Photoelectrochemical and theoretical investigations of spinel type ferrites (MxFe3−xO4) for water splitting: a mini-review

Abstract. Solar-assisted water splitting using photoelectrochemical cells (PECs) is one of the promising pathways for the production of hydrogen for renewable energy storage. The nature of the semiconductor material is the primary factor that controls the overall energy conversion efficiency. Finding semiconductor materials with appropriate semiconducting properties (stability, efficient charge separation and transport, abundant, visible light absorption) is still a challenge for developing materials for solar water splitting. Owing to the suitable bandgap for visible light harvesting and the abundance of iron-based oxide semiconductors, they are promising candidates for PECs and have received much research attention. Spinel ferrites are subclasses of iron oxides derived from the classical magnetite (FeIIFe2IIIO4) in which the FeII is replaced by one (some cases two) additional divalent metals. They are generally denoted as MxFe3−xO4 (M=Ca, Mg, Zn, Co, Ni, Mn, and so on) and mostly crystallize in spinel or inverse spinel structures. In this mini review, we present the current state of research in spinel ferrites as photoelectrode materials for PECs application. Strategies to improve energy conversion efficiency (nanostructuring, surface modification, and heterostructuring) will be presented. Furthermore, theoretical findings related to the electronic structure, bandgap, and magnetic properties will be presented and compared with experimental results.


Photoelectrochemical and theoretical investigations of spinel type ferrites (M x Fe 3−x O 4 ) for water splitting: a mini-review 1 Introduction
Solar energy is considered as one of the promising clean energy sources which is abundantly available (120,000 TW) 1 and can be utilized to meet the increasing energy demand of the world if it is coupled with a suitable means of capturing and conversion technology. One such avenue for *Address all correspondence to: Dereje H. Taffa, E-mail: dereje.hailu.taffa@uni-oldenburg.de This review manuscript is also part of the section on "Breakthroughs in Photonics and Energy," highlighting primarily recent advances in the last three years. energy storage is photoelectrochemical cells (PECs) for the production of hydrogen. With that, the energy is stored in the form of chemical bonds and is later available on demand. 2-10 PEC systems, in principle, are analogs to commercial electrolyzers, but the voltage required to electrolyze water comes directly from the photovoltage generated from absorbed solar photons. The photoabsorbing material (mostly semiconductors) should produce photovoltages sufficient to drive the water splitting reaction into hydrogen and oxygen, which necessitates band positions of the semiconducutor straddling the water reduction and oxidation potentials. Furthermore, the photoabsorbing material should be stable under solar irradiation, cheap and abundant, and should possess enough catalytic activity and selectivity. Thus, finding suitable semiconductors which satisfy these criteria poses a primary challenge for this technology to be used as an economical viable route for renewable energy. Numerous inorganic compounds from a variety of material classes have been studied in regard to their suitability as electrode materials for PEC application. 2,8,10 Metal oxides are one of the promising materials for PEC water splitting. The vast amount of research on metal oxide semiconductors for PEC is driven by (1) the cost reduction arising from the abundance of metal oxides, (2) stability under PEC operating conditions, and (3) the facile synthetic procedures which do not require vacuum facilities. Spinel ferrites, with the general empirical formula, M x Fe 3−x O 4 , are widely investigated as magnetic materials and used as spin filters in spintronics. 11,12 They also find wide applications in the area of electrochemical energy storage (batteries and electrochemical capacitors) and photocatalysis. [13][14][15][16] Spinel ferrites exhibit attractive photoelectrochemical activities originating from the (1) narrow optical bandgap (<2.2 eV) for efficiently harvesting light of the visible solar spectrum and (2) multiple oxidation states stabilized by the spinel structure with individual transition metals of known catalytic properties. Furthermore, as the constitute transition metals are abundant and are of low cost, they are promising candidates for PEC scaleup applications.
In the following sections of this mini-review, we cover a brief introduction of PEC to provide an overview of the working principles and the reactions involved. Then the structural properties and some fundamental aspects of spinel ferrite materials (M x Fe 3−x O 4 ) will be presented. Recent advances in the photoelectrochemical application of spinel ferrite for solar-assisted electroreduction or oxidation of water follow. Finally, theoretical investigations focusing on the magnetic, electronic, and optical properties of spinel ferrites will be summarized.

