Theory of charge and spin ordering in the nickelates - Physics ...

Theory of charge and
spin ordering in the
nickelates
Leon Balents, KITP
Cologne, 9/2010
$$

People
Collaborators
Sungbin Lee
Thanks to:
Susanne Stemmer
Junwoo Son
Jim Allen
Ru Chen
Dan Ouellette
Andy Millis

Outline
Introduction to Mott transitions and charge/spin order in the
RNiO3 nickelates
Hubbard model
itinerant limit: spin-density wave
Landau analysis of spin and charge order
role of orthorhombicity
Localized limit
spin and charge order
Other tests for itinerant versus localized physics

Outline
Introduction to Mott transitions and charge/spin order in
the RNiO3 nickelates
Hubbard model
itinerant limit: spin-density wave
Landau analysis of spin and charge order
role of orthorhombicity
Localized limit
spin and charge order
Other tests for itinerant versus localized physics

ates remain
temperature
ds, the key
ort high T c
y, spin oneg
antiferroperties
are
ered cobalhe
presence
0 where the
–localizedatistics
may
The multic
‘‘normal’’
icles, pseurconducting
y correlated
as Ti 3 and
2g hole) and
at possess a
hese comperties
[1];
from which
eracy is ‘‘to
etry of the
ck of both
bital degenkinematical
tly, a fermid
insulatorthe
pseudoormation
of
within just
correlations
lectrons are
ifferent orinteractions
that 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.
How to suppress
Mott
the orbital degeneracy and
interfaces
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
technology ([3–5] and references therein). While the proposed
compound has a pseudocubic ABO 3 structure, its
Lots of interesting suggestions!
low-energy electronic states are confined to the NiO 2
planes and, hence, are of a quasi-2D nature. A substrate
induced compression of the NiO 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
Chaloupka +
2D electronic structure. Arrows indicate the c-axis compression
of the NiO 6 octahedron Khaliullin, imposed by 2008 tensile epitaxial strain and
supported by Jahn-Teller coupling. (b) ,(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 .
Expected deformations are indicated by arrows.
Al
Ni
Ga
Ni
Ti
Ni
vary d to tune
Mott transition
d

Nickelates
But... we should understand the bulk first
One of the classic perovskites for studying
the Mott transition c.f. Goodenough + Raccah, 1965
Torrance et al, 1992

Bulk transitions
Transitions are all first order, w/ hysteresis
GARCÍA-MUÑOZ et al.
Resistance (ohms)
Nd
10 8
10 7
10 6
10 5
10 4
10 3
10 2
10 9 0 50 100 150 200 250 300
Magnetization (x 10 5 , emu/g)
3.0
2.6
2.2
180 190 200 210 220 230 240
T(K)
TABLE I. a Refin
in space group Pbnm.
50 K in space group P
Atom
a a=5.38712
Nd 4c 0.9958
Ni 4b 1/2
O1 4c 0.0692
O2 8d 0.7165
x
Torrance et al, 1992
10 1
T (K)
FIG. 1. Color online Resistance of NdNiO 3 on heating and
cooling showing an augment of 3 orders of magnitude after formation
of a charge Garcia-Munoz order phase. Inset: kink inet theal, susceptibility 2009 related
with the metal-insulator transition and the onset of the antiferromagnetic
order T N =T MI . Hysteresis on heating and cooling can be
appreciated.
Polycrystalline NdNiO 3 was synthesized under high oxygen
pressure 200 bar following the procedure described in
Ref. 28. The sample was extensively characterized by laboratory
x-ray powder diffraction, magnetic and electric measurements,
and synchrotron diffraction, which confirmed its
quality. High-resolution synchrotron x-ray powder-
290 K 2
Pbnm 4.53
Atom
b a=5.37783
Nd 4c 0.99321
Ni1 2d 1/2
Ni2 2c 1/2
O1 4e 0.07521
O2a 4e 0.71432
x

Nickelates
Ideally
RNiO3, with R 3+ , Ni 3+ = 3d 7
e
1 g
t
6 2g
Local moment and orbital degeneracy

Magnetic structure
Neutron scattering
R=Pr, Nd, Ho, Eu, Sm, Y all show the same,
unusual magnetic structure
k=(1/2,0,1/2) in orthorhombic coordinates,
equivalent to k=(1/4,1/4,1/4) in cubic ones
unusual pattern: along cubic axes
...
initially interpreted as evidence for orbital order

Charge order
Alonso et al, 1999: “rock salt” charge order
Since seen in R=Y, Nd, Ho, Y, Eu, Tm, Yb,
Er, Lu, by alternating expansion/
contraction of octahedra via neutrons/xrays
negligible Jahn-Teller distortions seen
Implication (observed in Ho, Y, Eu)
... ...

