PDF Proton transfer ferroelectricity/multiferroicity in rutile oxyhydroxides

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Cite this:Nanoscale, 2018,10, 9509

Received 20th February 2018, Accepted 4th April 2018 DOI: 10.1039/c8nr01456f rsc.li/nanoscale

Proton transfer ferroelectricity/multiferroicity in rutile oxyhydroxides †

Menghao Wu, *âTianci Duan,âChengliang Lu, âHuahua Fu, âShuai Dong^b and Junming Liu ^c

Oxyhydroxide minerals such as FeOOH have been a research focus in geology for studying the Earth’s interior, and also in chemistry for studying their oxygen electrocatalysis activity. In this paper thefirst-principle evidence of a new class of ferroelectrics/multiferroics is given. In this class are:β-CrOOH (guyanaite),ε-FeOOH,β-GaOOH, and InOOH, which are earth-abundant minerals which have been experimentally verified to possess distorted rutile structures, are ferroelectric with considerable polarizations (up to 24 µC cm⁻²) and piezoelectric coefficients. Their atomic-thick layer may possess vertical polarization will not be diminished by depolarizingfield because of the formation of O–H⋯O bonds that can be hardly symmetrized. Furthermore,β-CrOOH is revealed to be a combination of a high Curie temperature (TC) in-plane type-I multiferroics and vertical type-II multiferroics, which is strain tunable and may give a desirable coupling between magnetism and ferroelectricity. Supported by experimental evidence on reversible conversion between metal oxyhydroxides and dioxides and their good lattice match that gives convenient epitaxial growth, a heterostructure composed of oxyhydroxides and common metal dioxides (e.g., TiO2, SnO2and CrO2) may be constructed for various applications such as ferroelectricfield-effect transistors and multiferroic tunneling junctions.

Oxyhydroxide minerals such as AlOOH¹ (Boehmite) and FeOOH² in the Earth’s mantle have been a research focus of geologists for studying the water storage capacity of the Earth’s interior, and of chemists for studying oxygen electrocatalysis activity.^3–7They have also attracted considerable interest from physicists partially for studying the symmetrization of hydrogen bonds under high compression, which may have signifi- cant eﬀect on their crystal structures and physical properties.

This phenomena had been predicted or even demonstrated in various types of materials such as formic acid⁸and ice-X,⁹and recently the pressure induced hydrogen bond symmetrization has been characterized by evidence from a combination of various spectroscopies in oxyhydroxides such as AlOOH,¹⁰ FeOOH¹¹and also CrOOH.¹²It is also worth mentioning that many oxyhydroxide polymorphs have been verified. For example, there are three forms of CrOOH, denoted as α-CrOOH (grimaldiite), β-CrOOH (guyanaite), and Γ-CrOOH

(bracewellite), in which guyanaite is a common phase mineral with a distorted rutile structure. Some other oxyhydroxides such as β-GaOOH and InOOH share similar structures,^13,14 which are the usual byproducts in semiconductor industry.

In this research the focus was on an important property that has been scarcely noticed in oxyhydroxide minerals.

Although the antiferromagnetism in CrOOH and FeOOH have been investigated in some research,^11,12 their possible ferroelectricity because of the breaking of inversion symmetry by hydrogen bonds has not yet been explored. It is known that ferroelectric (FE) materials,^15–18which possess spontaneous electric polarizations switchable under external electric field, have a wide range of potential applications in electronics, micro- mechatronics and electro-optics. Ferromagnetic (FM) materials with switchable magnetization, FE materials with switchable electrical polarizations and ferroelastic materials with switchable strain^19,20 can find applications in non-volatile memory.

In commercial random access memories (RAMs), data writing in FM RAMs is energy consuming, while the reading operation in FE RAMs is destructive. To resolve both issues, multiferroic materials with both FM and FE properties were sought because of the combination of both eﬃcient writing and less energy cost for reading.²¹Because of the challenge in incorpor- ating both forms in the same compound, their existence in nature is rare and their Curie temperatures (TC) are usually far below room temperature.^22–25 Almost all the multiferroic

†Electronic supplementary information (ESI) available. See DOI: 10.1039/

c8nr01456f

aSchool of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China.