Basic Working Principle of Photoelectrochemical Cells
Photoelectrochemical water splitting into hydrogen and oxygen is thermodynamically an up-hill process with the free-energy barrier of G ¼ þ237 kJ∕mole or E 0 ¼ 1.23 eV under standard conditions. The photoelectrolysis of water consists of five main steps, as depicted in Fig. 1: (1) absorption of photons with energy greater than the bandgap of the semiconductor, (2) photogeneration of electron-hole pairs, (3) band bending at the semiconductor-electrolyte interface leading to separation of charge carriers, (4) diffusion of charge carriers toward the semiconductor-electrolyte interface, and (5) redox reaction involving charge carriers and solution species (oxidation of water to O 2 and reduction of water to H 2 ). Additionally, the protons are transported across the electrolyte through proton permeable membranes and the electrons travel to the external circuit to complete the process. The overall solar splitting of water involves two half reactions taking place at the photoanode and photocathode simultaneously. For a PEC system comprising an n-type photoanode and p-type photocathode material, the two half reactions in alkaline media (pH ¼ 14) can be expressed as follows: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1 1 6 ; 1 7 1 Reduction half recation∶2H 2 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 1 1 6 ; 1 3 9 Oxidation half recation∶2HO − → H 2 O þ 1∕2 þ O 2 þ þ2e − E o oxd ¼ 0.41 versus NHE; (2) E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 1 1 6 ; 1 1 3 Over all reaction∶H 2 Three types of PEC configuration are demonstrated: 9 (1) "photoanode coupled with metal electrode," (2) "photocathode coupled with metal electrode," and (3) "photoanode coupled with photocathode" [ Fig. 1(a)]. The latter configuration allows the use of only solar photons for the overall splitting of water without using precious metal electrodes (typically, Pt for H 2 evolution and Ru and Ir oxides for O 2 evolution are used) and can operate without external bias. 5,17 It can be arranged in stack or side-by-side layouts [Figs. 1(b) and 1(c)]. In a stack, the electrode with the smaller bandgap would be placed behind the electrode with the larger bandgap so that the high energy photons would be absorbed first and the lower energy photons transmitted to the back electrode. Using a combination of the two semiconductors with bandgaps of 1.84 eV for the top and 1.23 eV for the bottom electrode, a theoretical solar-to-hydrogen (STH) efficiency of 23% is predicted. 17 The side-by-side configuration is preferable when the two photoelectrodes have similar bandgaps (but different band alignments each optimized for water oxidation or reduction reactions), allowing each to have access to full solar illumination. In this case, the highest STH efficiency is reduced to 16% when the bandgap for the two semiconductors is 1.59 eV. Additionally, the bandgaps have to be close to each other to absorb the same number of solar photons in order to match the photocurrents for hydrogen evolution reaction (HER) and oxygen evolution reaction (OER). 18 Furthermore, this particular configuration allows the use of smaller bandgap materials which otherwise cannot be used for stacked configuration and can drive the two half reactions with a smaller photovoltage than that required for a single photoabsorber material. 17 Note that in both approaches, the STH efficiency prediction takes into account the major potential losses associated with (1) free-energy loss (the difference between the acquired photovoltage and the bandgap) ranging from 0.5 to 0.6 V for highly crystalline semiconductors but expected to be higher for oxide based semiconductors, (2) kinetic overpotentials for the HER and OER (highly dependent on the choice of the catalyst, e.g., 0.05 V for Pt and 0.4 V for RuO 2 ), 19 and (3) other potential losses including resistive and charge transport.  1 Schematic representations of (a) the band diagram of PEC in which both the photoanode and the photocathode have the required ideal band positions for spontaneous water splitting. The total photovoltage generated is large enough to split water and to overcome the electrochemical overpotentials η ox and η red for the oxidation and reduction of water, respectively. Note that the energy scale is V versus NHE at pH ¼ 14. The two types of PEC configurations: (b) dual stack and (c) dual side-by-side.
Notably, the required bandgap is well above the thermodynamic potential of 1.23 eV and should be sufficient to split water and overcome the electrochemical overpotentials (Fig. 3). However, most real systems have higher potential losses (entropy, reflection) even under the assumption of ideal band alignments, and the minimal bandgap required to split water can be as high as 2.0 to 2.3 eV. 20,21 Several excellent reviews appeared recently on topics related to solar water splitting with comprehensive coverage on the general principles of PEC and cell design and configurations, and readers are referred to these reviews for in depth discussions of the topic. 5 They are best known as magnetic materials and photocatalysts, with the most common photocatalytic application being the degradation of pollutants. 12,24 The structure of spinel ferrites is  derived from the mineral spinel, MgAl 2 O 4 , by replacing the trivalent Al atom with Fe 3þ and Mg atom by other divalent metal ions.
In the spinel ferrites, the oxide anions are arranged in a cubic close-packed lattice and the cations M and Fe occupy two different crystallographic sites, namely, the tetrahedral (A) and octahedral (B) sites. 25 The cubic unit cell consists of 56 atoms, 32 oxygen anions, and 24 cations, 8 of them occupying tetrahedral sites and the other 16 being located at the octahedral sites. Although the charges of M and Fe in the prototypical spinel structure (x ¼ 1) are þ2 and þ3, respectively, other combinations are also possible. The type and the distribution of the divalent metal cations govern the final ferrite structure and dictate the chemistry of ferrites. The main factors governing the preference of the individual ions for the two crystallographic sites are the ionic radii and coordination chemistry of the ions. For example, Zn 2þ and Cd 2þ preferentially occupy the tetrahedral sites, whereas Ni 2þ and Cr 3þ have strong preference for octahedral sites. When the tetrahedral sites are occupied by divalent metal ion M 2þ and the octahedral sites by Fe 3þ , the resulting ferrites are called normal spinels (e.g., ZnFe 2 O 4 ) [ Fig. 2(a)]. If the Fe 3þ cations fully occupy the tetrahedral sites and octahedral sites are occupied evenly by M 2þ and Fe 3þ , this leads to an inverse spinel [ Fig. 2 [26][27][28] Other ferrites, such as CuFe 2 O 4 , form crystalline solids with cubic or tetragonal unit cells depending on the synthetic conditions. 29 Ferrites are regarded to be chemically and thermally stable in aqueous systems. 15 Considering the Pourbiax diagrams, most ferrites are stable in the alkaline or near neutral media in which most PEC investigations are carried out, however, they suffer from corrosion in acidic media. 30,31 Most of them are semiconductors with bandgap energies allowing the excitation by visible light and possess energetic positions of the conduction and the valence band suitable for either reduction of protons and/or oxidation of water (Fig. 3). The theoretical and experimental bandgap energies E g are presented in Table 1, and the energetic positions of the valence band E VB and the conduction band E CB of some simple ferrites are shown in

Photoelectrochemical Application of Spinel Ferrites
Owing to the varied chemical composition, multiple valency states and choice of metal cation ferrites have attractive photoelectrochemical and catalytic activities. The improved electrical conductivity compared to the corresponding single component metal oxide (iron oxides) is mainly attributed to the presence of different metal cations which facilitate the electron transport process and/or support rich redox chemistry and also has significant importance in designing efficient photoelectrodes for PECs. 49 The early works on the fundamental (photo) electrochemical investigations of ferrite electrodes date back to the late 1970s and early 1980s. Kung et al. 50 reported one of the first ferrites employed for PEC, CdFe 2 O 4 , and in the following the years, other types of ferrites were investigated including Li 0. 5 41 Most of the early works focused on the basic properties of PECs, such as the determination of the flat band potentials and the energetic positions of the valance and conduction bands, however, the reported photocurrents and efficiencies were very low. Some of the fundamental semiconducting properties of these ferrites are summarized in Fig. 3 and the PEC performances are presented in Table 1.

