />
low temperature is dominated by a single Kramers doublet<br />
formed out of the underlyingJ =7/2 Yb 3+ spins in<br />
Yb2Ti2O7. This can be consideredas an effective spin<br />
S =1/2 moment, for which the strongest possible quantum<br />
effects are expected. This makes these materials<br />
nearly uniqueexamplesof strongly quantum magnets on<br />
the highly frustrated pyrochlore lattice. They are also<br />
nearly ideal subjects for detailed experimental investigation,<br />
existing as they do in large high purity single<br />
crystals, <strong>and</strong> with large magnetic moments amenable to<br />
neutron scatteringstudies.<br />
Theoretical studies have pointed to the likelihoodof<br />
unusual ground states of quantum antiferromagnets on<br />
the pyrochlore lattice. Most excitingisthepossibilityof<br />
a quantum spin liquid (QSL) state, which avoids magnetic<br />
ordering<strong>and</strong> freezingevenat absolute zero temper-<br />
FIG. 1. (color online) The measured S(Q,ω) atT=30mK,<br />
sliced along various directions in the [HHL] plane, for both<br />
µ0H=5T (first row) <strong>and</strong> µ0H=2T (third row). The second<br />
<strong>and</strong> fourth row show the calculatedspectrum for these two<br />
field strengths, based on an anisotropic exchangemodelwith<br />
five free parameters (see text) that were extracted by fitting<br />
to the 5T data set. For a realisticcomparison to the data, the<br />
calculated S(Q,ω) is convolutedwithagaussianoffull-width<br />
0.09meV. Both the 2T <strong>and</strong> 5T data sets, comprised of spin<br />
wave dispersions along five different directions, are described<br />
extremely well by the same parameters.<br />
ature, <strong>and</strong> whose elementary excitations carry fractional<br />
quantum numbers<strong>and</strong> are decidedlydifferentfrom spin<br />
waves 7 . Intriguingly, neutron scattering measurements<br />
have reported a lack of magnetic ordering <strong>and</strong> the absence<br />
of spin waves in Yb2Ti2O7 at low fields 8,9 . In a<br />
recent study, sharp spin waves emerged whenamagnetic<br />
field of 0.5T or larger was applied, suggesting that the<br />
systemtransitioned into a conventional state 9 . The pos-<br />
phenomenology<br />
(~model theory)<br />
WIEN2k<br />
ab initio<br />
VASP<br />
Balance of all these modes is essential to materials discovery,<br />
<strong>and</strong> the proper balance is not weighted to the right!
major discoveries<br />
from theory?<br />
High Tc cuprates<br />
Fe-based SCs<br />
(F)QHE<br />
CMR<br />
graphene<br />
topological insulators
Topological<br />
Insulators<br />
300<br />
225<br />
papers in WOS<br />
150<br />
75<br />
0<br />
2005 2006 2007 2008 2009 2010<br />
publication year
Topological<br />
Insulators<br />
300<br />
225<br />
papers in WOS<br />
150<br />
2d<br />
Discovery<br />
3d<br />
75<br />
0<br />
2005 2006 2007 2008 2009 2010<br />
publication year
1, 2, 3, 4 us<br />
Topological<br />
Insulators<br />
300<br />
225<br />
papers in WOS<br />
150<br />
2d<br />
Discovery<br />
3d<br />
75<br />
0<br />
2005 2006 2007 2008 2009 2010<br />
Quantum excitations <strong>and</strong> fluctuations in Yb2Ti2O7<br />
1 Kavli Institute for Theoretical <strong>Physics</strong>, University of California, Santa Barbara, CA, 93106-9530, etc.<br />
2 <strong>Department</strong>of<strong>Physics</strong><strong>and</strong>Astronomy, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada<br />
3 CanadianInstituteforAdvancedResearch, 180 Dundas St. W.,Toronto, Ontario, M5G 1Z8, Canada<br />
4 BrockhouseInstituteforMaterialsResearch, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada<br />
(Dated: March 10, 2011)<br />
A flu ry of recen theoretical <strong>and</strong> experimental work has highlightedexoticphysicsintheclas-<br />
sical dipolar spin ice compounds, Ho2Ti2O7 <strong>and</strong> Dy2Ti2O7, whic havebeenshowntoexhibitan<br />
emergent “artificial magnetostatics”, manifesting as Coulombicdiffusespincorelations<strong>and</strong>parti-<br />
cles behaving as diffusive “magneticmonopoles”. Here we discu s the related material Yb2Ti2O7,<br />
<strong>and</strong> extract its fu l set of Hamiltonianparameters from high field inelasticneutron sca tering experiments.<br />
These results show that Yb2Ti2O7 is in fact a highly analog of spin ice.<br />
Furthermore we show tha the Hamiltonianmaysupport a Coulombicquantumspinliquidground<br />
state in low field, which could explainsomepuzzlingfeatures prior experiments. This is the first<br />
potentialsightingofaquantumspinliquidstateinamaterial which the spin Hamiltonianis<br />
quantitativelyknown, <strong>and</strong> opensthedoortoawiderange o fascinatingphenomenathatuptonow<br />
have been discu sed only theoretica ly.<br />
Rare earth pyrochlores display a diverse set of fascinating<br />
physical phenomena. 1 One of the most interesting<br />
aspects of these materials from the point of view<br />