E-mail: [email protected]

bSchool of Physics, Southeast University, Nanjing 211189, China

cNational Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China

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materials reported to date are either antiferromagnetic (AFM) or ferrimagnetic, except for europium titanate (EuTiO3) which becomes FM under a large strain.^26,27They can be classified as either type-I or type-II multiferroics, where FE is induced by magnetism in type-II multiferroics with strong magnetoelectric coupling favorable for eﬃcient data reading and writing.²³ Recently a series of two-dimensional (2D) type-I multiferroics with almost independent FE and magnetism have been predicted theoretically,^20,28–32but these are still to be synthesized experimentally.

In this paper the focus is on distorted rutile-type oxyhydroxides,1,2,10–14,33–35 including β-GaOOH, InOOH, β-CrOOH, and ε-FeOOH, where the asymmetric O–H⋯O configuration at ambient pressure can result in proton transfer FE. Compared with conventional FE materials, it has already been concluded that proton transfer FE has many advan- tages:^24,32,36 the steric hindrance or high energy barriers during switching can be avoided, polarity can be formed spon- taneously for the directional preference of hydrogen bonding, and strong hydrogen bonds may also result in high-temperature FE. Now another advantage is demonstrated using first- principle calculations: their atomic thickness, thin-film can exhibit vertical FE which is robust against a depolarizing field, whereas the potential applications of traditional FE thin films are hindered by their polarization that disappears below critical film thickness.^37,38Furthermore, the coexistence of room- temperature magnetism and proton transfer FE, type-I and type-II multiferroicity, are predicted in β-CrOOH (guyanaite).

Because of the lattice match, heterostructures composed of diﬀerent oxyhydroxides and metal dioxides can be constructed for various applications such as FE field-eﬀect transistors, multiferroic tunneling junctions (MTJs),³⁹ or simply for enhanced FE upon epitaxial strain.

Results and discussion

The geometric structures ofβ-GaOOH, InOOH,β-CrOOH, and ε-FeOOH are displayed in Fig. 1(a), where the hydrogen bonding geometry of the rutile-type structures leads to a reduction of symmetry to space group Pmn21, which has already been verified in previous experiments.^11,12,34 Here proton transfer FE may stem from the asymmetric O–H⋯O configuration, as shown in Fig. 1(b), where the polarization can be switched upon the hopping of protons along the hydrogen bonds. There are two nearly independent O–H⋯O hydrogen bonds per unit cell aligned in two directions that are almost perpendicular, so two diﬀerent types of FE may emerge upon various combinations: switching from I to II along the

−Xaxis, or from III to IV along the−Yaxis, with diﬀerent directions and magnitude of polarizations. From the calculations in this research, for GaOOH, InOOH and FeOOH, the state I/II was slightly lower in energy compared with state III/IV, and for CrOOH this was reversed. So I/II and III/IV may sometimes be regarded as degenerate considering their negligible energy diﬀerence (∼meV fu⁻¹). As summarized in Table 1, GaOOH

possesses the largest polarization (∼24 µC cm⁻²) in the −y direction. If their metal ions such as iron (Fe) or Chromium (Cr) possess magnetism, the systems can be multiferroic.

Takingβ-CrOOH as an example, the FE state was revealed to be lower in energy compared with the anti-FE state (see Fig. S1, ESI†), and every unit cell contains two Cr atoms and each Cr atom possesses a magnetic moment of 3µB, which is marked in blue for the A spin and in purple for the B spin in Fig. 2(a). To determine the ground state of spin configuration, the Cr spin lattice composed of A and B spins is illustrated, where every A spin has eight adjacent B spins and two adjacent A spins. The exchange coupling constant between adjacent A–A (or equivalent B–B) and A–B are defined asJ1andJ2, respectively. For the AFM configuration where A and B spins are anti-parallel, denoted as AFM1, it will be 8J1 lower in energy compared with the FM state. If the unit cell is doubled in z direction, the AFM2 configuration (E-AFM), where adjacent A–A as well as B–B are anti-parallel, will be 8J1+ 4J2lower in energy compared with the FM state. It transpires that AFM2 is the ground state as when the energies of diﬀerent spin con- figurations obtained by DFT computations were compared:

E(AFM1)−E(FM) = 67.9 meV,E(FM)−E(AFM2) = 60.1 meV, so J1 andJ2are −8.5 meV and 32.0 meV, respectively. The magnetic frustration states were also compared by aligning the A spins along thezaxis and the B spins along thexory axis, which were all found to be higher in energy from noncollinear calculations.