Charge and spin
order
CO
CO+AF
Torrance et al, 1992

Valence skipping
Mazin et al, 2007: theoretically suggest mixed
valence PRL 98, state 176406 to (2007) enhance exchange
FIG. 1 (color online). Schematic electronic level diagram of Ni
ions in RNiO 3 in two cases: (a) two JT distorted Ni 3 ions
(energy gain E JT per site), and (b) charge disproportionation.
and in the fully delocalized limit, the additional Coulomb
energy due to CO is reduced to the Hartree energy, a very
strong reduction. Furthermore, delocalization often leads
PHYSICAL REVIEW LETTERS
even the magnetic inst
paramagnetic metal do
disproportionation. Ex
manifests itself in oxyg
netic moments on the tw
contrary to popular be
Mott-Hubbard insulato
tional band picture give
it is capable of expla
occurs in the crossover
band structure calculat
zation of the nonmag
The insulator-metal
structure in RNiO 3 are
0:7 B for Ni 2 in YNi
1:4 B and 0:6 B for H
A close inspection
erant states along the

Valence skipping
Mazin et al, 2007: theoretically suggest mixed
valence PRL 98, state 176406 to (2007) enhance exchange
FIG. 1 (color online). Schematic electronic level diagram of Ni
But: Why the complex magnetic ordering
ions in RNiO 3 in two cases: (a) two JT distorted Ni
pattern?
3 ions
(energy gain E JT per site), and (b) charge disproportionation.
c.f. Mizokawa, Khomskii, Sawatzky, 2000
and in the fully delocalized limit, the additional Coulomb
energy due to CO is reduced to the Hartree energy, a very
strong reduction. Furthermore, delocalization often leads
PHYSICAL REVIEW LETTERS
even the magnetic inst
paramagnetic metal do
disproportionation. Ex
manifests itself in oxyg
netic moments on the tw
contrary to popular be
Mott-Hubbard insulato
The insulator-metal
structure in RNiO 3 are
0:7 B for Ni 2 in YNi
1:4 B and 0:6 B for H
A close inspection
tional band picture give
it is capable of expla
occurs in the crossover
erant states along the
band structure calculat
zation of the nonmag

Naive expectations
Rock-salt ordering of Ni 2+ ions forms an fcc
lattice
FCC antiferromagnet is degenerate and
orders at (keeping original cubic conventions)
Q=(1/2,0,q) - usually (1/2,0,0)
“type I AF”
But Q=(1/4,1/4,1/4) found experimentally

Outline
Introduction to Mott transitions and charge/spin order in the
RNiO3 nickelates
Hubbard model
itinerant limit: spin-density wave
Landau analysis of spin and charge order
role of orthorhombicity
Localized limit
spin and charge order
Other tests for itinerant versus localized physics

Hubbard Model
A minimal model to consider is
H = ij;ab
t ab
ij c † iaα c jbα + i
Un 2 i − J( S i ) 2
Band energy
(hopping)
Coulomb
Hund’s
exchange

Hubbard Model
A minimal model to consider is
H = ij;ab
t ab
ij c † iaα c jbα + i
Un 2 i − J( S i ) 2
Band energy
(hopping)
Coulomb
Hund’s
exchange
vs

Phase Diagram
Which is more appropriate starting point?
and how do we tell experimentally?
J H /t
(localized)
strongly correlated insulator
intermediate correlation
(itinerant)
metal
U/t

Phase Diagram
Which is more appropriate starting point?
and how do we tell experimentally?
J H /t
(localized)
strongly correlated insulator
intermediate correlation
start here
(itinerant)
metal
U/t

Itinerant Limit
Ho
?

