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(Bi,RE)FeO www.pnas.org/cgi/doi/10.1073/pnas.1809004115 Pb(Zr,Ti) are substances inorganic in transitions (13–22). technological refrigerators electro-caloric and and 12), actuators, electro-mechanical 11, memories, nonvolatile (6, including characteris- chemistry applications condensed (7–10), from intriguing attention physics these considerable matter attracted of have Because they tics, entropy. (lattice and spontaneous structure strain), in crystalline change permittivity, large dielectric a polarization, by tran- accompanied antiferroelectric Phase often and are (6). phases ferroelectric, metal–organic systems paraelectric, (4), between supramolecular crystals sitions and liquid molec- (5), (3), organic polymers (1), frameworks (2), oxides inorganic solids in as ular observed such widely materials, are various phases These respectively. polarization, F transition phase structural crystal dipolar self- effects. for realization electro-mechanical and phase large principle order dipolar of the desired physical with crystal only fundamental a to not a strain. organization and provides control polarization finding to between coupling Our key the dipolar a also interactions, but is transition anisotropic interactions, of frustra- steric types energetic that and two reveal the we in between model, transition tion structural this com- important In this which system systems. of dipole, organic model essence permanent an a simple capture with may this a particles understand spheroid-like dipolar develop to of of essential posed we competition is a here order that of phenomenon, picture type physical another with a order organic of con- basis for unknown. the such still molecule On is behind a organization principle crystal–lattice of inorganic physical involving trollability shape basic for the the strain However, changing applying crystals. of by radius externally dipolar and ionic or of the crystals atom changing types to by constituent two made due a the been also practically of has but control and order The switchability electro-mechanical effects. as electrical such electro-caloric their effects to cross-coupling significance technological intriguing due of are only and not matter various condensed (received in of 2018 seen 16, types widely August are Mallouk antiferroelectricity E. Thomas and Member Ferroelectricity Board Editorial by accepted 2018) and 25, China, May Nanchang, review University, for Nanchang Xiong, Ren-Gen by Edited a Takae interaction Kyohei dipolar and shape between particle interplay the via crystals antiferroelectric and ferroelectric into Self-organization eateto udmna niern,Isiueo nutilSine nvriyo oy,Tko1380,Japan 153-8505, Tokyo Tokyo, of University Science, Industrial of Institute Engineering, Fundamental of Department yia xmlso ereeti–niereeti phase ferroelectric–antiferroelectric of examples Typical ogrnedplrodrn ihadwtotmacroscopic without and with ordering of dipolar manifestations are long-range antiferroelectricity and erroelectricity PbZrO 3 | ferroelectricity 1,2) hr Esad o aeerhmetal earth rare a for stands RE where 23), (14, a,1 3 o xml,sri eeae yaltiemis- lattice a by generated strain example, for , n aieTanaka Hajime and | ehnclswitching mechanical | antiferroelectricity a,1 | O 3 1 and (1) 1073/pnas.1809004115/-/DCSupplemental enivsiae o niiulsses(5 6 13) the 31–38), 26, (25, systems emer- individual has the for ordering for antiferroelectric investigated and responsible ferroelectric been modifications. of factor such each structural of by under- gence phase key physical each a the unified stabilize be Although to no to how is thought on there is standing the factor although in controlling shape, particular, key molecular In a parameter. substances, controlling organic certain a by intermolecular trolled steric controlling per- benzene- by (12). interactions of dielectric crystals (BTAs) in supramolecular ferroelectricity 1,3,5-triamides columnar vanishes anomaly in furthermore, case observed another recently, was former Quite while shown the remains. also pressure, mittivity in was high transition It at ferroelectric 30). (11, the respectively that acids, iodanilic chloranilic for iodanilic/chloranilic emerge and antiferroelectricity of and adduct ferroelectricity ple, 5,5 1:1 a with benzimidazoles For as acid such (29). (4) crystals crystals hybrid organic liquid organic–inorganic and 27), 6, also (28), (2, perovskites can the crystals molecular phases in in antiferroelectric seen coupling be of electro-mechanical Examples determining transition. of factor sug- phase 26), crucial importance (25, a the ordering be polarization gesting to and known structure is crystalline the substrate the to fit hsatcecnan uprigifrainoln at online information supporting contains article This Editorial the 1 by invited the editor under Published guest a is R.-G.X. Submission. Direct Board. PNAS a is article This interest. of conflict no declare paper. authors the The wrote and H.T. K.T. and research; K.T. performed and K.T. data; research; analyzed H.T. designed H.T. and K.T. contributions: Author owo orsodnemyb drse.Eal aaaisutkoa.por [email protected] Email: addressed. be may correspondence [email protected] whom To nswl rvd sflgiefrdsgigmtraswith materials designing for guide order. useful dipolar a provide find- will These ings phases. antiferroelectric to switch- and key mechanical ferroelectric a of as ability is such origins solids different of with properties anisotropy cross-coupling between of such interplay types the in two that the interactions competition reveal dipolar also of We and importance self-organization. steric the anisotropic controlled elucidate a between in we order dipolar Here desired sim- manner. of a structure is lattice missing a self-organization into still shows However, that model order. physical dipolar particle-based ple of science elec- type material the dielectric, depend on in crucially the properties issues thermoelectric because central and tromechanical, applications the of technological one crys- and is a of solid antiferroelectricity talline and ferroelectricity Controlling Significance nalo h bv xmls h yeo ioa re scon- is order dipolar of type the examples, above the of all In 0 -dimethyl-2,2 NSlicense. 