Table Of ContentDilute magnetism and vibrational entropy in Fe Al
2 5
Ji Chi,1 Xiang Zheng,1,2 Sergio Y. Rodriguez,1 Yang Li,3 Weiping Gou,1,2
V. Goruganti,1,2 K. D. D. Rathnayaka,1,2 and Joseph H. Ross, Jr.1,2
1Department of Physics, Texas A&M University, College Station, Texas 77843-4242, USA
2Materials Science and Engineering Program, Texas A&M University, College Station, Texas 77843-3003, USA
3Department of Engineering Science and Materials,
University of Puerto Rico at Mayaguez, Mayaguez, Puerto Rico 00681-9044, USA
(Dated: January 29, 2016)
6
1 Fe2Al5 containsaFe-Almatrixthroughwhicharethreadeddisorderedone-dimensionalchainsof
0 overlappingAlsites. Wereportmagnetic,NMR,andspecificheatmeasurementsaddressingitsmag-
2 neticandvibrationalproperties. TheCurie-typesusceptibilityisfoundtobeduetodilutemoments,
likelyduetowrong-siteFeatoms. 27AlNMRshiftandspin-latticerelaxationmeasurementsconfirm
n
these to be indirectly coupled through an RKKY-typeinteraction. Specific heat results indicate a
a
J large density of low-energy vibrational modes. These excitations generate a linear-T contribution
to the specific heat, which however freezes out below about 10 K. These results are attributed to
8
thepresence of anharmonic vibrational modes associated with thedisordered structural chains.
2
]
i I. INTRODUCTION
c
s
-
l Al-rich Fe aluminides, along with other transition
r
t metal aluminides, form complex atomic structures, for
m
examplethetriclinicstructureofFeAl ,1 andmonoclinic
2
. structure of Fe Al , the latter a decagonal quasicrys-
t 4 13
a tal approximant.2 In addition such compounds show a
m
variety of magnetic behavior, from non-magnetic or-
- dered FeAl and dilute-Fe alloys,3–5 to concentrated-
d
moment behavior in FeAl .6,7 Fe Al is a quasicrystal
n 2 2 5
approximantwith pentagonal channels (Fig. 1), through
o
c which are threaded one-dimensional arrays of partially-
[ occupiedaluminumsitesspacedverycloselyandexhibit-
ing anomalous vibrational properties.8 In this paper we
1
explore the magnetic and thermodynamic behavior of
v
4 this material, showing that it is an intrinsic dilute mag-
4 neticmaterialwithananomalouscontributiontotheen-
6 tropy at low temperatures. FIG. 1: [Color online] Fe2Al5 orthorhombic structure, show-
ing four adjacent unit cells. Larger spheres denote Al, and
7
In some ways, these transition-metal aluminides may smaller spheres Fe, as labeled. Undulating chains of overlap-
0
beviewedasdilutealloysofd-rankionsinametallicalu- ping Al(2) and Al(3) sites are shown here as if completely
.
1 minummatrix. However,the complex structuresalsoin- occupied.
0
clude regularly-spaced vacancies and partially-occupied
6
sites, stabilized in part by a combination of strong sp-
1
: d hybridization and the Hume-Rothery mechanism.9 In nels in the form of stacked pentagonal antiprisms. The
v
many cases this leads to the appearance of a pseudo-
singleinequivalentFesite(4/cell)hastwosomewhatdis-
i
X gap in the density of electronic states at the Fermi level tant (3.06 ˚A) Fe near neighbors, as well as eight Al(1)
[g(ε )],andassociatedunusualelectronicbehavior. Fur-
r F neighbors and a series of neighboring channel-centered
a thermore, it is believed that the structures of quasicrys-
Al sites. Al(1) sites (8/cell) are fully occupied, while
tals and approximants may lead to particularly narrow
the overlapping sites Al(2) (4/cell) and Al(3) (8/cell)
structures in the DOS near E ,10–12 which can dom-
F channel sites make up disordered chains, with site oc-
inate the electronic behavior. The possible presence
cupationfactors0.36and0.23,respectively,foundin the
of phason-type coherent vibrational excitations13,14 is studyofBurkhardtetal.8 Theseoccupationfactorsgives
also of interest, and there is experimental evidence for
a nominal composition of Fe Al . Reported composi-
4 10
an enhanced density of vibrational modes in this class tion ranges17,18 include variations as large as Fe Al to
4 9
of materials.15,16 Fe Al also includes closely-spaced Al
2 5 Fe Al , presumably through adjustment of Al(2) and
4 11
sites in the channels, and hopping between these sites Al(3) occupations. The close spacing (0.67 and 0.75 ˚A)
may have a large effect on the vibrational behavior.