p-Type Spinel Ferrites
As with many other materials investigated for photoelectrochemical reduction of water, spinel ferrites are also studied as photocathodes for HER. In order to reduce protons to H 2 , the conduction band edge of the photocathode must be more negative than the hydrogen redox potential. Considering the band diagrams in Fig. 3 4 40 have been studied in PECs. Furthermore, the mechanism of HER is pH dependent; in acidic media, the reaction mainly involves proton reduction while the reduction of water to hydroxide ions is the primary route in alkaline solutions. Hence, PEC studies involving spinel ferrites are preferably conducted in neutral or basic solutions, as most spinel ferrites are not stable in acidic media.
One of the most investigated p-type ferrite is CaFe 2 O 4 . Matsumoto et al. 55 reported a p-type CaFe 2 O 4 for the photoelectrochemical reduction of water. The CaFe 2 O 4 electrodes are prepared as pressed pellets and sintered at 1200°C followed by oxidation under O 2 at 1000°C. The CaFe 2 O 4 photocathode exhibits p-type behavior from Mott-Schottky analysis. However, the cathodic photocurrent for HER is negligibly low and when the electrode is coupled with an n-type Zn 1.2 Fe 1.8 O 4 , photoelectrolysis of water without external bias results in an STH conversion efficiency of <0.01%. Matsumoto 49 summarized his results on ferrites and other oxide semiconductors, compiled data on the bandgap, and formulated an empirical relation between the bandgap, the conduction band edge, and the valence band edge.
Cao et al. 36 have investigated the visible light-induced water splitting reaction employing a p-CaFe 2 O 4 photocathode. The photocathodes have been fabricated by depositing CaFe 2 O 4 thin films on fluorine-doped tin oxide (FTO) coated glass employing a pulsed laser deposition method. A hydrogen evolution rate of ∼4.8 μmol m −2 h −1 was observed under visible light irradiation (300 W Xe) using a Pt metal electrode without applying any additional bias. In a three-electrode configuration, a cathodic photocurrent was observed at values more negative than þ0.64 V. A photocurrent density of −0.117 mA cm −2 at −0.06 V was reported as being significantly larger than the values reported by Matsumoto et al. 55,56 for metal-loaded CaFe 2 O 4 photoelectrodes, probably due to shorter electron transfer distances in the thinner films and higher electric conductivity. 36 Furthermore  58 The quantum efficiency of a pristine p-CaFe 2 O 4 electrode was found to be relatively low, which is presumably due to the poor mobility of the photogenerated charge carriers. 56 Therefore, efforts have been made to improve the conductivity of CaFe 2 O 4 electrodes by doping the material. Doping with Na and Mg was performed by Matsumoto et al. yielding oxides of the type Ca 1−x Na x Fe 2−y Mg y O 4 . The authors suggested that as the ionic radii of Na þ and Mg 2þ are similar to Ca 2þ and Fe 3þ , respectively, Na þ will substitute for Ca 2þ and Mg 2þ will replace Fe 3þ . This will create acceptor levels in the bandgap leading to higher electronic conductivity; however, the reported photocurrents are still very small. The authors suggested that the formation of oxygen vacancies at higher amounts of Na (x > 0.2) lead to the decrease of conductivity, but the formation of oxygen vacancies is not supported experimentally. In an attempt to improve the low quantum efficiency for the light-induced water splitting reaction, Sekizawa et al. have prepared various metal-doped CaFe 2 O 4 electrodes by radio frequency magnetron cosputtering onto glass substrates coated with antimony-doped tin oxide (ATO) followed by postannealing at a low temperature. However, the doping metals were aggregated in the films after annealing as revealed by scanning transmission electron microscopy. Doping of CaFe 2 O 4 with Au and Ag resulted in an enhancement of the photocurrent without affecting the p-type conductivity. Doping with Ag resulted in an improvement of the carrier mobility together with a red-shift of the photoabsorption. Ag-doped CaFe 2 O 4 showed a 23-fold higher photocurrent than undoped CaFe 2 O 4 . 59 It is worth mentioning that the enhanced photoresponse may originate from the dopant metals (Ag, Au, Cu/CuO) as they are known as HER cocatalysts.
