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Physical Chemistry Chemical Physics View Article Online

DOI: 10.1039/C5CP04310G

Published on 16 September 2015. Downloaded by California Institute of Technology on 22/09/2015 07:04:21.

Yajun Zhanga, Jie Wanga* , MPK Sahooa, Takahiro Shimadab, and Takayuki Kitamurab a

Department of Engineering Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China b

Department of Mechanical Engineering and Science, Kyoto University, Nishikyo-ku, Kyoto 615-8540, Japan

Abstract Mechanical control of magnetism in perovskite oxides is an important and promising approach in spintronics. Based on first-principles calculations, we demonstrate that a negative pressure leads to a great enhancement of magnetic moment in deficient SrTiO 3 with oxygen vacancy, whereas a positive pressure results in the gradual disappearance of magnetism. Spin charge density, Bader charge analysis and electronic density of states successfully elucidate the origin and underlying physics of enhancement and disappearance of magnetism. It is found that the split electronic states of

and

in the 3d orbitals of Ti atom remarkably contribute

to the occupancy of majority spin states under negative pressure, which induces a large magnetic moment. Under positive pressure, however, the equal occupancy of both majority and minority t 2g and eg states leads to the disappearance of magnetization. In addition, both negative and positive pressure can largely lower the vacancy formation enthalpy, suggesting the oxygen vacancy is preferable with pressure. Our findings may provide a mechanism to achieve the pressure control of magnetization in nonmagnetic perovskite oxides. Keywords: First-principles calculations; magnetism; hydrostatic pressure; perovskite; oxygen vacancy

* E-mail:[email protected] 1

Physical Chemistry Chemical Physics Accepted Manuscript

Mechanical control of magnetism in oxygen deficient perovskite SrTiO3

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The ABO 3 -type perovskite oxides have received continuous attention over the last few Published on 16 September 2015. Downloaded by California Institute of Technology on 22/09/2015 07:04:21.

decades since they exhibit a multitude of interesting properties such as ferroelectricity, piezoelectricity, ferromagnetism and superconductivity.1 In particular, significant attention has been focused on the magnetism of perovskite compounds not only in fundamental research, but also in their potential applications in spintronics.2 However, widely used perovskite titanates are well-known to be nonmagnetic materials. This is because the formal d0 electron configuration (e.g., Ti4+) in these compounds contradicts with the partially occupied d states required for ferromagnetism.3 Much effort has been paid to find possible avenues to achieve magnetism in these oxides. Experimental measurements and theoretical calculations suggest that one of the practicable ways to achieve magnetism is defect engineering.4-8 This approach is feasible because intrinsic or extrinsic point defects are generally abundant in the oxide materials and can be easily realized in experiments.9-12 It has been reported that both cationic and anionic vacancies can induce magnetization in nonmagnetic perovskite oxides.6-8, 13-14 On the other hand, controlling the magnetic states by external stimulus is equally important for spintronics. Currently, the hydrostatic pressure, including the negative pressure,15-18 has become an important thermodynamic variable to tune the magnetic and electronic properties of materials. A number of experimental reports studied the pressure control of Curie temperature in transition metal alloys, diluted magnetic semiconductors, elemental ferromagnets and many other properties of materials.19-22 In a recent report, Thede et al. have investigated the influence of hydrostatic pressure on the magnetic behavior of quantum spin compound.23 Vanderbilt et al. have found that a large tetragonal strain can be induced in PbTiO 3 by application of a negative hydrostatic pressure.24 Zhao et al. show that the negative pressure has strong effect on the magnetic moment, band gap and magnetic Curie temperature of double perovskite oxides. 25-26 Previous reports successfully revealed the influence of hydrostatic pressure on the various properties of different materials. Nevertheless the influence of hydrostatic pressure on nonmagnetic perovskite oxides with intrinsic/extrinsic defects are less explored. It would be more advantageous and device worthy, if pressure could significantly increase the magnetization in perovskite oxides. Also, it would be more beneficial for practical usage when a high magnetization with reduced vacancy formation enthalpy can be achieved.