ofpartially-occupiedchannelsitesandhighlyanisotropic
The orthorhombic structure8 (Cmcm, s.g. #63) of thermal parameters deduced from crystallographic mea-
Fe Al is shown in Fig. 1. Its framework includes chan- surements also point to atomic hopping between sites
2 5
2
alongthe chains. A sizable Curie-type susceptibility was
previouslyreportedforFe Al ,19 withp =0.73. Here
2 5 eff
we report magnetization, specific heat and nuclear mag-
netic resonance (NMR) studies addressing the magnetic
and vibrational properties of this material.
II. EXPERIMENTAL METHODS
Samples were synthesized by arc melting appropriate
amounts of the elemental metals. The resulting poly-
crystallineingotswereannealedinvacuum-sealedquartz
◦
tubes at 600 C for one week. Samples were character-
ized by powder x-ray diffraction (Bruker D8 Advance)
using Cu K radiation, and also by wavelength disper-
α
sive x-ray spectrometry (WDS) using a Cameca SX50
equipped with four wavelength-dispersive x-ray spec-
trometers. Structural refinement of x-ray data was car-
ried out using the GSAS software package.20,21
We prepared samples with several starting composi-
tions, including Fe Al , Fe Al and Fe Al . WDS
4 10 4 11.2 4 11.8
measurements showed 2 phases, FeAl and Fe Al , in FIG. 2: Powder x-ray results for Fe2Al5, with results of re-
2 2 5
finementand differenceplot.
the samples with Fe Al and Fe Al starting compo-
4 10 4 11.2
sitions. However, for the starting composition Fe Al
4 11.8
no second phase was found. Also in the NMR measure-
ments to be described below, a separate peak due to the 0.012 )
u8000
concentratedmagneticphase7FeAl wasobtainedforthe m
2
e
Ffoeu4nAdl1i0naFned4AFel141A.8l.11W.2 DsaSmsphleosw,ewdhtihleeafinsianlgcleomppeaoksitwioans ol) mol /
roafythdeiffFrea4cAtilo1n1.8ressaumltpslfeotrothbiesFsae4mApll9e.8aareftsehrolowsnsoinfAFilg..X2-. u/m 0.008 1- ()40000
Atomic parameters obtained from the refinement are in m
reasonableagreementwiththosereportedearlier.8Unless e ( 0
( 0 50 100 150 200 250
otherwise noted, results reported here are for this sam- 0.004
T (K)
ple. Where necessary, samples are designated according
to the aluminum starting composition, for example sam-
Fe Al
2 5
ple Al .
11.8
Specific heat measurements were performed using a 0.000
0 100 200 300
Quantum Design Physical Property Measurement Sys-
T (K)
tem from room temperature to 1.8 K. DC-susceptibility
measurementswere carriedout using a Quantum Design
MPMS SQUID magnetometer. 27Al NMR experiments
FIG. 3: Fe2Al5 DC susceptibility (χ(T)) per mol Fe in an
were performed from 4.2 K to 450 K at two fixed fields applied field of 1000 Oe. Inset: (χ−χo)−1 vs. temperature.
usingawide-linepulsespectrometer. Forthesemeasure- Solid curves: Curie-Weiss fit.
ments the powdered sample was mixed with granular
quartz, and aqueous AlCl was used as shift reference
except as noted. MAS-N3MR measurements were also θ)+χo,withχo=+1.7 10−4emu/molasmallextrinsic
×
performed at room temperature using an Advance 400 contribution. The Curie constant is
spectrometer.