In a series of papers, Ida et al. 37,38,57 reported the light-induced water splitting employing p-CaFe 2 O 4 -based cathode coupled with different n-type semiconductors. In their first report, a suspension of presynthesized p-CaFe 2 O 4 powder was coated on a Pt substrate and annealed at 1100°C to 1200°C. 38 The sample annealed at 1200°C resulted in a flat, well-adhered crystalline film of p-CaFe 2 O 4 oriented in (320) and (420) planes. Under illumination (500 W Xe lamp), the PEC consisting of p-CaFe 2 O 4 and an n-TiO 2 photoanode generated a photovoltage of 0.97 V and short-circuit photocurrent density of 0.22 mA cm −2 , respectively. The obtained photovoltage is close to the difference between the two onset potentials of p-CaFe 2 O 4 (0.31 V) and n-TiO 2 (−0.75 V). The authors demonstrated generation of hydrogen under irradiation with visible light without applying a bias, however, the stoichiometric ratio H 2 ∕O 2 was an order of magnitude different than the expected value of 2. The slow rate of O 2 generation is accounted for from the weak absorption of O 2 on TiO 2 and slow water oxidation kinetics (indicating the need for an OER catalyst). The PEC configuration, the band diagram, and the amounts of gases generated as a function of time in this study are presented in Fig. 5.
Later, the same authors reported the presence of the Ca 2 Fe 2 O 5 impurity phase in the p-CaFe 2 O 4 , enhancing the short circuit photocurrent density (0.55 mA cm −2 ) and slightly increasing the photovoltage (1.09 V). 37 Additionally, the O 2 formation is enhanced, decreasing the H 2 ∕O 2 ratio to 3.7, which is, however, still higher than the theoretical value of 2. n-ZnO was also tested as a photoanode together with p-CaFe 2 O 4 and a photovoltage of 0.82 V was generated. When employing this PEC for unbiased water splitting, only H 2 gas was detected. 57 The photodissolution of n-ZnO is partly responsible for the absence of O 2 gas, but there is no obvious correlation between the amount of dissolved Zn 2þ ions and the H 2 gas evolved (which is much higher than the Zn 2þ ion concentration detected).
Very few additional spinel ferrites other than p-CaFe 2 O 4 are studied as photoathodes. Yang et al. have investigated the photoelectrochemical performance of porous CoFe 2 O 4 nanosheets on FTO. The electrodes have been prepared from an aqueous solution of Co and Fe nitrate through a template-free electrochemical deposition followed by a heat treatment at 933 K. The electrodes exhibited only a small cathodic photocurrent of ∼0.3 μA cm −2 in 0.1 M aqueous Na 2 S solution at zero bias voltage under visible light illumination (λ ≥ 390 nm, 30 mW cm −2 ). 39 The photoelectrochemical properties of p-NiFe 2 O 4 pellets prepared by sintering sol-gel synthesized particles at 850°C were investigated by Rekhila et al. The open-circuit voltage of and short-circuit current of a two electrode configuration consisting of Pt and p-NiFe 2 O 4 in a 0.5 M KCl cell were reported to be 0.43 V and 0.71 mA cm −2 under irradiation with visible light (50 mW cm −2 ). A photon-to-electron conversion efficiency of 0.28 was calculated. However, corrosion of the semiconductor electrode was observed under illumination as well as in the dark. 40 Considering the bandgaps presented in Fig. 3, less attention is given for other p-type ferrites (CoFe 2 O 4 , NiFe 2 O 4 , CuFe 2 O 4 ) and more tests and investigations are still required. Sometimes, even the fundamental optical properties are controversial. For example, most report the optical indirect bandgap of CoFe 2 O 4 as 1.3 to 1.4 eV, 62,63 but Xiong et al. reported a bandgap much lower than these values (0.8 eV). 64 In the authors' opinion, one of the main reasons is that these p-type ferrites are known to exist in a completely or partially inverted spinel structure. 24,63 Such a degree of inversion should be well controlled and require a rational design of synthetic strategy to accurately determine the optical properties and to enhance the PEC performance. In addition, they are prone to photocorrosion particularly in acidic media, which can be alleviated by applying suitable protective layers (TiO 2 , Al 2 O 3 ).

n-Type Spinel Ferrites
The photoelectrochemical oxidation of water to O 2 requires an n-type semiconductor with the valence band located more positive than the H 2 O∕O 2 oxidation potential (1.23 V versus NHE). In contact with an aqueous electrolyte, such a semiconductor results in an upward band bending which drives the holes toward the surface leading to the oxidation of water to O 2 . Additionally, good electrical properties and stability under water oxidation conditions are needed. Among the spinel ferrites, n-ZnFe 2 O 4 is the promising candidate and is the only n-type photoanode material reported for PEC application.
