Multiferroicity in Perovskite Manganite Superlattice
∗Yong-Mei Tao (>[r),1,† Xue-Fan Jiang (Æ),1 and Jun-Ming Liu (4d²)2
1Jiangsu Laboratory of Advanced Functional Materials, Department of Physics and Electronic Engineering, Changshu Institute of Technology, Changshu 215500, China
2Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
(Received February 29, 2016)
Abstract Multiferroic properties of short period perovskite type manganite superlattice ((R1MnO3)n/(R2MnO3)n
(n=1,2,3)) are considered within the framework of classical Heisenberg model using Monte Carlo simulation. Our result revealed the interesting behaviors in Mn spins structure in superlattice. Apart from simple plane spin cycloid structure which is shown in all manganites including bulk, film, and superlattice here in low temperature, a non-coplanar spiral spin structure is exhibited in a certain temperature range whenn equals 1, 2 or 3. Specific heat, spin-helicity vector, spin correlation function, spin-helicity correlation function, and spin configuration are calculated to confirm this non- coplanar spiral spin structure. These results are associated with the competition among exchange interaction, magnetic anisotropy, and Dzyaloshinskii–Moriya interaction.
PACS numbers: 75.80.+q, 75.40.Cx, 75.10.Hk, 73.21.Cd
Key words: manganite superlattice, non-coplanar spiral spin order, multiferroicity
1 Introduction
Orthorhombic perovskite oxides have simple structure and some of them are important multiferroic materials for their potential application in multifunctional devices.[1−3]
Among them, perovskite manganites attract more atten- tion. The interplay of spin, orbital, charge and lattice degrees of freedom in manganites gives rise to rich phys- ical phenomena.[4−7] There are many interesting spin or- ders in manganite compounds. For example, in TbMnO3, the spin order of Mn3+ is paramagnetic when the tem- perature is above 4 K, sinusoidal collinear order when the temperature is between 41 K and 28 K, and bc-plane cy- cloidal spin order (bc-CSO) when the temperature is below 28 K, respectively. The ferroelectric polarization (P) of TbMnO3is along thec-axis in thebc-CSO and the prop- agation vector is along the b-axis.[7] In GdxTb1−xMnO3
(0.2 ≤x≤0.4), with the decrease of temperature, simi- lar phenomena are observed, the spin order changes from paramagnetic, sinusoidal collinear order to ab-CSO, and the ferroelectric polarization P is along the a-axis when in the ab-CSO.[8] Both ab-CSO and bc-CSO are in-plane spiral spin orders. Their polarizations originate from spin-current model and/or inverse Dzyaloshinskii–Mariya (DM) interaction which related to Mn spin order and bends of Mn-O-Mn bonds.[9−10]
In addition, Tokura et al.[11] showed the conical spin structure for Eu1−xYxMnO3under rotating magnetic field around theb-axis. The orientation of the spiral plane and the direction of the cone axis can be determined from the
Pa and Pc values. Subsequently, Mochizuki’s theoretical paper revealed that under the externally applied magnetic field alongb-axis,ab-CSO converts to a conical spin order in TbMnO3.[12] This conical spin order can also be ob- served in spinel such as CoCr2O4 and ZnCr2Se4,[13−14]
and Y-type hexaferrite such as Ba0.5Sr1.5Zn2Fe12O22 and Ba2Mg2Fe12O22.[15−16]Our previous investigation on non- magnetic B-site substitution showed a coexistence of ab- CSO and bc-CSO phase when the doping concentration exceeded a threshold.[17] Therefore, spin order and po- larization in perovskite manganites can be modulated by temperature, magnetic field, doping etc.[11−12,18−20]
In recent years, superlattice has attracted much atten- tion in the experimental and theoretical research. The mismatch of lattice, stress, stain and other factors lead to the different properties from the bulk material. For example, in (SrCoO3)1/(SrTiO3)1 superlattice,[21] multi- ferroic state is found in tensile strained Pc structure. In the material where CaTiO3/BaTiO3 superlattice grow- ing on a SrTiO3 substrate, it is showed that the ferro- electric instability in TiO6 octahedra is enhanced by the interface.[22] The correlated manganite superlattices such as manganite-titanate, manganite-nickelate, manganite- BiFeO3 etc. and even pure manganite-manganite su- perlattices are investigated.[23−25] Spin glass behavior is found in BiFeO3/BiMnO3due to competition between an- tiferromagnetic (AFM) Fe-O-Fe, AFM Fe-O-Mn and fer- romagnetic (FM) Mn-O-Mn interactions at interfaces.[23]
In (LaMnO3)n/(SrMnO3)n (n=1, 2), tensile strain in-
∗Supported by the National Natural Science Foundation of China (NSFC) under Grant No. 11447136
†E-mail: [email protected] c
2016 Chinese Physical Society and IOP Publishing Ltd
http://www.iopscience.iop.org/ctp http://ctp.itp.ac.cn
duced A-type AFM and dx2−y2 orbital order at ground state, while compressive strain induced C-type AFM and d3z2−r2 orbital ordered.[24]
So far, the multiferroicity of manganite superlattices has not been discussed much. In this work, we use Monte Carlo simulation methods to study the perovskite man- ganites superlattice composed ofR1MnO3whose bulk ma- terial hasab-CSO andR2MnO3 whose bulk material has bc-CSO. The antisymmetric exchange interaction domi- nates in these materials and the symmetric exchange in- teraction is always ignored. In short period perovskite manganites superlattice, what phenomena will be brought about with the change of temperature? Will the phase be kept as ab-CSO and bc-CSO? Or there will be a coexis- tence ofab-CSO andbc-CSO phase, a conical spin phase, or other spin phase? Our results demonstrate that a non- coplanar spiral spin phase will appear in this superlattice, and it is still a multiferroic phase.
