Evidence for filamentary superconductivity nucleated at antiphase domain walls in antiferromagnetic CaFe$_2$As$_2$

0.44 MB·English

by  H. Xiao

Evidence for filamentary superconductivity nucleated at antiphase domain walls in
antiferromagnetic CaFe As
2 2
H. Xiao1,⋆, T. Hu1,4,†, A. P. Dioguardi2, N. apRoberts-Warren2, A. C. Shockley2, J. Crocker2, D. M. Nisson2,
Z. Viskadourakis1, Xianyang Tee3, I. Radulov1, C. C. Almasan4, N. J. Curro2, C. Panagopoulos1,3
1Department of Physics, University of Crete and FORTH, 71003, Heraklion, Greece
2Department of Physics, University of California, Davis, CA 95616, USA
3Division of Physics and Applied Physics, Nanyang Technological University, 637371, Singapore and
4Department of Physics, Kent State University, Kent, Ohio, 44242, USA
2
(Dated: January 30, 2012)
1
0 Resistivity, magnetization and microscopic 75As nuclear magnetic resonance (NMR) measure-
2 ments in the antiferromagnetically ordered state of the iron-based superconductor parent material
n CaFe2As2exhibitanomalousfeaturesthatareconsistentwiththecollectivefreezingofdomainwalls.
∗
a Below T ≈10 K, the resistivity exhibits a peak and downturn, the bulk magnetization exhibits a
J sharp increase, and 75AsNMRmeasurementsreveal thepresence ofslow fluctuationsof thehyper-
7 finefield. Thesefeaturesinboththechargeandspinresponsearestronglyfielddependent,arefully
2 suppressed by H∗ ≈ 15 T, and suggest the presence of filamentary superconductivity nucleated at
theantiphase domain walls in thismaterial.

]
n
o A. Introduction nomenonhasbeenobservedinheavyfermionmaterials,17
c
and enhanced superfluid density has been observed at
-
pr The interplay among competing ground states of cor- twin boundaries in Ba(Fe1−xCox)2As2.10 CaFe2As2 is
noteworthy,however,becausetheSCneverachievesbulk
u related electron systems can give rise to a rich spectrum
long-rangeorder,andsurprisinglythefilamentarySCap-
s of emergent behavior. The iron-based superconductors
. pears to be relatedto the presence of low frequency spin
t areparticularlynoteworthy,andhaveattractedextensive
a fluctuations. Measurements of the magnetotransport,
m interestsince the discoveryofLa[O1−xFx]FeAs in 2008.1 magnetization, and nuclear magnetic resonance (NMR)
Likethehightemperaturesuperconductingcuprates,su-
- reveal anomalies at T ≈ 10 K that are suppressed with
d perconductivity (SC) in the iron arsenides emerges from
magnetic field in a manner consistent with the suppres-
n an antiferromagnetic (AFM) parent state upon doping
sion of bulk SC in doped samples. Similar anomalies
o with excess charge carriers, and the superconducting
in the AFM state were reported recently to correlate
c pairing mechanism may be related to the AFM insta-
[ bility of the parent state.2–5 In both cases the electronic withthesuperconductingvolumefractioninSrFe2As2.18
2 degrees of freedom condense into an unusual coexistence ThesefeaturesaresubtleintheCaFe2As2,butaremani-
fest in both spinand chargeprobes. NMR spectra,spin-
v of both AFM and SC order parameters for intermedi-
lattice (T−1) and spin-spin (T−1) relaxation measure-
4 ate dopings.6,7 The nature of this coexistence is poorly 1 2
0 ments indicate slow dynamics and motional narrowing
understood. In general, a subdominant order parameter
9 consistent with the freezing of mobile DWs.19,20 The re-
can emerge locally in regions where the dominant order
0 sistivity and magnetization both change abruptly at the
vanishesorissuppressed.8Recentexperimentsintheiron
7. same temperatures and fields and analysis of the mag-
arsenidessuggestthatSCandAFMorderparametersare
0 netotransport indicates the presence of weakly pinned
indeed spatially modulated on a microscopic scale.9,10
1 superconducting filaments. This evidence suggests that
1 Among the iron based superconductors, the AFe2As2 the nucleation of finite superfluid density at DWs in
v: (A = Ca, Sr and Ba) materials are of particular interest CaFe2As2 drives the freezing of mobile antiphase do-
i because large single crystals of these oxygen-free com- mains. We thus find that this nominally pure stochio-
