Commensurate-Incommensurate Magnetic Phase Transition in Magnetoelectric Single Crystal LiNiPO$_4$

0.59 MB·English

by  D. Vaknin

Commensurate-Incommensurate Magnetic Phase Transition in Magnetoelectric Single
Crystal LiNiPO
4
D. Vaknin,1 J. L. Zarestky,1 J.-P. Rivera,2 and H. Schmid2
1Ames Laboratory and Department of Physics and Astronomy Iowa State University, Ames, Iowa 50011
2Department of Inorganic, Analytical and Applied Chemistry, University of Geneva,
Sciences II, 30 quai E. Ansermet, CH-1211-Geneva 4, Switzerland
(Dated: February 2, 2008)
4
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Neutron scattering studies of single-crystal LiNiPO4 reveal a spontaneous first-order
0
commensurate-incommensurate magnetic phase transition. Short- and long-range incommensurate
2
phases are intermediate between the high temperature paramagnetic and the low temperature an-

n tiferromagnetic phases. Themodulatedstructurehasapredominantantiferromagnetic component,
a giving rise to satellite peaks in the vicinity of the fundamental antiferromagnetic Bragg reflection,
J and a ferromagnetic component giving rise to peaks at small momentum-transfers around the ori-
2 gin at (0,±Q,0). The wavelength of the modulated magnetic structure varies continuously with
2 temperature. It is argued that the incommensurate short- and long-range phases are due to spin-
dimensionality crossover from a continuous to the discrete Ising state. These observations explain

] theanomalous first-ordertransition seen in the magnetoelectric effect of thissystem.
l
e
- PACSnumbers: 75.25.+z,75.50.Ee,78.20.Ls
r
t
s
. 2.0
t Common magnetic systems with simple colinear long-
ma range-ordergroundstatecanmelt intothe paramagnetic m) LiNiPO4
(disordered) state directly, usually via a second order s/
p1.5
- phasetransition,orthrougha seriesofintermediatespa- (
d
n tially modulated phases before losing all correlations[1, nts
o 2, 3]. The indirect melting through modulated phases cie1.0
c indicates the presence of competing interactions of next effi
[ o
nearest-neighbors, anisotropies in the spin Hamiltonian, C
1 and/ortopologicalfrustrations[2]. Therehasbeenacon- ME 0.5
v tinuousinterestinthespontaneousandmagnetic-fieldin- ar
e
1 duced commensurate-incommensurate magnetic (C-IC) Lin
4 transition over the years[4, 5, 6]. For instance, in the 0.0 5 10 15 20 25
4
semimetallic europium tri-arsenide (EuAs3), the ground Temperature (K)
1
state of the systemis commensurateand as temperature
0
4 increases the system undergoes a C-IC transition[4]. In FIG.1: Magnetoelectric coefficients of LiNiPO4 versus tem-
0 copper metaborate, on the other hand, the ground state perature measured by the dynamictechnique. The ME coef-
/ is incommensurate and undergoes a continuous phase ficients, αxz, and αzx, were measured under 5 kOe magnetic
t
a transitiontoanon-collinearcommensurateantiferromag- field along thec-axis and the a-axis, respectively[17].
m netic state[7]. It has also been demonstrated that the
- C-IC transition can be induced by the application of an
d
external magnetic field[5, 6].
n respectively, but with some anomalies[15, 16, 17]. In
o Here, we report a novel C-IC magnetic phase transi- particular, the ME effect measurements of LiNiPO4 as
c
tion in the weakly coupled antiferromagnetic planes of a function of temperature reveal a first-order AF tran-
:
v LiNiPO4 (S=1, Ni2+), its characteristics resemble IC sition, and an unusual decrease of the ME coefficient
Xi structural phase transitions[8]. LiNiPO4 is an antifer- at temperatures below a maximum close to TN[18].