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APPLIED PHYSICAL SCIENCES physical origin of the structural phase transition accompanying a crystal–lattice change between the two types of polarization ordering and its coupling to mechanics remain elusive. Further- A more, it is unclear whether there are any common underlying + physics behind ferro-to-antiferro ordering seen in a wide class of materials. As a first step toward the unified understanding of these phe- nomena, we propose a simple candidate mechanism, which may be relevant for the organic systems: competition between steric and dipolar interactions. To realize this by a simple particle- based model, we construct a system consisting of spheroid- like Lennard-Jones particles with a point dipole, whose shape anisotropy (i.e., the aspect ratio characterized by an anisotropy antiferroelectric order parameter η) is introduced as a key physical parameter to control the short-range repulsive interaction (Materials and Methods). ferroelectric order So far there have been many particle-based modelings of fer- B T roelectric ordering (39–44), but no reports on antiferroelectric 1.2 ordering and phase controllability. Our model may not be uni- Paraelectric versal [e.g., not directly applied to perovskite-type solids where a 1 Liquid point dipole moment cannot be well defined even approximately (45)], but captures essential physics behind self-organization of 0.8 dipoles into two types of long-range dipolar order into different 0.6 crystalline lattices: competing orderings. Fig. 1A schematically Ferroelectric shows a key idea of our model: The electric interaction between 0.4 point dipoles is intrinsically anisotropic, and its sign depends on 0.2 the particle arrangement (46). Thus, the particle arrangement Antiferroelectric favored by steric repulsions is not necessarily favored by dipo- 0 lar interactions. Such frustration is more significant for particles 0 0.5 1 1.5 2 2.5 with larger anisotropy η. Thus, the increase of η destabilizes the C D ferroelectric crystalline lattice structure and results in a struc- tural transition to an antiferroelectric phase with a different lattice structure (Fig. 1 A–D). In relation to this, it is worth not- ing that even in simple dipolar systems an interesting hysteretic response is observed under a specially designed arrangement of dipoles (47). In this article, we show a simple physical principle, by which we are able to control the tendency toward ferroelectric or antiferroelectric ordering, and discuss its relevance to material design. y -y E z -x -y Results Phase Diagram. We show the T − η phase diagram of our model -x x -x x in Fig. 1B, where η represents the degree of shape anisotropy x y and η = 0 corresponds to the spherical dipoles (43) (Materi- -z -y y als and Methods and SI Appendix, A). We fix the pressure at diagonal view top view bottom view a high value so that the crystalline state is stable for a broad temperature range. For η close to zero, there are three stable Fig. 1. Phase behavior. (A) Schematic representation of electro-mechanical coupling in our model. Since the dipolar interaction changes its sign phases: the equilibrium liquid, paraelectric crystal (plastic crys- depending on the particle arrangement, the ferroelectric/antiferroelectric tal characterized by long-range translational order but without ordering crucially depends on the aspect ratio of the spheroids and the orientational order), and ferroelectric crystal (Fig. 1C), from applied strain. (B) Equilibrium (η, T)-phase diagram of our model (see Mate- high to low temperature. Here the paraelectric–ferroelectric rials and Methods for the calculations). The solid and dashed lines are phase transition is of second order (SI Appendix, B). The crys- the phase boundaries between equilibrium phases and those between talline structure of the paraelectric phase is either face-centered metastable states, respectively. The phase transitions are first order for the antiferroelectric–ferroelectric/paraelectric transitions (black line) and the cubic (Fm3¯m) or hexagonal closed packed (P63/mmc) with almost equal probability; upon transition to the ferroelectric crystal–liquid phase transition (blue line). The transition between the stable phase, it transforms into a rhombohedral (R3m) or hexagonal ferroelectric and the paraelectric phase for η < 1.4 (solid red line) is sec- ond order, whereas the one between their metastable phases for η ≥ 1.4 (P63mc) structure by dipole alignment accompanying the asso- (dashed red line) is weakly first order due to the electrostrictive coupling ciated change of (111) interlayer spacing. With increasing η, between polarization and strain (SI Appendix, B). (C) A ferroelectric phase the paraelectric–ferroelectric transition temperature decreases observed for η = 1.0 and T = 0.6. The color denotes the molecular orien- since the ferroelectric attractive interaction decreases (Fig. 1A). tation; we can see that almost all of the particles align along the same Eventually, an antiferroelectric phase with a monoclinic (P2/m) direction. (D) An antiferroelectric phase observed for η = 1.6 and T = 0.6. structure (Fig. 1D) is formed from the ferroelectric phase via Two kinds of ferroelectric planes (distinguished by color) are stacked alter- a strongly first-order transition (see SI Appendix, C for the nately, leading to cancellation of macroscopic polarization. The snapshots details of the crystalline structure). At η = 1.4, the ferroelectric– in C and D are obtained from the low-T part on cooling from the simula- antiferroelectric phase transition temperature coincides with tions displayed in Fig. 2 A and B, respectively. In C and D, color fluctuation reflects orientation fluctuation, which is stronger in the ferroelectric state that of the paraelectric–ferroelectric phase transition, indicating (C) than in the antiferroelectric one (D) (Fig. 3). We note that time-averaged the presence of a triple point. Interestingly, a strong electrostric- orientation reduces fluctuation and coincides with that expected for the tive coupling for larger η changes the nature of the (metastable) assigned space groups in the main text. (E) Color legends of the dipole paraelectric–ferroelectric transformation from second order to orientation.