p2 µ2
eff B
C =N c , (1)
cw A
3k
B
III. RESULTS AND ANALYSIS
where N is Avogadro’s number, c the concentration of
A
magnetic ions per iron atom, and p the effective mo-
eff
A. Magnetic measurements ment. From least-squares fits we obtained θ = 1.1
−
K, and (p √c) = 0.51, somewhat smaller than the
eff
Thedc-susceptibility,χ(T),isshowninFig.3,forfixed previous report,19 the difference likely due to sample-
fieldof1000Oe. WefitthedatatoaCurie-Weissfunction dependent variations in atomic occupation parameters.
accordingtothestandardrelationship,χ(T)=C /(T Magnetization measurements vs. field at 150 K show
cw
−
3
atures the linewidth becomes progressivelylarger due to
the presence of paramagnetic moments [Fig. 5(b)]. The
pulse-length behavior23 confirms the central portions of
these lines to be central transitions for 27Al (I = 5/2)
connecting 1/2 +1/2 states. A room-temperature
− ←→
MAS-NMRspectrumisshowninFig.6. Theobservation
ofasinglepeakinthisgraphindicatesthatthestructure
inthestaticlineisdominatedbyorientationdependence
of a single site, rather than a splitting due to inequiva-
lent sites, even though the random paramagnetic contri-
butionistoolargetobeeffectivelynarrowedbyspinning
in this case. Since 8 of the nominal 10 Al atoms per cell
belong to Al(1), we can deduce that the main features
of the line correspond this site, with resonances due to
the other sites either overlapping this line or excessively
broadened due to channel disorder.
The field-dependence enables magnetic and
quadrupole contributions to be separated,24,25 since
the magnetic shift is proportional to B and the second-
order quadrupole shift (∆f2) is proportional to 1/B.
Q
Fitting the 295 K spectral center of mass obtained at
fixed fields of 7.00 and 8.75 T, we extracted a mean
magnetic shift, K = +0.020(1)%, and a corresponding
mean quadrupole contribution ∆f2B = 0.085MHz T.
Q −
The latter corresponds to the shift for a second-order
powder pattern having quadrupole parameters24 ν =
Q
1.9 MHz and η = 0 (or ν as small as 1.6 MHz with
Q
η increased to 1). However, in numerical calculations
starting with these values we found that the main
FIG.4: Fe2Al5 magnetization permol Fe. (a)Measurements features of the spectra could be fitted consistently vs.
at 150 K with Curie-Weiss fit described in the text. (b) 2.0
field only by using a larger ν , with η 0 and K =
K, with saturation fit described in text. Q ≈
+0.025%. Fig. 5(a) shows the superposition of such a
single-sitequadrupolespectrumwithν =2.39MHz for
Q
two different fields. The results are relatively insensitive
linear behavior [Fig. 4(a)]. The small vertical offset cor-
to the parameter η, however we found that computed
responds to the extrinsic contribution χo described pre- curves for η > 0.3 agreed poorly with the data. With
viously. The straight-line fit shown in Fig. 4(a) yields
this plot supe∼rposed, we find in addition a second peak,
(p √c) = 0.47. At 2.0 K [Fig. 4(b)] the magnetization
eff as shown from the difference curves plotted in Fig. 5(a).
is nonlinear,but with incomplete saturationatthe high-
This additional peak makes up 12–22% of the total
est field of 70 kOe. This curve could not be fitted to a
spectral weight. The difference in magnitude may be an
Brillouinfunctionrepresentingthemagnetizingbehavior
artifact of the fitting. According to the measured site
of independent local moments, presumably due to spin
occupations, 20% the Al reside on the two channel sites,
interactions corresponding to the small fitted θ obtained
so it is reasonable to conclude that the additional peak
fromthesusceptibility. However,thesaturationcouldbe
corresponds to these sites, while the fitted ν = 2.39
fitted to a function22 M = M A/H B/H2 [solid Q
sat − − MHz resonance is attributed to Al(1).
curve in Fig. 4(b)], yielding M = 281 emu/mol Fe.
sat
The low-temperature behavior of the NMR lines was
Since for local moments p = gpJ(J +1) while the
eff
measuredin8.8Tat79Kand4.2K;theextractedshifts
saturation moment corresponds gJµ per ion, J and c
B
and linewidths are plotted in Fig. 7. Widths are full
canbe determinedseparatelyfromthe MH curves,with
widthsathalfmaximum(FWHM)obtainedthroughline
g known. Assumingthatg =2(areasonableassumption
fitting, with the quadrupole contribution removed, and
for transition ions), this procedure yields J = 1.2 (hence
shifts are those of the spectral centers of mass. These
p = 3.2), and c = 0.021 per Fe atom.
