Contrasting spin dynamics between underdoped and overdoped Ba(Fe1-xCox)2As2.

Abstract

We report the first NMR investigation of spin dynamics in the overdoped nonsuperconducting regime of Ba(Fe1-xCox)2As2 up to x=0.26. We demonstrate that the absence of interband transitions with large momentum transfer Q{AF} approximately (pi/a,0) between the hole and electron Fermi surfaces results in complete suppression of antiferromagnetic spin fluctuations for x greater than or approximately 0.15. Our experimental results provide direct evidence for a correlation between T{c} and the strength of Q{AF} antiferromagnetic spin fluctuations.

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arXiv:0907.3875v3 [cond-mat.supr-con] 9 Jan 2010
APS/123-QED
Contrasting Spin Dynamics Between Underdoped and Overdoped Ba(Fe1−xCox)2As2
F. L. Ning1, K. Ahilan1, T. Imai1,2, A. S. Sefat3, M. A. McGuire3,
B. C. Sales3, D. Mandrus3, P. Cheng4, B. Shen4and H.-H Wen4
1Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S4M1, Canada
2Canadian Institute for Advanced Research, Toronto, Ontario M5G1Z8, Canada
3Materials Science and Technology Division, Oak Ridge National Laboratory, TN 37831, USA and
4National Laboratory for Superconductivity, Institute of Physics
and Beijing National Laboratory for Condensed Matter Physics,
Chinese Academy of Sciences, Beijing 100190, China
(Dated: January 9, 2010)
We report the first NMR investigation of spin dynamics in the overdoped non-superconducting
regime of Ba(Fe1−xCox)2As2 up to x = 0.26.
transitions with large momentum transfer QAF ∼ (π/a, 0) between the hole and electron Fermi
surfaces results in complete suppression of antiferromagnetic spin fluctuations for x ? 0.15. Our
experimental results provide direct evidence for a correlation between Tc and the strength of QAF
antiferromagnetic spin fluctuations.
We demonstrate that the absence of inter-band
PACS numbers: 74.70.-b, 76.60.-k
The critical temperature Tc of the newly discovered
iron-based superconductors [1] exceeds 50 K [2, 3]. In-
tensive research efforts are under way world-wide to in-
vestigate the physical properties of these exciting new
materials, yet the superconducting mechanism remains
enigmatic.The consensus reached so far is that the
undoped parent phase of iron-arsenide superconductors
(e.g.LaFeAsO and BaFe2As2) is a semi-metallic sys-
tem with a SDW (Spin Density Wave) ordered ground
state; upon doping a modest amount of electrons or holes,
a high Tcphase emerges from the magnetically ordered
state [2, 3]. Accordingly, it is natural to speculate that
residual antiferromagnetic spin fluctuations (AFSF) as-
sociated with the SDW phase may be acting as the glue
for the superconducting Cooper pairs.
Unlike the case of the high Tccuprates, however, elec-
trons in FeAs layers are always itinerant and there is
no Mott insulating state in the electronic phase diagram.
Therefore a sensible theoretical approach is to choose un-
correlated itinerant electrons as the starting point, and
crank up the electron-electron correlation effects.
the other hand, on the experimental front, past studies
exploring the possible relation between magnetism and
superconductivity focused almost entirely on the under-
doped side of the phase diagram near the SDW phase.
The evolution of the magnetic correlations on the over-
doped side has been unexplored to date.