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Fig. (SI at in transition shown temperature paraelectric–ferroelectric in the of change results the order to antiferroelectric and respond order ferroelectric how show Field. we External and Next Change phase Temperature by Induced competing Transitions Phase with systems melting-point of the 49). feature in 48, (24, universal minimum ordering large-η a the the is for of curve slope appearance the This although small. shape, boundary V phase a liquid–crystal has The the of 1A). increase (Fig. the anisotropy by particle stabilized is phase indicating antiferroelectric strongly the crystal, that antiferroelectric the to liquid the from > (η anisotropic strongly Appendix, (SI order first ecnseams h aeplrzto eairfrbt cool- both for behavior polarization same the almost see can around We steeply grows (see definition), order dipolar local of nitude EF C A η 0.2 0.4 0.6 0.8 10 10 10 10 -1 0 1 = 0 0.6 oaiainStrain(%) Polarization 0.6 1 2 3 4 and 1.0 nematic order< mrec ffrolcrcadatfrolcrcodr (A order. antiferroelectric and ferroelectric of Emergence constant dielectric External electricfield -0.2 =1.6 =1.0 T =0.6 =1.6 dipolar order< η Temperature Temperature = ,rsetvl.(C respectively. 1.6, 0 0.7 0.7 Q hP > i 0.2 n eai order nematic and .We h hr-ag neato is interaction short-range the When B). ,teei nyoepaetransition phase one only is there 1.7), rqec eedneo h edresponse field the of dependence Frequency ) =1.0 P > = and 1.6 0.8 -0.4 0 0.4 0.8 0.8 h hnei h ilcrcconstant dielectric the in change The ) B D 0.2 0.4 0.6 0.8 0.2 0.4 0.6 IAppendix, SI oaiain(e uv)adstrain and curve) (red Polarization ) -1 0 1 0 1 0 0.6 T 0.6 hP AF structuralorderparameter T 0 = = T Polarization h vrg ftemag- the of average the i, =1.0 =1.6 -0.2 External electricfield =0.65 5.See 0.65). =1.6 hQi .75/k Temperature Temperature o eprtr cycle temperature a for E 0.7 B < 0 0.7 < = o h detailed the for Q IAppendix, SI 40000 P pncooling. upon 4000 and 1.6 > > 800 400 iei quite is side 1 / η 0.2 = .The D). f =1.6 T and 1.0 and η = 0.8 D–G 0.8 0.6) are B) h rgno lwDnmc fteFrot-nier Transforma- Ferro-to-Antiferro the of Dynamics tion. Slow of Origin 1B. The Fig. in shown as boundary, phase the cru- to one close antiferroelectric on of an depends from degree state cially the ferroelectric a tuning induce by to field (η electric anisotropy polarization external particle the an and strain interest- to the the responses both highlights controlling This of possibility frequency. ing highest the at switching ('100t anti- time relaxation the the that to Appendix, fact the back by This confirmed transform modulation. be high-frequency to can a system such is under the there state for ferroelectric that time indicates enough dependence not phase frequency antiferroelectric This the disappears. of characteristic response hysteretic 2F polarization the (Fig. of dependence response frequency the by confirmed is this (see nucle- phase spontaneous ferroelectric for Appendix, the SI in time domains incubation antiferroelectric long of that ation a indicates This be transformation. should phase there the for barrier energy centrosymmetric is phase antiferroelectric space this the the that of since note piezoelectric, group We not polar- 2E. and Fig. the electrostrictive, strain in is curve model, large response blue a the our by by in shown along as accompanied particle response, automatically set spheroid is is the the response moment of of ization characteristic axis dipole response a long the hysteresis field, the Since double electric a phase. applied observe the antiferroelectric we to 2E, curve) field. Fig. (red electric in external an shown we to As order, response antiferroelectric dielectric has the only really examine value also state ordered nonzero this Appendix, a that (SI firm has phase antiferroelectric that the parameter in order structural cial in than same the phase for ferroelectric even the one in antiferroelectric the larger are Furthermore, hindrance. fluctuations steric less dipole to due orientational dipoles larger of allows fluctuations anisotropy the than smaller constant because large dielectric primarily at the in one change larger paraelectric–antiferroelectric much a by small dependence nied at transition temperature for paraelectric–ferroelectric the constant The show dielectric antiferroelectric the also the of We of temperature, nature transition. the first-order cycling phase phase The strong on 2C). hysteresis the (Fig. large indicating