X pounds can be easily synthesized.11 These materials un- metric materialcan spontaneouslybecome electronically
r dergo a tetragonal to orthorhombic transition followed inhomogeneousatthenanoscaleasaresultofcoupledlat-
a
by an AFM state upon cooling.12 Both chemical doping tice strain, antiferromagnetismand superconductivity.21
and applied pressure suppress the magnetostructuralor-
der of the parent compounds and give rise to SC, and
the phase diagrams are similar to those of other uncon- B. Experimental Details
ventional superconductors.2,13 The CaFe As system is
2 2
noteworthybecauseSC is inducedatonly0.4GPa(non-
High quality single crystals of CaFe As with typical
2 2
hydrostatic),whereastheSrandBamaterialsrequire2.8 dimension ∼ 2×2×0.1 mm3 were grown in Sn flux by
and 2.5 GPa, respectively.14–16 standard methods.19 Microprobe analysis indicates a Sn
In this paper we present evidence for coexisting fil- concentration<600ppminthebulk. Thein-planeresis-
amentary SC and AFM in the undoped parent com- tivity ρ was measuredusing the electrical contact con-
ab
pound CaFe As , in which the SC order remains local- figuration of the flux transformer geometry.22 Six elec-
2 2
ized within AFM domain walls (DWs). A similar phe- trodes were fabricated on each sample by bonding Au
2
below 25 K, revealing the presence of slow fluctuations
4
(a) (e) of the hyperfine field in the ab plane.
3 In the AFM ordered state, there are two types of do-
-1s) main boundaries that can give rise to slowly fluctuating
-1 (1 2 hyperfine fields: twin boundaries and antiphase bound-
T 1 -1-1T (s)120..000(b)4 8 lbaaretietenisc(edseestetercFatiiengd.aw1n(edel)la)b.r2ee0loiTmwwmTinoNbbiionleu.Bn25daaFArein2etAsipse2hm,aeasrengdeDatWorerselihlkiaeevvlyee
0 H (T) tobemobiledependingonthetemperature.26Bothtypes
(f) of DWs give rise to perturbations of the local hyperfine
-1ms)11..50 50 K field and could be responsible for the slow dynamics we
-1T (20.5 (c) 25 K tohbesesrpveec.2t7raTthheatDiWs cslegairvleyreivsiedetontainloFwigf.re1q(ufe).ncByytauislining
0.0
the known hyperfine couplings to the As, we model the
on 0.2 10 K resonancefrequencyasafunctionofpositionuponcross-
cti
Fra0.18 (d) 4.5 K ing such a DW as ω(x) = γH0 +ω0tanh(x/δ) where x
is the position perpendicular to the DW, δ is the DW
0.16 84.0 84.5 85.0 85.5
0 10 20 30 40 50 width, ω is the frequency arising from the hyperfine
Freq. (MHz) 0
T (K) field, ω = γH = 19.2 MHz, and γH = 65.4 MHz.28
0 hyp 0
We fit the spectra and extract the fraction f = 2δ/Λ
of the signal intensity arising from DWs, where Λ is the
FIG.1. (Coloronline)(a)T1−1 vs. T forH0=0(•,powder; domain width. This portion is roughly independent of
(cid:7),satellite),3T(◮),6T(◭)and9T((cid:4))(H kc). (b)T1−1vs. temperature down to 10 K, and then it decreases by ap-
H0 at8K(H kc). (c)T2−1 forH⊥cˆat9T(solid greenline proximately5%(Fig. 1(d)) andappearsto be correlated
is the like-spin second moment contribution.23) (d) Fraction
with the slow dynamics observed in T and T . Twin
1 2
f =2δ/∆ of signal intensity from DWs (see text for details)
boundariesaremostlikely the sourceofthe temperature
as a function of T. (e) Schematic of Fe spin orientations in
independent contribution. Motionalnarrowingfrommo-
plane indicating different types of domain walls: dotted blue
bile antiphase domain walls may be responsible for the
lines are twin boundaries, dashed red are antiphase bound-
aries alongtheaˆ-axis,anddash-dotgreen linesareantiphase the slow dynamics below 10 K, which may serve to sup-
boundaries along theˆb-axis. (f) Spectra of the upper central press δ and hence f. In this case the correlation time
transition (Hhyp || H || cˆ) at several temperatures; the red τc(T) & (γhhyp)−1 ∼ 10−6 s, where γ is the gyromag-
lines are fitsas described in thetext. netic ratio and h ∼ 1.4 kOe is the fluctuating com-
hyp
ponent of the hyperfine field in the ab plane at the DW,
which agrees with the calculated value at an antiphase
wires to the crystalwith H20E epoxy paste and the cur- boundary.