romagnetic (AF) insulator[9, 10] which belongs to the By contrast, the isostructural LiCoPO4, LiFePO4, and
r
a olivinefamilyoflithiumorthophosphatesLiMPO4 (M= LiMnPO4 exhibit continuous change of the ME coeffi-
Mn, Fe, Co, and Ni)[11]; space group is Pnma[12]. Neu- cients, indicative of second-order transitions[15]. Mag-
tron scattering studies demonstrated that LiMPO4 (M netic susceptibility studies of polycrystalline LiNiPO4
=Ni,Co)exhibitpropertiesbetweenthetwo-dimensional showed a significant deviation from the Curie-Weiss law
(2D) and three-dimensional(3D) with an interlayercou- in a temperature range much higher than T , and neu-
N
pling that is relatively stronger than the coupling found tronscatteringfromthesamepolycrystallinesamplegave
in the cuprates, for instance[13, 14]. These insulators rise to diffuse scattering at the nominal position of the
also exhibit a strong linear magnetoelectric (ME) effect, AFBraggreflectionuptoT ≈2T [13]. Recentmagnetic
N
with the observed ME tensor components, αxy,αyx, for susceptibility measurements of single crystal LiNiPO4
LiCoPO4 and, αxz,αzx, for LiNiPO4, in agreement with showed two features, one at TN = 20.8 K and one at
the antiferromagnetic point groups mmm’ and mm’m, T = 21.8 K associated with an AF transition and an
i
2
intermediate-phase,speculatedtobeIC,respectively[19].
Anirregularshapedsinglecrystal(0.396gramsinsize;
lattice constants at RT: a = 10.0317 ˚A, b = 5.8539
˚A,c=4.6768˚A),synthesizedbyaflux methoddescribed
elsewhere [20], was used for the neutron scattering stud-
ies. Neutron scattering measurements were carried out
on the HB1A triple-axis spectrometer at the High Flux
Isotope Reactor (HFIR) at Oak Ridge National Labo-
ratory. A monochromatic neutron beam of wavelength
λ = 2.368 ˚A (14.7 meV, k = 2π/λ = 2.653˚A−1)
o
was selected by a double monochromator system, us-
ing the (0,0,2) Bragg reflection of highly oriented py-
rolytic graphite (HOPG) crystals. The λ/2 component
in the beam was removed (to better than 1.3 parts in
106)byasetofHOPGcrystalssituatedbetweenthetwo
monochromatingcrystals. The collimating configuration
′ ′ ′ ′
40,40,Sample,34,68 was used throughout the exper-
iments. HOPG was also used as the analyzer crystal.
FIG. 2: A) Longitudinal scans along the (0,K,0) direction
Temperaturemeasurementsandcontrolwereachievedby
showing a single sharp (resolution limited) peak at the(010)
a Conductus LTC-20 temperature controller using Lake ∗
position (r.l.u is reciprocal lattice unit, in this case, b =
Shore silicon-diode temperature sensors (standard curve 1.0783 ˚A−2 units; the intensities of scans are shifted by two
10). ME effect measurements on thin polished plates decades each for clarity). A single Bragg reflection, due to
withevaporatedgoldlayersaselectrodeswereperformed theAFordering, is observed at low temperatures (2 - 19 K).
withthedynamictechniqueandquasistatictechniquefor At and above TN long-range IC order predominates and a
calibration, as described elsewhere[17]. Figure 1 shows third order reflection is also observed as shown for T=20.99
a strong ME effect with an abrupt transition, with an K. AboveT ≈ 21.7 K, broader peaks associated with the IC
anomalous temperature dependence of the ME coeffi- are observed up to ≈ 36 K. B) Longitudinal scans, close to
theorigin,alongthe(0,K,0)directionshowapeakcompatible
cients, αzx and αxz, with a maximum close to TN, in in position with the IC peaks observed at (0,1±Q,0). This
agreement with previous results[15, 18].
peak, due to a ferromagnetic component of the modulated
Relatively wide longitudinal scans along the (0,K,0) spin structure, is consistent with Model-I as described in the
direction at selected temperatures show the transition text (scans shown were obtained after subtraction of similar
fromtheAFtotheparamagneticstateproceedsthrough scanstakenat 40K;scansare shifted inintensityforclarity).
an infinite series of modulated structures. At low tem-
peratures (below T ≈ 19 K), a single Bragg reflection
at τ ≡ (010), due to the colinear AF ordering[10], is surate order persists in a narrow temperature range (≈
AF
observed,as shown in Fig. 2 for T = 9.81 K. At temper- 0.9 K) above the C-IC transition. In this temperature
atures higher than ≈19 K and lower than T =20.80 K, range, third order reflections of the modulated IC struc-
this Braggreflectionis superimposedona veryweakdif- ture(seeFig.2(A),T=20.99K)andapeakclosetothe
fuse scattering in the formof a broadLorentzian-shaped origin, characteristic of ferromagnetic modulations (Fig.
peak, also centered at (0,1,0). This broad peak (width 2(B)), are observed. No evidence for modulations along
0.235˚A−1),duetoshort-rangeinplanecoherence-lengths any other principal direction were observed.