of fundamental physics is the strong frustration experiencedbycoupledmagnetic<br />
moments on this lattice. The<br />
best explored materials exhibitingthisfrustration are the<br />
“spin-ice” compounds, Ho2Ti2O7, Dy2Ti2O7, inwhich<br />
the moments can be regarded as classical spins with a<br />
strong easy-axis (Ising) anisotropy 2,3 . The frustration of<br />
these moments resultsinaremarkable classical spin liquid<br />
regim exhibitingCoulombi correlations <strong>and</strong> emergent<br />
“magnetic monopole” excitations that have now<br />
been studiedextensivelyintheory <strong>and</strong> experiment 4–6 .<br />
Strong quantum effectsare absent in the spin ice compounds,<br />
but can be significant in rar earth pyrochlores<br />
with easy-plane rather than easy-axis anisotropy. The<br />
materials Yb2Ti2O7 <strong>and</strong> Er2Ti2O7 have been identified<br />
as of this type, <strong>and</strong> it has recently been argued that<br />
the spins in these materials are contro led by exchange<br />
coupling rather than the long-range dipolar interactions<br />
which dominate in spin ice 11,17 . Because of the strong<br />
spin-orbit <strong>and</strong> crystal field effects, the spin dynamics at<br />
low temperature is dominated by a single Kramers doublet<br />
formed out of the underlyingJ =7/2 Yb 3+ spins in<br />
Yb2Ti2O7. This can be consideredas an effective spin<br />
S =1/2 moment, for which the strongest possible quantum<br />
effects are expected. This makes these materials<br />
nearly uniqu examplesof strongly quantum magnets on<br />
the highly frustrated pyrochlore lattice. They are also<br />
nearly ideal subjects for detailed experimental investigation,<br />
existing as they do in large high purity single<br />
crystals, <strong>and</strong> with large magnetic moments amenable to<br />
neutron scatteringstudies.<br />
Theoretical studies have pointed to the likelihoodof<br />
unusual ground states of quantum antiferromagnets on<br />
the pyrochlore lattice. Most excitingisthepossibilityof<br />
a quantum spin liquid (QSL) state, which avoids magdering<strong>and</strong><br />
freezingevenat absolute zero temper-<br />
FIG. 1. (color online) The measured S(Q,ω) atT=30mK,<br />
sliced along various directions in the [HHL] plane, for both<br />
µ0H=5T (first row) <strong>and</strong> µ0H=2T (third row). The second<br />
<strong>and</strong> fourth row show the calculatedspectrum for these two<br />
field strengths, based on an anisotropic exchangemodelwith<br />
five free parameters (see text) that wer extracted by fi ting<br />
to the 5T data set. For a realisti comparison to the data, the<br />
calculated S(Q,ω) is convolutedwithagausianoffu l-width<br />
0.09meV. Both the 2T <strong>and</strong> 5T data sets, comprised of spin<br />
wave dispersions along five different directions, are described<br />
extremely we l by the same parameters.<br />
ature, <strong>and</strong> whos elementary excitations carry fractional<br />
quantum numbers<strong>and</strong> are decidedlydifferentfrom spin<br />
waves 7 . Intriguingly, neutron scattering measurements<br />
have reported a lack of magnetic ordering <strong>and</strong> the absence<br />
of spin waves in Yb2Ti2O7 at low fields 8,9 . In a<br />
recent study, sharp spin waves emerged whenamagnetic<br />
field of 0.5T or larger was applied, suggesting that the<br />
systemtransitioned into a conventional state 9 . The pos-<br />
publication year
1, 2, 3, 4 us<br />
Topological<br />
Insulators<br />
300<br />
225<br />
papers in WOS<br />
150<br />
2d<br />
Discovery<br />
3d<br />
75<br />
0<br />
2005 2006 2007 2008 2009 2010<br />
Quantum excitations <strong>and</strong> fluctuations in Yb2Ti2O7<br />
1 Kavli Institute for Theoretical <strong>Physics</strong>, University of California, Santa Barbara, CA, 93106-9530, etc.<br />
2 <strong>Department</strong>of<strong>Physics</strong><strong>and</strong>Astronomy, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada<br />
3 CanadianInstituteforAdvancedResearch, 180 Dundas St. W.,Toronto, Ontario, M5G 1Z8, Canada<br />
4 BrockhouseInstituteforMaterialsResearch, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada<br />
(Dated: March 10, 2011)<br />
A flu ry of recen theoretical <strong>and</strong> experimental work has highlightedexoticphysicsintheclas-<br />
sical dipolar spin ice compounds, Ho2Ti2O7 <strong>and</strong> Dy2Ti2O7, whic havebeenshowntoexhibitan<br />
emergent “artificial magnetostatics”, manifesting as Coulombicdiffusespincorelations<strong>and</strong>parti-<br />
cles behaving as diffusive “magneticmonopoles”. Here we discu s the related material Yb2Ti2O7,<br />
<strong>and</strong> extract its fu l set of Hamiltonianparameters from high field inelasticneutron sca tering experiments.<br />
These results show that Yb2Ti2O7 is in fact a highly analog of spin ice.<br />
Furthermore we show tha the Hamiltonianmaysupport a Coulombicquantumspinliquidground<br />
state in low field, which could explainsomepuzzlingfeatures prior experiments. This is the first<br />