constant zero a dielectric shows be the transition in not Thus, change fluctuation. need the in polarization with it change local of abrupt polarization, degree the local the of reflects antifer- and magnitude and define the paraelectric we of both since However, for phases. zero roelectric be should polarization lecre.Ti sacersgaueo h mrec fanti- of (Fig. emergence below vanishes the order of polarization signature long-range clear the ferroelectric a when is order This even curve). blue value dipolar 2B, large the discontinuously 2B, a increases (Fig. that have order to cooling nematic see the upon whereas can vanishes curve), We red almost and 2B. decreases Fig. abruptly in shown as large at tion (or particle. anisotropy (see each shape of the order along axis set long) is nematic moment dipole local the since of ing, magnitude of order the nematic nature Appendix, of local second-order the average that the note the We indicating transition. paths, phase this heating and ing hr eso h hneo spe- a of change the show we where 2D, Fig. also in can seen structure crystal clearly the be of transformation The 3). (Fig. later h ag ytrsslosi i.2 Fig. in loops hysteresis large The nteohrhn,tepreeti–niereeti transi- paraelectric–antiferroelectric the hand, other the On o ecnie h h epnei oso.Acrigto According slow. so is response the why consider we Now E K o h ealddfiiin,as eeosuo cool- upon develops also definition), detailed the for η slne hntetm eido field of period time the than longer is S8) Fig. and H sacmaidb ag eprtr hysteresis, temperature large a by accompanied is o h yaia rcs fnceto) Indeed, nucleation). of process dynamical the for :Wt nraigtefeuny h double- the frequency, the increasing With ): η h ytrsslo eoe mle for smaller becomes loop hysteresis The . normdl.Ide,tefil required field the Indeed, model). our in hP i pnpaetasto scorrelated is transition phase upon η 1 = .0 T B IAppendix, (SI 1.6 and = ∼ and NSLts Articles Latest PNAS h macroscopic The 0.66 η E η .T ute con- further To E). hc sdiscussed is which , hP ml ag free- large a imply .Ti is This 2C). 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APPLIED PHYSICAL SCIENCES Ferroelectric Antiferroelectric sion of the rotational motion in the antiferroelectric phase. As we 10 10 can see in Fig. 3, the ferroelectric phase has more low-energy (or softer) excitation modes of rotational nature compared with the 8 8 antiferroelectric phase. The presence of the distinct gap in the excitation frequency for the antiferroelectric phase indicates not 6 6 only the absence of low-frequency coherent rotational modes but also the presence of a resonance frequency, the latter of which 4 4 is reminiscent of the magnon dispersion relation in ferromag- frequency frequency netic and antiferromagnetic materials with uniaxial anisotropy 2 2 (50). We note that in our system the uniaxial anisotropy stems from the steric hindrance to the dipole moment. This implies that 0 0 the resonance frequency can be controlled by varying the shape 0 1 2 3 4 0 1 2 3 4 wavenumber wavenumber anisotropy of the spheroids. We note that we confirm that there is little difference in the translational vibrational modes and con-

Fig. 3. Rotational dynamical structure factor SR(q, ω) of ferroelectric and figurational entropy between the two phases (SI Appendix, J and antiferroelectric phases, showing the difference in vibrational dynamics Fig. S7). between ferroelectric and antiferroelectric states. See SI Appendix, J for the Here we note that the entropy difference between ferroelectric definition of SR(q, ω) and the calculation of vibrational density of states. and antiferroelectric phases implies an inverse electro-caloric effect (SI Appendix, K and Fig. S8), which has been observed in some antiferroelectric inorganic oxides (19, 51). classical nucleation theory, this timescale is determined by the free-energy barrier to overcome and the dynamics of elemen- Mechanical Control of Antiferroelectric Phase. Finally we show tary excitation. The free-energy gain comes from the formation interesting electro-mechanical coupling observed under exter- of the more stable phase, whereas the penalty comes from the nal stress, indicating the possibility of mechanical manipula- formation of the domain interface. In our system, the nucleation tion of the antiferroelectric phase. Larger particle anisotropy should be accompanied by cooperative displacement and reori- η means a stronger coupling between anisotropic mechani- entation of the particles in the same