(ξ ≈ 27 ˚A), is likely related to the lamellated domains Figure 3 shows transverse scans at the IC peak
recently observed by magnetic second-harmonic genera- (0,1±Q,0) with strong diffuse scattering below TN, sig-
tiontopographyonathinplateofLiNiPO4[21],andwith naling the onset of the incommensurate phases at ele-
the maximum observed in the ME effect(see Fig. 1). At vatedtemperatures. The onset for this diffuse scattering
T = 20.80 K, two extra satellite reflections at (0,1±Q,0) at T ≈ 19K correlates with the maximum observed in
appear, signaling a transition from the simple colinear the the ME-effect, shown in Fig. 1. The incommensu-
AF phase to the IC magnetic phase. The transition oc- rate peaks are observed up to TCO ≈ 36 K; however, in
curswithin0.005KofTN(theresolutionintemperature). the temperature range 20.8 - to 21.70 K, they consist of
Asshown,atthistemperaturecommensurateandincom- two superimposed peaks, one resolution limited and the
mensuratephasescoexist,asistypicaloffirst-orderphase other diffuse. This leads us to conclude that LiNiPO4
transitionsandconsistentwiththesuddendisappearance undergoes two transitions, one from the short-range IC
ofthelinearMEeffect(formerobservationsshowthatthe ordertothelong-rangeICstructureatTIC ∼=21.69,and
linear ME-effect cancels out in magnetically incommen- a second at TN from IC-LRO to AF as observed in the
suratestructures;e.g. BiFeO3[22],BaMnF4[23,24]). As ME effect measurements.
the temperatureisraised,theIC structurepredominates To account for the observations, two magnetic mod-
with correlation lengths comparable to those of the long els were considered in which each spin is rotated either
range AF ground state. In fact, long-range incommen- about the b-axis or the a-axis by an angle α with re-
3
spect to its nearest neighbor (Model I or Model II, re-
spectively). The angle of the j’th spin with respect to
the spin at some arbitraryoriginis givenby α =Q·r ,
j j
where Q is a vector along the (010) direction as the
AF propagation vector. The magnetic moment in the
plane varies as follows, S =µ(sinQ·r,0,eiτ·rcosQ·r)
for Model I and S = µ(0,sinQ · r,eiτ·rcosQ · r) for
Model II. Whereas Model I predicts ferromagnetic mod-
ulations with peaks near the origin at q = (0,±Q,0),
Model II does not. To determine the suitable model,
scans close to the origin(at small q’s)along allprincipal
directionswereconductedofwhichonlythe (0,K,0)scan
gave evidence to the IC structure. Figure 2(B) shows
background-subtractedscans along the (0,K,0) direction
(backgroundwasmeasuredatT=40K)withapeakob-
servedatthe intermediatelong-rangeIC phase(between
T=20.8KandT=20.7K).Theintensitiesofthesatel-
lite peaks close to the AF propagation vector (see Fig.
2) are about a hundred times stronger than the peaks
near the origin at (0,±Q,0), consistent with Model I as
shown below. The intensity ratio I(τ ±Q)/I(±Q) of
AF
these peaks can be estimated from the structure factors
oqf=thτe tw±onreQfl;ectinon=s,1F,3M, y∼ielPdinjgeiq·rjqˆ×(S ×qˆ) with FinIGL.iN4i:POA4)Taesmmpeearasuturered-doenpetnhdee(n0c,e1,o0f)tmheagonrdeteircpBarraagmgetreer-
AF flection. Intermediate phases between the paramagnetic (at
temperatureshigherthan≈36K)andtheAFphasesarein-
I(τ ±Q) |F(τ ±Q)|2 1
AF ≈ AF ≈( )2, (1) dicated. In the IC region two phases are identified, one with
I(±Q) |F(±Q)|2 Qb long-range and one with short-range order. Diffuse scatter-
ing at the nominal position persists up to TCO ≈ 36 K (a
where b is the lattice spacing along the direction of the crossover temperature). The transition from short- to long-
modulation. Equation(1)showstheintensityofthepeak range IC order occurs at TIC = 21.7K, and the C-IC tran-
near the origin vanishes as Q gets smaller, i.e., as the sition at TC−IC ≡ TN = 20.8 K. Illustration of the ground
temperature is loweredtowardsthe C-IC transition,giv- statemagneticorderingwithaprojectionoftherelevantions
ing rise to a maximum in peak intensity as qualitatively on the b-c plane is also shown. B) Temperature dependence
of the IC wave-vector. C) Simplified ground state (shaded
shown in Fig. 2.