potentialsightingofaquantumspinliquidstateinamaterial which the spin Hamiltonianis<br />
quantitativelyknown, <strong>and</strong> opensthedoortoawiderange o fascinatingphenomenathatuptonow<br />
have been discu sed only theoretica ly.<br />
Rare earth pyrochlores display a diverse set of fascinating<br />
physical phenomena. 1 One of the most interesting<br />
aspects of these materials from the point of view<br />
of fundamental physics is the strong frustration experiencedbycoupledmagnetic<br />
moments on this lattice. The<br />
best explored materials exhibitingthisfrustration are the<br />
“spin-ice” compounds, Ho2Ti2O7, Dy2Ti2O7, inwhich<br />
the moments can be regarded as classical spins with a<br />
strong easy-axis (Ising) anisotropy 2,3 . The frustration of<br />
these moments resultsinaremarkable classical spin liquid<br />
regim exhibitingCoulombi correlations <strong>and</strong> emergent<br />
“magnetic monopole” excitations that have now<br />
been studiedextensivelyintheory <strong>and</strong> experiment 4–6 .<br />
Strong quantum effectsare absent in the spin ice compounds,<br />
but can be significant in rar earth pyrochlores<br />
with easy-plane rather than easy-axis anisotropy. The<br />
materials Yb2Ti2O7 <strong>and</strong> Er2Ti2O7 have been identified<br />
as of this type, <strong>and</strong> it has recently been argued that<br />
the spins in these materials are contro led by exchange<br />
coupling rather than the long-range dipolar interactions<br />
which dominate in spin ice 11,17 . Because of the strong<br />
spin-orbit <strong>and</strong> crystal field effects, the spin dynamics at<br />
low temperature is dominated by a single Kramers doublet<br />
formed out of the underlyingJ =7/2 Yb 3+ spins in<br />
Yb2Ti2O7. This can be consideredas an effective spin<br />
S =1/2 moment, for which the strongest possible quantum<br />
effects are expected. This makes these materials<br />
nearly uniqu examplesof strongly quantum magnets on<br />
the highly frustrated pyrochlore lattice. They are also<br />
nearly ideal subjects for detailed experimental investigation,<br />
existing as they do in large high purity single<br />
crystals, <strong>and</strong> with large magnetic moments amenable to<br />
neutron scatteringstudies.<br />
Theoretical studies have pointed to the likelihoodof<br />
unusual ground states of quantum antiferromagnets on<br />
the pyrochlore lattice. Most excitingisthepossibilityof<br />
a quantum spin liquid (QSL) state, which avoids magdering<strong>and</strong><br />
freezingevenat absolute zero temper-<br />
FIG. 1. (color online) The measured S(Q,ω) atT=30mK,<br />
sliced along various directions in the [HHL] plane, for both<br />
µ0H=5T (first row) <strong>and</strong> µ0H=2T (third row). The second<br />
<strong>and</strong> fourth row show the calculatedspectrum for these two<br />
field strengths, based on an anisotropic exchangemodelwith<br />
five free parameters (see text) that wer extracted by fi ting<br />
to the 5T data set. For a realisti comparison to the data, the<br />
calculated S(Q,ω) is convolutedwithagausianoffu l-width<br />
0.09meV. Both the 2T <strong>and</strong> 5T data sets, comprised of spin<br />
wave dispersions along five different directions, are described<br />
extremely we l by the same parameters.<br />
ature, <strong>and</strong> whos elementary excitations carry fractional<br />
quantum numbers<strong>and</strong> are decidedlydifferentfrom spin<br />
waves 7 . Intriguingly, neutron scattering measurements<br />
have reported a lack of magnetic ordering <strong>and</strong> the absence<br />
of spin waves in Yb2Ti2O7 at low fields 8,9 . In a<br />
recent study, sharp spin waves emerged whenamagnetic<br />
field of 0.5T or larger was applied, suggesting that the<br />
systemtransitioned into a conventional state 9 . The pos-<br />
publication year
Why did it work?<br />
Very clear thinking by key theorists<br />
obviously correct <strong>and</strong> qualitatively new<br />
clear testable predictions made
Why did it work?<br />
Very clear thinking by key theorists<br />
obviously correct <strong>and</strong> qualitatively new<br />
clear testable predictions made<br />
Not correlated materials: traditional solid<br />
state physics methods apply
WIEN2k<br />
VASP<br />
Why did it work?<br />
Very clear thinking by key theorists<br />
obviously correct <strong>and</strong> qualitatively new<br />
clear testable predictions made<br />
Not correlated materials: traditional solid<br />
state physics methods apply<br />
theorists showed how to test for TIs in<br />
DFT calculation
TIs became the<br />
known <strong><strong>unknown</strong>s</strong>
<strong>and</strong> now ab initio<br />
methods can be<br />
very productive
But the key step<br />
was the idea <strong>and</strong><br />
the theory of how<br />
to search for TIs
What about the<br />
<strong>unknown</strong><br />
<strong><strong>unknown</strong>s</strong>?