hexagonal plane over the cal stress and particle alignment. Thus, an externally applied size of a critical nucleus. This is because such cooperativity is nec- anisotropic stress may affect the phase behavior via electro- essary to avoid charging (represented by ∇ · P, where P stands mechanical coupling. In Fig. 4, we show examples of such a for polarization field) at the interface, since it costs large elec- polarization response to a uniaxial stress. Depending on the trostatic energy (SI Appendix, H). Note that flipping of a dipole direction of the applied stress and temperature, the initial in a ferroelectric state inevitably results in charging at both ends at the dipole, but not in perpendicular directions. This requires cooperativity in dipole rotation along the direction of the long axis of spheroids. The probability to have such cooperative reori- entation may steeply decrease with domain size, simply because the number of particles involved increases. This extra physical constraint arising from the avoidance of charging, which is a uni- versal electrostatic factor governing the kinetics of the polariza- tion ordering, explains why the ferroelectric-to-antiferroelectric AF to AF transition exhibits a large hysteresis and requires a long incuba- tion time. T=0.65 Furthermore, the dipolar interaction also affects another compress important factor governing the slow dynamics: It is the dis- AF to F tance between adjacent spheroids, which controls steric hin- AF to P drance to rotational motion. This structural factor is responsible stretch for the asymmetry in the response between ferro-to-antiferro and antiferro-to-ferro transformations. To see this, we calcu- late the vibrational entropy difference in these phases, which stems from the difference in the degree of steric hindrance to particle rotation. As can be seen in Fig. 1A, spheroids have more space to fluctuate for the ferroelectric arrangement than compress for the antiferroelectric one: The nested structure of the lat- ter tends to inhibit rotational fluctuations. Indeed the average angular amplitude of rotational vibration of the dipoles relative to their average orientations becomes 23◦ for the ferroelectric state and 16◦ for the antiferroelectric state, although these fluc- T=0.67 T=0.65 tuations are isotropic for both states. The antiparallel dipole arrangement in the antiferroelectric phase causes both electro- static and steric constraints on the particle motion: The strong electrostatic attraction between adjacent antiparallel spheroids Fig. 4. Mechanical switching of antiferroelectric order. By applying a causes a strong constraint on the relative motion of spheroids. uniaxial compression to an antiferroelectric state, we can induce an anti- Furthermore, the distance between the nearest antiparallel ferroelectric to antiferroelectric (AF to AF) polarization reorientation. By applying a uniaxial stretching and compression to the same initial state in neighbors becomes shorter by approximately 5% upon phase appropriate directions, on the other hand, we can induce antiferroelectric transformation from the ferroelectric to the antiferroelectric to ferroelectric (AF to F) and antiferroelectric to paraelectric (AF to P) phase state by the attractive interaction (SI Appendix, I and Fig. S6), transitions, respectively, which are accompanied by large changes in the causing a strong geometrical constraint on rotational motions. dielectric permittivity. See SI Appendix, L for the details of the calculations These electrostatic and geometrical constraints result in suppres- and the kinetics of the phase changes.

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r σ ij ! 6 # , [1] r iru.T bancytliesae ihu eet,tenmeso par- of numbers the equi- defects, phase without examine are states low to ticles crystalline very temperature obtain the at To raise (67) librium. we barostat then Parrinello–Rahman and the temperature, and thermostat Hoover r ewe hss1ad2 where 2, ∂ and 1 h phases between (66) equation reads ary Clausius–Clapeyron model the our using the by them in equi- connect and antiferroelectric–paraelectric libria) and for diamonds liquid– antiferroelectric–ferroelectric black the and the for equilibria, squares liquid–antiferroelectric blue and paraelectric equilibrium, paraelectric–ferroelectric calculate the par- We for Widom’s potential. apply at chemical (η we various temperatures the hand, apply for calculate potentials other we chemical to the an the crystal, method on is a liquid, state insertion