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Introduction

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of perovskite oxides, we have selected a lead free SrTiO 3 (STO) as an example because

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vacancies has been observed in STO experimentally.27-28 In addition, STO exhibits a variety of properties that can be used in the field of photocatalysts,29-33 superconductivity,34-36 twodimensional electron gas37-39 and solar cell.40-41 If new properties can be induced, it could be possible to realize a wide variety of advanced applications. Previous first-principles calculations have explored the magnetism induced by intrinsic defects in STO,8 in which, however, oxygen octahedral rotation is not included. In particular, the effects of pressure on the magnetic property of defect perovskite system have not been investigated so far. Therefore, exploring the control of magnetism by hydrostatic pressure in prototypical perovskite oxides is of scientific significance and practical importance. In the present work, first-principles calculations are performed to study: (i) the influence of oxygen vacancy on the electronic and magnetic properties of STO with consideration of oxygen octahedral rotation, and (ii) the role of pressure in governing the magnetic states and formation of vacancies. Both spin polarized and non-spin polarized calculations are performed to determine the ground state of the deficient STO, and antiferromagnetic states are also considered. Bader charge analysis is used to show the contributions of atoms around the vacancies to the magnetic moment.42 We demonstrate that it is possible to switch the magnetic states from low spin to high spin by changing the pressure from positive to negative. Furthermore, it is found that both positive and negative pressures are beneficial for reducing vacancy formation energy, indicating the easy formation of vacancy under pressure.

Simulation models and procedure At low-temperature STO exhibits a tetragonal AFD phase with oxygen octahedral rotations along [001] direction. This octahedral rotation generates two inequivalent oxygen sites, as shown in Fig. 1. The oxygen atom indicated by „O 1 ‟ is located on the rotation axis, whereas other oxygen atom denoted by „O2 ‟ is slightly displaced from the rotation axis due to octahedral rotation. A 2 2 2 periodic supercell with 40 atoms is used in the present calculations, in whic h interactions between neighboring vacancies due to the periodic boundary conditions can be ignored.43-50 The corresponding vacancy is denoted by 3

(i = O 1 , O2 ) introduced by removing

Physical Chemistry Chemical Physics Accepted Manuscript

In order to address the effect of pressure on the magnetism and vacancy formation enthalpy

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controlled oxygen vacancy formation in CaMnO 3 in 2 2 2 supercell and give reasonable

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results.51 Another work has demonstrates that the energy difference between defect and prefect STO is not sensitive to the supercell size.52 First principles calculations are performed based on the density functional theory (DFT) using the projector-augmented wave (PAW) method, which are implemented in the Vienna ab initio simulation package (VASP).53 Here, Perdew-Burke-Ernzerhof (PBE) generalized- gradientapproximation (GGA) exchange-correlation functional plus the Hubbard parameter U (with Ueff = 4.36 eV for Ti ions54 ) is employed to describe the exchange-correlation potential.55-56 It is well known that the LDA or GGA calculations often underestimate the band gap, the energy position of some features such as conduction band minimum, valence band maximum and in-gap states. Compared with normally- used LDA or GGA, the present GGA+U calculations with an optimal value of U can give a qualitatively correct description of defect electronic structures as discussed in previous work.54 In addition, previous study has demonstrated that the GGA+U method can give the same trend as the one obtained by the HSE06 calculations for the electron localization of O vacancy in SrTiO 3 .57 Careful test calculations show that a relatively high plane-wave cutoff energy of 600

and a 5 5 5 Monkhorst-Pack k-point mesh58 give well-converged results and

are enough to accurately describe the electronic properties. The hydrostatic pressure ranging from -10 GPa to 30 GPa by steps of 5 GPa is imposed by the „PSTRESS‟ option. It is worthwhile to mention that under this pressure range and with GGA+U method, no significant structural phase transition observed, even though the phase transition is reported at room temperature.59 This discrepancy can be attributed to the limitations of DFT calculations which can only be done at 0 K. During the structural optimizations containing vacancies, the lattice parameters are kept fixed to the fully relaxed values without vacancies, while relaxing only internal coordinates of atoms. The atomic structures are fully relaxed using the conjugate gradient method until the Hellmann-Feynman forces on each atom are less than 0.01

.

