of 17
1
A
continuous
metal
-
insulator transition
driven by spin correlations
Yejun Feng
1
,
2
,
*
,
Yishu Wang
2
,3
, D. M. Silevitch
2
,
S. E. Cooper
1
,
D. Mandrus
4
,5
,
P
atrick
A.
Lee
2
,
6
,
T. F. Rosenbaum
2
,*
1
Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904
-
0495, Japan
2
Division of Physics, Mathematics, and Astronomy, California Institute of Technology,
Pasadena, California 91125, USA
3
The Institute for Quantum Matter and D
epartment of Physics and Astronomy, The Johns
Hopkins University, Baltimore, Maryland 21218, USA
4
Department of Materials Science and Engineering, University of Tennessee, Knoxville,
Tennessee 37996, USA
5
Materials Science and Technology Division, Oak R
idge National Laboratory, Oak Ridge,
Tennessee 37831, USA
6
Department of Physics,
Massachusetts
Institute of Technology, Cambridge, MA, USA
*
Corresponding author
s
.
Email:
yejun@oist.jp
,
tfr@caltech.edu
.
M
etal
-
insulator transition
s
involve a mix of charge, spin, and structural degrees of
freedom, and when strongly
-
correlated, can underlay the emergence of exotic
quantum states
.
Mott
insulators
induced by
the opening of a
Coulomb
gap
are
an
important and
well
-
recognized
class
of transitions
,
but
insulators
purely
driven by
spin
correlation
s
are
much less
common
,
as
the
reduced energy scale
often
invites
competition
from
other
degrees of freedom
.
Here we
demonstrate a clean
example
of
a
spin
-
correlation
-
driven
metal
-
insulator transition
in
the
all
-
in
-
all
-
out pyrochlore
antiferromagnet
Cd
2
Os
2
O
7
,
wh
ere
the lattice symmetry is
fully
preserved
by the
antiferromagnet
ism
.
After
the
antisymmetric
linear
magnetoresistance
from
conductive
,
ferromagnetic
domain wall
s
is
careful
ly
removed experimentally
,
the Hall
coefficient
of
the
bulk
reveal
s
four
Fermi
surfaces
, two of electron type and
two
of
hole type,
sequentially
depart
ing
the
F
ermi level
with
decreasing
temperature
below
the N
é
el temperature
,
T
N
.
C
ontrary to the common beli
ef of
concurrent
magnetic and
metal
-
insulator transition
s
in
Cd
2
Os
2
O
7
,
the
charge gap of
a
continuous
metal
-
insulator transition
opens
only
at
T
~10K, well below
T
N
=
227K
.
The
insulating
2
mechanism
resolved by the Hall coefficient
parallels
the
Slater picture
,
but
without
a
folded
Brillouin zone
, and contrasts sharply with the behavior of
Mott
insulator
s
and
spin density wave
s
, where the
electronic
gap opens above and at
T
N
,
respectively.
Unlike
insulators or semiconductors
derived
from
simple
metal
s such as
sodium
and lithium
[
1,2
],
metal
-
insulator transitions in correlated
-
electron
systems
reside
outside
the
paradigm
of
single
-
electron band
structure
.
Factors such as reduced dimensionality and
randomness [
3,
4
] enrich the description of the critical behavior
,
with possible separation
of spin and charge, and
deep connections
to
exotic
states
such as high
T
c
superconduct
ivity
and quantum spin liquids
[
5
]
.
In the limit of large electronic correlations, the starting point
for discussion is usually the opening of the Hubbard gap [
6
], with antiferromagnetic order
a subsidiary effect
.
There exist several major experimental
challenges
in
establishing
a
convincing
example
of
a
metal
-
insulator transition
driven by spin correlations
[
7
]
. First, t
he
spin
-
correlation
energy
is
typically much
smaller
than the direct Coulomb interaction
,
often
at
a
scale
comparable to
that of
the
structural
modification
s
induced by
the antiferromagneti
c
order
through
magnetostrict
ive
effect
s
and
symmetry
change
s
,
leading
to
a chicken
-
and
-
egg
conundrum
between
ascribing the insulating transition to
the
lattice
or
the
magnetism
[
8
,
9
]
.