Unknown <strong><strong>unknown</strong>s</strong><br />
We expect that the success of TIs in detailed<br />
prediction is an exception rather than the rule<br />
Better for theory to be more of a guide to<br />
materials classes than a detailed predictor<br />
In this case model-based theory is more<br />
informative because it gives direct intuition<br />
<strong>and</strong> dependence on essential parameters<br />
Some examples show how this can work
Ex. 1: Mott<br />
Interfaces<br />
Area has exploded since Hwang+Muller<br />
publicized it ~2002<br />
Vast majority of theory is ab initio<br />
H. Ohtomo et al, 2002
00.016404 PACS numbers: 71.27.+a, 74.78.Fk, 75.30.Et<br />
arch, cuprates remain<br />
the high-temperature<br />
ical grounds, the key<br />
that support high T c<br />
degeneracy, spin one-<br />
, <strong>and</strong> strong antiferrothese<br />
properties are<br />
ls (e.g., layered cobalhem.<br />
uprates is the presence<br />
& & 0:20 where the<br />
lane-wave–localized<strong>and</strong><br />
spin statistics may<br />
gy scales. The multiin<br />
an exotic ‘‘normal’’<br />
quasiparticles, pseuthe<br />
superconducting<br />
of strongly correlated<br />
23d ions as Ti 3 <strong>and</strong><br />
, Co 4 (a t 2g hole) <strong>and</strong><br />
lectron) that possess a<br />
onment. These comhysical<br />
properties [1];<br />
tal phase from which<br />
ng.<br />
bital degeneracy is ‘‘to<br />
igh symmetry of the<br />
ilding block of both<br />
s,—the orbital degend<br />
relaxes kinematical<br />
onsequently, a fermiing<br />
induced insulatorference<br />
to the pseudo-<br />
TiO 3 the formation of<br />
completes within just<br />
0:05 [2].<br />
duces AF correlations<br />
ysics), as electrons are<br />
ng on the different orthat<br />
result in a rich variety of magnetic states in S 1=2<br />
oxides such as RTiO 3 , Na x CoO 2 , Sr 2 CoO 4 , RNiO 3 ,<br />
NaNiO 2 . In contrast, spin correlations in single-b<strong>and</strong> cuprates<br />
are of AF nature exclusively <strong>and</strong> hence strong.<br />
Mott Interfaces<br />
How to suppress the orbital degeneracy <strong>and</strong> promote<br />
cupratelike physics in other S 1=2 oxides? In this<br />
Letter, we suggest <strong>and</strong> argue theoretically that this goal<br />
can be achieved in oxide superlattices. Specifically, we<br />
focus on Ni-based superlattices (see Fig. 1) which can be<br />
fabricated using recent advances in oxide heterostructure<br />
But technology the ([3–5] most <strong>and</strong> references influential therein). While the proposed<br />
compound has a pseudocubic ABO 3 structure, its<br />
theory paper - which<br />
low-energy electronic states are confined to the NiO<br />
really galvanized experiment 2<br />
- is<br />
planes <strong>and</strong>, hence, are of a quasi-2D nature. A substrate<br />
induced compression of the NiO<br />
phenomenological<br />
6 octahedra further stabilizes<br />
the x 2 -y 2 orbital. Net effect is a strong enhancement of<br />
(a)<br />
MO 2<br />
LaO<br />
NiO 2<br />
LaO<br />
MO 2<br />
a<br />
c<br />
b<br />
(b)<br />
(c)<br />
(d)<br />
substrate<br />
FIG. 1. (a) Superlattice La 2 NiMO 6 with alternating NiO 2 <strong>and</strong><br />
MO 2 planes. MO 2 layers suppress the c-axis hopping resulting in<br />
2D electronic structure. Chaloupka Arrows indicate+<br />
the c-axis compression<br />
of the NiO 6 octahedron imposed by tensile epitaxial strain <strong>and</strong><br />
supported by Jahn-Teller Khaliullin, coupling. (b) 2008 ,(c), (d) Strain-induced<br />
stretching of the NiO 2 planes occurs when superlattices with<br />
M Al, Ga, Ti are grown on SrTiO 3 or LaGaO 3 substrates<br />
having large lattice parameter compared to that of LaNiO 3 .<br />
Al<br />
Ni<br />
Ga<br />
Ni<br />
Ti<br />
Ni<br />
Quantum excitations <strong>and</strong> fluctuations in Yb2Ti2O7<br />
1, 2, 3, 4<br />
us<br />
1 Kavli Institute for Theoretical <strong>Physics</strong>, University of California, Santa Barbara, CA, 93106-9530, etc.<br />
2 <strong>Department</strong>of<strong>Physics</strong><strong>and</strong>Astronomy, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada<br />
