Two-gap superconductivity in single crystal Lu$_2$Fe$_3$Si$_5$ from penetration depth measurements

0.34 MB·English

by  R. Gordon

Two-gap superconductivity in single crystal Lu Fe Si from penetration depth
2 3 5
measurements
R. Gordon,1 M. D. Vannette,1 C. Martin,1 Y. Nakajima,2 T. Tamegai,2 and R. Prozorov1,∗
1Ames Laboratory and Department of Physics & Astronomy, Iowa State University, Ames, IA 50011
2Department of Applied Physics, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
(Dated: 31 December 2008)
Single crystal of Lu2Fe3Si5 was studied with the tunnel-diode resonator technique in Meissner
8 and mixed states. Temperature dependence of the superfluid density provides strong evidence
0 for the two-gap superconductivity with almost equal contributions from each gap of magnitudes
0 ∆1/kBTc = 1.86 and ∆1/kBTc = 0.54. In the vortex state, pinning strength shows unusually
2 strong temperature dependence and is non-monotonic with the magnetic field (peak effect). The
irreversibilitylineissharplydefinedandisquitedistantfromtheHc2(T),whichhintsontoenhanced
n
vortex fluctuations in this two-gap system. Altogether our finding provide strong electromagnetic
a
J - measurements support to the two-gap superconductivity in Lu2Fe3Si5 previously suggested from
specific heat measurements.
1

PACSnumbers: 74.25.Nf,74.25.Op,74.20.Rp,74.25.Ha
]
n
o
c Originally, the interest to iron - containing silicides the London and Campbell penetration depths, analyze
- M Fe Si was due to unusually high superconducting superfluid density as well as unusual vortex properties
r 2 3 5
p critical temperatures for compounds containing a crys- andconcludethatLu Fe Si is,indeed,atwo-gapsuper-
2 3 5
u tallographically ordered iron sublattice [1]. Three sili- conductor. It seemsthat multiband superconductivityis
s
cides,allhavingthesametetragonalstructure,havebeen morewidespreadanddevelopswhenthereisdifferentdi-
.
t
a foundtobesuperconductors,M=Y,ScandLuwithtran- mensionalityoftheFermisurfaceondifferentbandsthat
m sition temperatures of 2.4, 4.5, and 6.0 K, respectively. leads to a reduced interband scattering. In MgB there
2
- It turns out that iron in these materials is nonmagnetic are two- and three - dimensional bands [11, 12], whereas
d as was concluded from 57Fe Mo¨ssbauer effect measure- Lu Fe Si has quasi-one- and three- dimensional Fermi
2 3 5
n
ments [2, 3]. However, further detailed studies revealed surfaces [13].
o
that other superconducting properties are quite uncon-
c Measurements of Lu Fe Si single crystal were per-
2 3 5
[ ventional. The upper critical field Hc2(0) for Lu2Fe3Si5 formedusingatunneldioderesonator(TDR)[14,15,16].
has been found to be unusually large when compared
1 ExtendedreviewofusingTDRtostudysuperconductors
to other iron-containing superconductors [4, 5] and its
v is given in Ref.[14]. The main components of the TDR
9 temperature dependence differs from conventional. The
are an LC tank circuit and a tunnel diode. The tunnel
6 anisotropy and a pronounced peak effect in magnetic
diodehasaregionofnegativedifferentialresistanceinits
2 measurements was reported in [7]. The presence of a
0 I-Vcurve. IfaDCbiasvoltageisappliedacrossthediode
large residual electronic term in the specific heat below
. inthisregion,thenitactsasanACpowersourceforthe
1 T aswellasareducedspecificheatjumpatT havebeen
c c LC tank circuit. This results in a self-oscillating circuit,
0
observed and confirmed, indicating departures from the
8 whichresonatescontinuouslyataconstantfrequency for
standardBCS-likebehavior[6,7]. Non-magneticimpuri-
0 given values of L and C. The resonance frequency of the
v: tiessuppressedTc atasignificantrate,incompatiblewith circuit used in our measurements was near 14 MHz. All
isotropic s-wave BCS picture [8, 9]. On the other hand,
i throughoutthemeasurementsthecircuitiskeptatacon-
X ac Josephson effect indicated s-wave pairing mechanism
stanttemperature,4.8K±1mK,allowingforastability
r [10]. Vining et al. have proposed a two-band model
of0.05Hz in the resonancefrequencyoverseveralhours.