Systematic investigation of the photoelectrochemical activity ZnFe 2 O 4 was reported by Tahir and Wijayantha 33 and Tahir et al. 61 The electrodes were prepared by aerosol-assisted chemical vapor deposition (AACVD) of alcoholic solutions of a bimetallic precursor (½Fe 2 ðacacÞ 4 ðdmaeH 2 Þ 2 ½ZnCl 4 ) on FTO. The thickness, morphology, and nanostructure of the electrode were controlled by altering the solvent for dissolution of the bimetallic precursor and physical deposition parameters. 33,61 The photocurrents were found to be dependent on the solvent, as well as on the deposition temperature and the deposition time. A maximum photocurrent density of 0.35 mA cm −2 at 1.23 V versus RHE was obtained with a ZnFe 2 O 4 electrode synthesized using a 0.1 M solution of the bimetallic precursor in ethanol, the optimum deposition temperature of 450°C, and a deposition time of 35 min. This electrode showed an incidentphoton-to-electron conversion efficiency of 13.5% at 350 nm and an applied potential of 1.23 V versus RHE. 33 In the AACVD process, the aerosol droplet size (controlled by the solvent) and the enthalpy of combustion determine the decomposition pathway (homogeneous versus heterogeneous), thus varying the methanol/ethanol ratio of the solvent resulted in a change in the texture of the ZnFe 2 O 4 electrode. A compact ZnFe 2 O 4 film composed of hexagonal like particles was obtained in pure methanol, but the structure transformed in to porous ZnFe 2 O 4 nanorod films when ethanol was used as the solvent. Intermediate structures were obtained by varying the methanol/ethanol ratio. The textured electrodes exhibited a significantly higher photocurrent under AM1.5 illumination compared to their compact counterparts. The authors attributed this behavior to the improved collection of the photogenerated minority carriers at the ZnFe 2 O 4 ∕electrolyte interface as the average feature size gradually decreased from ∼500 nm (methanol) to ∼100 nm (ethanol). 61 In general, ferrites as photoelectrodes need high temperatures to crystallize (>1000°C). This limits the choice of support materials and poses a critical challenge to maintain the desired electrode material properties such as surface area and porosity. Recently, Kim et al. introduced a hybrid microwave annealing (HMA) postsynthetic heat treatment with graphite powder as the susceptor being compatible to most transparent conducting glasses. They treated solution processed β-FeOOH nanorods with a Zn nitrate solution and obtained ZnFe 2 O 4 nanorods after thermal treatment at 550°C for 3 h. Some unwanted ZnO on the nanorods was removed in NaOH. Subsequently, the ZnFe 2 O 4 nanorods were subjected to a second heating step at 800°C (20 min) or to HMA (5 min) to increase the crystallinity. The HMA-treated ZnFe 2 O 4 nanorods exhibited at 1.23 V versus RHE (1 M NaOH) and AM 1.5G illumination a photocurrent of 0.240 mA cm −2 , which was a 10-to 15-fold increase in comparison to conventional thermally treated electrodes and was stable for at least 3 h. The authors claimed that stoichiometric amounts of H 2 and O 2 can be measured with Faradaic efficiencies (= actual gas evolution rate/rate expected from current) of 90% to 100%. The improved performance after the HMA treatment was attributed to better crystallinity and reduced surface defects as evinced by electrochemical impedance spectroscopy. 65 Extending their work, the same authors recently reported the influence of the composition of the annealing atmosphere on the photoelectrochemical behavior of ZnFe 2 O 4 (Fig. 6). 34 in vacuum, the oxygen removal is represented by Eq. (5) and the concentration of the oxygen vacancies is given in Eq. (6): E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 5 ; 1 1 6 ; 1 9 7 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 1 1 6 ; 1 5 9 where n represents the electron density and ½O 2 is the partial pressure of the oxygen. In general, for most iron based n-type semiconductor oxide materials, the diffusion length of the minority carrier is very short leading to an inherently high charge recombination rate, which limits the efficiency of the PECs. Several strategies to address this issue were developed including nanostructuring 33,61,65 and doping. 59 Another attractive nanostructuring strategy is to use a structured transparent conductive oxide current collector to capture and tunnel the Recently, Hufnagel et al. 35 prepared mesoporous ZnFe 2 O 4 thin films on a macroporous ATO scaffold using atomic layer deposition (ALD). The photoresponse of the electrodes was tested in three electrode PECs and the electrodes exhibited 4-to 5-fold higher photocurrent density (0.26 mA cm −2 at 1.23 versus RHE) compared to nonstructured ZnFe 2 O 4 films prepared in a similar way (0.05 mA cm −2 at 1.23 versus RHE). Additionally, the authors show that such electrodes have more negative photocurrent onsets (0.9 V versus RHE) compared to reported values. 33 Spinel ferrites were recently investigated for construction of heterojunction electrodes to improve the photoelectrochemical performance of other widely used semiconductors. In this regard, heterojunction electrodes such as   0.0125, respectively. However, no data were given for the formation of molecular oxygen. The results of electrochemical impedance spectroscopy evinced a significantly lower interfacial charge transfer resistance of the ZnFe 2 O 4 ∕Fe 2 O 3 composite electrode than the ZnFe 2 O 4 electrode. 