Uniaxial strain-induced magnetic order transition from E-type to A-type in orthorhombic YMnO

Uniaxial strain-induced magnetic order transition from E-type to A-type in orthorhombic YMnO

from first-principles

S. X. Lin,¹X. G. Fang,¹A. H. Zhang,¹X. B. Lu,¹J. W. Gao,¹X. S. Gao,¹M. Zeng,^1,a) and J.-M. Liu^1,2,b)

1Institute for Advanced Materials and Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou, China

2Laboratory of Solid State Microstructures and Innovation Center for Advanced Microstructure, Nanjing University, Nanjing 210093, China

(Received 25 July 2014; accepted 13 October 2014; published online 29 October 2014)

The spin ordering magnetic structures of orthorhombic YMnO₃subjected to uniaxial strain have been investigated using first-principles calculations based on density functional theory. On applying com- pressive uniaxial strain of0.8% along theborientation, the spin ordering magnetic structure is pre- dicted to change from E-type to A-type antiferromagnetic orderings. The structure analysis also reveals that the uniaxial strain has a dramatic influence on the Mn-O bond lengths and Mn-O-Mn bond angles, allowing the gradual suppression of the alternation of the long and short Mn-O-Mn bonds in theabplane. These changes present very interesting possibilities for engineering the spin ordering along with ferroelectric property in orthorhombic YMnO₃.V^C 2014 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4899484]

I. INTRODUCTION

Orthorhombic YMnO₃ (O-YMO) has been extensively studied owing to their tendency towards a strong magneto- electric (ME) coupling, which stems from antiferromagnetic (AFM) spin-ordering-induced polarizations.^1–3 Currently, many studies on the O-YMO have been reported both in theory and experiment, including the origins of AFM order- ing and ferroelectric ordering, the microscopic mechanism of the anomalous dielectric constant, and the ME coupling effect near the Neel temperature.^4–19Theoretically, the exis- tence of polarization has been proposed in the E-type AFM (""##) phase, in which the polarization value was evaluated up to 2lC/cm²by the first-principles calculations based on the Berry phase method and theoretically optimized crystal structure.^12,13Experimentally, several synchrotron X-ray dif- fractions have been carried out to determine the magnetic structure and polarization mechanism of O-YMO. For examples, Solovyevet al.¹²reported that the mechanism of polarization generation originates from the ferroelectric dis- placements in the noncentrosymmetric E-type AFM state, which leads to the alternation of the long and short Mn-O- Mn bonds in the ab plane owing to the exchange-striction effects. Nakamura et al.¹⁴ investigated O-YMO thin films grown onto the YAlO₃(010) substrate and revealed a ferro- electric transition near 40 K with a large saturation polariza- tion of 0.8lC/cm²in the film. In particular, the ferroelectric polarization could be controlled by an external magnetic field, demonstrating a pronounced degree of ME coupling.

Actually, the ferroelectric polarization along with ME coupling exhibited in O-YMO materials are dependent greatly on the E-type AFM configuration. It is well known that O-YMO materials can form several different AFM

states, such as A-type AFM (A-AFM), E-type AFM (E-AFM), and cycloidal magnetic ordering depending on temperature and lattice constants, which in turn leads to dis- tinctly different electric properties.4,8,13,15–17 For instance, Fontcuberta et al.¹⁶ reported that the weakly strained O- YMO films are ferroelectric with a polarization alongc-axis switchable by 90 under an external magnetic field, while the reducing film thickness with an enlarged ratioa/bof the in-plane cell parameters, the ferroelectric order is progres- sively suppressed. This result indicates that strain plays a very important role for tuning the spin orderings, along with the ferroelectric and magnetoelectric properties. Therefore, the study on the transition of spin ordering magnetic struc- tures is important to engineering the ferroelectric and magne- toelectric properties. Generally, there are two types of strain sources. One is the intrinsic strain arising from lattice misfit by growing on different substrates, as the growth of O-YMO films has been limited by the selected substrates owing to their strong structural anisotropy or orthorhombicity; the other is the exter- nal strain originating from uniaxial strain or hydrostatic pres- sure. Currently, the study on uniaxial strain-induced magnetic order transition in O-YMO is limited, especially, in theory.