The energy required to flip one spin in the AFM2 configuration will beΔ= 2J2= 64.0 meV. Applying a tensile strain in the zdirection can greatly changeJ2 and convert the system from AFM to FM, as shown in Fig. 2(b). When there is a uniaxial tensile strain higher than 2%, FM will be the ground state and lower in energy when compared with AFM2, and as the strain increases to 3.3%, the valueE(AFM1)− E(FM) = 31.9 meV. A coarse estimation ofTCcan be performed simply by using the mean field theory and Heisenberg model which have been widely used in previous work:^40,41

TC¼ 2Δ 3kB;

where Δ= 8J1+ 2J2is the energy required to flip one spin in the FM state with the other spins fixed. Upon a strain of 2%

and 3.3%, the estimatedTCwere 510 K and 793 K, respectively.

If the FETCwas estimated using a similar method, as shown in Fig. 2(c), the energy barrier for one proton to flip to the other side in the FE lattice (with the other protons fixed) is about 39 meV using nudged elastic band calculations, which is induced by the asymmetry of O–H⋯O: the O⋯H/O–H distance ratio will be 1.44 Å/1.06 Å and the estimated FETCwill be 301 K.

This barrier will be lower if the nuclear quantum eﬀect is taken into account. However, upon a biaxial strain in thexyplane, this barrier will be enhanced and robust at ambient conditions even upon the nuclear quantum eﬀect of protons.

It seems that the proton transfer FE in the xy plane is almost completely independent of Cr spins in CrOOH, which should be type-I multiferroics. Meanwhile, it was noted that

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along thez axis, the AFM2 spin configuration with breaking inversion symmetry may give rise to a weaker switchable polarization: in CrOOH the adjacent Cr–Cr distance will increase by

∼0.020 Å when switching from a spin parallel state to an anti- parallel state because of magnetostriction,^42–44and from type-I to type-II and as shown in Fig. 3(a), the displacement of Cr Fig. 1 (a) Geometric structures ofβ-CrOOH,ε-FeOOH,β-GaOOH, and InOOH. (b) Two distinct types of FE switching from I to II and from III to IV, where blue arrows on the left denote the direction of the polarizations of the I–IV conﬁgurations, and the purple arrows denote the directions of proton transfer. White, red, pink, blue, orange, green spheres denote hydrogen (H), oxygen (O), gallium (Ga), chromium (Cr), indium (In), iron (Fe) atoms, respectively.

Table 1 Lattice constants, polarizations and energy diﬀerence between state I/II and state III/IV

|a|(Å) |b|(Å) |c|(Å) P_x(µC cm⁻²) P_y(µC cm⁻²) ΔE(meV fu⁻¹)

β-GaOOH 4.92 4.34 3.00 17.5 23.8 4.6

InOOH 5.33 4.59 3.32 7.9 17.4 3.0

β-CrOOH 4.88 4.32 2.98 10.9 20.5 −2.6

ε-FeOOH 4.93 4.40 3.00 23.1 20.3 12.5

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ions along thezaxis will be about∼0.016 Å. By these computations, this displacement can give rise to a switchable polarization of about 1300 µC m⁻², which was already much higher than the polarizations of common type-II multiferroics [e.g.,

∼600 µC m⁻²for terbium manganite (TbMnO3)].⁴⁵As a result, CrOOH is type-I multiferroic in the xy plane, and type-II multiferroic in the z direction where FE and magnetism are coupled. If an ideal thin layer model of three atomic thickness isolated from (001) surface is considered (see Fig. S3, ESI†), the ground state will be ferrimagnetic with a net magnetic moment of 3µBper unit cell: the Cr spins in the top layer are antiparallel to the spins in the bottom layer, so the spin direction of Cr atoms in the middle layer will determine the direction of both the total magnetization and the polarization. As a result, a vertical polarization of 1.2 × 10⁻¹¹C m⁻¹is formed. It is known that in traditional ionic FE ultrathin films, FE will disappear below the critical film thickness [24 Å in barium titanate (BaTiO3), 12 Å in lead titanate (PbTiO3), for example^37,38] because of the depolarizing field. Here the vertical polarization induced by type-II multiferroics is not diminished, and the proton transfer vertical FE of those oxyhydroxides can be even more robust against the depolarizing field.

