Evidence of spin lattice coupling in MnTiO 3 : an x-ray diffraction study
aa r X i v : . [ c ond - m a t . s t r- e l ] N ov Evidence of spin lattice coupling in MnTiO : an x-ray diffraction study R. K. Maurya , Navneet Singh , S. K. Pandey , and R. Bindu ∗ School of Basic Sciences, Indian Institute of Technology Mandi, Kamand, Himachal Pradesh- 175005, India School of Engineering, Indian Institute of Technology Mandi, Kamand, Himachal Pradesh- 175005, India (Dated: July 27, 2018)Here we investigate the temperature evolution of the structural parameters of a potential magne-toelectric material, MnTiO . The experimental results reveal interesting temperature dependenceof the c / a ratio and the Mn-O bonds which can be divided into three regions. In region I (300 Kto 200 K), the above parameters are seen to decrease with decrease in temperature due to thermaleffect. In the region II (200 K to 95 K), the decrement in the structural parameters are reduceddue the competing intra layer antiferromagnetic interaction setting in ∼
200 K. The c / a ratio areseen to display a minima around 140 K. Below 140 K, the short Mn-O bonds increase suggestingthe onset of inter layer antiferromagnetic interaction ∼
100 K. In region III (95 K to 23 K), the an-tiferromagnetic interaction is fully established. The behaviour of the calculated Mn-O bonds basedon first principle calculations are in line with the experimental results. This study demonstratesthe importance of spin lattice coupling in understanding the magnetic properties of the compoundwhich is expected to be helpful in revealing the origin of magnetically induced ferroelectricity.
PACS numbers: 75.85.+t, 61.05.cp, 71.27.+a, 75.47.Lx
The physical properties of a solid is governed by thebehaviour of the electrons in it. The properties becomemore complex and interesting if the motion of electronis decided by the interplay between charge, spin, latticeand orbital degrees of freedom. Such cross coupling isthe marked feature of strongly correlated electron sys-tems. One of the properties which has gained significantamount of attention from both application and funda-mental physics point of view is the multiferroicity . Inthese kinds of compounds, the magnetism can be con-trolled electrically and polarization can be controlledmagnetically. This phenomenon is possible when thereare significant couplings among spin, lattice and electri-cal dipole moment. MnTiO is one such system whichexhibits magnetically induced ferroelectricity. The thinfilms of this compound show ferrotoroidicity . For a ma-terial to undergo ferrotoroidicity, it is necessary to breakboth the inversion and time reversal symmetries. In viewof this, coupling of spin and lattice degrees of freedom isexpected to be present. In this paper, we employ the x-ray diffraction (XRD) technique to study the spin latticecoupling in MnTiO which is an important parameter tounderstand the multiferroic properties of this compound.MnTiO , an ilmenite, stabilizes in hexagonal struc-ture with centro symmetric R¯3 space group . Here theMn ions are magnetic and Ti ions are non mag-netic. This material undergoes paramagnetic (PM) toantiferromagnetic (AFM) transition at ∼
64 K with abroad anomaly ∼
100 K. The broad anomaly is at-tributed to the setting of two dimensional intra layerAFM interactions . Goodenough has worked out boththe intra and inter layer superexchange interactions andhave shown mainly two intra layer and three inter layersuperexchange interactions .MnTiO also reveals linear magnetoelectric couplingsimilar to that observed in Cr O . At zero magneticfield, the spins are aligned along the c -axis and no fer- roelectric behaviour is observed. With the applicationof field, the material becomes ferroelectric and beyond acritical applied magnetic field of 6.5 T along the c -axis,the spins tend to flop along the basal plane. At zero field,no anomaly is observed in the dielectric constant. Basedon this fact, Mufti et al. have pointed out that this ma-terial shows weak spin lattice coupling at the virgin statei.e. zero applied magnetic field. There are several factorswhich contribute to changes in the dielectric constantinduced by magnetization. These include spin latticecoupling, electronic structure, orbital