Under the above mentioned motivation, the effects of uni- axial strain applied along thebaxis on the spin orderings and magnetic properties in O-YMO were investigated by using first-principles calculations based on density functional theory.

In this letter, we performed the calculations and discussed possible implications of the obtained structure on the magnetic properties by assuming the collinear AFM spin alignment, as the collinear AFM alignment can be regarded as the first approximation to the true magnetic ground state and the cy- cloidal spin-spiral alignment.¹³We found that the changes of the spin orderings and the magnetic properties of O-YMO are dependent on the strain magnitude. The results, thus, evidently demonstrate the viability of tuning the spin-ordering proper- ties by controlling the strain induced in O-YMO materials.

a)E-mail: [email protected]

b)E-mail: [email protected]

0021-8979/2014/116(16)/163705/5/$30.00 116, 163705-1 VC2014 AIP Publishing LLC

II. CALCULATION METHODS

Our first-principles calculations were performed with collinear magnetism using the projector augmented wave (PAW) method within the generalized gradient approxima- tion plus the on-site repulsion (GGAþU)²⁰as implemented in the Vienna ab initio simulation package (VASP).²¹ We usedUeff¼2 eV on Mn 3dstates for a better description of the low-energy model of orthorhombic manganites.^10,11,13 We treated the basis with Y 4s²4p⁶4d¹5s², Mn 3p⁶3d⁵4s², and O 2s²2p⁴. The energy cutoff of 600 eV was used for the plane wave expansion of the PAW, and tetrahedron method was adopted for the Brillouin zone integrations. To model an O-YMO AFM alignment, we build a 121 super-cell, which contains four O-YMO formula units (40 atoms). The crystal structures for the equilibrium position of all the other atoms are relaxed in a 535 Monkhorst Pack grid of k points until the atomic forces are less than 1 meV/A˚ .

III. RESULTS AND DISCUSSION

The crystal structure of O-YMO withPna21space group is shown in Figure 1(a). The Mn and O atoms form oxygen-distorted octahedral environments, and the three- dimensional magnetic structure with Mn-O-Mn superex- change bonding leads to an AFM spin ordering. In order to reveal the effect of uniaxial strain on the magnetic orderings, we calculate the dependence of total energies of O-YMO with various magnetic phases on uniaxial strains. Here, only two possible spin orderings are considered, i.e., A-AFM and E-AFM, as sketched in Figure2. E-AFM and A-AFM order- ings have antiferromagnetic stackings along thecdirection, while E-AFM ordering has (""##) magnetic structure and A- AFM structure has the ferromagnetic order in theabplanes.

It should be noticed that this A-AFM ground state magnetic configuration is widely presented in manganite orthorhombic ReMnO₃ with light rare-earth cations (Re¼La, Pr, and Nd).^6,7In practical calculations, the external strain is applied along the b direction, which is the magnetization orienta- tion.^4,15,16 We define the uniaxial strain as e¼(bb0)/

b0100% based on the conventional mechanical definition, in whichb0is the experimental lattice parameters obtained

by a single crystal synchrotron X-ray diffraction.¹³The total energy as a function of strain is plotted in Figure3. The cal- culated results show the E-AFM into A-AFM phase transi- tion under uniaxial compressive strain of about 0.8%, which are consistent with experimental and theoretical reports.^16,17Meanwhile, the crystal structure analyses reveal that O-YMO is transformed from non-symmetric structure [space group Pna21] with to symmetric one [space group Pbnm] under compressive strain condition. Moreover, it is noticed the minimum energy of O-YMO for the E-AFM structure is not in e¼0%, but tensile strain of about 1%.

This means that the optimize lattice parameters bis larger than that from experimental result. The reason is mainly attributed to the assumption of a fully collinear spin struc- ture, as pointed out by Solovyevet al.¹²

In order to further reveal the magnetic ordering transi- tion, we summarize the calculated long (L) and short (S) Mn- O bond-lengths, Mn-Mn distances (d), and the bonding angle

FIG. 1. (a) The crystal structure of O-YMO and (b) sketch of Mn-O-Mn bonds in the E-AFM structure. Yellow, gray, and red spheres represent yt- trium, manganese, and oxygen, respectively.