2 Model and Method
Following the Mochizuki–Furukawa model,[26−27] we consider Mn S(Sa, Sb, Sc) = 2 spins on the orthorhom- bic perovskite manganite superlattice ((R1MnO3)n/ (R2MnO3)n). The Hamiltonian can be written as:
H =Hex+Hsia+HDM+Hcub. (1) Here the first term is exchange interaction which can be written as:
Hex=−Jab x,y
X
hi,ji
Si·Sj+
b
X
[i,j]
J2mSi·Sj+Jc c
X
hi,ji
Si·Sj.(2) Exchange interaction includes the FM interaction (Jab) between the in-plane nearest-neighbor (NN) Mn spins, the AFM interaction (Jc) between the NN Mn spins along the c-axis, and the AFM interaction (J2m) between the next- nearest-neighbor (NNN) Mn spins along theb-axis on the m-th-layer-plane. With the decreasing of R-ion radius, J2m increases, and the low temperature state ofRMnO3
changes from ab-CSO phase to bc-CSO phase. Here we chooseR1MnO3 andR2MnO3 who haveab-CSO andbc- CSO in bulk at different low temperature, respectively.
The second term is the single ion anisotropy term:
Hsia=DX
i
(Si·ζi/|ζi|)2+EX
i
(−1)ix+iy
×[(Si·ξi/|ξi|)2−(Si·ηi/|ηi|)2], (3) whereζi,ξiandηiare the tilted local about thei-th MnO6
octahedron. This term represents the magnetization of this material is hard along thec axis and the magnetiza- tion is alternatively hard and easy inab-plane.
The third term is the DM interaction and the last term represents the cubic anisotropy energy, respectively. They
are given by the following equations:
HDM=X
hi,ji
dαij·(Si×Sj), (4) Hcub=AX
i
(Sxi4 +Syi4 +Szi4). (5) We use specific heatC, spin-helicity vectorh, spin cor- relation functionφ, and spin-helicity correlation function Ψ to recognize the phase transitions. The definitions are expressed as:
C= 1 N
∂hHi
∂kBT ,
hα(T)(α=a, b, c) = 1 N
D
X
i
Si×Si+b
E.S2,
φα(k, T)(α=a, b, c) = 1 N2
X
ij
hSαiSαjieik·(ri−rj),
Ψα(k, T)(α=a, b, c) = 1 N2
X
ij
hhbαihbαjieik·(ri−rj), (6) where N is the number of Mn spins, kis the Boltzmann constant, ri is the coordinate of thei-th Mn ion, andh i denotes the thermal averaging. The spin-helicity vector hαis in proportion to the polarization vector, so multifer- roic phase is mainly confirmed by spin-helicity correlation function Ψαand spin order.
The parameters used in our simulations are (Jab, J2, Jc) = (0.80,0.80,1.25), (D, E) = (0.25,0.3),A= 0.0162. The three components of dij vector along the a-, b- and c-axis are (αab, βab, γab) = (0.10,0.10,0.14) on the ab-plane, and (αc, βc, γc) = (0.30,0.30,0) along the c-axis as earlier reports.[27]We start simulation on a 36×36×2n lattice whereJ2m= 0.62 (m= 1 :n)/0.80 (m=n+1 : 2n) with periodic boundary conditions. The replica exchange Monte Carlo method[28] is applied to accelerate the pro- cess toward the equilibrium state where 103 exchanges are performed for every 250 standard Monte Carlo steps (mcs). The initial 5×105 mcs are discarded for equilib- rium consideration, and another 2.5×105mcs are retained for statistic averaging.
3 Results and Discussion
A schematic diagram of perovskite manganite super- lattice ((R1MnO3)n/(R2MnO3)n) is provided in Fig. 1.
R1MnO3 has ab-CSO phase and R2MnO3 has bc-CSO phase in the bulk materials at different low temperature region, respectively.