degrees of freedom,etc. Non observance of anomaly in the dielectric constantdue to spin lattice coupling indicates that the nature ofthe spin structure is such that no break in spatial sym-metry is observed. It has been observed in CoCr O thatthe spiral spin structure would lead to the break in theinversion symmetry to obtain magnetically induced fer-roelectric order . Hence, the non observance of dielec-tric anomaly in the case of MnTiO does not guarantythat there is insignificant spin lattice coupling. In ad-dition, MnTiO exhibits quasi two dimensional AFM. Insuch low dimensional system, the intra and inter layer su-perexchange interactions are expected to depend on theMn-O, Mn-Mn bond lengths and Mn-O-Mn bond angles.Hence it is expected to show structural response acrossthe region of intra and inter layer magnetic interactions.In this work, we report the temperature evolutionof the various structural parameters of MnTiO acrossthe magnetic phase transition of the compound by us-ing XRD technique. Based on the behaviour of thermalexpansion coefficient, the temperature dependent struc-tural parameters are divided into 3 regions. In the re-gion I, the behaviour of the structural parameters aredue to simple thermal effect. As the material enters intothe region II, the decrement in the lattice parameters isdrastically reduced and is also reflected in the Mn-O andMn-Mn bonds. A minima is also observed in the c / a ra-
20 30 40 50 60 70 80 90 R p =10.8%; R wp = 14.8%; R e = 9.81%; S=1.5R p =11.8%; R wp = 16.1%; R e = 10.8%; S= 1.5 (b)23 K Θ (degrees) (a)300 K I n t en s i t y ( a r b . un i t s ) Obs Calc Residual BraggRef
FIG. 1: Rietveld refinement of the XRD patterns of MnTiO collected at (a) room temperature (300 K) and (b) 23 K.The open circle and solid line correspond to the observed andcalculated patterns, respectively. The Bragg reflections arerepresented by ticks. R p , R wp , R e and S correspond to profile,weighted profile, expected weighted profile factors and thegoodness of fit, respectively. tio. The experimental results were corroborated with thefirst principle calculations. These behaviours have beeninterpreted to the setting up of short range intra layerand inter layer AFM interactions ∼
200 and ∼
100 K, re-spectively. Apart from this, we also observe unusual be-haviour in the Ti-O bonds across the region of magneticphase transitions which still needs to be understood.The sample was prepared by conventional solid stateroute. The starting materials; MnCO and TiO wereground using mortar and pestle and sintered at 1200 ◦ Cfor 24 hours in air. The sample was characterized by us-ing powder XRD and dc magnetization techniques. Theresults show complete solid solubility. The temperaturedependent powder XRD experiments were performed us-ing Smart lab 9 kW rotating anode x-ray diffractometer.The diffraction patterns were collected for 12 differenttemperatures to understand the temperature evolution ofthe structural parameters. The dc magnetization mea-surements were carried out using PPMS set up in thetemperature range (300 K to 4 K) at applied field of 0.7T.The structures corresponding to the PM and AFMphases of MnTiO have been relaxed by using state-of-the-art full potential linearized augmented plane-wave(FP-LAPW) method . In these calculations we havefixed the lattice parameters to the experimental values ofcorresponding phases. The Muffin-Tin sphere radii were chosen to be 2.05, 1.76, and 1.59 a.u. for Mn, Ti, andO atoms, respectively. The recently developed PBESol exchange-correlation functional have been used in the cal-culations. The convergence was achieved by considering512 k points within the first Brillouin zone. The errorbar for the energy convergence was set to be smaller than10 − Ry/cell. The structure was considered to be relaxedwhen the total force became less than 1 mRy/a.u.In Fig.1, we show the Rietveld refinement of the XRDpatterns of MnTiO collected at room temperature (RT)and 23 K. The RT data was indexed using R¯3 space groupwith lattice parameters a = 5.1359(2) ˚ A , c =14.2782(5) ˚ A .The value of the lattice parameters are in line with otherreports . As the sample is cooled down to 23 K, thereoccurs no change in the number of reflections but shiftin the peak positions is observed. Hence, this compounddoes not show any structural transition down to 23 K.The magnetic susceptibility as a function of tempera-ture, Fig.2a, exhibits broad peak ∼