Tight-binding model
Keep just σ-bonding for 2 eg bands
t’
t
Ex Hopping Ni d x
2 O p x Ni
t
!"# $# !"#
Ex Hopping Ni d x
2 O px Ni d x
2
t
x
!"# $# !"#
x

3
2
1
1
0.5 1.0 1.5 2.0 2.5 3.0
Comparison w/ LDA
N. Hamada, 1993
NORIM
HAMADA
Best fit
w
0
t=0.75 eV
t’/t=0.07
-2
-4
P
X r X M r
Figure 1: Band structure of a cubic LaNiOs with a lattice parameter of 3,88A. The origin of
energy is taken at the Fermi energy.
Fits reasonably well the bands crossing the
Fermi energy, but misses some (t2g) states
below
M
V
Figure 2: Fermi surfaces of a cubic LaNKIs: (a) a electron pocket at the I? point contain~g 0.04
electrons, and (b) a large hole Fermi surface around the R point containing 1.04 holes inside.

Fermi surfaces
Variation with t’/t
0.24 0.06
t’/t
t’/t = 0.25 t’/t = 0.15 t’/t = 0

Comparisons
FERMI SURFACES, ELECTRON-HOLE ASYMMETRY, AND…
PHYSICAL REVIEW B 79, 115122 2009
Γ-X
a
R-M
b
X
R
Γ
M
X
R
Binding energy (eV)
0.0
0.5
1.0 0.5 0.0 1.0 0.5 0.0
Binding energy (eV)
Binding energy (eV)
k F 1 k F 2 k F 3 k F 4
1.0
X Γ X
R M R
soft x-ray ARPES, R.
FIG.
Eguchi
3. Color online a and
et
bal, EDCs along
2009
-X and R-M
direction, respectively. c and d The intensity maps of EDCs.
k F1-k F4 indicate the MDC peak positions at E F.
we measured ARPES at a fixed photon energy of 630 eV
k z 0 and 710 eV k z /c. The FS mapping in horizontal
k x -k y planes “” and “” of Brillouin zone in Fig. 1a
t’/t=0.15
was obtained as shown in Figs. 2b and 2c. In “” plane,
FIG. 2. Color online Fermi-surface mapping in a a vertical
the small electron FS around point is again observed. This
k result indicates that the 3D spherelike FS around point can
z-k x plane “” and b horizontal k x-k y planes “” and c “”
of Brillouin zone in Fig. 1a. Solid white lines correspond to the be observed by ARPES experimentally. The squarelike intense
area around M points obtained from raw data without
cubic Brillouin zone and dotted white lines correspond to the highsymmetry
lines. k F1-k F4 indicate the MDC peak positions at E F in symmetrization corresponds to the projection of the hole FS
Figs. 3c and 3d. Blue gray lines show nesting character hole centered at R point. In “” plane, no small FS is observed.
LNO
FSs. All the intensity maps are measured data over the displayed Instead large FSs centered at R point were observed. From
range and no symmetrization has been used to obtain the maps. the complete data set of energy and angle-dependent FS
RH
maps, the experimental FS obtained by soft x-ray ARPES is
to the Ni 3d6t 2g bands. In addition, EDCs for 600–660 eV in overall agreement with that predicted by the band
clearly show a dispersive band crossing at the E F arrows calculation. 24 However, the actual band dispersions reveal an
around the point. This dispersive band originates in Ni 3d important difference in electron and hole FSs as discussed in
e g states and forms a small electron pocket as predicted by the following.
the local-density 4 approximation LDA band calculation. The In order to discuss the band structures forming these FSs,
band disappears for energies below 600 eV and above 660 we measured the ARPES in the high-symmetry lines with
eV photon energy and an increase in intensity is observed detailed momentum steps and an energy resolution E
close to the M point at h=570 and 700 eV.
150 meV. The EDCs Figs. 3a and 3b and the intensity
plots Figs. 3c and 3d along -X and R-M directions
2
Figure 2a shows the FS mapping in a vertical k z -k x
plane “” of Brillouin zone as shown in Fig. 1a, which is are shown in Fig. 3. The FS crossing k F points are labeled as
obtained by a plot of the integrated intensity from −0.05 to k F 1-k F 4. The intensity plots in both directions Figs. 3c and
0.05 eV binding energy in EDCs. A small circle centered at 3d show an intense feature around 0.0–0.2 eV at and M
point is observed, while no 0.2 intensity is observed 0.1 around the 0.0points, corresponding 0.1 to the electron 0.2 t’/t
band and the hole band
X point. The existence of a nearly spherical small FS centered
at point, corresponding to the electron FS, was pre-
bottom at M point is around 0.25 eV, the band bottom at
derived from Ni 3d e g states, respectively. While the band
dicted by2
band calculations. 24 From photon energy point is not at 0.25 eV. The intensity remains in high bindingenergy
region about 0.5–1.0 eV at point Fig. 3c, in-
k z -dependent ARPES measurements, we can decide the
photon energy tracing the -X and X-M directions as shown dicating that the bands extend to high binding energies. Because
the t 2g bands also appear above 0.5 eV at X point, in Fig. 1b. 4 In order to observe the in-plane cuts of the FSs,
the
6
115122-3
c
d
S/T
3
2
1
1
2
3
optics, D. Ouellette et al, 2010
LNO
0.4 0.2 0.0 0.2 0.4
t’/t
“Hole like” Hall conductivity
“Electron like” thermopower