67 ZnFe 2 O 4 ∕Fe 2 O 3 nanorod composite photoanodes have also been prepared using hydrothermally grown FeOOH nanorods and subsequent treatment with different concentrations of Zn precursor. After calcinations at 750°C, a ZnFe 2 O 4 ∕Fe 2 O 3 composite electrode was obtained. 68 The photocurrent density for the composite electrode was 0.44 mA cm −2 at ∼1.2 V versus RHE, which was almost twice as high as that for a With this, the number of surface states that serve as electron-hole recombination centers is probably reduced. But it was also observed that both the formation of a ZnFe 2 O 4 layer and the incorporation of Al 3þ into the surface made the surface less catalytic for the OER. However, when Co 2þ was introduced into the surface of the ZnFe 2 O 4 ∕Fe 2 O 3 composite electrodes as oxygen evolution catalysts, the onset of the photocurrent was shifted to more negative voltage and the overall photocurrent was improved. 66 Furthermore, ZnFe 2 O 4 ∕TiO 2 heterostructures are also prepared using a combination of solution-phase materials growth techniques and ALD. 73 The TiO 2 nanowires were hydrothermally grown on FTO substrate and later infiltrated by Zn precursor using ALD. The ZnFe 2 O 4 ∕TiO 2 composite electrodes show an enhanced visible light photoresponse compared to bare TiO 2 photoelectrodes. The authors suggest that the extended visible light absorption by the ZnFe 2 O 4 , the nanowire morphology of the TiO 2 , and favorable band edge positions are the main reasons for the increased photoresponse. A related photoanode has been prepared by anisotropic growth of a β-FeOOH film on FTO from an aqueous solution containing Fe and Ca ions followed by two-step thermal annealing at 550°C and 800°C. The authors suggested that this procedure induces the formation of a p-CaFe 2 O 4 ∕n-Fe 2 O 3 heterojunction photoanode. The presence of Ca in the Fe 2 O 3 film, leading to the formation of CaFe 2 O 4 , has been proven by XPS measurements. Under illumination (AM 1.5G, 100 mW cm −2 ), the heterojunction photoanode exhibits a photocurrent density of 0.53 mA cm −2 at 1.23 V versus RHE, which is a 100% higher photocurrent response than that obtained using a bare α-Fe 2 O 3 electrode. Based on electrochemical impedance spectroscopy, the photocurrent enhancement has again been attributed to an enhanced charge carrier separation and a reduced resistance of the interfacial charge transfer between the electrolyte and the electrode. 69 Kim et al. 71,74 reported the preparation and characterization of p-CaFe 2 O 4 modified TaON and BiVO 4 p-n heterojunction photoanodes. Both n-type semiconductors are known to be suitable anode materials for solar-driven water splitting in PECs. The valence band of p-CaFe 2 O 4 is more positive than the water oxidation potential, and both semiconductors TaON and BiVO 4 form staggered relative band positions with the ferrite as required for an effective heterojunction photoanode. In both cases, p-CaFe 2 O 4 , which has been synthesized by a conventional solid state reaction, was deposited on top of the n-semiconductor/FTO electrode by electrophoresis. The pristine TaON electrode showed an anodic photocurrent density of 0.230 mA cm −2 at 1.23 V versus RHE (0.5 M NaOH, λ > 420 nm). The CaFe 2 O 4 layer on the surface of a TaON electrode resulted in a significant increase of the photocurrent density (1.26 mA cm −2 ). The observed photocurrent was found to be a result of overall water splitting yielding H 2 and O 2 in a ratio of 1.5, accompanied, however, by a deterioration of the TaON. Impedance spectroscopic analysis indicated that the formation of the heterojunction increased the photocurrent density by reducing the resistance of the charge carrier transport and, consequently, enhancing the electron-hole separation. 71 Anodic photocurrents have likewise been observed for both BiVO 4 and CaFe 2 O 4 ∕BiVO 4 electrodes (0.5 M Na 2 SO 4 , AM 1.5G 100 mW cm −2 ); the bare BiVO 4 electrode showed a photocurrent density of 0.58 mA cm −2 at 1.23 V versus RHE V while the CaFe 2 O 4 ∕BiVO 4 heterojunction photoanode exhibited 0.96 mA cm −2 , comprising an increase of 65% over that measured at the BiVO 4 electrode. The formation of the heterojunction was found to reduce the recombination of the photogenerated charge carriers on the electrode surface with little effect on bulk recombination as evinced by an investigation of the interfacial transfer of charge carriers using hydrogen peroxide as an electron donor. 74 In the above demonstrated heterojunction electrodes, efficient charge separation is the key factor for improved photoelectrochemical activity. This is demonstrated in the energy diagrams of the composite electrodes in Fig. 8. The ferrites (CaFe 2 O 4 and ZnFe 2 O 4 ) have valence band energies located between the water oxidation potential and that of the valence band of the second semiconductor. Thus, holes generated at the more positive valence band are extracted to the ferrite valence band reducing bulk recombination and allowing successful injection of the holes to the electrolyte. On the other hand, as the conduction band of the ferrites is situated at a more negative potential, the photogenerated electrons will be easily transferred to the conduction band of the second semiconductor for collection at the back contact.