For reference a ticle (66). the For Andersen follows where crystal. the method, Einstein as applying integration is by thermodynamic potential cubic the with chemical be system the to the culate box equilibrate simulation and the barostat of shape the and lattice, to fixed are pressure the and in moment described dipole the be of where condition, magnitudes metastable the including the state, each of potential chemical by surrounded Diagram. Phase is system the that ignores assuming which by simulations, walls. metallic numerical field in depolarization 66) the the (63, 10 in condition than error boundary less (65) root-mean-square ing” 64 torque the the is reduce and (FFT) to force interpolation transformation B-spline Fourier order fast for Ewald the size Here costs. 0.52/σ numerical reduce is to parameter (64) method Ewald mesh particle p spheroid to moment dipole a See introduce (62). also phase ferroelastic a duces small For re.Freape h iudpreeti hs onayadliquid– (η and at boundary meet phase boundary dT liquid–paraelectric phase the antiferroelectric example, For aries. moment spheroids: inertia ing the and tensor unit −( (43) as described is interaction dipolar the Then rmteJpnSceyfrtePooino Science. of Promotion the for (JP18H03675) Society Research Solid Japan Scientific by the for and supported Innova- from (JP17H06375), Institute was JP25000002), Softcrystal The study of (Grant Areas This at Research Tokyo. tive Promoted system of Specially hybrid University for the XA/UV Grants-in-Aid Uni- at ICE Kyoto (ISSP) SGI at Physics reading (YITP) the State careful Physics on on Theoretical the and performed for for partially versity Institute Yukawa were Yanagishima at calculations T. XC40 numerical CRAY to The grateful manuscript. the also of are We cussions. Clausius– the ACKNOWLEDGMENTS. by confirmed also is diagram phase the equation. of Clapeyron shape V the Thus, are field electric and moment dipole of dimensionless are in mass units presented and the are length, Then energy, article of tively. this units in the quantities where the form, of All 62). (43, 63), 62, (43, motion molecules of equation uniaxial the solving for by obtained is orientations and positions Units. cle Numerical and Motion of Equation (41). understood well been has behavior phase whose potential, For U /σ steetap e atce ycluaigtesaitclaeaeof average statistical the calculating By particle. per enthalpy the is ↔ /d /∂η 1 µ η −n 0 η 3 = = = epciey h lcrsai neato stetdb h smooth the by treated is interaction electrostatic The respectively. , n h nhly n a bantesoeo h hs bound- phase the of slope the obtain can one enthalpy, the and η i ,ti oeta orsod otewl-nw Stockmayer well-known the to corresponds potential this 0, 1.6 n −0.20/k − η i N ) hsptnilwl ersnsitrcigshrisadpro- and spheroids interacting represents well potential this , √ · T = N ∂ IAppendix, SI σ I U = ,0 o h C-ielattice, FCC-like the for 4,000 ln.TegnrlzdCasu–lpyo qainfor equation Clausius–Clapeyron generalized The plane. = /∂ 3 ,w aclt the calculate we 1B), (Fig. diagram phase the obtain To ,2 o h C-ieltie o iudsae efix we state, liquid a For lattice. BCC-like the for 4,320 η σ and n B 2 v dT i akdi h hs iga nFg 1B Fig. in diagram phase the in marked (1 h neato uofi elsaei 6.9σ is space real in cutoff interaction the , ij d o h omrand former the for ne naporaeesml blw.Here, (below). ensemble appropriate an under = /d A + etakY aaih n .Ieafrvlal dis- valuable for Ikeda A. and Takanishi Y. thank We P ij µ η 0with p)m/20 = = i = · 5/σ η C µ (λ [ ahsrcuei eae ne h Nos the under relaxed is structure Each . (n j /r 1 i − ij 3 3 · h rsa tutr fec hs is phase each of structure crystal The . r − λ ij ) 2 3(µ IAppendix , SI 2 I )/β , m + p sasmdt eta fcorrespond- of that be to assumed is −3 T ¨ r = i n bantepaeequilibrium phase the obtain and ) λ h ueia nerto fparti- of integration numerical The (n 2 i · /σ (h = dT = r (1 j ij · 1 N −∂ )(µ β + r /d eas dp h “conduct- the adopt also We . i − ij = (∂µ/∂η nprle to parallel in ) 2η j 2 η U N NSLts Articles Latest PNAS h , ,0.Temto ocal- to method The 4,000. · ] 2 T /∂ /r = 3 ) = r ntepaebound- phase the on ) 1/6 A n eaotfourth- adopt we and , 17 .5) where 0.755), (1.7, = ) ij ij 2 0.01/k )/r r ,3 o h HCP-like the for 4,032 . o ute eal.We details. further for i ) en h setratio aspect the being ij 5 and = . , β σ h∂ B I and , ( n ↔ U 1 o h latter. the for i /∂η as −n rdcircles (red h mesh the , √ respec- m, µ i i/N n i σ ↔ | 1 = i ) 3 · f6 of 5 sthe is µ n ¨ and and 0 i [2] [3] n e– ´ = i .

