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As-75 nuclear magnetic resonance study of antiferromagnetic
fluctuations in the normal state of LiFeAs
Citation for published version:
Jeglic, P, Potocnik, A, Klanjsek, M, Bobnar, M, Jagodic, M, Koch, K, Rosner, H, Margadonna, S, Lv, B,
Guloy, AM & Arcon, D 2010, 'As-75 nuclear magnetic resonance study of antiferromagnetic fluctuations in
the normal state of LiFeAs', Physical review B: Condensed matter and materials physics, vol. 81, no. 14,
140511, pp. -. https://doi.org/10.1103/PhysRevB.81.140511
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75
As nuclear magnetic resonance study of antiferromagnetic fluctuations
in the normal state of LiFeAs
P. Jeglič,
1
A. Potočnik,
1
M. Klanjšek,
1
M. Bobnar,
1
M. Jagodič,
2
K. Koch,
3
H. Rosner,
3
S. Margadonna,
4
B. Lv,
5
A. M. Guloy,
5
and D. Arčon
1,6
1
Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
2
Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
3
Max-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Str. 40, 01187 Dresden, Germany
4
School of Chemistry, University of Edinburgh, West Mains Road, EH9 3JJ Edinburgh, United Kingdom
5
Department of Chemistry and TCSUH, University of Houston, Houston, Texas 77204-5002, USA
6
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
共Received 16 December 2009; published 30 April 2010
兲
We present a detailed study of
75
As nuclear magnetic resonance Knight shift and spin-lattice relaxation rate
in the normal state of stoichiometric polycrystalline LiFeAs. Our analysis of the Korringa relation suggests that
LiFeAs exhibits strong antiferromagnetic fluctuations, if transferred hyperfine coupling is a dominant interac-
tion between
75
As nuclei and Fe electronic spins, whereas for an on-site hyperfine coupling scenario, these are
weaker, but still present to account for our experimental observations. Density-functional calculations of
electric field gradient correctly reproduce the experimental values for both
75
As and
7
Li sites.
DOI: 10.1103/PhysRevB.81.140511 PACS number共s兲: 74.70.⫺b, 76.30.⫺v, 76.60.⫺k
Following the discovery of superconductivity in
LaFeAsO
1−x
F
x
,
1
nuclear magnetic resonance 共NMR兲 pro-
vided one of the earliest evidences for unconventional pair-
ing in the superconducting 共SC兲 state,
2–4
multigap
superconductivity,
5–7
pseudogap 共PG兲 behavior in the normal
state,
2,3,8
and antiferromagnetic 共AFM兲 ordering of Fe
2+
spins in the undoped parent compounds of Fe-As
superconductors.
3,9,10
Although the SC pairing mechanism is
still under debate, it is commonly believed that AFM
fluctuations play an important role in promotion of
high-temperature superconductivity in this family. This
is indicated by the presence of the AFM phase next to
the SC ground state in the phase diagrams of REFeAsO 共Ref.
11兲共“1111,” RE=rare earth兲 and AFe
2
As
2
共Ref. 12兲
共“122,” A=alkaline-earth metal兲 compounds.
Recently, LiFeAs, the so-called “111” member of the
Fe-As superconductors, has been reported
13
to undergo a
transition to the SC state at T
c
=18 K without additional
doping and apparent AFM ordering or accompanying struc-
tural phase transition. Its structure is a simplified analog of
the “1111” or “122” members: FeAs layers comprised of
edge-sharing FeAs
4
tetrahedra are separated by double layers
of Li ions. However, the tetrahedra are deformed and the
Fe-Fe distance is considerably shorter compared to other
Fe-As superconductors. Moreover, T
c
linearly decreases with
applied pressure, similarly as in overdoped K
x
Sr
1−x
Fe
2
As
2
,
although the charge count of −1 per FeAs unit would rather
compare LiFeAs to undoped SrFe
2
As
2
.
14
LiFeAs is also
claimed to be a weakly to moderately,
15
or moderately to
strongly
16
correlated system. These conflicting results raise
an important question about the significance of AFM fluctua-
tions and the placement of LiFeAs in the general Fe-As su-
perconductor phase diagram.
Here we employ
75
As NMR to quantitatively account for
the extent of spin correlations in the normal state of LiFeAs
and compare it to a typical “122” member. We find that the
spin-lattice relaxation rate T
1
−1
is enhanced, compared to the
values calculated for the noninteracting electron scenario.
The quantitative comparison with cuprates and organic
superconductors
17
indicates that AFM correlations may also
play an important role in the LiFeAs superconductor.
Stoichiometric polycrystalline LiFeAs was synthesized
from high-temperature reactions as described in detail in Ref.
13. For magnetic resonance experiments the LiFeAs sample
was sealed into the quartz tube under vacuum to avoid con-
tamination with moisture during the measurements. To check
the quality of our polycrystalline LiFeAs samples, we per-
formed electron paramagnetic resonance measurements in
the vicinity of SC transition. A nonresonant microwave ab-
sorption effect
18
occurs sharply below 21 K 关Fig. 1共a兲兴, dem-
onstrating the onset of SC state at T
c
⬃20 K in agreement
with Ref. 13 and demonstrating the high quality of our
sample.
75
As 共I=3/ 2兲 NMR frequency-swept spectra were
measured in a magnetic field of 9.4 T with a two-pulse se-
quence

