Table Of ContentStudy of negative thermal expansion in the frustrated spinel ZnCr Se
2 4
X. L. Chen,1 Z. R. Yang,1,a) W. Tong,2 Z. H. Huang,2 L. Zhang,2 S. L. Zhang,2 W. H. Song,1 L. Pi,2,3 Y. P.
Sun,1,2 M. L. Tian,2 and Y. H. Zhang2,3
1)Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031,
People’s Republic of China
2)High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031,
People’s Republic of China
3)University of Science and Technology of China, Hefei 230026, People’s Republic of China
(Dated: 20 January 2014)
The origin of negative thermal expansion (NTE) in the bond frustrated ZnCr Se has been explored. ESR
2 4
4
and FTIR document an ideal paramagnetic state above 100 K, below which ferromagnetic clusters coexist
1
with the paramagnetic state down to T . By fitting the inverse susceptibility above 100 K using a modified
0 N
2 paramagneticCurie-Weisslaw,anexponentiallychangeableexchangeintegralJ isdeduced. Inthecaseofthe
variableJ,magneticexchangeandlattice elasticenergycouplewith eachother effectivelyviamagnetoelastic
n
interaction in the ferromagnetic clusters, where NTE occurs at a loss of exchange energy while a gain of
a
J lattice elastic one.
7
1
I. INTRODUCTION marked splitting of the low-frequency mode below T .20
N
This elucidates an essential spin-phonon coupling. Both
]
el Magneticfrustratedsystems haverecentlybeena sub- geometricaland additional bond frustrationare believed
- ject of continuing interests for a manifold of fascinating tobecrucialfactors.6,21 Inaddition,sinceCr3+ inanoc-
tr states such as spin ice, spin liquid and orbital glass et tahedralcrystalfieldisJahn-Tellerinactive,spin-phonon
s al. may be surviving down to T = 0.1–3 Among the couplingisofvitalimportanceinliftingfrustration. Nev-
.
at reportedmaterials,chromium-basedspinelswiththefor- ertheless,theveryoriginofNTEisyetfarfrombeingwell
m mula ACr X (X = O, S, Se) are of essential role not understood.
2 4
- only of being theoretical interests but also in explor- In the present paper, a set of experimental tech-
d ing potential multi-functional materials.4–7 For instance, niques is utilized to probe the spin-lattice correlation in
on cinapCacdiCtirv2eSc4o,utphleinfgerwroereelecotbrsiecritvyeda.n8dThcoelocsosmalpomuangdnewtaos- ZwnitChr2reSsep4e.cBtytocotnemsidpeerriantguraevoarrilaabtlteiceexcchonanstgaenitn,tNegTraEliJs
c
[ suggested to be a multiferroic relaxor. However, Scott attributed to a result of the competition between mag-
and coworkers argued its correctness and rather related netic exchange and lattice elastic energy via magnetoe-
1 it to be a conductive artefact.9 Recently, the conclusion lastic coupling.
v
of conductive artefact is further evidenced by Yang et
6
al., both experimentally and theoretically.10,11 As a re-
4
2 sult, the design or tuning of multi-functional materials
4 for potential applications enables the necessity to clear
. what stands behind the novel phenomena observed.
1 II. EXPERIMENTS
ZnCr Se withnegativethermalexpansion(NTE)isa
0 2 4
4 caseinpoint.6,12Thiscompoundexhibitsalargepositive
1 Curie-Weisstemperature.13 However,neutrondiffraction The polycrystalline sample of ZnCr Se was prepared
2 4
v: studyrevealedatTN =21Kacomplexhelicalspinscon- by standard solid state reaction method. High purity
◦
i sistedofFMlayersalong[001]withaturningangleof42 powdersofzinc(99.9%),chromium(99.9%)andselenium
X between the adjacent ones.14–16 Interestingly, this spin (99.9%) were mixed according to the stoichiometric ra-
r configuration allows a field-induced electric polarization tio. Next,thepowdersweresealedinanevacuatedquartz
a revealing magnetoelectric effect or multiferroicity.17,18 tube, and heated slowly to 850 ◦C in seven days. Then
WhileearlyX-raydiffraction(XRD)andneutronpowder the sample was reground, pelletized, sealed and heated
diffraction indicated a tetragonal structural transforma- again for another three days at 850 ◦C. The magnetic
tion at TN, subsequent neutron and synchrotron radi- data was collected on a Quantum Design superconduct-
ation results on single crystal showed an orthorhombic ing quantum interference device (SQUID) magnetome-
phase.15,16,19 Moreover, recent neutron powder diffrac- ter. The temperature dependent XRD patterns were ob-
tion found no sign of structural transition.12 In fact, the tainedusingXRD(RigakuTTRIII).ESRmeasurements
exact lattice symmetry is still subject of debate. On were performed using a Bruker EMX plus 10/12 CW-
the other hand, IR spectroscopy experiment reported a spectrometer atX-band frequencies (υ = 9.39GHz) in a
continuous He gas-flow cryostat for 2–300 K. The trans-
mittance spectra were collected in the far-infrared range
using the Bruker Fourier-transformspectrometer Vertex
a)Correspondingauthor: [email protected] 80v equipped with a He bath for 5–300 K.