Under constant temperature and pressure, the thermodynamic equilibrium state of a system can be determined by the Gibbs free energy: G = E − TS + PV = H − TS

(1)

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Physical Chemistry Chemical Physics Accepted Manuscript

one i atom, which can be written as SrTiO 3-x (x = 0.125). Spaldin et al. have study the strain-

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entropy, and P and V represent pressure and formation volume, respectively. Under 0 K

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temperature, the oxygen vacancy formation enthalpy is evaluated by (2) where vacancy,

and

are the enthalpy of the supercell with and without an oxygen

denotes the oxygen chemical potential.

Results and discussion Structure stability The optimal structures are determined by systematically seeking the ground-state structure. We perform structural relaxation of two possible vacancies with removing one i atom from the simulation supercell. Both spin-polarized and non-polarized calculations are considered here to determine the stability of magnetic state for these systems. The energies of nonmagnetic, ferromagnetic and antiferromagnetic states are calculated as -286.839, -286.849 and -286.839 eV, respectively, for zero pressure. The energies of the ferromagnetic states for the pressure from -10 Gpa to 20 Gpa are lower than those of the nonmagnetic and antiferromagnetic states. The predicted ferromagnetic ground state at zero pressure is consistent with previous result,4 which indicates the present result is reliable. On the other hand, the critical temperature is important for the appearance of ferromagnetic order. The ferromagnetic critical temperature can be estimated from the mean- field approximation. The calculated Curie temperature is 75 K without pressure and a negative pressure increases the temperature. These results indicate that the magnetic moments in the present work are ferromagnetic. The total magnetic moment driven by O1 and O 2 .The presence of oxygen vacancy doesn‟t have

vacancies are nearly the same, i.e., 0.56

significant effect on oxygen octahedral rotation. The calculated value of rotation angle with vacancy (6.6o ) is almost the same as that without vacancy. 54 However, the effect of pressure on octahedral rotation is nontrivial. It is found that positive pressure enhance the rotation while negative pressure suppress it, indicating the inclusion of oxygen octahedral rotation is indispensable to determine the most stable structures of defect STO. Besides, for both the vacancy sites the formation enthalpy is nearly the same, i.e., 5.72 eV. From the formation 5

Physical Chemistry Chemical Physics Accepted Manuscript

where E and H are the internal energy and the enthalpy, T and S denote the temperature and the

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is insensitive to the vacancy site. So in the following sections, we will focus on O 1 vacancy only.

Origin of the magnetism To qualitatively analyze the spin polarization induced by the O1 vacancy, we perform a comprehensive investigation of the spin charge density and density of states. Fig. 2(a) and (b) show the spatial distributions of spin density and the contour map of magnetization density around the vacancies, respectively. As can be seen from Fig. 2, the magnetization mainly appears around the VO1 site and the nearest-neighbor Ti atoms (Ti1 ), which are strongly bonded with the O atom in the perfect crystal. In addition, the second nearest- neighbor (Ti2 ) and third nearestneighbor Ti atoms (Ti3 ) also slightly contributes to it. In order to further quantitatively analyze the contribution of each atom to the magnetic moment, Bader charge analysis is adopted in our calculations. A detailed Bader analysis indicates that the local magnetic moment at the nearest Ti atoms to VO1 is 0.23

for the case without pressure. The second- nearest and third-nearest Ti

atoms also have local magnetic moments of 0.13 and 0.10 from all Ti- ions sites is 0.46