rent I was applied in the ab−plane. The NMR spectra
We now turn to the bulk transport and magnetiza-
and relaxation measurements were acquired on a single
tion experiments. Figure 2(a) depicts the temperature
crystalatthe upper ofthe twomagneticallysplitcentral
dependence of the resistivity ρ at H = 0 and 14 T
(I = +1 ↔ −1) resonances of the 75As (I = 3/2) using ab
2 2 (H k c), which exhibits a discontinuity at TN =169
standard pulse sequences.
K consistent with the reported phase transition.29 The
magnetoresistance ∆ρ/ρ = [ρ(14T) − ρ(0)]/ρ(0) (Fig.
2(b)) is almost zero for T > T , but increases below
N
C. Results and Discussion T and shows a sharp upturn at 10 K. Figure 2(c)
N
shows the zero-field-cooled (ZFC) and field-cooled (FC)
T−1 measurements in the AFM state of CaFe As re- magnetization M. The hysteresis below T suggests
1 2 2 N
vealasmallpeakat10Kthatwasattributedrecentlyto the presence of magnetic domains, and the low tem-
thepresenceofslowspinfluctuationspossiblyassociated perature increase in M may be due to free moments
withDWmotion.19 Totestthishypothesis,wemeasured present in the DWs; we estimate the percentage of free
T−1asafunctionoftemperatureindifferentappliedfield moments to be ∼7-18.7% for ordered moments of iron,
1
(Fig. 1(a),H kc)Surprisingly,wefindthattheintensity µ =0.3-0.8 µ . Figure 2(d) depicts the T dependence
eff B
ofthispeakissuppressedbymagneticfieldsontheorder of ∆M/M = [M(FC)−M(ZFC)]/M(ZFC). Below 10
of 10 T (Fig. 1(b), H k c). We also measured the spin- K the slope increases dramatically, indicating a collec-
spindecoherencerateT−1versusT forH ⊥c(Fig. 1(c)). tive freezing of the magnetic domains. It is clear from
2
In this configuration, T−2 = ∆ω2 + (γ2h2 τ (T))2, these data that the charge transport is strongly coupled
2 dip hyp c
where ∆ω2 =1.08×106 sec−2 is the temperatureinde- tothelowtemperatureanomalypresentintheNMRand
dip
pendentsecondmomentofthelike-spindipolarcouplings magnetization data.