On
The primary goal of the present study is to fill this
major void for the first time, and explore the magnetic
correlation effects utilizing75As NMR measurements in
the overdoped region of the Ba(Fe1−xCox)2As2 system
[4–11]. Unlike the LaFeAsO1−xFxsystem, one can trans-
form Ba(Fe1−xCox)2As2 into a non-superconducting
metal by increasing the Co concentration above x ∼ 0.15
[9, 10]. Moreover, as a model system, Ba(Fe1−xCox)2As2
has a major advantage over other iron-based supercon-
ductors in a systematic investigation of electronic prop-
erties; one can conduct high precision measurements for
homogeneous single crystals, and compare experimen-
tal results obtained by various techniques. For exam-
ple, recent ARPES [12] and Hall [10] measurements in
Ba(Fe1−xCox)2As2 showed that overdoped electrons al-
most completely fill the hole Fermi surface at the cen-
ter of the Brillouin zone when the doping level reaches
x ∼ 0.15, as schematically shown in Fig.1. These findings
imply that inter-band transitions with momentum trans-
fer QAF∼ (π/a, 0) between the hole and electron Fermi
surfaces gradually disappear when the level of electron
doping exceeds the optimal doping of x ∼ 0.08 (a is the
FIG. 1: (Color online) The SDW and superconducting (SC)
phase transition temperatures, TSDW and Tc, observed for
our samples. Also shown in the inset are the schematic repre-
sentations of the Fermi surface geometry in the unfolded first
Brillouin zone: the underdoped and optimally doped regimes
x < 0.15 (left), and the overdoped non-superconducting
regime (right). Dashed and solid arrows represent the intra-
band and inter-band transitions, respectively. Filling of the
hole Fermi surface by doped electrons results in the absence
of QAF ∼ (π/a, 0) inter-band transitions between the hole
and electron Fermi surfaces in the overdoped regime.

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distance between nearest neighbor iron sites). How do
the change of Fermi surface geometry and the absence of
inter-band transitions affect spin fluctuations? Is the ab-
sence of inter-band transitions the underlying cause of the
suppression of superconductivity in the overdoped region
[10, 12]? In what follows, we will demonstrate from our
75As NMR data that the filling of the hole Fermi surface
results in complete suppression of AFSF. Furthermore,
we will show that the strength of spin fluctuations ex-
hibits a clear correlation with Tcin the overdoped regime
above x = 0.08. Our findings suggest that AFSF asso-
ciated with the inter-band transitions play a crucial role
in the superconducting mechanism.
In Fig.2, we present representative field-swept75As
NMR lineshapes of the nuclear spin Iz= +1/2 to −1/2
central transition for single crystalline samples [10] with
x = 0.09, 0.14, and 0.26. The Co concentration x and the
superconducting critical temperature Tc for each piece
of crystal was determined from Energy Dispersive X-ray
(EDX) measurements and in-plane resistivity ρab, respec-
tively, as summarized in Fig.1. The sharp main peak in
the NMR lineshape, As(0), arises from As sites with all
four nearest neighbor (n.n.) sites occupied by Fe2+ions.
We also observe additional broad peaks for all concen-
trations, as reported earlier [5, 13, 14]. From systematic
measurements of the NMR lineshapes at different mag-
netic fields, we found that the cause of the line splitting is
second order nuclear quadrupole effects, and the Knight
shifts of different peaks are comparable. As shown in
Fig.2, we can assign three additional peaks as As(1),
As(2), and As(3) sites with 1, 2, and 3 of the n.n. Fe
sites occupied by Co, because the intensity ratio is con-
sistent with the probability of finding N (= 0 − 4) Co
at n.n. Fe sites, P(N;x) = C4
confirmed that spin dynamics measured at As(1) sites
show qualitatively the same temperature and concentra-
tion dependencies as at As(0) sites. We will discuss the
complete details elsewhere, and focus our attention on
As(0) sites in what follows.
In Fig.3, we present the temperature dependence of
the NMR Knight shift K in overdoped x = 0.09, 0.12,
0.14 and 0.26 samples measured for the main As(0) sites.
For comparison, we also present our earlier results for
optimum and underdoped samples x ≤ 0.08 [5, 6]. In the
metallic state above TSDW and Tc, all compositions ex-
hibit qualitatively the same behavior; K decreases mono-
tonically with decreasing temperature, then levels off be-
low ∼ 50 K. NMR Knight shift is related to the local
electron spin susceptibility χspinby K = Kspin+Kchem;
Kspin= Ahfχspin/NAµBis the spin contribution to the
Knight shift, where Ahf = 18.8 kOe/µB [15] is the hy-
perfine coupling constant between75As nuclear spins and
surrounding electrons, NA is Avogadro’s number, and
µBis the Bohr magneton. The temperature independent
chemical shift is Kchem∼ 0.22% for x = 0.08 [5], but has
a small concentration dependence, as shown below. Our
results in Fig.3 indicate that χspin shows qualitatively
the same behavior for all compositions regardless of the
N· xN· (1 − x)4−N. We
nature of the ground state.