3 CanadianInstituteforAdvancedResearch, 180 Dundas St. W.,Toronto, Ontario, M5G 1Z8, Canada<br />
4 BrockhouseInstituteforMaterialsResearch, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada<br />
(Dated: March 10, 2011)<br />
A flurry of recent theoretical <strong>and</strong> experimental work has highlightedexoticphysicsintheclas-<br />
sical dipolar spin ice compounds, Ho2Ti2O7 <strong>and</strong> Dy2Ti2O7, whichhavebeenshowntoexhibitan<br />
emergent “artificial magnetostatics”, manifesting as Coulombicdiffusespincorrelations<strong>and</strong>parti-<br />
cles behaving as diffusive “magneticmonopoles”. Here we discussthe related material Yb2Ti2O7,<br />
<strong>and</strong> extract its full set of Hamiltonianparameters from high field inelasticneutron scattering experiments.<br />
These results show that Yb2Ti2O7 is in fact a highly analog of spin ice.<br />
Furthermore we show that the Hamiltonianmaysupport a Coulombicquantumspinliquidground<br />
state in low field, which could explainsomepuzzlingfeatures prior experiments. This is the first<br />
potentialsightingofaquantumspinliquidstateinamaterial which the spin Hamiltonianis<br />
quantitativelyknown, <strong>and</strong> opensthedoortoawiderange of fascinatingphenomenathatuptonow<br />
have been discussedonlytheoretically.<br />
Rare earth pyrochlores display a diverse set of fascinating<br />
physical phenomena. 1 One of the most interesting<br />
aspects of these materials from the point of view<br />
of fundamental physics is the strong frustration experiencedbycoupledmagnetic<br />
moments on this lattice. The<br />
best explored materials exhibitingthisfrustration are the<br />
“spin-ice” compounds, Ho2Ti2O7, Dy2Ti2O7, inwhich<br />
the moments can be regarded as classical spins with a<br />
strong easy-axis (Ising) anisotropy 2,3 . The frustration of<br />
these moments resultsinaremarkable classical spin liquid<br />
regime exhibitingCoulombic correlations <strong>and</strong> emergent<br />
“magnetic monopole” excitations that have now<br />
been studiedextensivelyintheory <strong>and</strong> experiment 4–6 .<br />
Strong quantum effectsare absent in the spin ice compounds,<br />
but can be significant in rare earth pyrochlores<br />
with easy-plane rather than easy-axis anisotropy. The<br />
materials Yb2Ti2O7 <strong>and</strong> Er2Ti2O7 have been identified<br />
as of this type, <strong>and</strong> it has recently been argued that<br />
the spins in these materials are controlled by exchange<br />
coupling rather than the long-range dipolar interactions<br />
which dominate in spin ice 11,17 . Because of the strong<br />
spin-orbit <strong>and</strong> crystal field effects, the spin dynamics at<br />
low temperature is dominated by a single Kramers doublet<br />
formed out of the underlyingJ =7/2 Yb 3+ spins in<br />
Yb2Ti2O7. This can be consideredas an effective spin<br />
S =1/2 moment, for which the strongest possible quantum<br />
effects are expected. This makes these materials<br />
nearly uniqueexamplesof strongly quantum magnets on<br />
the highly frustrated pyrochlore lattice. They are also<br />
nearly ideal subjects for detailed experimental investigation,<br />
existing as they do in large high purity single<br />
crystals, <strong>and</strong> with large magnetic moments amenable to<br />
neutron scatteringstudies.<br />
Theoretical studies have pointed to the likelihoodof<br />
unusual ground states of quantum antiferromagnets on<br />
the pyrochlore lattice. Most excitingisthepossibilityof<br />
a quantum spin liquid (QSL) state, which avoids magnetic<br />
ordering<strong>and</strong> freezingevenat absolute zero temper-<br />
Keimer<br />
FIG. 1. (color online) The measured S(Q,ω) atT=30mK,<br />
sliced along various directions in the [HHL] plane, for both<br />
µ0H=5T (first row) <strong>and</strong> µ0H=2T (third row). The second<br />
<strong>and</strong> fourth row show the calculatedspectrum for these two<br />
field strengths, based on an anisotropic exchangemodelwith<br />
five free parameters (see text) that were extracted by fitting<br />
to the 5T data set. For a realisticcomparison to the data, the<br />