a
in order to explain their specific heat data [6]. Their
The sample to be studied is mounted on a sapphire rod
model assumes two-band Fermi surface with one band
withasmallamountofApiezonNgrease. Thesapphireis
being superconducting and gapped, and another being
inserted inside of the inductor coil of the tank circuit. It
normal. This represents an extreme case of multiband
is importantthatthe sample andits mountdo notmake
superconductivity as we know it today, for example in
physicalcontactwith the coilso that the temperature of
MgB superconductor where different bands have gaps
2 the sample may be changed while keeping the circuit at
of different magnitude [11, 12]. Later detailed measure-
a constanttemperature to maintainthe stability. As the
mentsofLu Fe Si crystalsandanalysishaveshownthat
2 3 5 magnetic susceptibility of the sample changes with tem-
specificheatdataarewellexplainedquantitativelywithin
perature, so does the inductance of the tank coil. This
two band model of superconductivity where both bands
results in a change in the TDR resonance frequency. By
are gapped but with different gap amplitudes [13].
measuring the shift in the resonance frequency, we are
In this letter we present precision measurements of able to sense changes in the penetration depth on the
2
order of 0.5 Angstroms. Specifically, the frequency shift,
∆f =f(T)−f , with respect to the resonant frequency
0
of an empty coil, f , is given by 1.8 4
0
1.5 -0.66
λ R from skin depth via (T)
∆f(T)=−G4πχ(T)=G 1− tanh (1)
(cid:20) R (cid:18)λ(cid:19)(cid:21)
) 1.2
m resonator data
where G≃ f V /2V (1−N) is the geometry dependent -0.68
0 s c ( 0.9
calibration constant, V is sample volume, V is the ef- b 6.0 6.5 7.0 7.5 8.0
s c a
fective coil volume and N is the demagnetization factor. T (K)
0.6
The effective sample dimension R is calculated by using
Ref.[15]. As described in detail in Ref.[16] it is difficult H c-axis
to obtain the absolute value of the penetration depth 0.3 H || c-axis
due to uncertainties in the sample dimension. How- ab(0)=0.2 m
ever, it is possible to calibrate the system with great 0.0
accuracy by using temperature-dependent skin depth, 0 1 2 3 4 5
δ(T), measuredrightabovetheTc. Inthatregime,both T (K)
real and imaginary parts of the susceptibility are taken
FIG. 1: (Color Online) λab(T) obtained from the measure-
into account and the frequency shift due to skin effect ments in two orientations. Inset: Evaluation of the calibra-
is ∆f(T) = G[1−(δ/2R)tanh(2R/δ)]. The skin tionconstantbymatching4πχ(T)fromtheTDRdata(empty
T>Tc
depth, δ(T)=c ρ(T)/2πω is evaluated independently points)tocalculatedfromthetheskindepth(solidredcurve)
obtained from theresistivity.