2
III. RESULTS AND DISCUSSION
0.12
The XRD data was analyzed using the standard Ri-
etveld technique, which shows a single-phase material
with cubic spinel structure at room temperature. Fig- u/g) ZFCFC
ure 1(a) shows the temperature (T) dependence of lat- m
e
(
tice constant a. With decreasing temperature, a first M
0.08 H = 100 Oe
decreases rapidly and then manifests a negative thermal TN
expansion behavior below about T = 60 K, which is
E
almost concordant with the previous results.6,12 Upon (a)
further cooling below 20 K, splitting of several peaks
in XRD spectra are observed. The representative peak 0 10 2 0 30 40
(440)at12Kthatsplitsinto(440)and(404)ispresented 60
inFig.1(b). Thissignalsacubictotetragonalstructural
transition with space group I4 /amd.15,19
1 )u ~ 180 K
m
e
ol/
m 30
(a) Oe
(
TN TE 1/
1.049
) 2aT (b)
m
n 0
( aC 0 100 200 300
a 1.048
T (K)
cT
FIG. 2. (Color online) (a) Low temperature dependence of
1.047 themagnetizationM forapolycrystallinesampleZnCr Se at
2 4
10 100 100Oe. (b)ACurie-Weissfittingoftheinversesusceptibility.
T (K)
(b) y (a. u.) 300 K40) 60 K40) ESKKxu12pm. 12 K40) ((((444440400404)))) KKKK1122 CmonGolymSeCunnrt3it+csa)ilocenuq.luaatlesdtoby3.8th7eµBfo,rimnualgareµeemffe=nt2w.8it3hpthCe/s2p(inin-
sit (4 (4 (4 The large positive Curie-Weiss temperature implies a
n dominant FM exchange interaction, however, the com-
e
r
n pound shows an AFM ordering at low temperatures.
I
Hence, we first investigate the lattice dynamic inspired
by the strong spin-lattice correlation. Within the wave-
48.5 49.0 48.5 49.0 48.5 49.0
number range inspected, three infrared modes, labeled
2 (deg.)
as I, II and III are observedsimultaneously. Generally
speaking, the phonon eigenfrequency follows an anhar-
monic behavior,whichcan be describedby the following
FIG. 1. (Color online) (a) Temperature dependent lattice
formula:
parameteravsT insemilogarithmicforZnCr Se . Errorbars
2 4
areaverageofrepeatedfittings. Thenegativethermalexpan-
osinoenTinNitaiarel tdermawpnerainturreedTdEotaenddlitnhees.a(nbti)feTrrhoemraegpnreesteicntoartdiveer ωi =ω0i(cid:20)1− exp(Θα/iT)−1(cid:21), (1)
peaks(440)at300K,60Kand12K.Circlesareexperimental
data; Solid and dashed lines are Lorentzian fits. where ω , α and Θ are the eigenfrequency of mode
0i i
i with decoupling of the spin and phonon at 0 K, the
Figure 2(a) presents the magnetization (M) versus weightfactor of mode i and the Debye temperature Θ =
T at low applied magnetic field of 100 Oe under 309K.20 Adetailedtemperature dependence ofeigenfre-
both zero-field-cooled (ZFC) and field-cooled (FC) se- quency is exhibited in Fig. 3. The solid line is a fitting
quences. At about TN = 22 K, M shows a sharp AFM of classical anharmonic behavior according to equation
transition.6,12,14–16 Figure 2(b) shows a fitting of the in- 1. Mode I shows negative shifts below T and Mode II
E
verse susceptibility 1/χ according to the paramagnetic shows positive shifts from about 100 K compared to the
(PM) Curie-Weiss law 1 = T−ΘCW0. A large positive normalanharmonicbehaviors,respectively. Accordingto
χ C
Curie-Weiss temperature Θ = 85 K and the coef- Lutz et al. and coworkers, the highest frequency mode
CW0
ficient C = 3.74 are obtained. The effective magnetic III is ascribed to the Cr-Se vibration, however,modes II
3
1.2
303
300 TN TE Oe) 0.8
k
III (PP
H
-1 m) 0.4
c
r ( 285
e
b (b)
m 0.0
u
e n 282 (a)
v
a
W II g = 1.996
e) 3.3
O 100 K
202 H (kres Hpp
3.2
200 Hres
I
10 100 3.1
T (K) 0 100 200 300
T (K)
FIG. 3. (Color online) Temperature dependence of wave FIG. 4. (Color online) (a) Temperature dependence of the
number of the infrared activated mode I, II and III for resonance field H . Inset: atypicalfittingof theESRspec-
res
ZnCr Se . Thesolid curveis a fit described in thetext. The trum at 100 K, where the definitions of the parameters are
2 4
characteristic temperatures are indicated. shown. (b) The peak-to-peak linewidth ∆H vs T. The
PP
dashed lines are guided by eyes.