I
t is
thus
preferable
to
search
for
candidate
system
s
in which
the magnetism
would
preserve
the crystalline symmetry.
Materials that demonstrate a
ll
-
in
-
all
-
out
(AIAO)
antiferromagnetic
order
on a
pyrochlore lattice
,
with all four spins on the corner of a
tetrahedron pointing either towards or away from the center,
meet th
is
criterion
.
The AIAO
order
induces
no symmetry
-
breaking magnetostriction
,
and causes
an
isotropic
expansion
of the
cubic
unit cell
by
a minimal
D
a
/
a
~10
-
5
,
only
becom
ing
experimentally
resolv
able
when
T
N
drops
below
40 K
[
10
,
11
]
.
For
AIAO order with
T
N
>
100
K, th
is
overall
magnetostriction
is
fully
camouflaged
by the thermal lattice contraction
[
10
]
,
which
broaden
s
bandwidth
s
but
introduces
no band splitting
. T
h
e
family of
AIAO
antiferromagnet
s
thus
provides
a
highly
desir
able
model system
to investigate
spin
correlations
with
little
lattice
interference
.
3
Identifying
a
n
AIAO
system
with
a
metal
-
insulator
transition
re
presents
the
next
experimental
challenge
.
Accompanying
the AIAO
order
, m
any
5
d
oxides
,
such as
R
2
Ir
2
O
7
(
R
= Eu, Sm, and Nd) and Cd
2
Os
2
O
7
(Ref. [
12
] and references in [
11
,
13
,
14
])
,
also
demonstrate
a
change of temperature
dependence
in
the
resistivity
at
T
~
T
N
[
9
,
13
,
15,
16
].
However
, the resistive behavior
of
R
2
Ir
2
O
7
(
R
=Nd, Sm, Eu)
, especially in the param
a
gnetic
phase,
is often
in
consistent
and
rai
s
es
concerns
about
their
intrinsic
,
disorder
-
free
behavior
[
13,
17
,
18
].
Cd
2
Os
2
O
7
has
present
ed
consistent behav
i
or
in both
the electron correlation
and metal
-
insulator transition.
S
amples from several groups [
9,
15
,
16
]
always
demonstrate
magnetic ordering
at
T
N
=
225
-
227K
,
metallic behavior above
T
N
,
a
nd a
three
-
to
-
four
-
decade rise of
the
resistivity
for
T
<
T
N
in
the best samples
. This
repeatability from crystal
to crystal
likely
indicat
es
a low level of
disorder
because of
the 2+/5+ valence condition o
f
Cd and Os
ion
s
as well as the
chemical transport
growth
procedure
at low
temperature
[
9,
15, 16
]
.
T
here exist
s
a
n
additional challenge arising from complications in modeling and
understanding the transport data in many 5
d
AIAO antiferromagnets due to
the
intrinsic
ally
conductive and
highly coercive ferromagnetic domain walls [
9,
19
-
21
]
.
F
erromagneti
c
domain
walls
introduce a Zeeman shift
in
the
metallic
paramagnetic band structure
,
but
they
are
not expected to gap the Fermi surface
like
the
antiferromagnetic
bulk
,
and
they
are
expected to
remain
metallic
down
to
T
= 0
.
A
s was pointed out recently
[
21
]
,
the highly
coercive
metal
l
ic
ferromagnetic domain walls
generate antisymmetric linear
magnetoresistance (MR)
of
the same functional form as the Hall resistance
. Moreover, the
anti
symmetric linear MR
is
detectable in
Hall channel
s
due to
distorted current paths
through
the
domain walls
[
21
]
.
This effect
is
likely
the root cause of the widely varying
Hall coefficient reported in the literature
for Cd
2
Os
2
O
7
[
9, 16
]
,
as
the
standard
procedure
for
extracting Hall resistance through
antisymmetri
zation
with respect to magnetic field
direction
lead
s
to erroneous results
.