For example, as shown in Fig. 3(b), a thin layer of InOOH is

isolated from (110) surface so half of the inner O–H⋯O bonds are almost fixed along the vertical direction, giving rise to a vertical polarization that can hardly be turned to in-plane. The obtained polarization of 3.9 × 10⁻¹¹ C m⁻¹ is much higher than previous predicted values in 2D materials (e.g., 0.2 and 1.1 × 10⁻¹¹C m⁻¹, for bilayer boron nitride²⁹and a functiona- lized phosphorene bilayer,²⁸respectively). It is known that the polarization direction of perovskites such as BaTiO3consisting of octahedral TiO6 may be aligned in any of six equivalent directions because of their symmetry, so the depolarizing field will symmetrize the ionic bonds or turn the vertical polarization to in-plane in the thin film. For the thin oxyhydroxide layer, however, the direction of O–H⋯O bonds are firmly aligned when the O atoms at two sides are embedded and almost fixed in the lattice. As a result, a large portion of O–

H⋯O bonds are fixed vertically, which can neither be symmetrized or driven in-plane.

It was noted that there was a good match for the lattice constants in Table 1, which may be favorable for constructing heterostructure devices. Furthermore, those metal oxyhydroxides share similar rutile structures with some metal dioxides [Fig. 4(a)], such as CrO2, which is a well-known room tempera- Fig. 2 (a) Cr lattice and two AFM spin conﬁgurations in CrOOH, where

A and B spins are marked by blue and purple spheres, respectively, and red arrows denote the spin direction. (b) Dependence of energy diﬀer- ence between the AFM2 and FM state with uniaxial strain in thezdirec- tion. (c) Hopping pathway for one proton toﬂip to the other side in FE lattice.

Fig. 3 (a) Opposite polarization directions on AFM2 conﬁgurations. (b) FE switching of a thin oxyhydroxide layer isolated from the (110) surface.

Olive and red arrows denote polarization and spin directions, respectively.

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ture half metal. In a previous report⁴⁶it was shown that supported CrO2can be reversibly reduced under hydrogen, produ- cing AFM CrOOH on titania (TiO2), whereas reoxidation to CrO2occurs at temperatures above 520 K in air, under oxygen, and under selective catalytic reduction conditions (NO + NH3+ O2), CrOOH and CrO2were decomposed at 770 K under argon to form AFM chromium oxide (Cr2O3). As a result, the heterostructure interface was composed of diﬀerent oxyhydroxides and oxides, such as CrOOH/TiO2, CrOOH/CrO2, CrOOH/

Cr2O3, can be synthesized using such an approach. In this research, the CrOOH/TiO2 was a FE/semiconductor interface that can be used for FE field eﬀect transistors,³¹as shown in Fig. 4(b). Considering the lattice constants of CrOOH (|a| = 4.88 Å, |b| = 4.32 Å) and TiO2(|a| = |b| = 4.65 Å), the CrOOH/

TiO2interface obtained should be the (110) surface, whereas the (001) surface can match the lattice constants of Cr2O3for the CrOOH/Cr2O3 heterostructure. Such a good lattice match will enable perfect epitaxial growth for a wider range of applications. If the dioxide substrate is metallic, it may also be

favorable for use as a bottom electrode, especially for piezo- response force microscopy measurements. FE or MTJs can also utilize the lattice match of CrOOH with CrO2, or other metallic rutile dioxides such as RuO2 and RhO2, according to their lattice constants |a| (= |b|) and |c| (listed in Table 2). As men- tioned previously, epitaxial growth of CrOOH on a substrate with relatively slightly larger lattice constants may also strengthen the ferroelectricity and ferromagnetism of CrOOH.

Fig. 4(c) is a design of MTJ composed of CrO2/CrOOH/RuO2. It is worth noting that such a junction with a high on/offratio requires two metallic electrodes with significantly different screening lengths. The difference in screening lengths between CrO2 and RuO2 gives rise to the asymmetry in the electrostatic potential profile that alters the effective barrier height upon FE switching, so that two distinct resistances can be obtained. Its on/off ratio is computed by using the non- equilibrium Green’s function and Landauer–Büttiker formula⁴⁷implemented in the QuantumWise ATK code⁴⁸(see the model in Fig. S4, ESI†). The transmission for spin-up and down channels are 1.3 × 10⁻⁶ and 4.6 × 10⁻²¹, respectively, when the polarization of CrOOH is towards the RuO2side, and this changes to 1.2 × 10⁻⁷ and 5.8 × 10⁻²²when it switches towards the CrO2 side, so a tunneling electroresistance (TER) as high as 1105% can be achieved. If the electrode RuO2 is replaced with RhO2, the TER will decline to 320%. Meanwhile, an intensive magnetoelectric effect can be obtained as the magnetic moment at the interface can vary by 1.05µB per supercell upon FE switching.