Furthermore, the modification of the heterojunction photoanodes by depositing OER cocatalysts results in higher photocurrent densities by decreasing the onset potential and facilitating the interfacial charge transfer. In this regard, "cobalt phosphate" (CoPi) is used widely as an OER catalyst. [75][76][77][78] For example, in the CaFe 2 O 4 ∕TaON 71 heterojunction electrode system, after deposition of CoPi and with an applied bias of 1.23 V versus RHE, H 2 and O 2 were generated with nearly of stoichiometric ratio of 2.1 (123 μmol H 2 and 59 μmol O 2 were produced within 3 h of illumination with λ ≥ 400 nm). The STH efficiency was 0.053% at 1.0 V versus RHE, but reached 0.55% when a PV device is coupled in tandem configuration (assuming the applied voltage is zero). However, the initial current decreased within 3 h to about 50%. The beneficial role of the CoPi cocatalyst was revealed by performing the gas evolution experiment with a CaFe 2 O 4 ∕TaON photoanode in the absence of CoPi. Under these experimental conditions, no constant photocurrent was obtained, the faradaic efficiencies decreased (50% to 70%), and the H 2 ∕O 2 ratio became less than stoichiometric (1.51) due to the self-oxidation of TaON. 71 Similar results have been obtained with CaFe 2 O 4 ∕BiVO 4 composite photoanodes. In this case, the CoPi modified CaFe 2 O 4 ∕BiVO 4 electrode exhibited a lower photocurrent density when compared to the CaFe 2 O 4 ∕BiVO 4 heterojunction electrode, but an improved stability of the current density was observed indicating that the presence of the OER cocatalyst is beneficial for the stabilization of the CaFe 2 O 4 ∕BiVO 4 heterojunction. The evolution of H 2 and O 2 during the photoelectrochemical water splitting reaction was measured in a three electrode set-up in phosphate buffer (pH ¼ 7) under applied bias. The total amounts of H 2 and O 2 evolved within 2 h of illumination with visible light (λ ≥ 400 nm) were 297 and 140 μmol, respectively. The resulting H 2 ∕O 2 ratio of 2.1 confirmed that the generation of the photocurrent was mainly due to the water splitting reaction. The Faradic efficiency during this reaction was reported to be about 78% to 88%. The photocurrent density was initially ∼4 mA cm −2 , but dropped rapidly during the first 30 min of illumination and decreased slowly afterward. 74 In general, the above few examples of spinel ferrite-based PECs demonstrated the attractive photoelectrochemical properties of these materials. The measured photocurrents of PECs with ferrite photoelectrodes are still low, but different strategies proved that higher photocurrents can be achieved. The main contributors for low photoelectrochemical performances are identified as (1) slow interfacial charge carrier transfer, (2) inherently high charge carrier recombination rates, and (3) loss of interfacial area due to the high thermal treatment. Strategies to address these bottle necks, including (1) nanostructuring, (2) forming heterojunction structures, (3) cocatalyst coating, and (4) control of the defect chemistry are shown to enhance the photoelectrochemical performance.
It is worth mentioning that the reported experimental band positions of some of the spinel ferrites related to HER and OER potentials are still arguable. Based on the energetic band diagrams of ferrites presented in Fig. 3, ZnFe 2 O 4 and MgFe 2 O 4 are, in principle, capable of producing hydrogen. However, to the best of the authors' knowledge, there is no literature report proving this. For example, the reported flatband potentials of ZnFe 2 O 4 (0.6 to 0.8 V versus RHE) 33,35 suggest the conduction band lies slightly below the HER potential. We also found that the conduction band edge is slightly positive (∼100 mV) to that of the proton reduction potential, but we are still in the process of verifying this. Thus, more experimental investigations are required to refine the existing photoelectrochemical data. Furthermore, MgFe 2 O 4 is also interesting for OER, but there are no reports except the fundamental investigation reported by Benco and Koffyberg. 52 However, there are a few reports on photocatalytic H 2 production using MgFe 2 O 4 which to some extent show the potential of this material. 53,72

Theoretical Investigations
Considering the above-mentioned PEC applications of spinel ferrites, several questions concerning the water splitting process arise that cannot be easily answered. Theoretical investigations allow an insight to material on an atomistic level that the experiment cannot provide in general. For example, theory allows one to study water and hydroxyl adsorption on different sites of differently terminated ferrite surfaces, and its effect on the degree of inversion, the magnetic structure, the bandgaps, and band positions. It is well known that the accuracy of theoretical predictions of electronic properties strongly depends on the choice of the method. During the last years, several quantum chemical protocols have been developed which go beyond the traditional independent-particle model at density-functional theory (DFT) level, the most refined being self-consistently vertex corrected GW. 79 A considerable number of theoretical investigations were devoted to the electronic, magnetic, structural, and energetic properties of ferrites. With a few exceptions, the quantum-chemical studies were performed at DFT level, in most cases employing the local (spin) density approximation (LSDA) or the generalized-gradient approximation (GGA). As is well known, the electronic properties of transition metal oxides are not accurately described within the LSDA or GGA, thus hybrid approaches combining DFT with unrestricted Hartree-Fock theory (HFT) are preferable. Global DFT-HFT hybrids have been demonstrated to provide accurate lattice constants, atomization energies, and bandgaps for a wide range of compounds 80 but are computationally much more demanding than GGA methods. Therefore, in most studies, a semiempirical on-site correction, the so-called LSDA+U or GGA+U approach, 81 is applied. In this method, the effective parameter U replaces one-center exchange and Coulomb integrals from unrestricted HFT. In principle, the value of U for each transition metal can be derived from exact theory, but in practical calculations, it is usually treated as an empirical parameter to adjust certain properties to experimental reference data.