Here we
present
high
-
fidel
i
ty
resistivity and Hall coefficient measurements
on
single crystal
Cd
2
Os
2
O
7
,
after
employing
a
n intricate
procedure
to
eliminate
the
influence
of
conductive ferromagnetic domain walls.
Unlike the common understanding of
a
4
concurrent metal
-
insulator transition
with
the AIAO magnetic transition at
T
N
, our results
reveal that
Cd
2
Os
2
O
7
is
metal
lic
for
a
broad
temperature range
below
T
N
,
despite
an
increasing resistivity with decreasing
T
. It
only
becomes
a
n
insulator
at
T
MIT
~
10
K
, when
four
sets of
Fermi
surfaces
have
sequentially
left
the Fermi
level
to open a true electronic
gap
. This
large
separation
in temperature for
spin
order (
T
N
)
and
the
charge gap (
T
MIT
)
,
with
T
N
>
>
T
MIT
,
unambiguously establishes spin ordering as the driving force in
Cd
2
Os
2
O
7
s metal
-
insulator transition.
Our
methodology
in separating the Hall behavior
of
the
bulk
from
the
influences
of the domain walls should
provide a generic
approach
to
parsing spin and charge effects in correlated antiferromagnetic insulators with metallic
domain walls
.
Our
single
-
crystal Cd
2
Os
2
O
7
sample
s
demonstrate
a
monotonic rise of resistivity
over three decades (~
3
000
́
)
from
T
N
to 1.
8
K
at zero
-
field
(Fig. 1),
consistent
with the best
samples
reported in the literature [
9, 15, 16
].
Instead of
using
bar
-
shaped samples for
both
resistivity and Hall measurements,
our key approach is to
utilize van der Pauw (vdP)
configuration
of
electrical
lead placement
o
n
plate
-
shaped
samples (
[
22
],
Schematics in
Figs. 1, 2a)
.
This choice
of putting four leads on equal footing
aim
s
to
comprehensively
evaluate the
effect
s
of
electrical current
path
s
which
constantly
redistribut
e
between
conductive
domain walls and
an
increasingly
insulating
bulk
as the
temperature
decreases
.
As
demonstrated by our samples, t
he vdP ratio, defined as
R
vdP
2
/
R
vdP
1
at zero field, stays
constant only in the paramagnetic phase above
T
N
.
B
elow
T
N
, the vdP ratios of both samples
have a
strong
yet continuous
temperature dependence (Fig
.
1 inset).
The resis
tivity
in Fig.
1
is calculated
from
R
vdP
2
and
R
vdP
1
at each
T
according to the standard vdP procedure
[
22
]
,
a
n
issue
w
e will revisit
below
.
T
he highly coercive, field
-
independent
magnetization
M
of
t
he
conductive
ferromagnetic domain walls
necessarily introduce
s
antisymmetric linear MR [
21
]
that
make
s the
Hall
resistance
s
of
the
two
reciprocal
channels
,
R
12,34
(
H
,
M
) and
R
43,12
(
H
,
M
)
,
have
different linear slopes
with
H
(Fig. 2a)
.
Due
to
the
cubic symmetry of
AIAO order, it
is not possible to create a single
antiferro
magnetic
domain
and
remove domain walls
altogether
by field cooling
.
T
he
separat
ion of
galvanomagnetic response
s
of
the
bulk
5
domain
s
and
the
domain walls
is instead
carried out
by introduc
ing
a var
iable
M
(
f
)
through
field
-
cooling
along 24 angular
directions
f
w
ithin the
sample
surface
plane
(Fig. 2,
Methods, and Ref. [
21
])
.
Here we first
examine
f
-
dependences of
two reciprocal
Hall
resistivity channels,
the vdP ratio
,
and
resistivity
r
(
H
=0),
at
temperatures 195K, 30K, and
1.8K
(Fig. 2)
,
where the ferromagnetic domain walls
have
different level
s
of
influence
as
gauged by
the
conductance and
the
bulk
Hall coefficient.