However, the qualitative similarity observed for K
must not be mistaken as evidence for overall similarity
of spin excitations between x = 0 and x = 0.26. After
all, K probes only the uniform q = 0 wave vector mode
of the spin susceptibility, χspin. In order to see the in-
fluence of doping on spin excitations, it is more useful
to look into the nuclear spin-lattice relaxation rate 1/T1
divided by T (i.e. 1/T1T) presented in Fig.4. 1/T1T
measures the q integral of the imaginary part of the
dynamical spin susceptibility, χ”(q,f), in the first Bril-
louin zone, i.e. 1/T1T ∝?
f ∼ 56.5 MHz is the NMR frequency. It is important to
note that 1/T1T reflects the summation of all different
q modes of spin fluctuations, i.e. both inter-band spin
excitations with large momentum transfer ∆q ∼ QAF
and intra-band spin excitations with smaller momentum
transfers.
We start our discussion on the evolution of spin exci-
tations from the non-superconducting metallic phase at
x = 0.26. A crucial difference between x = 0.26 and the
optimally doped superconductor x = 0.08 is that 1/T1T
of the former levels off to a very small constant value
below ∼ 50 K. We recall that, within a canonical Fermi
liquid picture, 1/T1T ∝ N(EF)2due to Fermi’s golden
rule (where N(EF) is the density of states at the Fermi
energy). On the other hand, Kspin∝ χspin= µ2
from Pauli spin susceptibility. Accordingly, the Korringa
relation, (1/T1T)0.5= (constant) × Kspin, is a bench-
mark test for the applicability of the Fermi liquid the-
ory to a strongly correlated electron system.
q|Ahf(q)|2χ”(q,f)/f, where
BN(EF)
Plotted
FIG. 2: (Color online) Field swept75As NMR lineshapes of
overdoped Ba(Fe1−xCox)2As2 with x = 0.09 at 20 K (> Tc),
x = 0.14 at 4.2 K (> Tc), and non-superconducting x = 0.26
at 4.2 K with external magnetic field B // c-axis. The NMR
frequency is fixed at f = 56.555 MHz. The grey dashed line
marks the expected resonance position for K = 0. Notice the
systematic increase in the relative intensity of the As(N) peaks
(N = 1−3) for larger x. Inset : schematic representations of
the Fe and Co coordinations of As(0) and As(1) sites.

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0.1
0.15
0.2
0.25
0.3
050100 150200250300
0%
4%
8%
9%
12%
14%
26%
K (%)
Temperature (K)
0
0.1
0.4
0.25
1/T1T and (1/T1T)0.5
K (%)
26%
1/T1T
(1/T1T)0.5
Kchem
FIG. 3: (Color Online) q = 0 uniform susceptibility as mea-
sured by75As NMR Knight shift K for As(0) sites in represen-
tative compositions. The dashed curve is a fit of x = 0.26 data
to an activation form, K = 0.20 + 0.23 × exp(−∆/T), with
∆/kB = 450 K. Inset : (1/T1T)0.5and 1/T1T for x = 0.26
plotted as a function of K with temperature as the implicit
parameter.
0
0.4
0.8
050100150200 250 300
0%
4%
5%
8%
9%
10%
12%
14%
26%
1/T1T (sec-1K-1)
Temperature (K)
TSDW=135K
FIG. 4: (Color Online) 1/T1T measured at As(0) sites for
various concentrations x with magnetic field B applied along
the ab-plane. Solid and dashed arrows mark Tc and TSDW,
respectively. Solid and dashed curves are the best fits with
(for x ≤ 0.14) and without (for x = 0.26) a Curie-Weiss term
arising from AFSF; see the main text for details.
in the inset to Fig.3 is (1/T1T)0.5as a function of K,
where temperature has been chosen as the implicit pa-
rameter. We find a good linear relation between these
two quantities for the whole temperature range between
4.2 K and 290 K. This means that, when only intra-band
electron excitations exist, the nature of spin excitations
in x = 0.26 is consistent with a Fermi liquid picture.