−
−

−
−echo, a pulse length

=5
s, inter-
pulse delay
=100
s, and repetition time 100 ms at room
temperature. The reference frequency of
共
75
As兲
=68.484 MHz was determined from a NaAsF
6
standard. The
75
As T
1
−1
was measured with inversion-recovery technique.
The band-structure calculations were performed within the
local-density approximation 共LDA兲, as described in detail in
Refs. 10 and 19. As basis set Li共/2s2p3d +3s3p兲,
Fe共3s3p / 4s4p3d+5s5p兲, and As共3s3p / 4s4p3d +5s5p兲 were
chosen for semicore/ valence+polarization states. A well-
converged k mesh with 1183 k points in the irreducible part
of the Brillouin zone was used. The structural parameters
were taken from Ref. 13. The calculated V
zz
component of
the electric field gradient 共EFG兲 tensor is converted into the
experimentally measured quadrupole splitting
Q
using the
relation
Q
=3eV
zz
Q/ 关2hI共2I −1兲兴 with the quadrupole mo-
ment Q and nuclear spin I given in Table I.
Representative
75
As NMR spectra of the central
共−
1
2
↔
1
2
兲 and the satellite 共⫾
3
2
↔ ⫾
1
2
兲 transitions for the
polycrystalline LiFeAs sample are shown in Fig. 1共b兲 for
PHYSICAL REVIEW B 81, 140511共R兲共2010兲
RAPID COMMUNICATIONS
1098-0121/2010/81共14兲/140511共4兲 ©2010 The American Physical Society140511-1
temperatures between room temperature and T
c
. Over the
entire temperature range the line shape remains characteristic
for an axially symmetric EFG tensor, in accordance with the
75
As site symmetry 4mm, indicating the absence of a struc-
tural phase transition, as encountered in the undoped “1111”
and “122” members of the Fe-As superconductors family.
Analysis of the splitting between both singularities belonging
to the satellite transitions reveals only a moderate tempera-
ture dependence of
Q
, which monotonically decreases from
21.35 MHz at room temperature reaching 20.87 MHz at low
temperatures 关inset to Fig. 1共c兲兴. There is no indication of
AFM ordering down to T
c
, which would be seen as an abrupt
broadening of the NMR line shape due to the appearance of
internal magnetic fields.
3,9,10
In Fig. 2共a兲 we show the
7
Li 共I =3/ 2兲 NMR spectrum
measured at 300 K. Contrary to the
75
As resonance the shift
of the
7
Li NMR line is small and negative 关Fig. 2共a兲兴. How-
ever, the value of −61共5兲 ppm cannot be attributed to the
pure orbital shift 共typical values are an order of magnitude
smaller兲, which may indicate an incomplete charge transfer
from the Li layer to the FeAs layer. From the
7
Li NMR
linewidth
␦
⬇90 kHz, we conclude that
7
Li has a very
small
Q
. In order to extract
7
Li
Q
we performed an echo-
decay measurement. The
7
Li echo amplitude clearly shows
characteristic quadrupole oscillations as a function of inter-
pulse delay
in the two-pulse