among the 75As for the central transition with H||[100] In order to highlight the low temperature magneto-
(solidlineinFig. 1(c)).23,24T−1clearlyincreasessharply transport anomaly, Fig. 3(a) shows the low tempera-
2
3

1.01
12 T H||c (a) H||c (b)
400 8 6 T
p
(a) TN (c) TN 2.0 )/di 6 1.005
T
( cm)23ab 0000 H || c HH = 5c0 Oe 1.5 M (10em -4 (1.00 42 TPeak H6 0T cT dip(T)/
14 T u/g 0.5
)
100 0 T FC 1.0 TPeak
ZF C
0
30 8 0.99 1.000
3 6 9 12 3 6 9 12
10 K
T (K) T (K)
(%) 20 10 K 6M/M 15 H||c Co0.06 30H
/ 4 (%) T)10 H || a 1200c2(T)
10 TN 2 H ( H || c
TN 0 5 10 15 0
(b) (d) 5 T (K)
0 0
0 100 200 300 0 100 200 300
1mA
T (K) T (K) 0 (c) 3mA
0 2 4 6 8
T (K)
FIG. 3. (Color online) (a) T dependence of the reduced
resistivity ρ(T)/ρdip measured at H = 0, 0.5, 2, 4, 6, 8, 12 T
(H kc)andI =3mA.(b)H =0and6TforbothH kcand
FIG.2. (Coloronline)(a)TemperatureT dependenceofthe
H ⊥ c with I = 3mA. (c) T and H dependence of the peak
in-plane resistivity ρ for applied magnetic fields H=0 and
ab positionforI =1and3mA.Inset: µ0Hc2−T phasediagram
14 T and an applied current I = 1 mA. (b) T dependence ofCaFe1.94Co0.06As2. (FromRef.33). Thesolidblacklinesare
of magetoresistivity ∆ρ/ρ where ∆ρ = ρ(14T)−ρ(0). (c) T
fits to the GL expression for upper critical field; the dotted
dependence of ZFC and FC (H = 50 Oe) magnetization M
red lines are fitsby WHH relation.
curves. (d) ∆M/M vs. T where ∆M =M(FC)−M(ZFC).
CaFe Co As (upper inset).33 We find H is nearly
1.94 0.06 2
ture resistivity normalized by ρdip, the value at the lo- linear in Tpeak with a slope of -2.4 T/K for both cur-
cal minimum at ∼ 13.5 K. Below this temperature the rent values. Linear extrapolations to zero temperature
resistivity exhibits a local maximum around 10 K, an yields critical field values of 18.3 and 16.7 T, respec-
observationthatisconsistentwithotherreports.30,31 In- tively, representing the applied fields necessary to com-
creasing the magnetic field reveals a semiconducting like pletely suppress the downturn in ρ. In fact, our ob-
backgroundwithanenhancedresistivitybelow10K.Be- servations are consistent with the development of fila-
low this temperature, however, the resistivity exhibits mentary superconductivity, in which only a small vol-
a field-dependent peak and downturn at lower temper- ume fraction of the material becomes superconducting.
ature. The peak position Tpeak (marked with an arrow This fraction is responsible for the suppression of resis-
in Figs. 3(a) and 3(b)) shifts to lower T with increasing tivity,butisnotsufficientlyextendedspatiallytoleadto
field. Tpeak is suppressed with field and ρ no longer ex- a diamagnetic signature or a completely zero resistance
hibitsapeakbyH >12T,butcontinuestorisedownto state. The facts that T is on the same scale as T
peak c
thelowesttemperaturemeasured. Theresistivitypeakis in fully superconducting samples and that both temper-
similar for both H k c and H ⊥ c (Fig. 3(b)) indicating atures are suppressed with field in similar manners sug-
a very small anisotropy consistent with earlier reports gest that the phenomena we observe are not associated
in SC samples of this family.32 Tpeak shifts slightly as a with an impurity phase. This observation is supported
function of the applied field direction, and is smaller for by fits to the Ginzburg-Landau (GL) expression for the
H kc. upper critical field, H (T) = H (0)[1−(T/T )2]/[1+
c2 c2 c
The field dependence of T is summarized in Fig. (T/T )2] (solid black lines, yielding H (0) = 15.1 T,
peak c c2
3(c) and bears a striking resemblance to the reported T (0) = 8 K for 1 mA and 12.6 T and 7.6 K for 3
c
upper critical field H vs T phase diagram for SC mA) andthe Werthamer-Helfand-Hohenberg(WHH) re-
c2
4
lation, H (0) = −0.7T (dH /dT ) (dotted red lines, 90
c2 c c2 c
yielding 13.3 T and 12 T for 1 mA and 3 mA, respec- (a) (b)
80
tively). The value of H (0) obtained from GL is larger
c2
than WHH, a behavior similar to that reported for SC z)
H 70
CaFe1.94Co0.06As2. Furthermore, the high temperature M
ftoarilH(cr2e(dT)dainshtehdeilrionnes-b)aisnedosuurpHerc−ondTucctuorrvse.34isTthyepfiaccatl Freq ( 60
that T is suppressed with increasing current density
peak 50
further suggests that the superconducting filaments are
weakly pinned.
