Neutron Scattering Study on Spin Dynamics in Superconducting (Tl,Rb)2Fe4Se5

1.8 MB·English

by  Songxue Chi

Neutron Scattering Study on Spin Dynamics in Superconducting (Tl,Rb) Fe Se
2 4 5
Songxue Chi,1 Feng Ye,1,2 Wei Bao,3,∗ Minghu Fang,4 H. D. Wang,4
C. H. Dong,4 A. T. Savici,5 G. E. Granroth,1 M. B. Stone,1 and R. S. Fishman6
1Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
2Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA
3Department of Physics, Renmin University of China, Beijing 100872, China
4Department of Physics, Zhejiang University, Hangzhou 310027, China
5Neutron Data Analysis and Visualization Division,
3
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
1
6Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
0
2
We observed in superconducting (Tl,Rb)2Fe4Se5 spin-wave branches that span an energy range

n from6.5to209meV.SpindynamicsaresuccessfullydescribedbyaHeisenberglocalizedspinmodel
′
a whosedominantin-planeinteractionsincludeonlythenearest(J1andJ1)andnextnearestneighbor
J (J2 and J2′) exchange terms within and between the tetramer spin blocks, respectively. These

1 experimentally determinedexchangeconstants would crucially constrain thetheoretical viewpoints
1 on magnetism and superconductivity in the Fe-based materials.

] PACSnumbers: 74.25.Ha,74.70.-b,78.70.Nx
n
o
c
OneastonishingaspectoftherecentlydiscoveredT selenide superconductors to bound the discussion.
- c ∼
r 30 K iron selenide superconductors [1–5] is the coexis-
Here we report inelastic neutron scattering measure-
p
tence of a large magnetic moment (3.3µ /Fe) and high
u B mentscoveringthewholespinexcitationspectruminthe
s transition-temperature (TN 470-560 K) antiferromag- (Tl,Rb) Fe Se superconductor. Four doubly degener-
≈ 2 4 5
. netic order [6, 7]. Different from all other families of
t
a the Fe-based superconductors, the new iron selenide su-
m
perconductors consist of Fe plates with highly ordered
- √5 √5vacancysuperstructure[6–8]. Sampleswithless
nd dev×eloped√5 √5 orderare known to not be supercon-
×
o ductingeitherwhentheircompositionsarecloseto[9]or
c deviate significantly from [10] the ideal A Fe Se formu-
2 4 5
[
las. Inthelattercase,anadditionalphaseoforthorhom-