At
all three temperatures
(Figs. 2b
-
2d
)
,
the average
slopes
of
two Hall
resistivity
channels
are
always
f
-
independent
,
while
the
result
ant
f
-
dependent
components
behave
differently
.
At 195K and 30K,
the
f
-
dependent
Hall
resistivity
slopes
of
the reciprocal
channels
follow two constrain
t
s
, as
they are
(1)
of opposite sign at each
f
,
canceling out
for
the
f
-
independent average,
and
also
(2)
identical
at
f
and
f
+
p
respectively
,
lead
ing
to
identical
f
-
average
d
resistivity slope
s
of
both
Hall
channels
.
From previous analysis [
21
],
constrain
t
(1)
reflects
voltage
-
current reciprocity, while
constrain
t
(
2
)
manifests
Onsager’s
reciprocity
relation
with regard to
ferromagnetic domain wall
M
.
A
t
1.8
K,
the
f
-
depende
nt
Hall resistivity slopes
(Fig. 2d)
behave
different
ly.
Only constrain
t
(1) is
sustained
, while
constrain
t
(2)
can
not be satisfied
by
any choice of
the
f
-
independent
component
s. The
result is that
the
f
-
average
d
resistivity slope
s
of
individual Hall
channel
s are
no longer
necessarily equal
to each other
and
to
the
f
-
independent component.
The breakdown of constraint (2)
seemingly
implies a violation of Onsager’s
reciprocity
relation
between
f
and
f
+
p
states
.
H
owever,
the
established
Onsager’s
reciprocity
in our
system
hinges
on the
invers
e
relationship
between
domain wall
magnetization
s
M
(
f
)
an
d
M
(
f
+
p
)
through
separate
field
-
cooling processes
at
f
and
f
+
p
.
The
ir
invers
e
relation
ship
is
generally
robust
in
that
both
r
and
the
vdP ratio
at zero field
demonstrate
a
p
-
periodicity
at all temperatures
(Figs. 2b
-
2d)
. At 1.8K,
the conducti
on
patterns
at
f
and
f
+
p
are
similar
enough to be
reproducibly differentiate
d
from
th
ose
at
neighboring
f
positions
,
judging
by
r
and
the
vdP ratio
(Fig
s
.
2d
)
.
Nevertheless
,
because
of the
separate
cooldowns
,
there exist differences beyond an inversion between
M
(
f
) and
M
(
f
+
p
)
.
With the
increasingly insulating
bulk, the
electrical
current
is
more
concentrated
6
along
a fraction
of
the domain walls,
as reflected by the
dramatic
ally
oscillating
vdP ratio
f
rom
3:1
to
1:4 (Fig. 2d).
While the
entire
sample
volume bring
s
better
averaged
galvanomagnetic
behavior
and
demonstrate
s
Onsager reciprocity
(Fig. 2c), probing only a
small
number
of domain walls enh
ances the relative difference
between
M
(
f
) and
M
(
f
+
p
)
.
Even at a
fixed
f
, multiple
field
-
cool
ing
s
c
an
lead to significant difference
in
individual
Hall
channel
s
at 1.8K (Fig. 2d)
,
despite
the
consisten
cy
at 30K
(Fig. 2c)
.
We
note that
the
assumed uniform medium
for
t
he
vdP technique [
22
]
is justified
a posteriori
at 195K and
30K,
as the
calculated
r
(
f
)
varies
within
±
0.1
%
and
±
3
%
,
respectively
.
C
onstraint (2)
remains satisfied (Figs. 2b
,
2c).
At
1.8K,
r
(
f
)
calculated
from
the vdP
formula [vdP1958]
varies by ±50% (Fig.
2
d)
.