40
It is worth noting that this low temperature anomaly -40 -20 0 20 84.0 85.0 86.0
around 10 K is about the same for the maximum T of
c Lattice position (a )
the material with applied pressure.15 Furthermore, it is O Freq (MHz)
presentnotonlyinCaFe As ,butalsointheothermem-
2 2
bers of the AFe2As2 family. For example, BaFe2As2 at FIG. 4. (Color online) (a) The resonance frequency of the
ambientpressuredisplaysabroadmaximumintheresis- upper satellite of the As along the b direction upon crossing
tivity around 20 K, and pressure studies show that even an antiphase DW oriented along the a direction, assuming a
verymoderateuniaxialstresscaninduceatleastfilamen- DW thickness δ =5a. (b) The expected lineshape of the As
tary SC and a maximum T around that temperature.35 resonance for such a DW.
c
6
D. Summary
) 5
s
EnhancedsuperfluiddensityatDWs maybeanatural nit
consequence of the coupling between SC and AFM U
orders. Indeed, model calculations exhibit an enhanced b. 4
r
local density of states and superconducting order at A
(
twin boundaries in the iron pnictides.36 It is therefore al 3
r
not surprising that superconductivity could nucleate at g
e
antiphase domain boundaries. However, the fact that nt 2
the emergence of SC coincides with the freezing of the o I
h
AFM DWs is striking, and implies that the former is Ec 1
drivenby the latter. In other words,defects in the AFM
background are pinned by the emergence of SC order,
0
which would be unstable if the DWs were mobile.
85.85 85.90 85.95 86.00 86.05 86.10
Acknowledgments We thank S. Roeske at the Freq. (MHz)
UCD Electron Microprobe lab and T. Devereaux, P.
Hirschfeld, L. Kemper, K. Kovnir and R. Singh for FIG. 5. The central resonance of the As in a field of 11.72
fruitful discussions. We acknowledge financial support T at 300K. The solid line is a fit to a Guassian with second
by MEXT-CT-2006-039047, EURYI, National Research moment σ=18(1) kHz.
Foundation,SingaporeandtheNationalScienceFounda-
tionunderGrantNo. DMR-1005393andDMR-1006606.
by the vector sum of contributions from the four nearest
TH acknowledges support from ICAM Branches Cost
neighbor Fe sites. The hyperfine coupling is given by:
Sharing Fund of the Institute for Complex Adaptive
Matter and NSF Grant DMR-0844115.
H =γ~ˆI· B ·S(r ), (1)
hf i i
iX∈nn
where the sum is overthe four nearestneighbor Fe spins
I. APPENDIX S(r ), and the components of the hyperfine tensor B are
i
givenfor CaFe As by: B =B =5.8 kOe/µ , B =
2 2 aa bb B cc
A. NMR Spectra of Domain Walls 6.0 kOe/µ and B =8.2 kOe/µ .27,37
B ac B
The exact structure of the ordered Fe moments in the
In the presence of either a twin boundary DW or an vicinity of the domain walls depends on details of the
antiphaseboundaryDW, the localmagnetic orderofthe magnetic model and the exchange couplings, which has
Femomentswillbe perturbedfromtheequilibriumanti- not been completely resolved. However, in general one
ferromagnetic structure. This perturbations will modify can expect the magnetic order to recover to the equi-
the local hyperfine field at the As sites, which is given librium structure within several lattice constants. As a
5
where Λ is the domain size. This distribution, however,
7
10
should be convoluted with a Gaussian in order to repro-
duce the experimental data. The width of this Gaussian
is determined in part by the intrinsic width of the spec-
s)106 trum, as wellasthe disorderof the domainstructure. In
Unit this case, the spectrum is given by:
b.