FIG. 2. The schematic illustrations of two antiferromagnetic orderings with E-AFM and A-AFM. The arrows denote the spin alignment of the magnetic moments. Gray and red spheres represent manganese and oxygen, respectively.

FIG. 3. The total energy as a function of latticebor the uniaxial strain for O-YMO with E-AFM and A-AFM structures, respectively. The vertical line is the guide line for the experimental parameter.

h, see Fig.1(b), in two different spin states. One is E-AFM at e¼0% and other is A-AFM ate¼ 1%. Detailed results are listed in TableI. The calculatedL andSin the E-AFM state are 2.219 A˚ and 1.910 A˚, respectively, which are close to those for the reported bulk.^4,13 For the A-AFM state, while the bong-lengthLis shorted to 2.153 A˚ , and the bond-lengthSis elongated to 1.917 A˚ , which are in good agreement with the reports in a strained O-YMO film.^15,16Moreover, for A-AFM structure, only one kind of Mn-O-Mn bond with an angle of 143.96 is presented in the basal ab-plane, while in the E- AFM structure, there are two non-equivalent bonds of Mn- O(1)-Mn and Mn-O(2)-Mn in the ab-plane, whose bond angles are 144.09 and 143.78, respectively. It is the varia- tion of bonding-angles that make a E-AFM magnetic structure to be expected, as in bulk O-YMO. While a magnetic structure approaching the A-AFM ordering should be induced for the large strained O-YMO. These results are in good agreement with the experimental reports in Refs.16and17, demonstrat- ing the viability of tuning the spin-ordering by controlling the external strain induced in O-YMO materials.

Next, to reveal the electronic mechanism of uniaxial strain-driven magnetic ordering transition in O-YMO, we investigate the electronic density of states (DOS) for the AFM states (E-AFM ate¼0% and A-AFM at e¼ 1%) in the range of88 eV, as shown in Figure4. It is seen that the total DOS [Fig.4(a)] in the two spin orderings are very similar because Mn atoms remain in an octahedral site. In fact, the total DOS consists of a broadening O 2pderived peak, approximately 8 2 eV below the Fermi energy, see Fig.4(b), and then follows another gap of a manifold of Mn 3d derived bands, ranging from 2 to 2 eV, see Fig.

4(c). Finally, they change to the Y 4din the region of the high energy, see Fig. 4(d). For the E-AFM structure, the band gapEgis found to be 0.81 eV, which is slightly lower than the band gap energy of 1.17 eV of the hexagonal YMnO₃estimated using LDA method.²² Whereas an exter- nal strain (<0.8%) applied in the b direction leads to a large compression of the MnO₆octahedrons so that the dis- torted Mn-O octahedron makes the occupied Mn and O states lowering their energy. From partial DOSs of O and Mn atoms, see Figs.4(b)and4(c), it can be found that both of O 2p and Mn 4d orbits are shifted by 0.35 eV towards lower energy level. In particular, the unoccupied Mn 4dorbit [Fig.4(c)] is almost rigidly shifted into the band gap, which leads to the decrease of the band gap by 50% to 0.41 eV in the strained structure.

It is well known that the ferroelectricity of O-YMO orig- inates from the spin ordering of E-AFM state. That is to say that the magnetic properties can be an important factor of tuning the polarization as well as multiferroic ME coupling.

To illustrate the relationship of magnetic properties with spin structures, we calculate and compare the spin-density distributions of E-AFM structure at e¼0% and A-AFM structure at e¼ 1%. The contour maps of the spin-density distributions in the (001) direction for the two films are dis- played in Figure5. One can clearly observe the spin interac- tion of Mn-O-Mn states with ferromagnetic "" Mn spin arrangement is stronger than that in antiferromagnetic"#Mn spin arrangement. It is worth noting that the spin magnetic moment of Mn ions is 3.428lBin the E-AFM state, while it is slightly increased to 3.496lB for the A-AFM state.