1 bic vacancy order with a √2 √2 or 2√2 √2 unit
× ×
v cell also exists at intermediate temperatures. The large-
3
moment block antiferromagnetic order developed on the
1
vacancy ordered Fe lattice [Fig. 1(a-b)] exists in super-
4
2 conducting as well as insulating samples [10].
.
1 The perfect √5 √5 vacancy order demands one va-
0 ×
cancy per five Fe ions and the charge neutrality enforces
3
a proportional number of intercalating A ions. While
1
: superconductivity can tolerate, or even requires, a small
v
composition deviation from the ideal A Fe Se to dope
i 2 4 5
X charges,the crystalstructure has to deform,as expected
r in any non-stoichiometric samples, such that the “va-
a
cant” Fe1 site is found to be occupied by a few percent
of Fe on average[6, 8] and fine-scale structural variation
[11, 12] and phase-separation[13] are observed in super- FIG.1. (coloronline)(a)Schematicdiagramoftheblockan-
conducting samples. Nonetheless, the block antiferro- tiferromagnetic structure in the I4/m unit cell. Only Fe ions
magnetic order not only coexists with superconductivity withtheirspindirectionsareshown. Jc istheexchangeinter-
action between spins in adjacent Fe planes. (b) Each shaded
in the same sample [6, 7, 12, 14], but also the interac-
square highlights a block of four ferromagnetically coupled
tion between these two long-rangeordered states reveals Fe2+ ionsintheFeplate. Theopen(orange)andthecrossed
itself inananomalousmagnetic orderparameternearT
c (blue) balls represent spins with opposite directions perpen-
[6, 7, 15]. Irrespective of the current theoretical debate dicular to the ab-plane. The black line marks the unit cell.
on the role played by spin excitations in forming the su- Thefouruniquein-planeexchangeinteractions considered in
perconducting Cooper pairs [16–18], it is important to this work are labeled. (c) Theoretical spin wave dispersions
investigatespindynamicsexperimentallyinthenewiron calculated using experimentally determined parameters.
2
FIG. 2. (color online) Constant energy slices of the acoustic branch of the spin wave excitations projected on the (H,K,0)
plane. The energy transfer is specified on each figure. The relative intensity is indicated by the color scale. The sample was
aligned on oneof thetwocrystalline twinsin theI4/m unitcell. Thedatawere collected at SEQUOIAwith Ei=50 meVfor
(a-b) and 100 meV for theother panels.
ate spin wave branches, one acoustic and three optical, Theimportanceofthenearestandnextnearestneigh-
form in three groups and span an energy range up to borexchangeinteractionsintheFeplanewasidentifiedin
210meV[Fig.1(c)]. AHeisenbergmodel,involvingthe theinitialab initiostudyexaminingtheironpnictidesu-
∼
intra- and inter-block nearest and next nearest neighbor perconductors[23]. Thelatticetetramerizationformsthe
interactions in the Fe plane and the nearestneighbor in- spinquartetblock[Fig.1(b)]makingtheintra-andinter-
teractionbetweenthe planes,issufficienttodescribeour block exchange interactions inequivalent [24]. Therefore,
data. Consistentwithabinitiotheoreticalworks,thereis the effective Heisenberg Hamiltonian
no need to resortto the third nearest neighbor exchange
interaction J3. H =XJi,jSi·Sj −∆XSi2z (1)
i,j i
Single crystals of (Tl,Rb) Fe Se (T 32 K) were
2 4 5 c
≈
grown using the Bridgman method [5]. A small single- is used which includes five exchange constants J , J ,
1 2
′ ′
crystal was used in a neutron diffraction study to de- J , J and J as depicted in Fig. 1(a-b), and the single-
1 2 c
termine the crystalline and magnetic structural proper- ion anisotropy constant ∆ that quantifies the observed
ties [7]. For the inelastic studies, 240 plate-like crystals Fe spin S = 3.2(1)/g alignment along the c-axis [7].
were mutually aligned on Al plates using an X-ray Laue This spin model on the √5 √5 vacancy ordered lat-
×
diffractometer. Thefinalassemblyhasanetsamplemass tice has been theoretically investigated [25, 26], and
of 19.5 g. The sample was sealed with He exchange gas as to be shown later, describes the spin dynamics of
inside an Al can [19] and measured with the SEQUOIA (Tl,Rb) Fe Se .
2 4 5
[20, 21] fine resolution and the ARCS [22] wide angu- Figure 2 shows the evolution of the acoustic branch
lar range Fermi chopper spectrometers at the Spallation of spin waves with increasing energy in (Tl,Rb) Fe Se .
2 4 5
NeutronSource(SNS)atOakRidgeNationalLaboratory The orientationof the tetramer Fe block with respect to
(ORNL).NeutronbeamsofincidentenergyE =50,100, theI4/munitcellcanbeclockwise[Fig.1(b)]orcounter-
i
200and350meVwereprovidedbythecoarserresolution clockwise. Thecorrespondingtwinsleadtoeight,instead
Fermi chopper [21] spinning at 180,240,360 and420 Hz of four, Bragg spots for the magnetic 1,0,1 peaks pro-