Fig. 4 (a) Reversible conversion between metal dioxides and metal oxyhydroxides. (b) Model of FEﬁeld eﬀect transistor based on the interface of metal oxyhydroxide and semiconducting metal dioxide. (c) MTJ based on metal oxyhydroxide located between two distinct metal dioxides.

Table 2 Lattice constants of rutile metal dioxides. (CrO2: Chromium dioxide, RhO2: rhodium oxide, RuO2: ruthenium oxide, SnO2: tin dioxide, TiO2: titanium dioxide)

TiO2 SnO2 CrO2 RhO2 RuO2

|a|(Å) 4.65 4.83 4.49 4.56 4.54

|c|(Å) 2.97 3.24 2.98 3.13 3.14

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Previously it was predicted that doped-BaTiO3/SrRuO3may enable electric control of spin injection into FE semiconductors because of the transition between the Schottky and Ohmic contacts upon FE switching.⁴⁹A similar mechanism may be utilized at the CrOOH/RuO2or CrOOH/RhO2interface as long as CrOOH can be doped. Based on the experimental work⁴⁶ that shows that CrO2 can be reversibly reduced under hydrogen, the electronic and magnetic structure may be tuned by controlling the density of the hydrogen atoms. The hydrogen vacancy in CrOOH can be regarded as p doping, which also makes FM more favorable than AFM. For the structure of CrOOH0.75in Fig. S5(a) (ESI),†the FM state will be 33 meV per fu lower in energy compared with AFM2. Another report on the synthesis of rutile Cr_1−xFexOOH (0 < x< 1) also revealed the possibility of tuning its properties by doping.⁵⁰For the structure of Cr0.5Fe0.5OOH in Fig. S5(b) (ESI),†the results show that Cr spins (∼3µBper atom) are all antiferromagnetically coupled with Fe spins (∼5µB per atom) in the ground state, so that Cr0.5Fe0.5OOH is ferrimagnetic with a magnetic moment of 1.0µBfu⁻¹.

Conclusion

In summary, first-principle evidence is provided of proton transfer FE inβ-GaOOH, InOOH, β-CrOOH and ε-FeOOH. In particular, not only was the coexistence of room temperature magnetism and proton transfer FE, but also a hitherto un- reported combination of type-I and type-II multiferroicity, are predicted inβ-CrOOH (guyanaite), giving a desirable coupling between magnetism and FE. A tiny strain may turn it from anti-FM to FM, whereas the polarization as well as the Curie temperature can also be greatly enhanced. Their atomic-thick thin layer may possess vertical polarization that will not be diminished by the depolarizing field because of the formation of vertical O–H⋯O bonds that cannot be symmetrized.

Because of the lattice match for convenient epitaxial growth, heterostructures composed of diﬀerent rutile oxyhydroxides and metal dioxides, which have been partially synthesized in previous reports, can be constructed for various applications such as FE field-eﬀect transistors and multiferroic tunneling junctions.

Computational methods

Density functional theory (DFT) calculations were carried out using the ViennaAb initioSimulation Package (VASP).^51,52The projector augmented wave (PAW) potentials⁵³for the core and the generalized gradient approximation (GGA) in the Perdew–

Burke–Ernzerhof (PBE)⁵⁴ functional for the exchange–corre- lation functional were applied. The kinetic energy cutoﬀwas set at 530 eV, and the Brillouin zone was sampled by 7 × 7 × 9 k points using the Monkhorst–Pack scheme. Here following previous models that fit well with experimental data, GGA + U, GGA + D2 were both checked and finally the GGA + U method

on FeOOH was adopted where on-site Coulomb and exchange interaction U–J = 5.3 eV was used to treat the d electron states in Fe atoms,¹¹and pure GGA was used in CrOOH so the para- meters obtained were closer to the values measured in neutron diﬀraction experiments.¹²Finally the Berry phase method was used to evaluate crystalline polarization.⁵⁵For the slab calcu- lation, the errors introduced by the periodic boundary conditions could be counterbalanced by setting an electric field to compensate for the dipole–dipole interaction between the image slabs.

Con ﬂ icts of interest

The authors declare that there are no competing financial interests.

Acknowledgements

MHW and JML are supported by the National Natural Science Foundation of China (No. 21573084, 51721001 and 51431006) and the National Key Research Programme of China (Grant No. 2016YFA0300101). We wish to thank Prof. Ju Li (MIT) for helpful discussions, and the Shanghai Supercomputing Center for providing computational resources.

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