Although the uniformity assumption
no longer
holds
at 1.8K
to
legitimize
both the
vdP
-
derived
resistivity
and constraint (2)
,
our procedure to extract
the
Hall coefficient
R
H
through the average
slope
of
two
Hall
resistivity
channels
is
protected
by
the
fundamental principle of voltage
-
current recipr
ocity
.
With the understanding of
how to
extract
R
H
through
a
f
-
dependence
study
at
three
fixed temperatures
, we
now
explore the temperature
evolution
of
R
H
by
taking the
averag
e
Hall resis
t
ivity
slope
of
two reciprocal channel
s
at a fixed
f
(Fig. 2e)
.
R
H
(
T
)
measured on
two
different Cd
2
Os
2
O
7
single
crystal
s
(
Fig. 3
)
demonstrates
a consistent picture
that
represents
the major
finding
of
this
work
.
R
H
(
T
)
remains stable
above
T
N
=227K,
and
all
bands only start to
evolve
at
T
N
,
maintaining
a delicate balance
between
them
until the first
sharp
change
at 220 K.
D
espite
a rise of
nearly
three
orders of magnitude in
r
(
T
)
from
T
N
down
to 10 K
,
R
H
(
T
)
remains
finite and
oscillates between positive and negative values
.
r
(
T
) reflects
a fast
drop
in
total
carrier
density
with
decreasing temperature
(Fig. 1)
,
and
the
oscillating
R
H
(
T
)
reflects
the changes in the bands, with
an alternati
ng
dominance by
either electron
s
or hol
e
s
as the
itinerant carriers
.
A
temperature dependence
of
the
carrier
mobility
would
not
account for this
metallic
behavior
.
When a
band
move
s
out
from
the
Fermi
level
,
th
e
relative contributions of charge carriers
(electron or hole)
changes,
signa
l
ed
by
a turn
in
direction
in
of
R
H
(
T
)
.
The first
surface
moves out
from
the Fermi level
at
~
220K
(Fig.
3
, top inset
)
, and with
R
H
(
T
)
turn
ing
more electron
-
like, the
departed
carriers
are
of
hole type.
As
thermal excitation at finite temperature still populates the departed
band
s
close to
the Fermi level,
R
H
(
T
) remains a smooth function of
T
.
Here we count four
7
characteristic temperatures below
T
N
at
22
0K, 1
6
5K,
8
0K, and 10K
that
reflect
four
sets of carriers
leaving
the Fermi
level
(arrows
and
T
1
-
T
4
in Fig. 3
inset
s
)
.
Below
T
~
10K
,
a
sharply
divergent
R
H
indicates
that
a
full
gap
emerges
in the bulk
,
and
a
ll
itinerant
carriers
are due to thermal excitation
,
predominately of electron type
from the last departed band
.
Our results
can be compared with
existing
band structure calculation
s
[
23
]
that
suggest the Fermi surface is made
up
of th
ree
sets of carriers
in the paramagnetic phase
of
Cd
2
Os
2
O
7
:
hole
surfaces around the W point, an electron shell at the
G
point, and a family
of electron ellipsoids along the
G
-
X line, solely of Os 5
d
t
2g
origin.
Our observation reveals
a
fourth
set
of
hole ellipsoids, potentially locate
d
along the
G
-
X line [
23
],
but
which
have
an energy difference too small to be resolved by the band structure calculation
given that
they
drop below
the Fermi level
at 220K, only 7K below
T
N
.
Infrared reflectivity also
illuminates
t
he metal
-
insulator transition in Cd
2
Os
2
O
7
[
24
-
25
]
.
While the direct optical gap
has been consistently verified
, t
he interpretation
varies from
either a
spin
-
density
-
wave
gap
opening at
T
N
[
24
]
or
a
n indirect
gap
opening
at
~
21
0K
because of
a
Liftshitz type of
mechanism
[
25
]
. Th
e lat
t
er
is partially consistent with our observed first
set of carriers
depart
ing
the Fermi level at 220K.