Nesting
Large fermi surface contains rather flat
portions
Approximate “nesting” leads to a large
susceptibility at some wavevectors, and a
tendency to CDW or SDW order

Susceptibility
Susceptibility is peaks for k=(k,k,k), with
k≈0.4π (close to π/2), for the FS closest to
ARPES
Χk, Ω0
1200
1000
800
600
400
200
t't0.1 0.05
t't0.2 0.1
t't0.3 0.15
0
000 100 110 111 000 101
kΠ
Due to JH, this drives a Spin Density Wave
instability (in e.g. RPA)

Hartree-Fock
Two SDW phases appear
SDW
Ɵ =0
0 < Ɵ < π/4
Ɵ = π/4
PM+M : paramagnetic metal
SM : semimetal+SDW
SDW+CO+I : spin density wave +
charge ordering + insulator
SDW+M : spin density wave + metal
n.b. calculated for ideal cubic structure

Outline
Introduction to Mott transitions and charge/spin order in the
RNiO3 nickelates
Hubbard model
itinerant limit: spin-density wave
Landau analysis of spin and charge order
role of orthorhombicity
Localized limit
spin and charge order
Other tests for itinerant versus localized physics

Landau Theory
SDW order parameter
in reality there are 4 (2)
S i = Re ψe iQ·r equivalent Q a by cubic
i (orthorhombic)
symmetry, but we expect
the system to choose only
one to order into

Landau Theory
SDW order parameter
S i = Re ψe iQ·r i
Charge order parameter
n i =(−1) x i+y i +z i
Φ
Symmetry allows the term
F = λΦRe [ψ · ψ]
Φ ∝ Re [ψ · ψ]

Cubic symmetry
Landau free energy
F = rψ ∗· ψ + u 1 (ψ ∗· ψ) 2
+u 2 |ψ · ψ| 2 + u 3
(ψ · ψ) 2 +h.c.
Physics of u2:
u20: spiral state

Cubic symmetry
Landau free energy
F = rψ ∗· ψ + u 1 (ψ ∗· ψ) 2
+u 2 |ψ · ψ| 2 + u 3
(ψ · ψ) 2 +h.c.
Physics of u2:
u20: spiral state

Cubic symmetry
Landau free energy
F = rψ ∗· ψ + u 1 (ψ ∗· ψ) 2
+u 2 |ψ · ψ| 2 + u 3
(ψ · ψ) 2 +h.c.
Physics of u3:
fixes phase of SDW
ψ = |ψ|ˆn e iθ
F = constant +u 3 |ψ| 4 cos 4θ
find θ=0 or π/4

SDW states
Look along axis
θ=0
“site centered”
max Φ
θ=π/4
“bond centered”
Φ=0

Cubic lattice
“site centered”
“bond centered”
“MCO”
c.f. Mizokawa et al, 2000
“OCO”
m 1 =m, m 2 =0 m 1 =m 2 =m