eff
data could be fit to Curie-Weiss functions, as plotted in
the figure. The fitted Weiss temperatures are 3.8 and
−
2.6K,respectively,comparabletothesmallθ obtained
B. NMR measurements −
fromthesusceptibility. Thereforethelocalfieldsatthese
temperatures are dominated by these paramagnetic mo-
The 27Al NMR spectrum at room temperature has a ments. The nonzero average shift indicates RKKY-type
two-peaked structure [Fig. 5(a)], while at lower temper- ratherthan simple dipolar nuclearcoupling to the dilute
4
FIG. 7: 27Al NMR lineshifts and widths, plotted with fitted
Curie-Weiss curves described in text.
paramagnetic moments, since the dipolar coupling has
zero spatial average.
27Al NMR spin-lattice relaxation times (T ’s) were
1
measured using the inversion recovery method, record-
ingthesignalstrengthbyintegratingthespinechoFFT.
For the central transitions, the T ’s were extracted by
1
fitting to multiexponential curves26 for magnetic relax-
ation of the I = 5/2 27Al central line. In Fig. 8 we show
thetemperaturedependencebetween4and450K.These
data were measured in 8.8 T; measurements at selected
temperatures also indicated no field-dependence to the
T . ThestraightlineinFig.8representsafittothedata
1
below 200 K of the form
T−1(T)=aT +T−1, (2)
1 1P
witha=4.44 10−2 K−1s−1,andT−1 =0.87s−1. The
× 1P
first term in Eq. 2 follows the expected Korringa behav-
iorformetals. SubtractingthesmallnegativeCurie-type
FIG.5: 27AlNMRlineshapesforFe2Al5. (a)295Kmeasure- shift(obtainedfromthefitshowninFig.7,andamount-
ment, with calculated quadrupole powder pattern for Al(1) ing to 0.007% at room temperature) from K for the
−
sites (upper curve) and difference curve attributed to Al(2) main Al(1) site as described above, we obtain a baseline
andAl(3)sites(lowercurve). Inset: lower-fieldmeasurement, room-temperature metallic shift, K = 0.032%. Multi-
m
withcurvescalculatedusingsameparameters. (b)4.2Kmea-
plying by the fitted slope fromEq. 2 yields the Korringa
surement. product25 K2(T T) K2a−1 = 2.3 10−6 sK. Com-
pared to the sta1ndar≡d 27Aml Korringa×value, 3.9 10−6
×
sK, the smaller value obtained here likely indicates the
presenceofanegativecross-polarizationterm,anddcon-
tributions to g(ε ) that will tend to reduce K , and
F m
thereby the Korringa product.
The additive term T−1 in Eq. 2 can result from the
1P
presence of paramagnetic moments interacting through
a constant RKKY-type coupling field. We can estimate
such a contribution by calculating the nuclear transfer
hyperfine coupling as follows: the fitted paramagnetic
contribution to the shift in Fig. 7 at 79 K is 24 kHz,
−
whichcorrespondsto a22Geffective fieldfor27Al. Also
at this temperature the paramagnetic response will be
linear; the parameters used for Fig. 4(a) yield M = 0.27
µ perparamagneticionatthistemperatureandfield,so
FIG.6: 27AlMAS-NMRspectrumforFe2Al5,in9.4T.Spin- B
the transferfield is 81 G/z,where z is the effective coor-
ning rate = 12 kHz. Shift reference: Al2O3.
dination number for paramagnetic ions interacting with
5
FIG.9: C/T vs. T2 forFe2Al5 between0and30K,forsam-
ples and fields as indicated. Calibration is per mole formula
unit, Fe2Al5. Solid lines correspond to the fitted parameters
FIG.8: Temperaturedependenceofrelaxationratesfor27Al, described in thetext.