area) beside the model of the IC structure within one plane.
The IC magnetic structure occurs as an intermedi-
Here, each spin is rotated at a finite angle with respect to
ate phase between two high symmetry phases. As the
a neighboring spin about the a-axis (Model II in the text).
Model I is similar to the one shown above, except the spins
are rotated about the b-axis, giving rise to a FM modulated
structurewith a detectablepeakat theorigin (small angles).
temperature is loweredfrom the paramagneticphase,an
onset for the IC occurs at TCO ≈ 36 K, with a grad-
ual increase in the wavelength of the modulation and
the correlation length. At TIC = 21.7 K, the coher-
ence length diverges and higher and new harmonics ap-
pear until the modulation wavelengthcoincides with the
high symmetry AF phase at TN = 20.8 K (See Fig.
4). The origin of the IC structure may be induced by
subtle charge distortions, or it could be innate to the
spin Hamiltonian. Since no evidence for a structural in-
commensurability was found, we hypothesize that the
IC phases (long- and short-range) originate from spin-
FIG. 3: A) Transverse scans along L B) and along H at
roughlythepositionoftheICpeak. Inthetemperaturerange dimensionality crossover, i.e., from a continuous Heisen-
20.8 - to21.7 K(i.e., from TN ≡ TC−IC toTIC) abroad dif- berg (orXY) type model to anIsing-model. The ground
fusepeakissuperimposed onaresolution limited peak(both state of the system is AF with no modulations, indi-
Lorentzians). Short range IC phase persists up to TCO ≈ 36 cating a spin Hamiltonian that does not include strong
K. terms that invoke an IC ground state (for instance, a
4
Dzyaloshinsky-Moriya term), as recently suggested by temperature-dependence of the ME coefficient of weakly
Kharchenkoetal.[25]. Thus,theoccurrenceofintermedi- ferromagnetic/ferroelectric/ferroelasticboraciteshas,for
ate magnetic incommensurate phases in LiNiPO4 has all the first time, been explained by considering the con-
the characteristicsof typical structuralIC phases,which tribution of the symmetry-allowed spontaneous toroidal
also manifest soft-phonon modes[8]. In preliminary spin moment[29, 30, 31]. Neutron scattering studies under
wave studies of LiNiPO4, a temperature-dependent gap applied magnetic field may shed light on the anomalous
(1.5-2meV),andaminimuminthespin-wavedispersion behavior of the ME-effect. We hope that our findings
curve was observed[26]. Theoretical predictions suggest will stimulate theoretical microscopic studies on the na-
that frozen magnons are possible in a 2D system with tureofthisICphaseobservedinLiNiPO4,butnotinthe
random-distribution couplings[27], as recently suggested isostructural LiCoPO4.
for these systems[13, 14]. This work was supported (in part) under the auspices
In summary, our observations of a C-IC first-order of the United States Department of Energy. The HFIR
phase transition, and the short-range order below TN Center for Neutron Scattering is a national user facility
explain the abrupt jump and the maximum in the ME- funded by the United States Department of Energy, Of-
effect of LiNiPO4 (as observed in Fig. 1). Our results fice of Basic Energy Sciences- Materials Science, under
however do not explain the anomalous temperature de- Contract No. DE-AC05-00OR22725 with UT-Battelle,
pendence ofthe MEcoefficientwhichmaybe due to ME LLC. The work was supported by the Department of
contributionsofthespontaneoustoroidalmoment,which Energy, Office of Basic Energy Sciences under contract
ismagnetoelectricinnature[28]. Recently,theanomalous number W-7405-Eng-82.
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