, respectively. The contribution

, whereas the contribution from other ions sites is 0.10

the total magnetic moment from all ions sites is 0.56

. Thus

. The Bader charge analysis reflects the

same physical picture with above spin density distribution. To get insight into the origin of ferromagnetism induced by the vacancies, the total density of states (DOS) and projected density of states (PDOS) of Ti1 and Ti2 atoms are shown in Fig. 3. The energies are plotted relative to the Fermi level (

= 0). As shown in Fig. 3(a)-(b), the O vacancy causes the Fermi level to move

into the bottom of the conduction band, indicating an n-type character. We can find that the ingap state is singly- occupied and the associated Fermi level is located at about 0.50 eV below the conduction band minimum (CBM), which is consistent with previous results. 57 As shown in Fig. 3, the in-gap states are mainly due to localized electrons in 3

orbitals. Nevertheless, it is also

true that the GGA+U method still underestimate the band gap and will lead to a small deviation from experimental values. This deviation has no significant influence on the mechanical control of magnetism in the present study. The more accurate description of band gap energy can be realized if a hybrid functional is employed.57,60 Meanwhile, the DOS below the Fermi level are asymmetric for the spin- up and spin-down states resulting in the spin-polarized state. To

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Physical Chemistry Chemical Physics Accepted Manuscript

enthalpy and magnetic moment it can conclude that magnetic properties in oxygen deficient STO

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needed. The O h -type crystal field in the perovskite structure can split the 3d orbitals of the Ti

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atom into two

(

,

) and

(

,

,

) states. These states distribute toward the

six neighboring O atoms and toward four neighboring Sr atoms, respectively. The PDOS shows that the formation of oxygen vacancy can contribute to the asymmetry in spin polarized majority and minority states for neighboring Ti atoms. For Ti1 atom, an asymmetry is observed in orbital, whereas for Ti2 atom the asymmetry is observed in (

and

(

orbital. It is clear that both

orbitals can form spin-polarized state and contribute to the magnetization.

Switching of magnetic state from low to high spin states Above results are about oxygen vacancy induced magnetism in deficient STO at ambient pressure. It is well known that the electronic structures, dielectric, magnetic and thermodynamics properties of materials can be modified with external pressure. So, the control of magnetic states by pressure will be of great importance. Fig. 4 gives the magnetism as a function of pressure. It is interesting to note that the magnetic moment is very high (~ 1.93 µB) at negative pressure. Bader charge analysis results show that the magnetization mainly comes from the nearestneighbor and the second nearest-neighbor Ti atoms with the values of 0.40 and 0.45

,

respectively. The increase of positive pressure gradually decreases the magnetic moment to zero. Correspondingly, switching of magnetic state from low spin to high spin is realized by pressure. The pressure control of magnetism is promising for spintronics. To provide more insight into the variation of ferromagnetism with pressure, we plot the PDOS at negative and positive pressures for five 3d states of Ti atoms nearest and second-neatest to VO1 . Fig. 5(a)-(c) illustrate the projected DOS of Ti1 atom under positive, and Ti1 and Ti2 atoms under negative pressure, respectively. In addition, Fig. 5(d)-(f) describe the details of states near the Fermi level shown in Fig. 5(a)-(c). Negative pressure affects different Ti atoms in different manners. For Ti1 atoms, under negative pressure,

,

and

remarkably contribute to the occupancy of majority spin

states making them spin polarized, which induces large magnetism. However,

and

states do not possess any spin polarized state either above valence band maximum (VBM)

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Physical Chemistry Chemical Physics Accepted Manuscript

investigate the composition of the spin-polarized state, the analysis of PDOS for the 3d states is