measuredat8.75T.Solidline: fittoKorringa+paramagnetic
relaxation. Upper curve is guide to the eye. Inset: Low-
temperature portion of data. wellasinquasicrystalapproximants,14,16,30 andinglassy
systems,31,32 due to thermal excitation of localized vi-
brational modes. For comparison, the 27Al T−1 contri-
1
eachnuclearspin. Dividing by the nuclear gyromagnetic bution (quadraticat hightemperatures) due to ordinary
ratio we obtain the transfer coupling parameter, A/h = phonons in AlSb is roughly 10 times smaller.33
89 kHz/z. The contribution of the paramagnetic mo-
ments with spin J to the T can be expressed26
1
T−1 =(2π)−3/2(A/h)2(3ω )−1J(J +1)z. (3) C. Specific heat
1P E
Inthiscaseω istheaverageRKKYexchangefrequency, Thespecificheat(C)wasmeasuredinthetemperature
E
which may be expressed, [8J2 zJ(J +1)/3h¯2]1/2, where range1.8–300K.C/T vs. T2plotsbelow30Kareshown
ex
J is the interaction strength. In the paramagnetic in Fig. 9, for the Al and the Al sample, the latter
ex 11.8 10.0
regime27,J isrelatedtotheCurietemperaturethrough including a small FeAl minority phase. In both cases
ex 2
J z = 3kBθ . Combining, and using the fitted θ = the straight-line behavior is equivalent to that of typical
ex 2J(J+1)
1.1 K and J = 1.2, we obtain T−1 = 2.1 s−1/√z. As- metals, however with a downturn at low temperatures.
− 1P A fit to C(T) = γT + βT3 for Al yielded γ = 48
suming the dilute moments to be randomly positioned, 11.8
mJ/molK2 and β = 0.147mJ/molK4 with zeroapplied
the value for z is unclear, however it should be a small
field(solidlineinFig.9). Datawith6Tappliedfieldare
number on order of unity. Thus this estimate is in quite
goodagreementwiththefittedT−1=0.87s−1,providing alsoshown;asimilarfityieldsγ=52mJ/molK2andβ=
1P 0.143 mJ/mol K4. For sample Al the results are γ =
additional evidence supporting the picture of a nonmag- 10.0
83mJ/molK2 andβ =0.141mJ/molK4 (shownininset
netic matrix containing weakly coupled dilute moments.
Above 300 K, there is an increase in T−1 beyond the plot). The essentially identical β values correspond to a
1 Debye temperature Θ = 460 K, however in both cases
linear Korringa fit. Similar behavior has been observed D
inanumberofquasicrystalinealloys28,29,andattributed the fitted γ is quite large for a nonmagnetic metal. The
low-temperaturedownturnis anomalous,andappears in
in some cases to a pseudogap near the Fermi energy,
bothsamples. Henceforth,wewillfocusonsampleAl ,
whereby an increase in temperature leads to an increase 11.8
on which the previously-described magnetic and NMR
in the number of carriers available for Korringa relax-
measurements were also performed.
ation. Howeverweseenoevidenceforacorrespondingin-
The inset in Fig.10 showsthe specific heatfor the en-
creaseintheKnightshift. Whilewehavenotmappedout
tire temperature range. On this scale the 6 T and 0 T
thedetailedfield-dependenceofthelineshapesabove295
data appear superposed. One can solve for the Debye
K, we measured lineshapes at 7.0 T at several tempera-
temperature by solving the standard integral equation,
tures up to 403 K. We found no change in the center-of-
mass centralline positionbetween 295and403 K within C =9NR(T/ΘD)3R0ΘD/T x4exdx/(ex−1)2, with ΘD as
experimental error. Thus a more likely explanation for a parameter.34 Assuming C to be entirely vibrational,
the increase in T−1 is vibrational. Indeed, there are a we obtain the lower curves displayed in the main plot
1
number of reports of enhanced density of localized vi- of Fig. 10. The large drop in Θ below 50 K signals the
D
brationalmodesathightemperaturesinquasicrystalsas presenceofadditionallow-energyexcitationsinthistem-
6
FIG. 10: Debye temperature extracted from Fe2Al5 specific
heat,forB=0and6T.Solidcurve: calculatedafterremoval FIG. 11: Specific heat difference for zero and 6 T data, with
of γT as described in text (6 T data). Inset: specific heat calculated B = 6 T multilevel Schottky anomaly for fitted
measured in B = 0 and 6 T, per mole formula unit. density of paramagnetic defects. Normalization is per mole
formula unit.