APPLIED PHYSICAL SCIENCES 1. Lines ME, Glass AM (1977) Principles and Applications of Ferroelectrics and Related 36. Hlinka J, et al. (2014) Multiple soft-mode vibrations of lead zirconate. Phys Rev Lett Materials (Oxford Univ Press, Oxford). 112:197601. 2. Horiuchi S, Tokura Y (2008) Organic ferroelectrics. Nat Mater 7:183–208. 37. Ishii F, Nagaosa N, Tokura Y, Terakura K (2006) Covalent ferroelectricity in hydrogen- 3. Furukawa T (1997) Structure and functional properties of ferroelectric polymers. Adv bonded organic molecular systems. Phys Rev B 73:212105. Colloid Interface Sci 71–72:183–208. 38. Osipov MA, Fukuda A (2000) Molecular model for the anticlinic smectic-CA phase. 4. Takezoe H, Gorecka E, Cepiˇ cˇ M (2010) Antiferroelectric liquid crystals: Interplay of Phys Rev E 62:3724–3735. simplicity and complexity. Rev Mod Phys 82:897–937. 39. Weis JJ, Levesque D (2005) Simple dipolar fluids as generic models for soft matter. 5. Zhang W, Xiong RG (2012) Ferroelectric metal–organic frameworks. Chem Rev Adv Polym Sci 185:163–225. 112:1163–1195. 40. Hynninen AP, Dijkstra M (2005) Phase diagram of dipolar hard and soft spheres: 6. Tayi AS, Kaeser A, Matsumoto M, Aida T, Stupp SI (2015) Supramolecular ferro- Manipulation of colloidal crystal structures by an external field. Phys Rev Lett electrics. Nat Chem 7:281–294. 94:138303. 7. Landau LD, Lifshitz EM, Pitaevskii LP (1984) Electrodynamics of Continuous Media 41. Groh B, Dietrich S (2001) Crystal structures and freezing of dipolar fluids. Phys Rev E (Butterworth-Heinenann, Amsterdam). 63:021203. 8. Chaikin PM, Lubensky TC (1995) Principles of Condensed Matter Physics (Cambridge 42. Groh B, Dietrich S (1997) Orientational order in dipolar fluids consisting of nonspheri- Univ Press, Cambridge, UK). cal hard particles. Phys Rev E 55:2892–2901. 9. Onuki A (2002) Phase Transition Dynamics (Cambridge Univ Press, Cambridge, UK). 43. Takae K, Onuki A (2017) Ferroelectric glass of spheroidal dipoles with impurities: Polar 10. Blinc R (2011) Advanced Ferroelectricity (Oxford Univ Press, Oxford). nanoregions, response to applied electric field, and ergodicity breakdown. J Phys 11. Horiuchi S, Kumai R, Ishibashi S (2018) Strong polarization switching with Condens Matter 29:165401. low-energy loss in hydrogen-bonded organic antiferroelectrics. Chem Sci 9:425– 44. Johnson LE, Benight SJ, Barnes R, Robinson BH (2015) Dielectric and phase behavior 432. of dipolar spheroids. J Phys Chem B 119:5240–5250. 12. Zehe CS, et al. (2017) Mesoscale polarization by geometric frustration in columnar 45. Resta R, Vanderbilt D (2007) Theory of polarization: A modern approach. Physics of supramolecular crystals. Angew Chem Int Ed 56:4432–4437. Ferroelectrics: A Modern Perspective, eds Rabe KM, Ahn CH, Triscone JM (Springer, 13. Scott JF (2007) Applications of modern ferroelectrics. Science 315:954–959. Berlin), pp 31–68. 14. Sando D, Barthel´ emy´ A, Bibes M (2014) BiFeO3 epitaxial thin films and devices: Past, 46. Luttinger JM, Tisza L (1946) Theory of dipole interaction in crystals. Phys Rev 70: present and future. J Phys Condens Matter 26:473201. 954–964. 15. Martin LW, Rappe AM (2016) Thin-film ferroelectric materials and their applications. 47. Concha A, Aguayo D, Mellado P (2018) Designing hysteresis with dipolar chains. Phys Nat Rev Mater 2:16087. Rev Lett 120:157202. 16. Damodaran AR, et al. (2016) New modalities of strain-control of ferroelectric thin 48. Tanaka H (2012) Bond orientational order in liquids: Towards a unified description of films. J Phys Condens Matter 28:263001. water-like anomalies, liquid-liquid transition, glass transition, and crystallization. Eur 17. Pesiˇ c´ M, Hoffmann M, Richter C, Mikolajick T, Schroeder U (2016) Nonvolatile random Phys J E 35:113. access memory and energy storage based on antiferroelectric like hysteresis in ZrO2. 49. Russo J, Romano F, Tanaka H (2018) Glass forming ability in systems with competing Adv Funct Mater 26:7486–7494. orderings. Phys Rev X 8:021040. 18. Uchino K (2016) Antiferroelectric shape memory ceramics. Actuators 5:11. 50. Lifshitz EM, Pitaevskii LP (1980) Statistical Physics, Part 2 (Pergamon, Oxford). 19. Moya X, Kar-Narayan S, Mathur ND (2014) Caloric materials near ferroic phase 51. Geng W, et al. (2015) Giant negative electrocaloric effect in antiferroelectric La-doped transitions. Nat Mater 13:439–450 Pb(ZrTi)O3 thin films near room temperature. Adv Mater 27:3165–3169. 