calculated S(Q,ω) is convolutedwithagaussianoffull-width<br />
0.09meV. Both the 2T <strong>and</strong> 5T data sets, comprised of spin<br />
wave dispersions along five different directions, are described<br />
extremely well by the same parameters.<br />
Khaliullin<br />
ature, <strong>and</strong> whose elementary excitations carry fractional<br />
quantum numbers<strong>and</strong> are decidedlydifferentfrom spin<br />
waves 7 . Intriguingly, neutron scattering measurements<br />
have reported a lack of magnetic ordering <strong>and</strong> the absence<br />
of spin waves in Yb2Ti2O7 at low fields 8,9 . In a<br />
recent study, sharp spin waves emerged whenamagnetic<br />
field of 0.5T or larger was applied, suggesting that the<br />
systemtransitioned into a conventional state 9 . The pos-
00.016404 PACS numbers: 71.27.+a, 74.78.Fk, 75.30.Et<br />
arch, cuprates remain<br />
the high-temperature<br />
ical grounds, the key<br />
that support high T c<br />
degeneracy, spin one-<br />
, <strong>and</strong> strong antiferrothese<br />
properties are<br />
ls (e.g., layered cobalhem.<br />
uprates is the presence<br />
& & 0:20 where the<br />
lane-wave–localized<strong>and</strong><br />
spin statistics may<br />
gy scales. The multiin<br />
an exotic ‘‘normal’’<br />
quasiparticles, pseuthe<br />
superconducting<br />
of strongly correlated<br />
23d ions as Ti 3 <strong>and</strong><br />
, Co 4 (a t 2g hole) <strong>and</strong><br />
lectron) that possess a<br />
onment. These comhysical<br />
properties [1];<br />
tal phase from which<br />
ng.<br />
bital degeneracy is ‘‘to<br />
igh symmetry of the<br />
ilding block of both<br />
s,—the orbital degend<br />
relaxes kinematical<br />
onsequently, a fermiing<br />
induced insulatorference<br />
to the pseudo-<br />
TiO 3 the formation of<br />
completes within just<br />
0:05 [2].<br />
duces AF correlations<br />
ysics), as electrons are<br />
ng on the different orthat<br />
result in a rich variety of magnetic states in S 1=2<br />
oxides such as RTiO 3 , Na x CoO 2 , Sr 2 CoO 4 , RNiO 3 ,<br />
NaNiO 2 . In contrast, spin correlations in single-b<strong>and</strong> cuprates<br />
are of AF nature exclusively <strong>and</strong> hence strong.<br />
Mott Interfaces<br />
How to suppress the orbital degeneracy <strong>and</strong> promote<br />
cupratelike physics in other S 1=2 oxides? In this<br />
Letter, we suggest <strong>and</strong> argue theoretically that this goal<br />
can be achieved in oxide superlattices. Specifically, we<br />
focus on Ni-based superlattices (see Fig. 1) which can be<br />
fabricated using recent advances in oxide heterostructure<br />
But technology the ([3–5] most <strong>and</strong> references influential therein). While the proposed<br />
compound has a pseudocubic ABO 3 structure, its<br />
theory paper - which<br />
low-energy electronic states are confined to the NiO<br />
really galvanized experiment 2<br />
- is<br />
planes <strong>and</strong>, hence, are of a quasi-2D nature. A substrate<br />
induced compression of the NiO<br />
phenomenological<br />
6 octahedra further stabilizes<br />
the x 2 -y 2 orbital. Net effect is a strong enhancement of<br />
(a)<br />
MO 2<br />
LaO<br />
NiO 2<br />
LaO<br />
MO 2<br />
a<br />
c<br />
b<br />
(b)<br />
(c)<br />
(d)<br />
substrate<br />
FIG. 1. (a) Superlattice La 2 NiMO 6 with alternating NiO 2 <strong>and</strong><br />
MO 2 planes. MO 2 layers suppress the c-axis hopping resulting in<br />
2D electronic structure. Chaloupka Arrows indicate+<br />
the c-axis compression<br />
of the NiO 6 octahedron imposed by tensile epitaxial strain <strong>and</strong><br />
supported by Jahn-Teller Khaliullin, coupling. (b) 2008 ,(c), (d) Strain-induced<br />
stretching of the NiO 2 planes occurs when superlattices with<br />
M Al, Ga, Ti are grown on SrTiO 3 or LaGaO 3 substrates<br />
having large lattice parameter compared to that of LaNiO 3 .<br />
Al<br />
Ni<br />
Ga<br />
Ni<br />
Ti<br />
Ni<br />
c.f. S. Stemmer<br />
6pm today
Ex.2: Quantum Spin<br />
Liquids<br />
Ψ =<br />
Anderson 1973: a material with localized<br />
electrons where the spins never order but<br />
instead form “resonating valence bonds”<br />