perature range, which can be associated with the large
T-linear term fitted as γT. Subtracting this term from
the measured specific heat before solving for Θ yields
D
the upper curve in Fig. 10, which brings Θ back into
D
agreement with the value, 460 K, corresponding to the
measuredβT3. However,the continuedriseofthis curve
asroomtemperatureisapproachedisunphysicalandin-
dicatesthatthelargeγT contributiondoesnotextendto
hightemperaturesaswouldtheelectroniccontributionin
an ordinary metal. Instead, these additional excitations
are apparently confined to a plateau in C/T.
The small low temperature difference between specific
heatcurvesfor6Tand0TisconsistentwithaSchottky
anomalyfor paramagneticspins. The difference between FIG. 12: Reduced C/T with β T2 and magnetic Schottky
thetwomeasurementsisplottedinFig.11,allowingother terms removed (left scale). Also plotted: entropy obtained
contributionstoberemovedinamodel-independentway. from reduced C/T (right scale). Units are per mole formula
Also plotted is a multilevel Schottky curve34 for B = 6 unit.
T correspondingto paramagneticdefects withg =2 and
c = 0.021 as obtained from the magnetic measurements,
and using J = 3/2 to approximate the fitted J = 1.19. above 20 K. The integrated entropy [S = R(C/T)dT] is
Above10KwheretheB =0contributionhasapparently also shown, obtained from the reduced C/T. This curve
diedout,themagnitudesareinagreement. Thenegative is still rising at 30 K (above which temperature addi-
peak near 2 K corresponds to the zero-field upturn in tional terms in the ordinary phonon expansion must be
C/T at low T, and is consistent with spin freezing due included), however the change in S over these tempera-
to a distribution of local fields. The contribution of the turesprovidesanestimateofthemagnitudeoftheexcess
measureddilutemomentstothespecificheatisdescribed vibrational contribution.
entirely by these low-temperature effects, and thus the
low-energy excitations corresponding to the plateau in
C/T must be attributed to nonmagnetic features. IV. DISCUSSION
WithboththefittedβT3andSchottkytermsremoved,
theremaininglow-temperatureC/T contributionisplot- Fromthe NMRandmagneticmeasurementsitis clear
ted in Fig. 12. In typical metals this would yield a con- thatthisisanordinarymetalcontainingrelativelydilute
stant equal to the electronic γ, however in this case the paramagneticdefects. Thesizeofthesemomentsiscom-
curve trends toward zero as T approaches zero. The parable in size to that found for thermally-generated Fe
Schottky term is likely overestimated, as J = 3/2 was antisite defects35 in Fe VAl. In the present case a likely
2
used as an approximation for the fitted J = 1.2. Thus scenariomaybethatFeatomsrandomlysubstitutingon
theremainingmetallicγ islikelynonzero,butitisclearly chain sites8 may be magnetic due to the more closely
significantly smaller than the apparent γ of the plateau connected Fe neighbors of these sites. It is also possi-
7
ble that built-in chain-site disorder induces moments on tation spectrum, with an energy close to 1 meV corre-
a small fraction of the otherwise nonmagnetic Fe sites; sponding to the observedlossofexcitationstrengthnear
generally for dilute Al-Fe alloys the presence of a local 10K.Thiscutoffcouldplausiblybeattributedtotheen-
moment is a sensitive function of the coordinating atom ergyrequiredforhoppingbetweenneighboringpartially-
positions.4,36 Furthermore,ashasbeenproposedforMn- occupied chain sites. The large linear coefficient of spe-
aluminide quasicrystals9 complexoverlappingRKKYin- cific heat in both measured samples implies a high den-
teractions in these aluminides can reinforce dilute mag- sity of these vibrational modes. For example the inte-
netic momentsoncertainsiteswithinthe otherwisenon- gratedentropyshowninFig.8reaches0.14R at30K;if
magnetic material. attributed to two-level localized anharmonic states this
K , the baseline metallic shift as extracted here for impliesapproximately0.14/ln2=0.2suchmodesperfor-
m
the metallic matrix, is about 20% of the value for Al mulaunitbecomingactivatedbelow30K,orasignificant
metal. This is likely associated with a broad minimum fraction of the chain sites, assuming that each localized
intheAlpartialg(ε)nearε asistypicalofhybridization vibrationalstate correspondsto asingle chainatom. We
F
gap systems.5 However we found no evidence for a tem- assume that the breadth of the vibrational spectrum is
perature dependence to K , as has been found in some be due to the disordered arrangement on these sites.