Although the bond-lengths (LandS) in the E-AFM structures are different, the magnetic moment distributions for all Mn

TABLE I. Calculated long (L) and short (S) bond-lengths, Mn-Mn distances (d), and Mn-O-Mn bonding angle (h), which are close to that for the reported bulk YMO and the 49 nm thin film YMO. The magnetic structure in each case is indicated in the last column.

Sample S(A˚ )60.01 A˚ L(A˚ )60.01 A˚ d(A˚ )60.005 A˚ h()60.35 Magnetic structure

e¼0% (cal.) 1.89 2.22 3.90 142.72 E-type

1.90 2.20 3.92 145.11

e¼ 1% (cal.) 1.90 2.167 3.88 144.58 A-type

YMO (other cal.) 3.82 143.7 E-type¹²

3.91 146.8 (LSDAþU¼2.2 eV)

Bulk YMO 1.90 2.20 3.91 144.5 E-type^4,13

Film YMO 1.90 2.12 3.88 149.4 CycloidalþA-type^15,16

FIG. 4. Total and partial DOS for O-YMO. The shaded areas and straight lines are corresponding E-AFM structure ate¼0% and A-AFM structure at e¼ 1%, respectively. The Fermi energy is set to zero.

atoms are uniform in the whole unit cell. Furthermore, the hybridizations of Mn-O play the leading role for the spin magnetic moments of O atoms. Owing to the enhanced Mn- O hybridizations in the A-AFM structure (see the iso-lines of O atoms in Fig.5), the magnetic moments are increased to 0.057lBfor all O atoms from 0.045lB for O1 and 0.017lB

for O2 in the E-AFM structure. Our results reveal that the external tensile strain applied in thebdirection can enhance the spin moments of Mn and O atoms in the O-YMO materi- als. Meanwhile, we analyze different contributions to the fer- roelectric polarization in the E-AFM structure ate¼0% and A-AFM structure at e¼ 1% of O-YMO by using the Berry phase method. The optimized structure in the E-AFM state shows a non-symmetric with space groupP21nm. Table IIlists the optimized ion coordinates of O-YMO with the E- AFM structure ate¼0%, which is consistent with the theo- retical reports.¹² Taking the optimized crystal structure, the calculated value of ferroelectric polarization is 0.35lC/cm², which is slightly larger than the experimental results in the bulk (e.g., 0.24lC/cm²at 2 K),¹²but smaller in comparison with some theoretical calculated results (e.g., 1.4lC/cm²) based on the assumption of non-collinear spin alignment¹⁰

and the experimental data in the films (e.g., 0.8lC/cm²).¹⁴ The inconsistency may be attributed to the simplification of a real cycloidal spin-spiral alignment in the O-YMO.

However, ferroelectric polarization vanishes in O-YMO with A-AFM spin ordering owing to the highly symmetric struc- ture with space groupPbnm, where there lacks the ionic dis- placement. Thus, it can be concluded that a tradeoff exists between the strain/magnetization and crystal structure to optimize magnetic field-modulated electric polarization in the O-YMO materials.

IV. CONCLUSIONS

We have performed the first-principles calculations on the origin of strain-driven transition from E-AFM to A-AFM magnetic orderings in O-YMO. Our calculated results expected that the spin ordering magnetic structure is changed from E-AFM to A-AFM orderings under a compressive uniaxial strain of0.8%applied along theborientation. The structure analysis revealed the differences in bond lengths and bond angles to determine a ground state of AFM order- ing. On applying compressive uniaxial strain, the energy band gap decreased, while the spin magnetic moments of Mn and O atoms are both increased. Our results, thus, indicate a very promising way in tuning the spin-ordering along with multiferroic properties by controlling the strain induced in O-YMO.

ACKNOWLEDGMENTS

This work was supported by the National Science Foundation of China (Grant Nos. 51101063, 51272078, and 51332007) and the program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT1243).

The Program for International Innovation Cooperation Platform of Guangzhou (No. 2014J4500016).

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