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to the magnetization comes from all the three

orbitals. In contrast to negative pressure, the

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magnetization completely disappeared at high positive pressure (> 25 GPa). Under positive pressure both nearest and second nearest Ti atoms show similar trend. Thorough investigation of PDOS reveals that the majority and minority spin states of

and

orbitals are equally

occupied. Therefore, the possibility of magnetization at positive pressure completely ruled out. Now we will explore the reason behind the dissimilar magnetic behavior at negative and positive pressures with reference to the zero pressure. As mentioned before, the crystal field experienced by

can split the 3d state into doubly degenerate high energy

triply degenerate low energy

(

,

,

) levels. These

and

(

,

) and

levels are free to be

linked with the ligands, here O 2-. In case of perfect STO at zero pressure, it is inferred that the orbital of oxygen atom have a chance to form a strong bond with whereas the

orbital of the oxygen atom points toward the

orbital of Ti1 atom,

orbital of Ti2 atom. When

oxygen vacancy is created, the foremost probability is that the spin density should migrate to the nearest

of Ti1 and

from high energy

(

of Ti2 atom. Thus the magnetic contribution at zero pressure comes ) and low energy

(

) orbitals of Ti1 and Ti2 atoms respectively.

Under negative pressure, tetragonal distortion is enhanced. Due to this distortion, the z axis is elongated and the x and y axes are compressed. This breaks the degeneracy of energy of

is found to be lowered in comparison to

orbitals and the

. If the tetragonal distortion is large,

then the true square planner arrangement can be realized. In this arrangement, the energy of level further drops below that of

. The true square planner arrangement is shown in Fig.

6(c). This lowering of energy with structural deformation is one of the examples of John Teller distortion. For Ti1 atom, John Teller distortion leads to a true square planner structure, which can be realized from the PDOS of Ti1 atom. Because the

, and

these orbitals are occupied leaving the high energy

and

have lower energy than

,

unoccupied. For Ti2 atom,

which is far from the vacancy site, undergoes small John Teller distortion and don‟t exhibit the true square planner arrangement. Fig. 6(b) describes the energy levels for Ti2 atom. If we compare the PDOS for Ti2 atom both at negative and at zero pressures, it is observed that the spin density shifted from

orbital at zero pressure to

at negative pressure. This can be

explained as, under negative pressure the John Teller distortion leads to 90o rotation of 8

Physical Chemistry Chemical Physics Accepted Manuscript

or below CBM, and hence do not contribute to the magnetization. For Ti2 atom, the contribution

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pressure supports this rotation. Thus

orbital. Also, the volume expansion due to negative orbital show spin polarized majority states. This spin

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polarized state is responsible for magnetic contribution of Ti2 atom. In addition to

orbital,

orbital also contributes to the magnetism. However, it is very small in comparison to

.

Our quantitative estimation of magnetic moment unfolds that the magnetic contribution of Ti2 is a little bit larger than that of Ti1 atom. Further, at high positive pressure, the lattice is under high compression. This compression restores the orbital degeneracy, Fig. 6(a). From the PDOS (both Ti1 and Ti2 exhibit similar trend) it is evident that all

and

levels with majority and

minority spin states are equally occupied and looks like symmetric. This symmetry leads to cancellation of magnetic moments. Thus, at high positive pressure, STO is nonmagnetic even with vacancy. To further support our results, we studied the spin charge density of the oxygen deficie nt STO at high negative and positive pressures in Fig. 7, respectively. It is observed from the spin charge density that the contribution of Ti2 atom to magnetization is more than that of Ti1 . For Ti1 atom, the shape of the spin charge density is much similar to the shape of the

orbital, as

shown in Fig. 7(a). This supports the fact that the dominant contribution to magnetization comes from as that of

orbital in case of Ti1 atom. For Ti2 atom, the shape of the spin charge density is similar orbital, which contributes to magnetization. For high positive pressure, if we look

at the color of the contours and the scale given on left side, a nonmagnetic behavior of STO is confirmed. The present work provides a general mechanism to achieve the mechanical control of magnetization in nonmagnetic perovskite oxides. The concept of hydrostatic pressure control of magnetism can be translated to the biaxial epitaxial strain control of magnetism in lowdimensional perovskite oxides. It is found that oxygen vacancies and charge imbalance at the interfaces can induce magnetism in low-dimensional LAO/STO heterostructures61-62 . The induced magnetism can be controlled by the biaxial epitaxial strain in a similar way to the hydrostatic pressure control of magnetism in the bulk. There is a possibility to realize the enhancement of magnetic moment of oxide heterostructures by strain engineering.