from the temperpature-dependent resistivity, ρ(T), mea-
sured by the four-probe technique. In addition to excel-
lent stability and sensitivity, the advantage of this tech-
nique is very low excitation fields, ∼ 20 mOe which en-
sures that the sample is in Meissner state. Furthermore, penetration depth, Fig. 1. The solid red curve is the to-
by superimposing an external DC field we canprobe the tal superfluid density calculated from the α model that
vortex state in so-called Campbell regime where small assumes two independent contributions to the total su-
excitationensures thatvorticesremainin their potential perfluid density and has been successfully applied to the
wells. well known two-gap superconductor MgB [11, 12]. In
2
Single crystal of Lu2Fe3Si5 was grown by the floating- thismodel,eachsuperconductinggap,∆1(T)and∆2(T)
zone technique using an image furnace followed by an havesimilartemperaturedependence givenbythe weak-
annealingasdescribedindetailelsewhere[13]. Thesam- couplingBCSself-consistencyequation[14],butwithdif-
ple was a rectangular slab having dimensions 0.99 × ferent ratio of ∆(0)/k T that become two fit parame-
B c
0.84 × 0.15 mm3 with the c-axis perpendicular to the ters. A third fitting parameter gives the relative con-
largestface. Tostudypossibleanisotropyoftheresponse, tribution of each band to the total superfluid density,
themeasurementswereperformedfortheexcitationfield ρ (T) = xρ (T) + (1-x)ρ (T). Each superfluid den-
total 1 2
bothparallelandperpendicular to the c-axisofthe sam- sity is calculated by using full temperature range semi-
ple. A 3He cryostatwithsample invacuumandexternal classical BCS treatment as described in detail elsewhere
field up to 9 T was used for the reported studies. [14]. Thesepartialρ (T)andρ (T)areshownbymarked
1 2
Figure 1 shows the temperature dependence of the solid lines in Fig. 2. The best fit was achieved with
London penetration depth, λab(T) obtained from the x = 0.51, ∆1/kBTc = 1.86, and ∆1/kBTc = 0.54. The
measurements along and perpendicular to the c-axis. firstgapisquiteclosetotheweak-couplingvalueof1.76,
Both orientations give λab(T), because sample is a thin whereasthe secondgapismuchsmalleranditis surpris-
plate and apparently λc(T) is not too different from the ing that earlier two-band model assumed it to be fully
λab(T) - otherwise the results would not coincide. The normal [6]. Similarly to MgB2, the two gaps contribute
value of λab(0) = 0.2 µm was obtained as described equally to the superfluid density. A dashed line, which
in Ref.[14] from the reversible magnetization dM/dlnH almost follows the data is calculated from the param-
measuredindependentlyonthesamesampleusingQuan- eters obtained analyzing specific heat data, x = 0.47,
tum Design magnetometer. In the further analysis, pos- ∆ /k T = 2.2, and ∆ /k T = 0.55 [13], which is in
1 B c 1 B c
sibleuncertaintyofthisnumberupto25%wasexamined a quite good agreement given very different nature of
and and confirmed not to change our conclusions in any the measurements. To further highlight the qualitative
way. difference between single and two gap behavior, we plot
Symbols in Fig. 2 show temperature dependent super- dρ /dt in the inset to Fig. 2. Note characteristic non-
s
2
fluid density, ρ (T)=(λ(0)/λ(T)) calculatedfrom the monotonic behavior in the case of two gaps. It is not
s
3
0
1.0 Hac || c-axis /dts s-wave 0.0 4 T
d 2 T
-1 d-wave
600 Oe
-0.2 Tc2(H)
0.8 d-wave two-gaps irr zfc-w
-20.0 0.3 0.6 0.9 Tirr(H)
T/Tc -0.4
0.6
s from Cp x=0.51 kBT1c 1.86 4 -0.6 fc-c-w
0.4
-0.8 rev zfc-w
0.2 2 0.54 fc-c-w
kBTc
-1.0 H || ab-plane
0.0
0.0 0.2 0.4 0.6 0.8 1.0 0 1 2 3 4 5 6 7 8
T/T T (K)
c
FIG. 3: (Color Online) 4πχ(T) from the TDR data at three
FIG. 2: (Color Online) TDR data (symbols) fitted to a two-
different values of an applied magnetic field along the c-axis.
gap model with indicated parameters. The red curve shows
Each curve was obtained after cooling in zero field and then
thetotalsuperfluiddensity. Alsoshownandlabeledtwopar-
warming and cooling twice. The labels and arrows indicate
tial superfluid densities as described in thetext. The dashed
various characteristic points used in later analysis.
lineiscalculated frotheparametersderivedfrom thespecific
heat data. Inset: dρs/dt for pured-wave,s-wave and present
case of two-band superconductivity.
cessfully used to explain the data for Bi Sr CaCu O
2 2 2 8+y
superconductor.
4πχ(T) in the vortex state of Lu Fe Si is shown in
2 3 5
present either in pure d-wane, nor pure s-wave cases.