Expected to have many exotic properties<br />
(spin-charge separation, etc) <strong>and</strong> may be a<br />
good platform for quantum computing<br />
c.f. L.B., Nature 464,199 (2010)
Ex.2: Quantum Spin<br />
Liquids<br />
But...the c<strong>and</strong>idate materials are hard to<br />
model, <strong>and</strong> DFT (even DMFT) fails to<br />
describe ground state properties<br />
These local moment systems usually have<br />
some exchange model description (<strong>and</strong> it is<br />
useful!)<br />
but: this is not known <strong>and</strong> really hard to<br />
calculate from first principles<br />
c.f. L.B., Nature 464,199 (2010)
Be precise. A lack of<br />
precision is dangerous<br />
when the margin of error<br />
is small<br />
J
Yb2Ti2O7<br />
ature, <strong>and</strong> whose elementary excitations carry fractional<br />
quantum numbers<strong>and</strong> are decidedlydifferentfrom spin<br />
waves 7 . Intriguingly, neutron scattering measurements<br />
have reported a lack of magnetic ordering <strong>and</strong> the absence<br />
of spin waves in Yb2Ti2O7 at low fields 8,9 . In a<br />
recent study, sharp spin waves emerged whenamagnetic<br />
field of 0.5T or larger was applied, suggesting that the<br />
systemtransitioned into a conventional state 9 . The possingle<br />
crystals<br />
crucial!<br />
Complete phenomenological Hamiltonian can<br />
be quantitatively extracted from INS with<br />
B=5T<br />
Quantum excitations <strong>and</strong> fluctuations in Yb2Ti2O7<br />
The first QSL c<strong>and</strong>idate where H is known!<br />
K. Ross, L. Savary, B. Gaulin, <strong>and</strong> LB, in preparation<br />
1, 2, 3, 4 us<br />
1 Kavli Institute for Theoretical <strong>Physics</strong>, University of California, Santa Barbara, CA, 93106-9530, etc.<br />
2 <strong>Department</strong>of<strong>Physics</strong><strong>and</strong>Astronomy, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada<br />
3 CanadianInstituteforAdvancedResearch, 180 Dundas St. W.,Toronto, Ontario, M5G 1Z8, Canada<br />
4 BrockhouseInstituteforMaterialsResearch, McMasterUniversity, Hamilton, Ontario, L8S 4M1, Canada<br />
(Dated: March 10, 2011)<br />
A flurry of recent theoretical <strong>and</strong> experimental work has highlightedexoticphysicsintheclas-<br />
sical dipolar spin ice compounds, Ho2Ti2O7 <strong>and</strong> Dy2Ti2O7, whichhavebeenshowntoexhibitan<br />
emergent “artificial magnetostatics”, manifesting as Coulombicdiffusespincorrelations<strong>and</strong>parti-<br />
cles behaving as diffusive “magneticmonopoles”. Here we discussthe related material Yb2Ti2O7,<br />
<strong>and</strong> extract its full set of Hamiltonianparameters from high field inelasticneutron scattering experiments.<br />
These results show that Yb2Ti2O7 is in fact a highly analog of spin ice.<br />
Furthermore we show that the Hamiltonianmaysupport a Coulombicquantumspinliquidground<br />
state in low field, which could explainsomepuzzlingfeatures prior experiments. This is the first<br />
potentialsightingofaquantumspinliquidstateinamaterial which the spin Hamiltonianis<br />
quantitativelyknown, <strong>and</strong> opensthedoortoawiderange of fascinatingphenomenathatuptonow<br />
have been discussedonlytheoretically.<br />
Rare earth pyrochlores display a diverse set of fascinating<br />
physical phenomena. 1 One of the most interesting<br />
aspects of these materials from the point of view<br />
of fundamental physics is the strong frustration experiencedbycoupledmagnetic<br />
moments on this lattice. The<br />
best explored materials exhibitingthisfrustration are the<br />
“spin-ice” compounds, Ho2Ti2O7, Dy2Ti2O7, inwhich<br />
the moments can be regarded as classical spins with a<br />
strong easy-axis (Ising) anisotropy 2,3 . The frustration of<br />
these moments resultsinaremarkable classical spin liquid<br />
regime exhibitingCoulombic correlations <strong>and</strong> emergent<br />
“magnetic monopole” excitations that have now<br />
been studiedextensivelyintheory <strong>and</strong> experiment 4–6 .<br />
Strong quantum effectsare absent in the spin ice compounds,<br />
but can be significant in rare earth pyrochlores<br />