Our results demonstrate
that
the transition at
T
N
=227K
in
Cd
2
Os
2
O
7
should be
regarded as only the magnetic
-
ordering transition, and there is no concurrent metal
-
insulator transition despite
the fact that the
resistivity
r
(
T
) chang
es
its temperature
dependence around
T
N
(Fig. 1 inset
)
.
Given
the
well
-
defined changes obser
ved for
R
H
(
T
)
at
T
N
(Fig. 3),
the driving
mechanism
behind
the
electronic
evolution
should
be attributed
to
Os 5
d
t
2g
band renormalization by
t
he AIAO
order
[
7
]
,
with the effect
grow
ing
with
the
increasing
strength of
the
magnetic
order parameter,
the
staggered moment <
m
>
, with
decreasing
T
.
From
a
direct
x
-
ray
magnetic diffraction study
[
12
]
,
<
m
>
continu
es
to grow
to
the zero
-
temperature
limit
without saturation
.
This
spin
-
dependent
shift of
the
quasiparticles
self
-
energy
happens within the antiferromagnetic phase and the
electronic
gap
is
opened
by
developed
antiferromagnetic
order
.
I
t
is analogous
to
a Slater
mechanism
without
Brillouin
zone
-
folding
[
7
]
.
8
The entire
density of states
within ±1.5eV of the Fermi level
is
made
of
the
Os 5
d
t
2g
manifold
of
twelve
bands
total
(two
Cd
2
Os
2
O
7
units in the primitive unit cell
,
with three
t
2g
bands
from
individual
Os ion
s
)
[
23
]
.
D
ue to the Os
5
+
(5
d
3
) valence,
these bands are
filled
between
the sixth and seventh bands
, with dispersion across the Fermi surface to create the
electron
-
type and hole
-
type carriers.
S
pin correlation
renormalizes
the
t
2g
manifold
to
create a
true gap
at
the half
level
between the sixth and seventh ban
ds
.
T
he
Mott
-
Hubbard picture
of
the metal
-
insulator transition
split
s
a single
band
to
open a gap by
strong
charge correlation energy
(
U
~2
-
6
eV)
.
In Cd
2
Os
2
O
7
, an AIAO
antiferromagnet with no structural instability, the transition
relies on
a
small spin
-
correlation energy (
T
N
~
20meV
)
to
essentially create a
band insulator
.
The spin and charge
gaps are
widely
separated in temperature
.
However, they remain experimentally obscure
until the confounding effects of metallic domain wall conduction can be separated from the
intrinsic bulk behavior. The methods introduced here clarify the contributions from the
bulk and the role of the spin an
d charge degrees of freedom. They also promise a means to
quantify the conductive properties of coercive ferromagnetic domain walls winding their
way through an insulating antiferromagnet.
Method
s
:
Galvanomagnetic
measurements:
H
igh quality Cd
2
Os
2
O
7
si
ngle crystals
were
grown by
vapor transport techniques [
9
] and
polished from individual tetrahedra to plates of 17
-
20
μ
m thickness with a (1, 1, 0) surface norm
al
[
14
].
The transport samples were
selected with
a
typical mosaic of
0.0
1
o
-
0.02
o
FWHM
characterized
during
a
previous synchrotron
x
-
ray
diffraction study
[
14
]
. As the current distribution could
potentially
change under
temperature between domain walls and bulk, a strict Hall bar
shaped sample
geometry is
not useful
.
Instead
,
w
e employ a van
der Pauw (vdP)
sample
geometry
[
22
]
to
allow the
measure
ment of
both Hall and magnetoresistance
with their reciprocal
configurations
(Fig
s
.
1&
2a inset
s
)
[
21
]
.
Four
25
-
μ
m diameter
gold wires
we
re
attached to the transport
samples of typical
2
00
μ
m lateral sizes by conductive silver epoxy
.
The
transport
samples were mounted on
the
standard
sample
holder
of
a
horizontal
9
rotator
probe in a
14
-
T
esla
Physical Property Measurement System (
PPMS
,
Quantum
Design
, Inc.
).