−
−

−
−echo experiment
关Fig. 2共b兲兴.
21
Oscillations with the period t
Q
=59
s yield
Q
=2/ t
Q
⬇34 kHz. The
7
Li 共 I =3/ 2兲 NMR line-shape simu-
lation taking into account the quadrupole splitting
Q
=34 kHz and the magnetic anisotropy of 160共5兲 ppm
共both obeying axial symmetry in accordance with the
7
Li site
symmetry兲 fits the experimental NMR spectrum very well
关Fig. 2共a兲兴.
Next we compare the experimental values of quadrupole
splittings for
75
As and
7
Li with those obtained from the
band-structure calculations. As usually encountered in Fe-As
superconductors, the displacement of As site along the z axis
has a huge influence on the EFG at the As site, see
Fig. 2共c兲. Experimental
Q
matches the calculated one for
⌬z =z −z
exp
=0, where z
exp
=0.2635 is the experimental As z
position
13
共see Table I for details兲. The minimum in energy
with respect to the As z position predicts the displacement of
As by almost ⌬z=0.3 Å 关marked by the black arrow in Fig.
2共c兲兴. The corresponding
Q
⬃0 fails to correctly reproduce
the measured
75
As
Q
. This is in line with findings in the
“122” compounds
22
but in striking contrast to studies of the
“1111” compounds, where the calculated and measured
Q
’s
agree well for the optimized As z position.
10,19
Calculated
EFG at the Li site is much smaller, less dependent on the As
z position, and does not reach the value
Q
=0 in the covered
interval of ⌬z 关inset to Fig. 2共c兲兴. This can be understood by
different bonding situations: whereas Fe and As build a
polyanionic sublattice formed by covalent bonds, Li only has
a slightly filled 2p shell. As such, the EFG at the Li site does
not provide such a stringent test for the quantity ⌬z, in con-
trast to the EFG at the As site. Anyway, the measured
7
Li
Q
TABLE I. Comparison between calculated and experimental
Q
’s for
75
As and
7
Li sites. Quadrupole moments Q are taken from
Ref. 20.
Site I
Q
共fm
2
兲
V
zz
calc
共V/ m
2
兲
Q
calc
共MHz兲
兩
Q
exp
兩
共MHz兲
75
As 3/2 31.4 −5.82⫻ 10
21
−22.1 21.35
7
Li 3/2 −4.01 −0.11⫻10
21
0.054 0.034
FIG. 1. 共Color online兲. 共a兲 Microwave absorption near the SC
transition at low magnetic field indicating T
c
⬃20 K. Arrows show
different field sweep directions. Sharp peaks at around 1700 G
originate from a dielectric resonator. 共b兲
75
As NMR spectrum at 300
and 20 K for a chosen orientation of LiFeAs polycrystalline sample.
A comparison with simulated powder spectrum with
Q
=21.35 MHz and K
iso
=0.32% demonstrates that the sample con-
tains at least few tens of grains. Inset shows the experimental
Q
as
a function of temperature. 共c兲 Temperature dependence of the high-
frequency singularity of the
75
As NMR central transition.
∆
µ
µ
FIG. 2. 共Color online兲共a兲 Experimental 共solid red line兲 and cal-
culated 共dotted black line兲
7
Li NMR spectra at 300 K and magnetic
field 4.7 T 关
ref
共LiCl兲=77.7247 MHz兴 of LiFeAs polycrystalline
sample. 共b兲
7
Li echo amplitude as a function of interpulse delay
measured at 300 K 共see text for details兲. 共c兲 The calculated V
zz
at
the As 共green diamonds兲,Li共red circles兲, and Fe 共blue squares兲
sites as a function of ⌬z 共see text for details兲, together with experi-
mental data for Li 共black circle兲 and As 共black diamond兲. The mini-
mum in energy regarding the As z position is marked by the black
arrow. The inset shows the Li values on a smaller scale.
JEGLIČ et al. PHYSICAL REVIEW B 81, 140511共R兲共2010兲
RAPID COMMUNICATIONS
140511-2
compares relatively well to the range of calculated values.
We now focus on the role of AFM correlations in LiFeAs.
We begin with the determination of the spin part of the
75
As
NMR Knight shift from the temperature dependence of the
high-frequency singularity of the
75
As central transition
关Fig. 1共c兲兴. The position of this singularity is given by
=
0
共1+K
iso
兲+3
Q
2
/ 共16
0
兲, where
0
is the
75
As Larmor fre-
quency and K
iso
=K
orb
+K
s
represents an isotropic
75
As shift.
The latter has two contributions, the orbital part K
orb
and the
spin part K
s
. Taking into account the slight temperature
variation in
Q
关inset of Fig. 1共b兲兴 we can extract the precise
temperature dependence of K
iso
. For the
75
As orbital
contribution we assume K
orb
=0.15%, which leads to
K
s
共T → 0兲=0 关inset of Fig. 3共a兲兴 in accordance with the spin-
singlet Cooper pairing.
4
We find that K
s
is strongly reduced
with decreasing temperature and changes from K
s
=0.16% to
K
s
=0.055% between room temperature and T
c
=15 K at 9.4
T 关Fig. 3共a兲兴. Such suppression of K
s
is reminiscent of the
PG behavior observed in many Fe-As superconductors.
2,3,8
Because it has been reported for a wide range of x in
Ba共Fe
1−x
Co
x
兲
2
As
2
,
23
the observation of the PG-like behavior
is not yet conclusive about the positioning of LiFeAs in the
Fe-As superconductor phase diagram.
We obtain complementary information from the tempera-
ture dependence of
75
As spin-lattice relaxation rate T
1
−1
关Fig. 3共b兲兴. The nuclear magnetization recovery curves fol-
low M共t兲− M
0
⬀0.1 exp共−t/ T
1
兲+0.9 exp共−6t / T
1
兲共Ref. 6兲 in
the whole temperature range. Below 40 K we detect a slight
enhancement in 共T
1
T兲
−1
followed by a sharp decrease below
T
c
. However, since 共T
1
T兲
−1
does not follow the PG-like be-
havior seen in K
s
, we conclude that AFM fluctuations are
present already above 40 K, which is the reason for almost
temperature-independent 共T
1
T兲
−1
above T
c
. Enhancement
and divergent behavior of 共T
1
T兲
−1
due to the slowing down
of AFM fluctuations has been reported for underdoped “122”
superconductors.
23
With increasing doping the AFM fluctua-
tions become less pronounced and 共T
1
T兲
−1
shows PG behav-
ior in the overdoped regime. Our results suggest that LiFeAs
is somewhere in between these two limits with properties
analogous to those of optimally doped Fe-As superconduct-
ors. It seems that this can explain the relatively high T
c
, its
decrease with the applied pressure and the absence of AFM
ordering.
In order to quantitatively verify the presence of AFM
fluctuations in the normal state of LiFeAs, we turn to the
analysis of the Korringa relation for
75
As,
T
1
TK
s
2
=
ប
4
k
B
␥
e
2
␥
n
2