Our finding is also consistent with the fact that in-plane
resistivity varies as ρab ∼ T2in x = 0.26 [9, 10], an-
other benchmark for Fermi liquid behavior. We estimate
Kchem= 0.15 % from the extrapolation of the linear fit
to the (1/T1T)0.5vs. K plot. The net spin contribu-
tion to the Knight shift below 50 K can then be deter-
mined as Kspin = K − Kchem = 0.2 − 0.15 = 0.05 %,
hence χspin ∼ 1.5 × 10−4emu/mol-Fe.
be slightly underestimated because we ignored possible
small orbital contributions to 1/T1T, hence χspinmay be
slightly overestimated.) According to LDA band calcula-
tions, the bare density of states No(EF) ∼ 4.6 eV−1/f.u.
in Ba(Fe1−xCox)2As2[4, 16], hence we expect bare Pauli
spin susceptibility χband
factor of ∼ 2 enhancement of χspinover χband
consequence of mild mass enhancement of electrons due
to electron-electron interactions. We caution, however,
that we also found a linear relation between 1/T1T and K
as presented in the inset to Fig.3. In fact, we can fit both
1/T1T and K of the x = 0.26 sample with the same em-
pirical activation form, α+β·exp(−∆/kBT), and a com-
mon phenomenological gap ∆/kB∼ 450±40 K, as shown
by the dashed curves in Fig.3 and Fig.4. This might be an
indication that spin excitations in the overdoped metallic
phase are still dominated by over-damped paramagnons.
In this scenario, we obtain Kchem ∼ 0.18 % from the
inset to Fig.3, and χspin∼ 0.6 × 10−4emu/mol-Fe.
How do spin excitations evolve when we reduce the
level of electron doping below x ∼ 0.26? We recall that a
hole pocket will begin to grow once we reduce the doping
level below x ∼ 0.15 [10, 12]. This means that if the
presence of the hole Fermi surface is playing a crucial
role in the spin excitations in the superconducting regime
below x ∼ 0.15, we may find a qualitative change in
spin excitations below this concentration. In fact, our
results in Fig.4 show that 1/T1T exhibits an upturn for
x ≤ 0.12 due to the growth of AFSF. Further reduction
of the doping level results in divergence of 1/T1T toward
TSDW due to that of AFSF with ∆q ∼ QAF (1/T1T
does not blow up at TSDW = 135 K for the undoped
x = 0 sample, because the SDW transition is first order
for x = 0 [15]).
We can see the systematics more clearly by plotting the
concentration x dependence of 1/T1T observed at 25 K
(? Tcof x = 0.08), as shown in Fig.5a. The strength of
spin fluctuations at 25 K, as reflected by the magnitude
of 1/T1T, shows only a mild concentration dependence
from x = 0.26 down to x ∼ 0.15, but grows dramatically
below x ∼ 0.15. Equally interesting is the fact that the
growth of spin fluctuations with decreasing x correlates
with that of Tcin Fig.1. Thus our 1/T1T data clearly es-
tablish that (a) robust AFSF remain even in the optimum
(x = 0.08) and slightly overdoped (x = 0.09 − 0.10) su-
perconducting samples, and (b) it is unlikely that AFSF
and the superconducting mechanism compete with each
other. If the presence of AFSF was genuinely detrimen-
tal to the formation of superconducting Cooper pairs,
the x = 0.08 sample with strong enhancement of AFSF
below ∼ 100 K would not have the maximum Tc.