Using
the horizontal rota
tion
, w
e first cool our samples through
T
N
with
a 2
-
T
esla
magnetic
field
applied
along an in
-
plane direction
f
(Fig. 2a insets),
then
the sample
is
rotated
below
T
N
to allow
the
measurement
magnetic
field
of both the Hall
effect
and
the
MR
to be
applied perpendicular to the sample surface. A
n additional
home
-
built
indexing
-
stage
on the sample
holder
provides degree of freedom
s
to set
field
-
cooling
along 24
discrete
angular
positions
of
f
within the sa
mple surface plane
[
21
]
;
the origin of
the
f
-
angle has no
specific
relationship
to either
the wiring position
s
of
the
electrical leads
or
the
crystalline
structure
.
G
alvanomagnetic response
s
of both reciprocal Hall channels
and vdP
channels
w
ere
measured
at selected temperatures
of
195K, 30K, and 1.8K for the full
f
-
dependence
(Fig. 2b
-
2d)
.
The
data set at
195K w
as
measured independently from th
ose at
the
other two
temperatures
.
At
30K and 1.8K
, measurement
s
were
repeated
at
three
and
eleven
f
positions
respectively
for
a
check of
reproducibility
through
an
additional
field
-
cool
ing
proce
ss
.
For measurements at 30K, all data except two (
one each
at
f
=30
o
and
195
o
) have a corresponding measurement at 1.8 K during the same field
-
cooling p
rocess
in
order
to compare the
f
-
dependence at both temperatures.
For
the
full temperature evolution
in Figs. 1, 2e, and 3, both samples were field
-
cooled along one in
-
plane
f
posi
tion
to base
temperature, then the
galvanomagnetic
measurements were performed at
each
stabilized
temperature
along
the
warming
trajectory
.
We observe
no
degrading
or change in
our
samples after
many
thermal cycl
es (>
6
0
in COO
-
2
)
.
The r
esistivity was measured using a Lakeshore LS3
72
AC
resistance bridge
,
working at 9.8 Hz
, together with a low
-
noise 3708 preamp
and a home
-
built vdP
switching
box
based on
low
-
resistance
CMOS
relay
switches
.
At zero field, the vdP relationship is
satisfied
to
D
R
/
R
max
= (
R
Hall1
+
R
vdP1
-
R
vdP2
)/Max(
R
vdP1
:
R
vdP2
)
<
±
0.05% at 30K
and
<
±
0.25%
at 1.8K
.
R
(
H
) curves
we
re measured
over
a
magnetic field
loops
of
±
4
T
esla
.
Since n
o
field
hysteresis was observed,
R
(
H
)
values are averaged at each field
, exemplified by
Fig. 2a
,
and fit to a polynomial form to the second order. The linear slope is taken for plots in Figs.
2 and 3. O
ur sample
s
demonstrate
a
very
low
level of
positive parabolic MR
~
0.3% over
±14 Tesla
,
consistent from
1.65K to
80K,
and is thereby
unappreciable
at low field
s
.
10
Acknowledgments
Y.F. acknowledges support from the
Okinawa Institute of Science and Technology
Graduate University, with subsi
dy
funding from the Cabinet Office, Government of Japan.
The work at Caltech was supported by National Science Foundation
Grant No. DMR
-
1606858. P.A.L. acknowledges support from the US Department of
Energy, Basic Energy
Sciences, Grant No. DE
-
FG02
-
03ER4607
6. D.M.
acknowledge support from the US
Department of Energy, Office of Science, Basic Energy
Sciences, Division of Materials
Sciences and Engineering.
Author contributions
Y.F.
,
Y.W.
, P.A.L.,
and T.F.R. conceived of the research; D.M. provided samples; Y.F.,
Y.W.,
D.M.S.,
and
S.E.C. performed experiments; Y.F.
,
Y.W.
, P.A.L.,
and
T.F.R. analyzed data
and
prepared
the manuscript.
Competing interests
The authors declare no competing interests.