Magnetic structures
Refinements give no materials with
momentless Ni sites
material m1(µB) m2(µB) Reference
Ho 1.4 0.6 PRB 64, 144417 (2001)
Y 1.4 0.7 PRL 82, 3871 (1999)
Eu 1.2 1.2 PRB 57, 456(1998)
Sm 0.9 0.9* PRB 57, 456(1998)
Nd 0.9 0.9* PRB 50, 978 (1994)
Pr 0.9 0.9* PRB 50, 978 (1994)
* observed charge order is inconsistent with equal moments

1918 J B Good
Orthorhombic
Distortion
orthorhombicity
Figure 2. Cooperative MX 6/2 rotations giving (a) tetragonal (projection on (001) of MX 3
(b) rhombohedral and (c) orthorhombic (Pbnm axes) symmetry. Note: Pbnm axes a, b, c, b
c, a, b, in Pnma.
The equilibrium (A–X) and (M–X) bond lengths are calculated for ambient cond
from the sums of the ionic radii available in tables [1]; they were obtained from x-ray data

Orthorhombicity
Orthorhomic distortion quadruples the unit cell
and allows an additional term:
In the collinear SDW this becomes
Now the minima are at
u30: θ=π/4 + δ, with δ ~ v/u

SDW states
Look along axis
θ=0
θ=π/4
+ δ
Charge order grows with orthorhombicity!
“site centered”
max Φ
zero moments
due to I center
Φ ∝ δ
“off center”
develops unequal
moments and CO

Unequal moments
orthorhombicity

Hartree-Fock
With orthorhombicity, charge order is
everywhere
θ=0
↑0↓0
θ=π/4±δ
SDW+CO
↑↑↓↓
Ɵ =0
0 < Ɵ < π/4
Ɵ = π/4
PM+M : paramagnetic metal
SM : semimetal+SDW
SDW+CO+I : spin density wave +
charge ordering + insulator
SDW+M : spin density wave + metal
But, there are still 2 types of magnetic states

Outline
Introduction to Mott transitions and charge/spin order in the
RNiO3 nickelates
Hubbard model
itinerant limit: spin-density wave
Landau analysis of spin and charge order
role of orthorhombicity
Localized limit
spin and charge order
Other tests for itinerant versus localized physics

Back to the Mott
Transition
What about the separation of charge and spin
ordering for smaller rare earths?
Ho
?

Phase Diagram
Which is more appropriate starting point?
and how do we tell experimentally?
J H /t
(localized)
strongly correlated insulator
look here
intermediate correlation
(itinerant)
metal
U/t

Strong Coupling
Approach
Consider perturbation theory in the hopping
t=t’=0:
E=2U-3J H /2
E=4U-2J H

Strong Coupling
Approach
Consider perturbation theory in the hopping
t=t’=0:
E=2U-3JH/2
E=4U-2J H
JH/t
paired
J H =4U
electrons are bound
into S=1 bosonic pairs
intermediate correlation
(itinerant)
metal
U/t

Ordering of pairs
Half of sites should be occupied (Ni 2+ )
or
or...

Ordering of pairs
Half of sites should be occupied (Ni 2+ )
or
or...
At second order in hopping, the ordering is
determined to be of rock salt (fcc) type
virtual hopping processes favor Ni 2+
neighboring Ni 4+
TCO ~ t 2 /JH

Magnetism
The spin of each Ni 2+ electron pair is totally free
at O(t 2 /J H )
exchange coupling sets TAF ~ t 4 /JH 3

Magnetism
The spin of each Ni 2+ electron pair is totally free
at O(t 2 /J H )
exchange coupling sets TAF ~ t 4 /JH 3 |J1| (needs t’)
But: the ↑0↓0 state is expected here

Put it together
Strong coupling picture agrees with HF
↑0↓0
θ=0
↑0↓0
θ=π/4±δ
SDW+CO
↑↑↓↓
Ɵ =0
0 < Ɵ < π/4
Ɵ = π/4
PM+M : paramagnetic metal
SM : semimetal+SDW
SDW+CO+I : spin density wave +
charge ordering + insulator
SDW+M : spin density wave + metal