In order to gain additional insight into the relation
between AFSF and superconductivity, we fit the 1/T1T
(Kchem may
spin∼ 0.8 × 10−4emu/mol-Fe. The
spinmay be the

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0
0.2
0.4
0.6
00.050.10.150.20.25
x
1/T1T at 25 K (sec-1K-1)
(a)
SDW ordered
-100
0
100
00.050.10.150.20.25
x
? (K)
(b)
FIG. 5: (Color online) The concentration dependence of (a)
the strength of paramagnetic spin fluctuations as measured
by 1/T1T observed at 25 K, and (b) Weiss temperature θ
obtained from the fit in Fig.4. Solid curves are guides for the
eyes.
data with a simple phenomenological two-component
model, 1/T1T = (1/T1T)inter+ (1/T1T)intra, where we
represent the contributions of the inter-band AFSF with
a Curie-Weiss term, (1/T1T)inter = C/(T + θ). Since
the temperature dependence of 1/T1T above ∼ 150 K is
similar for a broad concentration range, it is reasonable
to assume that the intra-band contributions may be rep-
resented by the same phenomenologocal activation form,
(1/T1T)intra= α + β · exp(−∆/kBT), employed earlier
for x = 0.26. We take the same ∆/kB = 450 K for all
compositions as determined from the fit of x = 0.26, since
the Knight shift data show nearly identical temperature
dependence except for constant offsets. For simplicity,
we also fix the constant α (= 0.11) and β (= 0.63) from
the best fit of the 1/T1T data for x = 0.14 sample. In
principle, (1/T1T)intramay be slightly concentration de-
pendent below x = 0.14; however, we found that floating
the values of α, β and ∆ does not alter the essential
conclusions, because (1/T1T)inter is the dominant con-
tribution for x ≤ 0.1.
Despite the simplicity of our minimalist model, the
fits presented in Fig.4 capture the essential aspects of
the temperature and concentration dependences of our
1/T1T data remarkably well for all compositions. The
resulting value of the Weiss temperature θ is summarized
in Fig.5b. The negative value of θ for x ≤ 0.05 implies
that these samples are gradually approaching a magnetic
instability from T >> TSDW. On the other hand, the
relatively large positive value of θ ∼ 119 K for x = 0.12
reflects the fact that the overdoped sample is far from
magnetic instabilities, hence the growth of AFSF is only
modest. The small positive value of θ = 31 K for x =
0.08 is evidence for the close proximity of the optimally
doped superconducting phase with a magnetic instability,
i.e. high Tcsuperconductivity is realized near a quantum
critical point, where we expect θ = 0. In passing, C =
24 ± 4 sec−1is independent of x from x = 0 to x = 0.1,
then decreases to C ∼ 12 sec−1for x = 0.12 and C ∼
0 sec−1for x = 0.14. That is, the contribution of the
Curie-Weiss term associated with inter-band transitions
becomes negligibly small for x = 0.14.
that we arrive at analogous conclusions even if we employ
the 1/T1T data measured with magnetic field B applied
along the c-axis [6].
To summarize, we have investigated the spin excita-
tions of Ba(Fe1−xCox)2As2over the entire doping range
for the first time. Our NMR data for the overdoped
metallic phase x = 0.26 is consistent with the Kor-
ringa relation expected for canonical Fermi liquid sys-
tems. However, as we decrease the level of doping across
x ∼ 0.15, where a hole Fermi surface emerges in the cen-
ter of the Brillouin zone, we find a dramatic enhancement
of QAF∼ (π/a, 0) antiferromagneticspin fluctuations as-
sociated with inter-band transitions. The superconduct-
ing critical temperature Tcis optimized when these spin
fluctuations are modestly enhanced, to the extent that
SDW ordering does not set in. The correlation observed
between the strength of QAFantiferromagnetic spin fluc-
tuations and Tcsuggests the former plays a crucial role
in the superconducting mechanism.
The work at McMaster was supported by NSERC,
CFI, and CIFAR. Research at ORNL was sponsored
by the Division of Materials Sciences and Engineering,
Office of Basic Energy Sciences, U.S. Department of
Energy. The work at Beijing was supported by NSF, the
Ministry of Science and Technology of China, and the
Chinese Academy of Sciences.
We also note
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