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Physical Chemistry Chemical Physics Accepted Manuscript

orbital about z-axis and transforms as

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The oxygen vacancies are inevitable in perovskite oxides such as SrTiO 3 . Confining and Published on 16 September 2015. Downloaded by California Institute of Technology on 22/09/2015 07:04:21.

controlling the oxygen vacancies can provide scope to realize the full potential of the perovskite oxides for multiple device applications. Thus for tailoring the oxygen vacancies, it is necessary to have understanding of defect chemistry and its role on physical properties of the materials such as magnetization. The formation of oxygen vacancies can be achieved by annealing pure SrTiO 3 at elevated temperature (> 400 0 C) in oxygen poor atmosphere.63 By following standard Kroger-Vink notaion, the formation of oxygen vacancy can be expressed as, 64 ↔ Here,

,

and



(3)

lattice oxygen, oxygen vacancy and electron respectively.

The equilibrium for this reaction can be expressed as, 65 [ Here,

]

indicates oxygen pressure,





or [ ]

(4)

is the equilibrium constant, and

denotes the carrier

concentration. From equation 4 it can be understood that under reducing atmosphere, high concentration of oxygen vacancy can be achieved. In the present case, it has been observed that the electron generation (equation 1) may further lead to the reduction of Ti4+ to Ti3+. This can be expressed as,64 (5) Here,

and

denotes Ti4+ and Ti3+ respectively.

Further, the reduced Ti may combine with

to form defect dipole which is expresses as, (6)

The electronic structure of oxygen deficient perovskite oxides is highly sensitive to the presence of either free

or

. According to Ref. 64, the presence of defect dipole (here,

) can result in lowering of the energy of whereas for free

the energy of

orbital in comparison to the

should be lower than 10

,

state. In addition, lattice

Physical Chemistry Chemical Physics Accepted Manuscript

Defect chemistry and easy formation of vacancy under pressure

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STO, a deep analysis of defect states in the vicinity of conduction band explores the existence of

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defect dipole from a negative pressure as large as (-10 GPa) to a positive pressure (20 GPa). At pressure > 20GPa, the lattice compression results in overlapping of the Ti orbitals close the defect center restoring the degeneracy of the 3d electrons which is reflected as symmetric 3d states below the conduction band edge. Fig. 8 illustrates the oxygen vacancy formation enthalpy for STO as a function of pressure at an oxygen chemical potential of −5 eV,51 which corresponds to typical growth conditions under air. It is interesting to find that both positive and negative pressure can largely lower the formation enthalpy, which means that pressure can not only control the magnetization, but also can make the oxygen vacancy easy to form. It is noted that hydrostatic pressure can induce volume expansion (negative pressure) and compression (positive pressure), more like tensile and compressive strain respectively, whereas anionic defects lead to considerab le volume expansion.66-67 Also both these entities are thermodynamically related to Gibbs free energy and defect formation enthalpy. In general, the presence of an anionic defect, here O 2-, supplies the electrons to the neighboring octahedral cations, here Ti+4 , which effectively reduces the oxidation state, from +4 to +3, of the cations and results in increased ionic radius. This increased ionic radius finally leads to the volume expansion. The negative hydrostatic pressure favors the volume expansion required for anionic defect and therefore, greatly reduces the vacancy formation enthalpy. However, when positive pressure leads to lattice compression, it imposes constraint to the lattice expansion required for anionic defect (due to the reduction in oxidation state). Thus, unlike the negative pressure, relatively higher energy is required to stabilize the structure under positive pressure. Furthermore, the decrease in vacancy formation enthalpy with increase in positive pressure is attributed to the domination of crystal field over electrostatic field, which often accommodates the lattice compression created by positive pressure as change in the bond length and overlapping of

states (as observed in DOS and spin charge density plots).

From above analysis, we can draw the conclusion that the dependence of formation enthalpy on pressure is rather strong and seems to be of greatly beneficial from the application point of view.