{ }
respectivelyonSEQUOIA.ForARCSE =400meVwas jecting on the (H,K,0) plane. As energy transfer is in-
i
providedby the 700meV Fermi chopper spinning at 420 creased, these spots broaden [Fig. 2(a-b)] and then de-
Hz. The sample was kept in its ground state by a closed velop into well-resolved circular rings above 30 meV
∼
cyclerefrigeratoroperatingatT 6K. Wewilllabelthe [Fig. 2(c-g)]. The spin wave dispersions along the high
≈
wavevector transfer Q = (H,K,L) using the tetragonal symmetry direction [100] and [110] are demonstrated in
I4/m unit cell [6] of a=8.683 and c=14.39˚A. Fig. 3(a) and (b), respectively. There exists featureless
3
FIG. 3. (color online) Slices of the spin wave spectrum (a)
along the [100] and (b) the [110] direction, measured with
Ei = 100 meV. The solid line is the theoretical spin wave FIG. 4. (color online) Constant energy slices of the op-
dispersion described in the text. The spectral weight of the
tic branches of the spin wave excitations projected on the
acousticbranchalongthe(c)[100]and(d)[110]directionwas (H,K,0) plane at the energy transfer of (a) E = 107 −
obtainedfrom theconstant-E cutsat differentLvalues. The 113meVand(c)E =190−220meV.(b)Theconstant-Qcut
solid lines are calculated intensities at corresponding L.
at (1.5,0.5,0) with a background at (3,-1,0) subtracted. (d)
The constant-Q cut at (2,1,0) with a background at (3,1,0)
subtracted.
scattering below 40 meV whose intensity increases with
Q and is attributed to multi-phonon scattering.
experimenttothespinwavesolutionofEq.(1)yieldsthe
Across an energy gap, and above the acoustic branch,
parameters:
are two optic branches. Another gap proceeds a third
optic branch at higher energy. The projection of the SJ = 30(1)meV, SJ′ =31(13)meV,
1 − 1
optical modes at 110 3 meV and 205 15 meV on the ′
SJ =10(2)meV, SJ =29(6)meV,
± ± 2 2
(H,K,0) plane are shown in Fig. 4(a) and (c), respec-
SJ =0.8(1)meV, S∆=0.3(1)meV. (2)
tively. To obtain eigenvalues of the optic modes at high c
symmetry points, constant-Q cuts at peak and back- Theresultingspinwavedispersioncurvesinvarioushigh
groundpositionswereperformedandtheirdifferencewas symmetrydirectionsareshowninFig.1(c). Theyarealso
fit to a Lorentzian. Example curves and fits are shown reproduced as the solid lines in Fig. 3(a-b) and Fig. 5(a-
in Figs. 4(b) and (d). The peak at E = 209(1) meV in b), and are in excellent agreement with the measure-
Fig.4(d)presentsthehighestenergymagneticexcitation ments. To further check the reliability of the fits, the
mode in (Tl,Rb)2Fe4Se5. inelastic neutron scattering intensity was also calculated
At the low energy end, the single-ion anisotropy ∆ using these fitting parameters and over-plotted with the
in Eq. (1) breaks the Heisenberg spin rotation symme- observed intensity in Figs. 3(c) and (d). The theory
try, thus, opening a gap in acoustic spin waves at mag- agrees well with experimental results.
netic Bragg points. The inter-plane coupling Jc, which The J1, J1′, J2′, Jc and ∆ in Eqs. (2) have the cor-
stabilizes the antiferromagnetic order at finite tempera- rect sign to stabilize the observed block antiferromag-
ture, also introduces a modulation in spin wave disper- netic order, while the weaker antiferromagnetic J frus-
2
sion along the c-axis. Fig. 5(a) and (b) show the details tratestheferromagneticallyalignedspinblock[Fig.1(b)].
ofthelow-energyspinwaveexcitationsobtainedwiththe The strong difference of the exchange constants be-
finer E-resolution spectrometer configurationof Ei =50 tween the intra and inter-block nearest neighbor and
meV. The energygapinmagnetic excitations is obvious. next nearest neighbor Fe spin pairs highlights the elec-
Constant-Qcutthroughthemagneticzonecenter(back- tronic consequence of the lattice tetramerization in the
ground) is shown in Fig. 5(c). The difference intensity √5 √5 structure uncovered in structural refinement
×
wasfittoastepfunctionconvolutedwiththeinstrument studies [6,8]andemphasizedby electronicstructurecal-
resolution to obtain the intrinsic gap value 6.5(3) meV. culations [24, 27, 28]. In particular, the recent ab initio
InFig.5(b),thedispersivecurveofbandwidth 18meV linear response theory concludes that the significant in-
along the c-axis is clearly observed. ∼ plane exchange interactions include only J , J , J′ and
1 2 1
′
The simultaneous fit of the data from all branches J , whose calculated values [27], remarkably, agree with
2
alongthe multiple symmetry directions measuredin this our experimental results in Eqs. (2) qualitatively.
4
nearest neighbors on the √5 √5 vacancy ordered lat-
×
tice. Theoretical work has investigated the stability of
these spin configurations [24–26]. According to the cal-