Put it together
Strong coupling picture agrees with HF
↑0↓0
Ɵ =0
θ=0
↑0↓0
θ=π/4±δ
SDW+CO
↑↑↓↓
0 < Ɵ < π/4
Ɵ = π/4
PM+M : paramagnetic metal
SM : semimetal+SDW
SDW+CO+I : spin density wave +
charge ordering + insulator
SDW+M : spin density wave + metal
Off-center SDW seems most compatible with expt

Outline
Introduction to Mott transitions and charge/spin order in the
RNiO3 nickelates
Hubbard model
itinerant limit: spin-density wave
Landau analysis of spin and charge order
role of orthorhombicity
Localized limit
spin and charge order
Other tests for itinerant versus localized physics

How to tell?
Itinerant vs.
Localized?
Magnetism: “off center” SDW (itinerant) vs.
“site centered” SDW (localized)
Order of phase transitions (1st order)
Other ways?
Electronic structure
c.f. arXiv:1008.2373v1
Heterostructures: response of charge+spin
order to confinement, strain

Electronic
structure
Another way to distinguish two SDWs is by
electronic properties
c.f. DOS (cubic symmetry taken here)
DOS
0.08
0.06
DOS
0.07
0.06
0.05
0.04
0.04
0.03
0.02
1.0 0.5 0.0 0.5 1.0 1.5 2.0
E
gap
Ɵ =0
0 < Ɵ < π/4
Ɵ = π/4
0.02
0.01
1 0 1 2
E
linear DOS

semi-metal state
In Hartree-Fock, one finds a semi-metallic
solution in the cubic system
This corresponds to the bond-centered SDW,
and essentially electrons of one spin
polarization are confined to a pair of
parallel planes
This forms a honeycomb lattice
looks familiar?

Hartree-Fock
graphene-like band structure!
t’=0
t’=0.15
protected by topology and inversion symmetry
but: orthorhombic distortion will open up a gap

Hartree-Fock
small gap opens with orthorhombicity
before
after

Anisotropy
SDW wavevectors
cubic unit cell 4 wavevectors top down view
Transport along Q is the “hard” direction - expect large
in-plane anisotropy for a single-domain film

Films, Interfaces
Landau analysis can be readily adapted:
include terms reflecting lowered symmety
Example: interface
z-translation symmetry is removed
δF = λ e iα ψ 1 · ψ 3 +c.c.
Q 1 = 1 4 (1¯1¯1)
Q 2 = 1 4 (¯11¯1)
leads to “two-q” state near interface
Similar effects can lead to switching of SDW
wavevector and hence can turn charge order on/off

Nesting
Confinement affects Fermi surfaces
N=4 layers N=3 N=2 N=1

1
0
1
0
0
0
1
0
1
1
1
2
Spin susceptibility
0 1 2 3 3 2 1 0 1 2 3
2
3
3
3
Spin susceptibility
3 2 1 0 1 2 3
usceptibility
70
200
60
3 2 1 0 1 2 3
1
2
2
3
3 2 1 0 1 2 3
k z Π4
t't0.05 t't0.05
t't0.1 t't0.1
2
3
200
3 2 1 0 1 2 3
t't0.15
k z Π4
k z Π2
50
150
t't0.15
t't0.15
150
k z 3Π4
Χk, Ω0
40
30
Χk, Ω0
100
Χk, Ω0
100
20
50
50
10
0
0
00 10 11 00
00 10 11 00
kΠ
kΠ
0
00 10 11 00
N=1 N=3
kΠ
Single layer is enhanced for broad range of t’/t
N=3 layers is peaked at 2π(1/4,1/4,1/8)

Summary
Theory of the nickelates must bridge the gap between itinerant
and localized behavior
There are sharp ways to define the two regimes, that can be
experimentally distinguished
“site centered” versus “off-center” magnetic order
electronic structure
behavior in heterostructures
These methods can readily be applied to heterostructures and
interfaces, and lead to testable predictions
e.g. Expect conductivity anisotropy enhanced in SDW state
Reference: arXiv:1008.2373v1