100 K and no anomalyis observed ∼ T N . Our experimental data are in line withthe reported data .The broad peak corresponds to 2 di-mensional AFM interaction.The non appearance of sharpanomaly ∼ T N has been attributed to the accidental can-cellation of different interlayer interactions existing inthis compound . Here, T N marks the transition fromPM to 3 dimensional AFM phase. The value of T N isobtained by taking the first derivative of the susceptibil-ity as a function of temperature which is ∼ ± ′ . This value is in line with the reportedvalue .To obtain the structural parameters across the re-gion of magnetic phase transition, Rietveld profilerefinement were carried out at all the temperatures.In Figs.1a and b, we show typical Rietveld refinementof the XRD patterns. The goodness of fit (S) obtainedat all the temperatures is close to 1.5. The temperatureevolution of the lattice parameters a and c are shown inFig.2b. The careful analysis of the data shows that thelattice parameters decrease with decrease in temperaturebut this decrement is not uniform throughout the tem-perature range of study. We observe that the decrementis significant until 200 K and later on until ∼
95 K, thisdecrement decreases. On further reduce in temperaturethe lattice parameter a decreases marginally until 50 Kand later on remains almost the same while c shows anincrease below 95 K. Quantitatively, in the temperaturerange 300 K to 200 K, both the lattice parameters de-crease by 0.07%; in the range 200 K to 95 K, it decreasesby 0.04%; in the range below 95 K, the parameters showsmarginal decrease until 50 K and later on it remains thesame while the c -parameter increases by 0.014%. To ob-tain the thermal contribution, thermal expansion coeffi-cient α was calculated for the lattice parameters in allthe above mentioned temperature ranges. Here, we findthat in the first temperature range, the value of α for a and c parameters are ∼ − K − and 8.3 x 10 − K − , respectively . In the second temperature range, itis 4.15 x 10 − K − and 2.7 x 10 − K − and in the third
20 40 60 80 0.0000.0010.0020.003
Temperature (K) d χ / d T ( e m u / g m . K ) IIIIII (a) χ ( e m u / g m ) (b) c ( Å ) T N a ( Å ) (c) c / a (a') Temperature (K)
FIG. 2: Temperature evolution of (a) DC magnetic suscepti-bility carried out at applied magnetic field 0.7 T; (a ′ ) Firstderivative of susceptibility; (b) the lattice parameters and (c) c / a ratio. range, it is 2.03 x 10 − K − and -1.898 x 10 − K − , re-spectively. Considering above facts, the behaviour of thestructural parameters can be divided into 3 regions. Theregion I lies in the range 300 K to 200 K; region II in therange below 200 K to 95 K and region III is the rangebelow 95 K to 23 K. The behaviour of the c / a ratio isshown in Fig.2(c). Here, we observe that in the region I,the ratio decreases; in region II, it reaches a minima ataround 140 K and in region III an increase is observed.To understand this behaviour, it is important to lookinto the Mn-O, Ti-O, etc. bond distances. In the region I,the short Mn-O bonds (Mn-O(S)) decrease with decreasein temperature, Fig.3(a). In the region II, it is found toincrease below 140 K, then decreases in the region IIIand later on remains almost the same. The long Mn-Obond (Mn-O(L)) lengths, Fig.3(b); are found to decreaseuntil region II and in the region III, it increases from 75K and below 50 K, it decreases. The Mn-Mn bonds arefound to decrease in region I and a marginal increase isobserved in the region II and in the region III, it remainsalmost the same.In regions I and II, the short and long Ti-O bonds,Fig.4(a and b) are found to increase and decrease, respec-tively with decrease in temperature. On further reduce intemperature, both the bonds reveal opposite behaviour.Reduction in the Mn-Ti bonds, Fig.4(c) is observed in theregion I and in the regions II and III, it remains almostthe same. (b) M n - O ( L ) ( Å ) III II I (a) M n - O ( S ) ( Å ) (c) Temperature (K) M n - M n i n t r a ( Å ) FIG. 3: Temperature evolution of (a) Mn-O(S); (b) Mn-O(L)and (c) Mn-Mn intra bond lengths.