with easy-plane rather than easy-axis anisotropy. The<br />
materials Yb2Ti2O7 <strong>and</strong> Er2Ti2O7 have been identified<br />
as of this type, <strong>and</strong> it has recently been argued that<br />
the spins in these materials are controlled by exchange<br />
coupling rather than the long-range dipolar interactions<br />
which dominate in spin ice 11,17 . Because of the strong<br />
spin-orbit <strong>and</strong> crystal field effects, the spin dynamics at<br />
low temperature is dominated by a single Kramers doublet<br />
formed out of the underlyingJ =7/2 Yb 3+ spins in<br />
Yb2Ti2O7. This can be consideredas an effective spin<br />
S =1/2 moment, for which the strongest possible quantum<br />
effects are expected. This makes these materials<br />
nearly uniqueexamplesof strongly quantum magnets on<br />
the highly frustrated pyrochlore lattice. They are also<br />
nearly ideal subjects for detailed experimental investigation,<br />
existing as they do in large high purity single<br />
crystals, <strong>and</strong> with large magnetic moments amenable to<br />
neutron scatteringstudies.<br />
Theoretical studies have pointed to the likelihoodof<br />
unusual ground states of quantum antiferromagnets on<br />
the pyrochlore lattice. Most excitingisthepossibilityof<br />
a quantum spin liquid (QSL) state, which avoids magnetic<br />
ordering<strong>and</strong> freezingevenat absolute zero temper-<br />
FIG. 1. (color online) The measured S(Q,ω) atT=30mK,<br />
sliced along various directions in the [HHL] plane, for both<br />
µ0H=5T (first row) <strong>and</strong> µ0H=2T (third row). The second<br />
<strong>and</strong> fourth row show the calculatedspectrum for these two<br />
field strengths, based on an anisotropic exchangemodelwith<br />
five free parameters (see text) that were extracted by fitting<br />
to the 5T data set. For a realisticcomparison to the data, the<br />
calculated S(Q,ω) is convolutedwithagaussianoffull-width<br />
0.09meV. Both the 2T <strong>and</strong> 5T data sets, comprised of spin<br />
wave dispersions along five different directions, are described<br />
extremely well by the same parameters.
Ex. 3: SOC<br />
+Interactions<br />
Schematic phase diagram from Pesin<br />
+Balents, 2010<br />
heavily influenced by experiments <strong>and</strong><br />
materials grown <strong>and</strong> studied by Y. Maeno,<br />
Y. Matsuhira, H. Takagi, Y. Tokura, B.-J.<br />
Kim, G. Cao
Ex. 3: SOC<br />
+Interactions<br />
Schematic phase diagram from Pesin<br />
+Balents, 2010<br />
U/t<br />
“traditional” Mott<br />
insulators<br />
strong SO Mott<br />
insulators<br />
“simple”<br />
materials<br />
TIs, SO-semimetals<br />
λ/t
What <strong>and</strong> where?<br />
Most important thing is intuition<br />
correlations: d electrons<br />
strong SOC: 4d or 5d <strong>and</strong> orbital<br />
degeneracy<br />
U/W is crucial parameter<br />
Must choose carefully because for 4d+5d’s,<br />
U/W is usually smallish
What <strong>and</strong> Where?<br />
Iridates: λ ~ U ~ t <strong>and</strong> favorable (t2g) 5<br />
configuration: Ln2Ir2O7, Sr2IrO4, Na2IrO3,...<br />
Topological Mott insulator, topological 3d<br />
Dirac semimetal, magnetic topological<br />
insulator, high T c superconductor, Kitaev spin<br />
liquid...<br />
Double perovskites: anomalously low b<strong>and</strong>width:<br />
Ba2YMoO6, Ba2LiOsO6, Sr2MgReO6, ...<br />
Multipolar order, quantum spin liquid...
Recommendations<br />
Pure theory <strong>and</strong> phenomenology are at least<br />
as important in materials discovery as ab initio<br />
Really works best when theory <strong>and</strong> growth/<br />
measurement work closely together<br />
Theorists need to be trained in how to<br />
develop models for new materials
Recommendations<br />
Pure theory <strong>and</strong> phenomenology are at least<br />
as important in materials discovery as ab initio<br />
Really works best when theory <strong>and</strong> growth/<br />
measurement work closely together<br />
Theorists need to be trained in how to<br />
develop models for new materials<br />
If you are not criticized,<br />
you may not be doing<br />
much