, 共1兲
where
␥
e
and
␥
n
are the electron and nuclear gyromagnetic
ratios, respectively. The phenomenological parameter

,
called the Korringa factor, characterizes the extent of spin
correlations.
24
In case
75
As couples to the noninteracting
Fe 3d electrons 共i.e., Fermi gas兲 via the on-site Fermi contact
interaction, the Korringa factor is

=

0
=1. Strong ferro-
magnetic fluctuations increase the value of

while AFM
fluctuations decrease it. However, it has been recently pro-
posed for the Fe-As superconductors
4
that the
75
As nuclei are
coupled to the localized Fe electronic spins via the isotropic
transferred hyperfine coupling.
25,26
According to Millis
et al.
25
this renormalizes the noninteracting

0
value.
Namely, T
1
−1
due to the q-dependent spin fluctuations is ob-
tained from Moriya’s expression
1
T
1
T
⬀
兺
q
兩A共q兲兩
2
⬙
共q,
n
兲
n
, 共2兲
where
⬙
共q ,
n
兲 is the imaginary part of the electron spin
susceptibility at the wave vector q and at the nuclear Larmor
frequency
n
. In case
75
As nucleus is coupled to the local-
ized Fe electronic spins via isotropic transferred hyperfine
coupling, we have 兩A共q兲兩
2
⬀cos
2
q
x
a
ⴱ
2
cos
2
q
y
a
ⴱ
2
, where a
ⴱ
is the
distance between two neighboring Fe
2+
spins. For noninter-
acting spins,
⬙
共q ,
n
兲 has no strong singularities in the q
space, and can be taken out of the summation 共integrals兲 in
Eq. 共2兲. Compared to the on-site scenario, we get an extra
factor 兰兰dq
x
dq
y
/ 兰兰dq
x
dq
y
cos
2
q
x
a
ⴱ
2
cos
2
q
y
a
ⴱ
2
=4, which renor-
malizes the noninteracting