The above results show interesting temperature evolu-tion of various structural parameters across the magneticphase transitions. However, the changes in bond lengthsare small and in some temperature range these changesare within the error bar. At this stage it is important tonote that x-ray diffraction technique provides extremelyaccurate value for lattice parameters. The presence oferror bar in fourth decimal place, as mentioned above,is an indication to this fact. However, this technique isnot very accurate for determining the atomic positionsof lighter elements especially the oxygen ions. This isbecause the x-rays interact with the electron cloud, sothe contribution of the diffracted intensity for the heav-ier element is more as compared to the lighter elements.In the light of this fact the small changes seen in thebond lengths within the error bar may not be so reli-able. In order to confirm the reliability of the experi-mental results across the magnetic phase transitions wehave performed the DFT based first principles calcula-tions by using Wien2k code where the structure of thecompound is relaxed in both PM and AFM phases. Thecomputational details are given above. The structuralparameters corresponding to both the phases obtainedafter relaxations are shown in Table 1. One can clearlysee that the Mn-O(S) increases by +0.271 ˚ A and Mn-O(L) bonds decreases by 0.0863 ˚ A as the compoundsenter from PM to the AFM phase. The Mn-Mn (in-tra) bond lengths are seen to increase by 0.0772 ˚ A . Thechange in the calculated Mn-O and Mn-Mn bond lengths (b) T i - O ( L ) ( Å ) (a) III II I T i - O ( S ) ( Å ) (c) Temperature (K) M n - T i ( Å ) FIG. 4: Temperature evolution of (a) Ti-O(S); (b)Ti-O (L)and (c) Mn-Ti bond lengths across the magnetic phase transition is in line with theexperimental data. However, the changes observed in thecalculated bond lengths are more as compared to the ex-perimental results. This is due to the fact that thermalcontribution to the structural parameters is absent in thecalculation which is competing with the magnetic contri-bution. Hence the experimentally observed changes instructural parameters are expected to be less than thatobserved in the calculations.The above results clearly show the discernible changesin the structural parameters in the temperature rangewhere various magnetic interactions set in. Thus theelectronic and magnetic properties of this compound isexpected to be closely related to the Mn-O and Mn-Mnbonds. This expectation appears to be a reality in thelight of the fact that the magnetoelectric effect in thismaterial arises due to Mn ions and the superexchangeinteraction depends strongly on the bond distances andbond angles. The behaviour of the structural parameterscan be understood in the following way. In the regionI, the structural parameters namely lattice parameters,Mn-O and Mn-Mn bonds show simple thermal contrac-tion as the value of α are in line with the general ilmenitestructures . As the material enters region II, ∼
200 K,the reduction in the α value suggests the evolution of theshort range intra layer AFM. To observe any effect on thediffraction pattern due to onset of intra layer AFM or-dering, the coherence length should be atleast some hun-dreds of angstroms. So the signature of the short range magnetic cluster in the diffraction pattern suggests thespatial extent of the magnetic phase is sufficient enoughto be reflected in the structural parameters.Paramagnetic Antiferromagnetic M n − O ( s ) (˚ A ) 1.9801 2.2511 M n − O ( L ) (˚ A ) 2.1743 2.0880 M n − M n ( intra ) (˚ A ) 2.9663 3.0435Table 1: Bond lengths obtained using first principlecalculations in the paramagnetic and antiferromagenticphases.In MnTiO , Goodenough et al have shown that thereare five superexchange interactions in this material. Outof these two are intra layer and the rest are inter layerones. The sign of the exchange interaction depends onthe number of electrons in the orbitals which are inter-acting. For half-filled interacting orbitals superexchangeinteraction is antiferromagnetic. When there is morethan one electron per interacting orbital, the interactionis ferromagnetic. Following the Goodenough Kannamorirules , the intra layer AFM interaction occurs throughthe overlap of half-filled orbitals at the Mn sites. Hence inthe region II, ∼