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Figure
c
aptions:
Fig. 1.
T
ransport signature
s
of
Cd
2
Os
2
O
7
at zero field.
Resistivity
r
(
T
)
of
Cd
2
Os
2
O
7
measured over two single crystals
(COO
-
1 and COO
-
2)
using
the
vdP configuration
(Schematics).
At each temperature, both vdP
channels were measured in order to account
for the changing current path
between
the
insulating bulk and conductive domain walls
.
(Top inset)
The
resis
tance
ratio
R
vdP
2
/
R
vdP
1
between two vdP channels
manifest
s
the
changing current path below
T
N
=227K.
(bo
ttom inset) Details of
r
(
T
)
near
T
N
, showing
both metallic behavior above
T
N
, and also a
n
upturn of
r
near
but still above
T
N
,
which is
often attributed to dynamical spin fluctuation effects
without long
-
range order.
T
N
is
determined
precisely
from
magnetic susceptibility
c
(
T
),
individual
R
vdP
2
(
T
)
and
R
vdP
1
(
T
)
(not shown)
,
and
R
H
(
T
)
in Fig. 3
.
Fig. 2.
Separating
the influence
of
metallic
ferromagnetic domain wall
s
.
(
a
)
Raw data
of Hall resistances
R
(
H
) between two reciprocal channels
.
The
difference in slopes
indicates the influence of
asymmetric linear magnetoresistance
from ferromagnetic domain
walls [
21
]
.
(Top
s
chematics)
The f
ield
-
cooling process
in two
-
stages:
(i)
field aligned
parallel to the sample surface during cooldown; and
(ii) sample rotated to have field
pe
r
pendicular to its surface for galvanomagnetic measurements.
The in
-
plane
magnetizing
direction
is defined by angle
f
at 24
discrete
positions.
(Bottom schematics)
vdP
configuration for the two reciprocal Hall channels.
(
b
-
d
)
f
-
dependence of Hall resistivity
slopes in two reciprocal channels (red and blue) and their average (
fresh green
),
in addition
to resistivity (green) and vdP ratio (orange), measured
in sample COO
-
2
at three
temperatures 195K, 30K, and 1.8K.
(Methods
)
(
e
)
Hall resistivity slopes from two
reciprocal channels
(red and blue)
are plotted alongside the
ir
average
(fresh green)
for
two
14
different
single crystal
Cd
2
Os
2
O
7
s
amples.
Although
the
resistance slopes of
an
individual
Hall channel are very different
for
each sample,
with
occasional cross
ing
s
at various
temperatures
,
the average
s
are similar
in shape
between
the
two samples
, and
determine
the
bulk Hall coefficient
R
H
(
T
)
.
This irregular behavior
of
resistance slopes of
individual
Hall
channel
highlights
potential
experimental deficienc
ies
in
previous Hall measurements
.
Fig. 3.
M
etal
-
insulator transition
in
Cd
2
Os
2
O
7
revealed
through
bulk Hall coefficient
.
The bulk
Hall coefficient
R
H
(
T
)
from
two
Cd
2
Os
2
O
7
samples in
Fig. 2e
are
compared
in
detail
.
While
R
H
(
T
) evolves slowly above
T
N
, it starts
to
deviat
e
from the high temperature
behavior right at
T
N
, indicating
th
at the onset of
AIAO
antiferromagnetic
order
influen
c
es
the
band
structure
a
round
the Fermi level
.
Nevertheless,
R
H
(
T
)
does not
diverge until
it
reaches a
temperature
below
10K
~ 0.
044
T
N
,
whe
n
the true
charge
gap opens
.
In between,
each
sharp change in
in
R
H
(
T
) indicates a band leaving the Fermi level, marked by
arrows
a
t four different temperatur
es,
T
1
=220K,
T
2
=165K,
T
3
=
80
K,
and
T
4
=10K
.
T
wo bands are
of hole type and the other two of electron type.
15
Fig. 1.
16
Fig. 2.
17
Fig. 3.