and I originate from combined vibrations of Cr-Se and
Zn-Se. Formode II,the ratioof contributionfromCr-Se Thegfactoris1.996,inagreementwellwiththeprevi-
andZn-Seis78: 18,whileformodeItheratioofCr-Seto ous works.6,25,26 The linear decrease of ∆H with tem-
PP
Zn-Se is 21 : 73.22 Cr-Se bond relates to the ferromag- peraturecanbeattributedtoasingle-phononspin-lattice
netic (FM) spin super-exchange interaction and Zn-Se relaxation mechanism.27,28 Both the constant g-factor
links to the antiferromagnetic (AFM) super-exchanges.4 and linear behavior of ∆H evidence a well-defined
PP
As a result, FM Cr-X-Cr bonds dominate modes II and paramagnetic(PM)stateatleastabove100K.Notethat
III while AFM linkages Cr-X-A-X-Cr determine mainly H starts to decrease and ∆H broadens at 100 K.
res PP
theeigenfrequencyofmodeI.23,24 Thedeviationofmode Meanwhile, an FM-related positive shift for Mode II is
II below 100 K due to spin-phonon coupling indicates observed in the IR modes in Fig. 3. These can thereby
that FM fluctuations involve already at this tempera- be correlated to the onset of FM fluctuations and spin-
ture. Furthermore, the opposite shifts of modes I and II phonon coupling. As we know, H is a sum of H
res int
in the NTE temperature region may refer to a dynamic and H , where H and H are the equivalent inter-
ext int ext
competition of FM and AFM superexchanges. nal and the external actural fields, respectively. For the
The temperature dependent ESR spectrum is further case H > 0, the internal field may shift the resonance
int
investigated. A PM signal is observed at room temper- line to lower field; on the contrary, the resonance signal
ature and it vanishes below T (not drawn). The reso- wouldappear at higher field with negative internalmag-
N
nantfield(H )andpeak-to-peakline-width(∆H )as netic field. The decreasingofH below 100Kindicates
res PP res
afunctionoftemperatureareplottedinFig.4(a)and(b), an increasing of H , which may be caused by the inter-
int
respectively. A typical ESR spectrum at 100 K and fit- action between the localized magnetic moments and the
tingusingthefirst-orderderivativesymmetricLorentzian demagnetization effect.27 Therefore, the enhancement of
function are presented in the inset of Fig. 4(a). As H andonsetofFMfluctuationsrevealgraduallygrow-
int
can be seen from Fig. 4(a), with decreasing temperature ing FM clusters, forming an FM-cluster and PM mixed
from 300 K to 100 K, H shows a constant value while state from 100 K to T . The existence of FM clusters
res N
∆H decreases almost linearly. Upon further cooling, is also supported by the following NTE analysis. Below
PP
H drops drastically and accordingly ∆H broadens T , the signaldisappearsdue tothe AFMorderingtran-
res PP N
greatly, in accordance with Ref.6. sition.
4
As is discussed above, the system keeps a pure PM
state at least above 100 K, so the inverse susceptibility 60
should be described by the PM Curie-Weiss law down
to this temperature. However, it departs from the lin- )u
m
ear behavior at a temperature as high as about 180 K, e
see Fig. 2(b). Recalling the fitting process in Fig. 2(b), ol/
m
we have assumed a constant Curie-Weiss temperature e 30
O
ΘCW0, i.e., a constant magnetic exchange interaction J. (
The behavior of IR modes below 100 K implies a com- 1/
petition of FMand AFM superexchangeinteractions. In
(a)
addition, the nearest neighbor FM Cr-Se-Cr and other
0
neighbor AFM Cr-Se-Zn-Se-Cr superexchange interac- 0 100 200 300
tions depend strongly on the lattice constant.4 It means
that the total J may change since a decreases dramat-
80
ically upon cooling [Fig. 1(a)]. Accordingly, the tradi-
tional Curie-Weiss behavior should be modified within
) 40
K
the present case to bridge the gap mentioned above. In
specific,oneshouldtakeavariableΘCW (orJ)asafunc- (CW
0
tion of T or a into account.