200 K, there occurs onset of the magneticinteraction within the layer and is depicted as decreasein the Mn-O (L) and Mn-Mn (intra) bond lengths above140 K. It is interesting to note that the increase in the c / a ratio below 140 K and also increase in the Mn-O(S)bonds suggest the onset of the weak interlayer super su-perexchange interaction between the cations through theoxygen-oxygen ions. The increase in the Mn-O(S) bondlength leads to the decrease in the separation between theO-O bonds lying along the c -axis and hence enhancementin the super superexchange interactions between the lay-ers. So the critical temperature for setting up of the intraand inter layer AFM interactions occurs in the region II.So far there are no reports regarding this aspect.In the region III, for temperatures below 50 K, contri-bution due to thermal effect and AFM interaction to the a parameter is almost the same. Hence almost no changein the value of a is observed. While for the c parameterthe magnetic interaction dominates thereby leading toits increment. The behaviour of the lattice parametersare more evident in the c / a ratio plot shown in Fig.2(c).It is also observed that the Mn-O(S) bonds initially de-crease and remains the almost the same until the lowestcollected temperature while the Mn-O(L) bonds showsan increase at around 50 K and later on remains almostunchanged.Apart from the Mn-O bonds, the Ti-O bonds also re-veal significant changes across the region of intra andinter layer AFM interaction. However, it is still not clearabout the role of Ti in magnetism and magnetically in-duced ferroelectricity exhibited by this system. We hopethat careful observation of the local structural studieswill provide clue towards answering this question.In summary, we have studied the temperature evolu-tion of the structural parameters of MnTiO using x-raydiffraction technique. The temperature behaviour of thestructural parameters was divided into three regions; (i)300 to 200 K, (ii) 200 K to 95 K and (iii) 95 K to 23K.In region I, the decrease in the c / a ratio and the Mn-O bonds with decrease in temperature is attributed tothermal effect. In region II, ∼
200 K, decrement in theabove parameters is altered as a result of the competi-tion between the intra layer AFM interaction and thethermal effect. Around 140 K, a minima is observed inthe c / a ratio. The short Mn-O bonds shows an increase below this temperature suggesting the onset of intra layerAFM interaction. The bond lengths obtained using firstprinciple calculations is in consonance with the experi-mental results. From the present results, it appears thatspin lattice coupling plays significant role in stabilisingmagnetically induced ferroelectricity in this system. X-ray diffraction studies in the presence of magnetic fieldis expected to be helpful in addressing the origin of mag-netically induced ferroelectricity in this compound. ∗ Corresponding author: [email protected] K.F. Wang, J.-M. Liu and Z.F. Ren, Adv.Phys. , 321(2009). H. Toyosaki, M. Kawasaki, and Y. Tokura, Appl. Phys.Lett. , 072507 (2008). G. Shirane, S. J. Pickart, and Y. Ishikawa, J. Phys. Soc.Jpn. , 1352 (1959). J. Akimitsu, Y. Ishikawa and Y. Endoh, Solid State Com-mun. , 87 (1970). Yasuhiko Syono, Syun-Iti Akimoto, Yoshikazu Ishikawaand Yasuo Endoh J.Phys.Chem.solids , 1665 (1969). H. Yamauchi, H. Hiroyoshi, M. Yamada, H. Watanabe,and H. Takei, J. Magn. Magn. Mater. , 1071 (1983). Jun akimitsu and Yoshikazu Ishikawa, J.Phys.Soc.Japan, , 462 (1977) N. Mufti, G. R. Blake, M. Mostovoy, S. Riyadi, A. A. Nu-groho, and T. T. M. Palstra, Phys. Rev. B , 104416(2011). John J. Stickler, S. Kern, A. Wold and G.S.Heller, Phys.Rev. , 765 (1967) John B. Goodenough and John J. Stickler Phys. Rev. ,768 (1967) G. Lawes,B. Melot,K. Page,C. Ederer,M. A. Hayward,Th.Proffen,and R. Seshadri, Phys. Rev. B , 024413 (2006) P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, and J. Luitz, WIEN2k, An Augmented Plane Wave PlusLocal Orbitals Program for Calculating Crystal Properties(Karlheinz Schwarz, Technische Universit¨ a t Wien, Austria,2001). J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov,G.E. Scuseria, L.A. Constantin, X. Zhou, K. Burke, Phys.Rev. Lett. , 136406 (2008). H. M. Rietveld, Acta Crystallogr. , 151 (1967); J. Appl.Cryst. , 65 (1969); A. W. Hewat, Harwell Report No.73/239 (1973),ILL Report No. 74/H62S (1974); G. Malm-ros and J. O. Thomas,J. Appl. Cryst. , 7 (1977); C. P.Khattak and D. E. Cox, ibid. , 405 (1977). J. R. Carvajal, FULLPROF, a Rietveld refinement andpattern matching analysis program, Laboratoire Leon Bril-louin, CEA-CNRS,France, 2000. Review in mineralogy, volume 40, Chapter 9 by Joseph R.Smyth, Steven D. Jacobsen and Robert M. Hazen , 2000 Magnetism and the chemical bond, J.B. Goodenough, In-terscience (Wiley), New York, 1963 S. W. Chen, P. A. Lin, H. T. Jeng, S. W. Fu, J. M. Lee, J.F. Lee, C. W. Pao, H. Ishii, K. D. Tsuei, N. Hiraoka, D. P.Chen, S. X.Dou, X. L. Wang, K. T. Lu, and J. M. Chen,Appl. Phys. Lett.104