To determine phase transition of the superlattice, we calculate specific heatCand spin-helicity vectorhα(α=a, b,c) as a function of temperature for different total layer number. In Fig. 2, short period superlattice is considered for the cases of (a) n = 1, (b) n = 2 and (c) n= 3. In general, three sharp peaks all appear at T = TN, Tlock
and Tflop which correspond to the three successive mag- netic phase transitions respectively, i.e. transition from the paramagnetic (PM) phase to the sinusoidal collinear (sc)-AFM phase, from the sc-AFM phase to an unknown phase, from the unknown phase to ab-CSO phase. We will discuss this unknown phase later. Here, kBTN=2.3, kBTlock = 1.5 and kBTflop = 0.9 for n= 1; kBTN = 3.6, kBTlock = 2.5 and kBTflop = 1.2 for n= 2; kBTN = 3.9, kBTlock = 2.9 and kBTflop = 1.2 for n = 3. Considering spin-helicity vector, the PM and sc-AFM phases are non- ferroelectric with their spin-helicities are nearly equal to zero. Theab-CSO phase exhibits a large spin-helicity vec- tor alongc-axis (hc) and the others (ha andhb) are close to zero. Between the sc-AFM phase andab-CSO phase, the unknown phase where ha and hc should not be ne- glected, andhb nearly equals to zero. It is marked as the yellow shadow portion in Fig. 2. This phase andab-CSO phase are all multiferroic phases.
Fig. 1 (Color online) A schematic diagram of (R1MnO3)n/(R2MnO3)n. R1MnO3 has ab-CSO phase and R2MnO3 has bc-CSO phase in the bulk materials, respectively.
Subsequently, in order to distinguish this phase from the others, we look at the spin correlation functionφand spin-helicity correlation function Ψ in this superlattice.
As we all know, collinear Mn spins are modulated along b-axis in sc-AFM phase, so the component of b-axis in spin correlation function is nonzero, while the other two components are nearly equal to zero. At the same time, three components of spin-helicity correlation functions are small enough to be neglected. In theab-CSO phase, Mn spins rotate in theab-plane resulting spin correlation func- tionφa andφb show sharp peaks which do not appear in φc. Spin-helicity correlation function Ψc exhibits sharp peak but not on Ψa and Ψb. The pictures of spin cor- relation function and spin-helicity correlation function in sc-AFM phase and ab-CSO phase are not plotted here.
What should be mentioned here is that one can observe the different values from above in between the sc-AFM
phase andab-CSO phase region where we plot the yellow shadow area in Fig. 2. We see that a, b and c compo- nents of spin correlation function values are all too small and can be neglected. And we do not show them here.
However, two components of spin-helicity correlation func- tions Ψa and Ψc of the first layer exhibit sharp peaks at kBT = 1.96 meV, but no peak on Ψb as displayed in Figs. 3(a)–3(c). Now, we can deduce that this phase is not sc-AFM phase, ab-CSO phase orbc-CSO phase. Is it a coexistence of ab-CSO or bc-CSO phase as our earlier works? If not, what phase is it actually?
Fig. 2 (Color online) Calculated specific heatC and spin-helicity vectorhα (α=a,b,c) as a function of tem- perature for different layers of (R1MnO3)n/(R2MnO3)n superlattice with (a)n= 1, (b)n= 2 and (c)n= 3. Here the yellow shadow region indicates non-coplanar spiral spin (NCSS) phase.
In order to know this, the snapshots of Mn spins of the first layer in (R1MnO3)2/(R2MnO3)2 superlattice at kBT = 1.96 meV are presented in Fig. 4(a) on (Sa, Sb) plane and Fig. 4(b) on (Sb, Sc) plane. The Mn spins struc- tures on the other layers in (R1MnO3)2/(R2MnO3)2 su- perlattice are similar with the first layer and we do not show here. For clearness, we give the spin structures in
Figs. 4(c) and 4(d), which are amplified from the rectan- gle marked region in Figs. 4(a) and 4(b). And we can see the none negligible value of Sa, Sb and Sc. Thus, a non-coplanar spiral spin structure is confirmed. And this non-coplanar spiral spin is not a conical one. Due to the different ion radii of R1 and R2, the NNN Mn spins interactions along b-axis on R1MnO3 and R2MnO3 are different. In short period superlattice, the size mismatch
of R-site ions leads to different Mn-O-Mn bond, which brings about different NNN interaction energy, thus, the competitions of energy for DM interaction and single ion anisotropy result in the different Mn spin order such as non-coplanar spiral spin structure. And this three dimen- sion spiral spin structure needs to be proved by further experiments.
Fig. 3 (Color online) Spin-helicity correlation function (a) Ψa(b) Ψb(c) Ψcof the first layer atkBT = 1.96 meV in (R1MnO3)2/(R2MnO3)2 superlattice.
Fig. 4 (Color online) Mn spins configuration of the first layer in (R1MnO3)2/(R2MnO3)2, on theab-plane (a) andbc-plane (b) atkBT = 1.96 meV. The orange rectangle marked region is amplified in (c) and (d), respectively.
In summary, we apply a classical Heisenberg model proposed by Mochizuki and Furukawa to investigate the multiferroicity in perovskite manganite superlattice ((R1MnO3)n/(R2MnO3)n). The lattice mismatch ef- fects are significant in short period superlattice. Com-
paring with the bulk perovskite manganite materials, ((R1MnO3)n/(R2MnO3)n) (n = 1,2,3) superlattice has different spin-helicity vector, spin correlation function, and spin-helicity correlation function in a non-coplanar spiral spin order phase at a certain temperature region.
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