20. Liu Y, Scott JF, Dkhil B (2016) Direct and indirect measurements on electrocaloric 52. Yethiraj A, van Blaaderen A (2003) A colloidal model system with an interaction effect: Recent developments and perspectives. Appl Phys Rev 3:031102. tunable from hard sphere to soft and dipolar. Nature 421:513–517. 21. Aida T, Meijer EW, Stupp SI (2012) Functional supramolecular polymers. Science 53. Assoud L, et al. (2009) Ultrafast quenching of binary colloidal suspensions in an 335:813–817. external magnetic field. Phys Rev Lett 102:238301. 22. Han S, Zhou Y, Roy VAL (2013) Towards the development of flexible non-volatile 54. Sacanna S, Pine DJ, Yi GR (2013) Engineering shape: The novel geometries of colloidal memories. Adv Mater 25:5425–5449. self-assembly. Soft Matter 9:8096–8106. 23. Kan D, Cheng CJ, Nagarajan V, Takeuchi I (2011) Composition and temperature- 55. Newman HD, Yethiraj A (2015) Clusters in sedimentation equilibrium for an induced structural evolution in La, Sm, and Dy substituted BiFeO3 epitaxial thin films experimental hard-sphere-plus-dipolar Brownian colloidal system. Sci Rep 5:13572. at morphotropic phase boundaries. J Appl Phys 110:014106. 56. Li B, Zhou D, Han Y (2016) Assembly and phase transitions of colloidal crystals. Nat 24. Tokura Y (2006) Critical features of colossal magnetoresistive manganites. Rep Prog Rev Mater 1:15011. Phys 69:797–851. 57. Gundermann T, Cremer P, Lowen¨ H, Menzel AM, Odenbach S (2017) Statistical anal- 25. Reyes-Lillo SE, Rabe KM (2013) Antiferroelectricity and ferroelectricity in epitaxially ysis of magnetically soft particles in magnetorheological elastomers. Smart Mater strained PbZrO3 from first principles. Phys Rev B 88:180102. Struct 26:045012. 26. Mani BK, Chang CM, Lisenkov S, Ponomareva I (2015) Critical thickness for 58. Frenkel D, Mulder B (1985) The hard ellipsoid-of-revolution fluid I. Monte Carlo antiferroelectricity in PbZrO3. Phys Rev Lett 115:097601. simulations. Mol Phys 55:1171–1192. 27. Hochli¨ UT, Knorr K, Loidl A (1990) Orientational glasses. Adv Phys 39:405–615. 59. Rex M, Wensink HH, Lowen¨ H (2007) Dynamical density functional theory for 28. Li PF, et al. (2017) Unprecedented ferroelectric–antiferroelectric–paraelectric phase anisotropic colloidal particles. Phys Rev E 76:021403. transitions discovered in an organic–inorganic hybrid perovskite. J Am Chem Soc 60. Dijkstra M (2014) Entropy-driven phase transitions in colloids: From spheres to 139:8752–8757. anisotropic particles. Adv Chem Phys 156:35–71. 29. Horiuchi S, et al. (2012) Above-room-temperature ferroelectricity and antiferroelec- 61. Schreck CF, O’Hern CS (2010) Computational methods to study jammed systems. tricity in benzimidazoles. Nat Commun 3:1308. Experimental and Computational Techniques in Soft Condensed Matter Physics, ed 30. Horiuchi S, Kumai R, Tokura Y (2007) A supramolecular ferroelectric realized by Olafsen J (Cambridge Univ Press, Cambridge, UK), pp 25–61. collective proton transfer. Angew Chem Int Ed 46:3497–3501. 62. Takae K, Onuki A (2014) Orientational glass in mixtures of elliptic and circular par- 31. King-Smith RD, Vanderbilt D (1994) First-principles investigation of ferroelectricity in ticles: Structural heterogeneities, rotational dynamics, and rheology. Phys Rev E perovskite compounds. Phys Rev B 49:5828–5844. 89:022308. 32. Ghosez P, Cockayne E, Waghmare UV, Rabe KM (1999) Lattice dynamics of BaTiO3, 63. Allen MP, Tildesley DJ (1989) Computer Simulation of Liquids (Oxford Univ Press, PbTiO3, and PbZrO3: A comparative first-principles study. Phys Rev B 60:836– Oxford). 843. 64. Essmann U, et al. (1995) A smooth particle mesh Ewald method. J Chem Phys 33. Rabe KM (2013) Antiferroelectricity in oxides: A reexamination. Functional Metal 103:8577–8593. Oxides, eds Ogale SB, Venkatesan TV, Blamire MG (Wiley-VCH Verlag GmbH & Co. 65. Deserno M, Holm C (1998) How to mesh up Ewald sums. I. A theoretical and numerical KGaA, Weinheim, Germany), pp 221–244. comparison of various particle mesh routines. J Chem Phys 109:7678–7693. 34. Ponomareva I, Lisenkov S (2012) Bridging the macroscopic and atomistic descriptions 66. Frenkel D, Smit B (2001) Understanding Molecular Simulation: From Algorithms to of the electrocaloric effect. Phys Rev Lett 108:167604. Applications (Academic, San Diego). 35. Tagantsev AK, et al. (2013) The origin of antiferroelectricity in PbZrO3. Nat Commun 67. Parrinello M, Rahman A (1981) Polymorphic transitions in single crystals: A new 4:2229. molecular dynamics method. J Appl Phys 52:7182–7190.

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