culated phase diagram [26], the exchange constants de-
termined in the present study put (Tl,Rb) Fe Se near
2 4 5
theboundarybetweentheblockantiferromagneticphase
and a non-collinear antiferromagnetic phase. Further-
more, such a non-collinear antiferromagnetic order has
recently been observedin a spin-flop transition from the
block antiferromagneticorder at 100K in TlFe Se (or
1.6 2
Tl Fe Se ) [30]. Therefore we postulate that composi-
2.5 4 5
tion tuning has pushed Tl Fe Se just across this phase
2 4 5
boundary.
The success of the Heisenberg localized spin model in
describing spin dynamics in the (Tl,Rb) Fe Se super-
2 4 5
conductor may be attributed to the fact that the ob-
served saturated magnetic moment 3.2(1)µ /Fe is very
B
large [7]. Therefore the system is close to the local spin
limit. In the iron chalcogenide Fe1+yTe1−xSex super-
FIG.5. (coloronline) Slicesoftheacousticspin wavebranch conductorswithout the intercalatinglayerandFe vacan-
along (a) the [110] and (b) the[001] direction. (c) Constant- cies, the spin excitations belong to the itinerant class as
Q cuts through the magnetic Bragg point (2,1,1) and the those in the antiferromagnet Cr which are described by
background point (1.3,0.3,1). The difference intensity curve
more complex theories than linearized spin-wave theory
was fitted to the spin wave excitations convoluted with the
[31, 32]. Even-though, the binary iron chalcogenides are
instrumental resolution to obtain the energy gap at 6.5(3)
not simple antiferromagnetic metal like Cr: Their par-
meV.
entcompoundshaveamagneticwavevectorthatcannot
be accounted for by Fermi surface nesting, and have the
The block antiferromagnetic order not only exists in largestsaturatedmagneticmoment(2µB/Fe)amongthe
superconducting samples, but also in insulating samples previously discovered families of Fe-based superconduc-
with a less ordered √5 √5 vacancy structure. Experi- tors [33].
×
mentallythistypeoforderisobservedevenfor29%filling Moreover,adiffusive spinexcitationcomponentinthe
ofthevacantFesite[10]andabinitiocalculationsat25% binary iron chalcogenides was recently resolved as origi-
fillingsupportthestabilityoftheblockantiferromagnetic nating from interstitial Fe-induced short-range spin pla-
order [27]. Recently, the spin dynamics in an insulating quettes that contain the same four-spin blocks as found
Rb Fe Se sample with the block antiferromagnetic in the block antiferromagnetic order [34]. Such fluctu-
0.89 1.58 2
order were investigated with inelastic neutron scattering ating spin quartets have been shown to contribute pro-
[29]. The overall energy scale of spin dynamics is sim- nouncedfeaturesinthespindynamicsintheparentcom-
ilar to the system under study in this paper. However poundFeTe [35]. Thecloselinkamongtheseantiferro-
1.1
the published analysis of that data provides a somewhat magneticstatesdiscoveredexperimentallyinironchalco-
anomalousresultascomparedtoourresultandtheafore- genides with or without vacancies, was anticipated in a
mentioned ab initio works. Specifically their data could theory including both itinerant and localized electronic
be least-squared fit only by a model that includes an states [28].
inter-block J3 term in Eq. (1), where the preponderance In summary, in this inelastic neutron scattering work,
ofotherresultsfindsnoneedforthis term. Thisdiscrep- we contribute fresh insights to the understanding of iron
ancy can be reconciled in two ways: One is to introduce chalcogenide superconductors by determining the spin
asubtlephysicaleffectintheabinitiostudiesthatmakes Hamiltonian for a new block antiferromagnetic order in
theinsulatingsamplesubtlydifferentfromthesupercon- the (Tl,Rb) Fe Se superconductor. Our results agree
2 4 5
ducting sample. The other is to consider a small overlap with the majority of theoretical studies that state that
of the observed excitation with the Q-resolution tail of the dominant exchange interactions extend only to the
its twin. We minimized this latter effect in our data by next nearest neighbor Fe pairs in the plane. The block
usingthefineQresolutionofSEQUOIAforouracoustic antiferromagnetic order is frustrated only by the intra-
mode measurements. block next nearest exchange J , the weakest among the
2
Inadditiontotheobservedblockantiferromagneticor- four dominant in-plane exchange interactions. Combin-
der [6, 7, 10], many other magnetic order configurations ingourexperimentalexchangeparameterswiththeoreti-
are possible with the Heisenberg model Eq. (1) with in- calcalculationsshowsthatthissystemisnearthebound-
plane exchange interaction extending only to the next ary of the block antiferromagnetism regime. A unified
5
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