In AFM spinel oxides, the Curie-Weiss temperature
changesexponentially withthe lattice parameter.23 Nat- -40 (b)
urally,anempiricaldescriptionofΘ (T)=Θ −α×
CW CW0
e−T/β ispostulated. Thefittingoftheinversesusceptibil- 0 100 200 300
T (K)
ityabove100Kusingthe modifiedCurie-Weissbehavior
1 = T−ΘCW(T) is exhibitedinFig.5(a). Theparameters
χ C FIG. 5. (Color online) (a) A fitting of the inverse suscep-
are α = 226 and β = 45. Furthermore, a remarkable de- tibility above 100 K in red solid line using 1 = T−ΘCW(T)
viation below 100 K in blue short dashed line indicates taking a temperature or lattice constant a deχpendent CCurie-
the appearance of the effective internal field originating Weiss temperature into account. The short dashed blue line
from FM clusters. Next, based on the obtained α and is an extension of the fitting to low temperatures. (b) Θ
CW
β, Θ (T) is extrapolated to low temperatures as ex- vsT and thered dashed line indicates Θ = 0 at 45 K.
CW CW
hibited in Fig. 5(b). It shows a derivation at about 180
K from the nearly constant value. With further lower-
ingtemperature,itdecreasesfasterandfasterandbelow
When the systemstays atanFM state with a change-
T ≈ 45 K, Θ (T) even becomes negative. These fea-
CW able J, there may exist a competition between E and
ex
tures may interpret qualitatively the fact that ZnCr Se
2 4 E since the former is negative while the latter always
el
is dominated by ferromagnetic exchange interaction but
positive. Indeed, it has been concluded above that J de-
orders antiferromagnetically at low temperatures. Since
creases exponentially [Fig. 5(a)] and some FM clusters
the exchange integral and the Curie-Weiss temperature
forms gradually below 100 K. Therefore, the concomi-
are linked by J(T)∝Θ (T) [J(a)∝Θ (a)], we will
CW CW tant decrease of J and a causes an increasing E but
ex
use J(T) [J(a)] instead in the following discussion.
decreasingE intheFMclusters. Atsomecriticalpoint,
el
GiventhatJ ischangeable,magneticexchangeandlat-
a totally compensation between them may present. If a
tice elastic energies can link effectively with each other
further decreases as cooling, the variation of E would
ex
viamagnetoelasticcoupling. ThefreeenergyF inamag-
gradually exceed that of E in magnitude. Especially
el
netoelastic system is expressed as
when J drops sharply with respect to a, say here at T ,
E
a tiny decrement of a will give rise to a dramatic in-
−→ −→ 1 crement of E whereas E keeps nearly constant. The
F(T)=−J(T) S ·S + Nω2△2(T)−T·S(T), (2) ex el
i j 2 state in a system subjected to stimuli, such as cooling,
Xi,j
always tends to develop towards one that can lower F.
where N the number of the ion sites, ω the averaged In this sense it is favorable to lowering F by expand-
vibrationalangularfrequency and △ the averagedstrain ing the lattice parameter a to increase J (J > 0) and
relative to the equilibrium lattice constant. The first thereby to decrease E due to its negative value, at the
ex
term is exchange energy (E ) as a function of J, the same time at a cost of few increases of E in magni-
ex el
second is lattice elastic energy (E ) related mainly to tude. This means that a negative thermal expansion of
el
the lattice parameter a (or equivalent T) and the last is the latticeoriginatingfromtheFMclusterswithaexpo-
the entropy. From the above equation we know that if nentiallychangeableJ isexpected. Itisworthyofnoting
the system stays atan ideal PMstate, then E = 0. So thatwhenapplyingamagneticfieldtothe systeminthe
ex
E and E will show no coupling, as is observed from NTE temperature region,NTE in magnitude enhances.6
ex el
the IR spectra above 100 K. This is becausethe sizeorpopulationofthe FM clusters
5
increases when applying a magnetic field. 6J.Hemberger,H.-A.KrugvonNidda,V.Tsurkan,andA.Loidl,
On the contrary, when an AFM ordering appears, J Phys.Rev.Lett.98,147203(2007).
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Park,J.-H.Chung,andK.H.Kim,Appl.Phys.Lett.94,042505
notmetanymore. Normalthermalexpansionuponcool-
(2009).
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which is consistent to lowering F. In fact, a normal ex- Nidda,V.Tsurkan,andA.Loidl,Nature434,364(2005).
pansionfeatureisobservedbelowT .6 Itshouldbenoted 9G.Catalan,andJ.F.Scott, Nature448,E4(2007).
N
that the existence of NTE6,12 evidences in turn that J 10Y.M.Xie,Z.R.Yang,L.Li,L.H.Yin,X.B.Hu,Y.L.Huang,
H.B.Jian,W.H.Song,Y.P.Sun,S.Q.Zhou,andY.H.Zhang,
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el
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