Fig. 3 for three representative fields. In each case, sam-
WhilstthesituationisquiteclearfortheLondonpene- ple was cooled in zero applied field to the base temper-
trationdepth,measurementsinanappliedmagneticfield ature and indicated magnetic field was applied. Then
reveal more puzzling behavior of the studied compound. measurements were taken while warming up the sample
When an external DC field is applied and small - am- above T (zfc-w). Then, sample was cooled and warmed
c
plitude AC response is probed, vortices respond elasti- twice without changing the field and while taking the
cally and the overall susceptibility is governed by the data (fc-c and fc-w). For low field values, there is no
Campbell penetration depth, λ2 = λ2L +λ2C, where λL hysteresis observed, while at intermediate fields the hys-
is the usual London penetration depth described above teresis becomes very pronounced. Clearly, the hysteresis
and λC(B,T,j) is the Campbell penetration depth [17], is associated with the static Bean current, j, induced by
λ2C = φ0B/4πα(j). Here φ0 is the flux quanta and α(j) applyingfield. We alsonotethatthiseffectisnotassoci-
is the Labusch parameter that generally depends on the atedwith the vortexdensity (e.g. less vorticesafter zfc),
biasing Bean current generated in the sample, for exam- because then initial Campbell length would be smaller
ple,afterapplyingfieldaftercoolinginzerofield. Sample than equilibrium, not larger as observed.
magnetic susceptibility (and the frequency shift) in the By measuring many 4πχ(T) curves at different mag-
vortex state is still given by Eq. 1, but with generalized netic fields, we extracted field dependence of the initial
penetration depth. susceptibility obtained after zfc and fc. Figure 4 shows
In conventional type-II superconductors there is no the resulting 4πχirr(H) (open circles) and 4πχrev(H)
hysteresis for zero-field cooled (zfc) and field cooled (closed squares) curves at T = 0.7 K. The inset shows
(fc) curves of the small amplitude AC response. How- the difference between the two curves. This difference
ever, in materials where j is strongly temperature de- is directly related to the strength of pinning and magni-
c
pendent (e.g. high-T cuprates) large hysteresis is ob- tude of the apparent Bean current density, j, ∆χ∼j/j
c c
served [17]. As shown in Ref.[17], cubic correction to where we assumed j ≪ j . There is a clear peak effect
c
a parabolic potential well for vortex pinning leads to and its location is well compatible with direct measure-
α(j)=α 1−j/j , where j = cα r /φ is the criti- ments reported in Ref. [7].
0 c c 0 p 0
cal currenpt and rp is the radius of the pinning potential. Finally, we construct the H − T phase diagram ob-
This model explains why zero-field cooled curve differs tainedfromourmeasurementsforbothdirections. While
from subsequent cooling and warming and it was suc- Meissner response is governedby currents flowing in the
4
10
0.2
0.0
4 0.1 8 Hc2 H || c
specific heat
0.0 TDR
-0.3
0 1 2 3 4 5 6 6
H (T) )
irr T
4 ( Hirr
H
-0.6 4
H || ab
2
-0.9 rev T=0.7 K
0 1 2 3 4 5 6
0
0 1 2 3 4 5 6
H (T)
FIG. 4: (Color Online) Open circles: 4πχirr(H) at T = 0.7 T (K)
K measured byapplyingfield after zfc as indicated in Fig. 3. FIG. 5: (Color Online) H −T phase diagram for Lu2Fe3Si5
Closed squaresindicate4πχrev(H)obtainedonfc. Inset: the crystal in two orientations.
differencebetweenzfcandfccurvesshowninthemainframe,
4π∆χ=4πχirr−4πχrev.
was supported by the Department of Energy-Basic En-
ergySciencesunderContractNo. DE-AC02-07CH11358.
ab-plane, in magnetic field the response is anisotropic
Work at the University of Tokyo was supported by a
andis determinedby orientationofvorticeswith respect
Grant-in-AidforScientificResearchfromtheMinistryof
to crystal axes. We observe large anisotropy of the up-
Education, Culture, Sports, Science and Technology. R.
percriticalfield,H (T),downto1KasshowninFig.5,
c2
P.acknowledgespartialsupportfromNSFgrantnumber
which has not been reported in earlier papers. Further-
DMR-05-53285and the Alfred P. Sloan Foundation.
more,H (T)determinedfromtheTDRmeasurementsis
c2
in excellent agreement with the specific heat data. Note
thatH (T)islinearintemperaturedownto0.15T . Fig-
c2 c
ure 5 also shows position of the irreversibility line (see
Fig. 3 for definition) for both orientations. Unlike con- ∗
corresponding author: [email protected]
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