Ar105 +∞
al ( S(ω)=Z−∞ P(ω′)e−(ω−ω′)2/2σ2dω′ (3)
r
g
e 4 δ +Λ/2δ (ω−ω tanhy)2
nt10 = exp − 0 dy. (4)
o I ΛZ−Λ/2δ (cid:20) 2σ2 (cid:21)
h
c
E103 We fitthe experimentalspectrato this function withω0,
σ and δ/Ω as variable parameters. We find that σ ≈ 62
kHz, about 3.5 times the paramagnetic state width.
102 Therelativeweightcontainedinthelowfrequencytail
0.0 0.5 1.0 1.5 2.0 2.5
from the domain walls is given roughly by f = 2δ/Λ.
τ (ms) For the case of twin domains, transmission electron mi-
croscopyand optical measurements find domain sizes on
the order of 40 - 400 nm.25 Our observation of f ≈ 0.2
FIG. 6. (Color online) Echo decay curves for the As cen-
implies that δ is on the order of 8 - 80 nm, or 10a -
tral transition in a field of 5 T for the external field aligned O
100a , where a = 0.554 nm is the orthorhombic unit
perpendicular to the c axis. The echo integral is shown as a O O
◦ ◦ celllength. Itisimportanttonotethatatatwinbound-
functionofpulsespacing,τ,betweenthe90 and180 pulses
ary,the structuraldistortioncan be fairly small, but the
atseveraltemperatures,offsetverticallyforclarity. Thetem-
peratures are (in order of increasing vertical offset): 4.5 K, 6 magnetic response can be extended spatially depending
K,8K,12.5K,15K,17.5K,20K,25K,and30K.Thesolid on the details of the magnetic couplings.
lines are fitsto as described in thetext.
result, the As hyperfine field will have a similar recov- B. Lineshape in Paramagnetic State
ery length at which point the hyperfine field will point
alternately along ±cˆ. Within the distance δ from the Fig. 5showsthe spectrumofthe upper satellite above
boundary, Hhyp will be tilted away from the cˆ-axis and TN, which shows a Gaussian form with second moment
have components in the ab-plane. This arrangement 18(1) kHz.
will modify the resonance frequency, which is propor-
tional to the vector sum |H +H |. We therefore ap-
0 hyp
proximate the spatial dependence of the resonance fre-
quency along a direction perpendicular to the DW as C. Spin Echo Decay Curves
ω(x) = γH +ω tanh(x/δ) where δ is the DW width,
0 0
ω0 = γHhyp = 19.2 MHz, and γH0 = 65.4 MHz. For The echo decay is shown in Fig. 6 for a series of
example, this would be the case for an antiphase DW temperatures, as well as fits to the function M(2τ) =
orientedalongthe ab direction,where x points alongthe M exp(−2τ/T ). Theechodecayclearlyshowsexponen-
0 2
b-direction (see Fig. 1(e)). This dependence is shown in tialbehavior,andtherateT−1 increaseswithdecreasing
2
Fig. 4(a). For such a one-dimensional model, the his- temperature. The temperature dependence is shown in
togram of resonance frequencies is shown in Fig. 4(b). Fig. 1(d).
In order to model the spectrum, we first calculate the ⋆Permanent address: Institute of Physics, Chi-
histogram:
nese Academy of Sciences, Beijing 100190, China.
Email: [email protected]. †Permanent address: Insti-
1 +Λ/2 tute of Microsystem and Information Technology, Chi-
P(ω)= δ(ω−ω(x))dx, (2) nese Academy of Sciences, Shanghhai, China.
ΛZ
−Λ/2
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