Summary and conclusions 11

Physical Chemistry Chemical Physics Accepted Manuscript

expansion (negative pressure) facilitates the formation of defect dipoles. For oxygen deficient

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and pressure are investigated through first-principles calculations. The calculation results reveal

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that oxygen vacancy leads to the emergence of magnetism, which is convincingly demonstrated through spin density, Bader charge analysis and density of states. In particular, we demonstrate that it is possible to control the magnetic states from “low spin” to “high spin” by changing the pressure from positive to negative. It is found that the split electronic states of

and

in

the 3d orbitals of Ti atom leads to the occupancy of majority spin states under negative pressure, which gives a large magnetic moment. Under a positive pressure, equal occupancy of both majority and minority

and

states results in the disappearance of magnetization. The

results further indicate that pressure can largely reduce the vacancy formation enthalpy due to the chemical expansion and crystal- field effects, which means that an oxygen vacancy is easier to form under pressure. The present work implies a promising way for the mechanical control of magnetic properties in deficient perovskite oxides.

Acknowledgements The authors acknowledge the financial support for J.W. from the National Natural Science Foundation of China (Grant No. 11321202, 11472242), and for T.S. and T.K. from the Grant- inAid for Specially Promoted Research (Grant No. 25000012) and the Grant- in-Aid for Scientific Research (B) (Grant No. 26289006) from the JSPS.

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Physical Chemistry Chemical Physics Accepted Manuscript

In summary, enhancing and controlling of magnetization through coupling between vacancy

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Sr

O1

Ti

O2 O y [010]

x [100]

Fig. 1 Simulation models for oxygen vacancies with inequivalent oxygen positions, with one atom on the rotation axis (O 1 ), and another located at the oxygen site displaced due to the rotation (O 2 ). (a)

(b)

VO

b

c

a

Fig. 2 Spin charge density in O 1 -deficient SrTiO 3 under zero pressure. (a) Isosurface of magnetization density (yellow-colored region). (b) Contour map of magnetization density in (100) plane. The corresponding color scale is shown on the left of the figures.

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(b)

(a)

Fig. 3 Total and projected density of states for the nearest-neighbor Ti atom (a) and (b) second nearest- neighbor Ti atom in O1 -deficient SrTiO 3 . The red and blue curves correspond to the majority and minority spins, respectively. The solid vertical line denotes the Fermi level.

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Low spin

High spin

Fig. 4 Magnetic moment as a function of pressure for O 1 -deficient SrTiO3 . Negative pressure enhances the magnetic moment while a positive pressure eliminates it which means switching of magnetization from “high spin” and “low spin”.

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(a)

(a) (b) (e)

(c) (f)

(e)

(c) (f)

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(d)

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pressure (25 Gpa) for nearest- neighbor Ti atom, (b) negative pressure (-10 Gpa) for nearest-

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neighbor Ti atom and (c) negative pressure (-10 Gpa) for second nearest-neighbor Ti atom. (d), (e) and (f) describe the details of states near the Fermi level of (a), (b) and (c), respectively.

Fig. 6 Energy band diagram showing the splitting of eg and t 2g levels under small (b) and large tetragonal distortions (c). The arrows shown in (b) and (c) indicate the occupied orbitals.

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Fig. 5 The d projected density of states of Ti atom in O 1 -deficient SrTiO 3 for (a) positive

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(b)

Fig. 7 Spin charge density in O 1 -deficient SrTiO 3 for (a) negative pressure (-10 Gpa) and (b) positive pressure (25Gpa) in the (100) plane. The corresponding color scale is shown on the left of the figures.

Fig. 8 Vacancy formation enthalpy as a function of pressure for O 1 -deficient SrTiO 3 , which shows a decrease with pressure regardless of negative or positive.

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(a)

Mechanical control of magnetism in oxygen deficient perovskite SrTiO3.

Mechanical control of magnetism in perovskite oxides is an important and promising approach in spintronics. Based on the first-principles calculations...
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