m
systems37,38 for which narrow pseudogap features domi- V. CONCLUSIONS
nate nearε . Thus fromthis standpointFe Al behaves
F 2 5
asanordinarymetal. Additionalexcitationsidentifiedin
MagneticmeasurementsofFe Al showittobeanon-
2 5
this material take the form of localized modes excited at
magneticmetalwithalargedensityofparamagneticmo-
high temperatures, evidenced by an enhancement in T ,
1 ments, likely connected to wrong-site Fe atoms on the
and low-energy features that dominate the specific heat, disordered chains. 27Al NMR results confirm that these
shown to be nonmagnetic in origin.
are indirectly coupled through an RKKY-type interac-
Low-energyEinstein oscillator-type vibrational modes
tionviathenonmagneticmatrix. WeidentifiedKorringa
have been observed previously in metallic systems,39,40
behavior in NMR shifts and relaxation rates; an addi-
howeverthe low-temperature specific heat observedhere
tional contribution to the latter was identified as due
is not consistent with a single oscillator with a well-
to localized vibrational excitations. Specific heat mea-
defined frequency. Onthe otherhandthe alternativeex-
surements and analysis demonstrate in addition a large
planation of a narrow electronic pseudogap, which could
densityoflow-energymodescontributingto asignificant
produce the low-temperature reduction in specific heat
linear-T enhancement in the specific heat. An anoma-
as observedhere, seems unlikely since an extremely nar-
lousfreeze-outofthesemodesisobservedatlowtemper-
row gap would be required. In addition the observed
atures. We showed these to be nonmagnetic, and likely
field-independence would rule out magnetic Kondo be-
attributable to atomic motion on the partially-occupied
havior as a source of such a feature. Thus we conclude
chains threading the structure of this material.
that the enhanced low-energy excitations are due to an
extended spectrum of localized anharmonic vibrations.
We attribute these to atomic motion along the unusual
Acknowledgments
partially-occupied chains found in this material.
An enhanced specific heat nearly linear in the tem-
perature is observed in insulating glasses41 as well as This work was supported by the Robert A. Welch
orientational glasses,42 and these are modeled as local- Foundation, Grant No. A-1526, by the National Science
izedatomichoppingsitesproducingabroadspectrumof Foundation (DMR-0315476), and by Texas A&M Uni-
two-levelsystems. For this model to work in the present versitythroughthe TelecommunicationsandInformatics
case, a low-energy cutoff must be present in the exci- Task Force.
1 R. N. Corby and P. J. Black, Acta Crystallogr., Sect B: 7 J.Chi,Y.Li,F.G.Vagizov,V.Goruganti,andJ.H.Ross,
Struct.Crystallogr. Cryst. Chem. 29, 2669 (1973). Jr, Phys. Rev.B 71, 24431 (2005).
2 J.Grin,U.Burkhardt,andM.Ellner,Z.Kristallogr. 209, 8 U.Burkhardt,Y.Grin, andM.Ellner, Acta.Cryst.B50,
479 (1994). 313 (1994).
3 D.GuenzburgerandD.E.Ellis,Phys.Rev.Lett.67,3832 9 G. T. de Laissardi`ere, D. Nguyen-Manh, and D. Mayou,
(1991). Prog. Mater. Sci. 50, 679 (2005).
4 P.G.Gonzales,L.A.Terrazos,H.M.Petrilli,andS.Frota- 10 T. Fujiwara and T. Yokokawa, Phys. Rev. Lett. 66, 333
Pessˆoa, Phys.Rev. B 57, 7004 (1998). (1991).
5 R. E. Watson and M. Weinert, Phys. Rev. B 58, 5981 11 J. Delahaye, T. Schaub, C. Berger, and Y. Calvayrac,
(1998). Phys. Rev.B 67, 214201 (2003).