0
value to

0
⬘
=4. From here we
proceed as usual: in case

⬎4 ferromagnetic fluctuations are
predicted, whereas AFM fluctuations should lead to

⬍4.
For instance, in cuprates,
25
a prototypical example of a sys-
tem where AFM fluctuations are important,

is reduced by a
factor of 15, compared to the noninteracting electron sce-
nario with transferred hyperfine coupling. A similar factor is
found in some organic superconductors.
17
The experimentally extracted Korringa factor

for
75
As
in LiFeAs is displayed in Fig. 3共c兲. It amounts to ⬃0.7 at
room temperature and then monotonically reduces to ⬃0.1
approaching T
c
. We stress that the absolute values of

de-
pend on our choice of K
orb
. For K
orb
=0.13% and
K
orb
=0.17% the low-temperature value of

changes to 0.17
and 0.03, respectively. Regardless of this uncertainty, the
analysis above demonstrates the enhancement of T
1
−1
at low
temperatures with respect to noninteracting electron limits in
both scenaria considered above, and demonstrates the
strength of AFM fluctuations in LiFeAs. For comparison we
FIG. 3. 共Color online兲 Temperature dependence of the
75
As
NMR: 共a兲 spin part of Knight shift, 共b兲共T
1
T兲
−1
, and 共c兲 Korringa
factor

above T
c
, measured for LiFeAs 共green circles兲 and
SrFe
2
As
2
共red squares兲. Horizontal dashed lines indicate expected
values for

in case of noninteracting electrons for on-site 共

0
兲 and
transferred coupling 共

0
⬘
兲共see text for details兲. The inset to 共a兲
shows the behavior of K
s
below T
c
=15 K 共vertical dashed line兲 at
9.4 T.
75
As NUCLEAR MAGNETIC RESONANCE STUDY OF… PHYSICAL REVIEW B 81, 140511共R兲共2010兲
RAPID COMMUNICATIONS
140511-3
add

values for SrFe
2
As
2
共Ref. 27兲 to Fig. 3. In this case,

is systematically larger by a factor of ⬃1.6 compared to
LiFeAs, and above 250 K

is larger than

0
. In case of the
hyperfine transferred coupling scenario, the experimental

should be compared to

0
⬘
rather than to

0
. Then, the en-
hancement of T
1
−1
in LiFeAs for a factor as large as 40⫾20
at low temperatures suggests strong AFM fluctuations, as
recently predicted by quantum chemical calculations.
16
How-
ever, our LDA calculations, which correctly predict
Q
for
both
75
As and
7
Li sites without taking into account strong
electronic correlations, speak against well-defined localized
moments at the Fe sites as assumed in the transferred hyper-
fine coupling scenario. In this case, the correct reference
valid for the on-site coupling is

0
=1 and the enhancement
of T
1
−1
in LiFeAs is reduced to a factor of 10⫾ 5 speaking for
weaker AFM fluctuations. It is not clear at the moment how
strongly

is enhanced since cross terms between different
bands in the LiFeAs multiband structure can influence T
1
−1
values,
28
while they do not affect NMR Knight shifts, so that
we cannot unambiguously discriminate between the on-site
Fermi contact and the transferred coupling mechanisms. The
ambiguity in the analysis above opens three important issues,
which will have to be addressed in future studies: 共i兲 is the
coupling of
75
As to itinerant electrons in LiFeAs really on-
site while it is transferred in “122” members? 共ii兲 If this is
the case, is it related to structural differences of the FeAs
layer between the two families? And, 共iii兲 should LiFeAs
really be treated as a strongly correlated system?
In summary, NMR and band-structure investigations were
employed to investigate the normal-state properties of the
LiFeAs superconductor. The presence of a PG in the uniform
spin susceptibility measured by the
75
As Knight shift is over-
shadowed by AFM fluctuations in the T
1
−1
measurements. Al-
though the precise determination of the strength of AFM
fluctuations should be a subject of further investigations, we
believe that LiFeAs is the simplest Fe-As superconductor
where correlation effects might be important and should be
considered in future studies.
We acknowledge stimulating discussions with P. Pre-
lovšek, I. Sega, and D. Mihailović. This work was supported
in part by the Slovenian Research Agency. A.M.G. and B.L.
acknowledge the NSF 共Grant No. CHE-0616805兲 and the
R. A. Welch Foundation 共Grant No. E-1297兲 for support.
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