6 C. S. Lue, Y. O¨ner, D. G. Naugle, and J. H. Ross, Jr., 12 R.Widmer,P.Gr¨oning, M.Feuerbacher,andO.Gr¨oning,
Phys. Rev.B 63, 184405 (2001). Phys. Rev.B 79, 104202 (2009).
8
13 G. Coddens, Eur. Phys.J. B 54, 37 (2006). 28 J.Dolinˇsek,M.Klanjˇsek,andT.Apih,Ferroelectrics250,
14 M. Widom, Phil. Mag. 88, 2239 (2008). 195 (2001).
15 E.Abe,S.J.Pennycook,andA.P.Tsai, Nature421,347 29 P.JegliˇcandJ.Dolinˇsek,Phys.Rev.B71,014204(2005).
(2003). 30 J.Dolinˇsek,T.Apih,P.Jegliˇc, M.Feuerbacher,M.Calvo-
16 R.A.Brand,F.Hippert,andB.Frick,J.Phys.: Condens. Dahlborg, U. Dahlborg, and J. M. Dubois, Phys. Rev. B
Matter 21, 045405 (2009). 65, 212203 (2002).
17 Z. W. Chen, R. M. Sharp, and J. T. Gregory, Mater. Sci. 31 J. Szeftel and H. Alloul, Phys. Rev.Lett. 34, 657 (1975).
Technol. 6, 1173 (1990). 32 E.Mammadov,P.C.Taylor,A.Reyes,S.Mehdiyeva,and
18 M. K¨oster, B. Schuhmacher, and D. Sommer, Steel Res. P. Kuhns,Phys.Status Solidi A 207, 635 (2010).
72, 371 (2001). 33 R.L. Mieher, Phys. Rev.125, 1537 (1962).
19 F.Mu¨ller,M.Rosenberg,W.Liu,andU.K¨oster,Materials 34 A. Cezairliyan, Specific Heats of Solids (Hemisphere Pub-
Science and Engineering A134, 900 (1991). lishing Corporation, New York,1988).
20 B. H.Toby,J. Appl.Cryst. 34, 210 (2001). 35 C. S. Lue, J. H. Ross, Jr., C. F. Chang, and H. D. Yang,
21 A.C. Larson and R.B. vonDreele, Tech. Rep.LAUR86- Phys. Rev.B 60, R13941 (1999).
748, Los Alamos National Laboratory (2000). 36 M.Mantina,S.L.Shang,Y.Wang,L.Q.Chen,andZ.K.
22 S. Chikazumi and C. D. Graham, Physics of Ferromag- Liu, Phys.Rev. B 80, 184111 (2009).
netism (Oxford UniversityPress, 1997). 37 C.-S.LueandJ.H.Ross,Jr.,Phys.Rev.B58,9763(1998).
23 O.KanertandM.Mehring,inNMR:BasicPrinciplesand 38 X.-P. Tang, E. A. Hill, S. K. Wonnell, S. J. Poon, and
Progress, edited by E. Fluck and R. Kosfeld (Springer- Y. Wu,Phys.Rev.Lett. 79, 1070 (1997).
Verlag, NewYork, 1971), vol. 3, p. 1. 39 A. D. Caplin, G. Gru¨ner, and J. B. Dunlop, Phys. Rev.
24 G. Stauss, J. Chem. Phys. 40, 1988 (1964). Lett. 30, 1138 (1973).
25 G. C. Carter, L. H. Bennett, and D. J. Kahan, Metallic 40 Z.Zhou,C.Uher,D.Xu,W.L.Johnson,W.Gannon,and
Shifts in NMR (Pergamon, 1977). M. C. Aronson, Appl.Phys.Lett. 89, 031924 (2006).
26 A.Narath,inHyperfine Interactions, editedbyA.J.Free- 41 W. A.Phillips, Rep.Prog. Phys.50, 1657 (1987).
manandR.B.Frankel(AcademicPress,NewYork,1967), 42 C. Tal´on, M. A. Ramos, and S. Vieira, Phys. Rev. B 66,
p. 287. 012201 (2002).
27 N. W. Ashcroft and N. D. Mermin, Solid State Physics
(Saunders, 1976).