Absolute band positions thus, the work functions and fundamental bandgaps can only be obtained from two-dimensional slab model calculations of surfaces. However, recently, very accurate results for both properties were obtained for binary systems (e.g., ZnO, CdO, GaAs, GaP, InP) from self-consistent GW calculations. 79 So far, most theoretical investigations of ferrite surfaces, however, have focused on the adsorption of water and other small adsorbates. The following sections provide a survey of recent theoretical studies on bulk and surface properties of ferrites.

Electronic Structure of the Bulk
The effect of charge ordering in the octahedral sites of Fe 3 O 4 and CoFe 2 O 4 on their electronic structure was investigated using DFT+U. 82 A precise description of charge ordering was found to be crucial in determining the bandgaps of the compounds. GGA+U calculations of the electronic structure of antiferromagnetic CaFe 2 O 4 yield an indirect bandgap of ∼1.9 eV. 83 The ionicity of Fe 3 O 4 has been determined using DFT calculations. 84 Furthermore, a new developed quantum mechanical estimation method for the ionicity of spinel ferrites has been proposed and tested. On the basis of this, the ionicities of the spinel ferrites MFe 2 O 4 (M: Co, Cu, Fe, Mn, Ni) were calculated. The electronic structure of NiFe 2 O 4 has been investigated using LSDA+U and hybrid-DFT in 2012. 85 According to the theoretical results, the system is an indirect gap material in one of the minority channels and slightly larger direct bandgaps can be found both in the minority and majority channels. The electronic structure of MFe 2 O 4 (M: Ca, Mg, Zn) was investigated in a combined experimental and theoretical study. 86 The DFT calculations reveal that the M-ion controllably affects the density of states of the Fe d-orbitals near the Fermi level. The electronic structure of ZnFe 2 O 4 was studied using GGA+U. 87 Taking the effect of spin arrangement on symmetry into account, ZnFe 2 O 4 was classified as a semiconductor. The impact of cation distribution in CuFe 2 O 4 on electronic structure and magnetic properties has been investigated by Feng et al. 88 The lattice structure was optimized on the GGA level and the electronic structure was calculated with GGA+U. The calculated density of states shows that the distribution of Cu ions significantly impacts the electronic structure. Multilayer bispinel composites, in which one member is Fe 3 O 4 and the other is MFe 2 O 4 (M: Co, Mg, Mn, Ni), were modeled using GGA+U by Wells et al. 89 It was found that substitution of the transition metal sites in the supercell produces cation charge transfers and magnetization modulation. Band shifts and gap modulation were comparable to the chemically similar bulk compounds. Two different distributions for the octahedralsite cations in ZnFe 2 O 4 and CdFe 2 O 4 have been investigated using LDA and GGA, as well as LDA+U and GGA+U. 90 It was shown that a different octahedral-site distribution impacts the density of states as well as the bandgaps in both the normal and inverse spinel configurations of these compounds. Magnetic properties and the electronic structure of NiFe 2 O 4 have been studied using hybrid-DFT. 91 The calculated density of states suggests that NiFe 2 O 4 is an insulator. The electronic structure of normal and inverse spinel ferrites MFe 2 O 4 (M: Co, Fe, Mn, Ni) was investigated by self-interaction corrected LSDA. 92 For both structures, all studied compounds were found to be insulating but with smaller gaps in the normal spinel structure. The calculated spin magnetic moments and exchange splitting of the conduction bands were dramatically increased when moving from the inverse spinel structure to the normal spinel. A first principle investigation of the electronic structure of MFe 2 O 4 (M: Co, Fe, Mn, Ni) compares the performance of LSDA and LSDA+U. 93 For the LSDA+U approach, the charge ordering is stable in contrast to a metallic state given by the LSDA approach. Calculated x-ray absorption spectra as well as the x-ray magnetic circular dichroism spectra were in good agreement with the experiment. The electrical and magnetic properties of the normal and inverse spinel structures of MnFe 2 O 4 were calculated with DFT by Zuo and Vittoria. 94 The calculated bandgap suggests that MnFe 2 O 4 is a complex insulator, in contrast to earlier LSDA and GGA calculations which suggest a half-metallic behavior. MnFe 2 O 4 has been investigated theoretically at DFT level. 95 The calculated band structure shows a low carrier density half-metal in the fully ordered state, in contrast to experimental characterizations. The computations yield a strong coupling of the energy bands at the Fermi energy to the internal structural parameter u as well as strong effects on the electronic structure upon partial interchange of Fe and Mn atoms.
Calculations of the K-edge x-ray absorption near-edge structure (XANES) in elemental iron and MFe 2 O 4 (M: Mg, Mn, Ni, Zn) were carried out by Safontseva and Nikiforov. 96 It was shown that the Fe K-edge energy shift found experimentally occurs upon the transition from elemental iron to the spinel ferrites. This shift was demonstrated to be identically directed for ferrites with a normal and inverted spinel structure. A computational study of ferrimagnetic Zn x Ni 1−x Fe 2 O 4 compounds using the pseudofunction method was carried out in 1996. 97 Substitution of Ni with Zn enhances the localization of the 3d states of Fe on the octahedral sites, so that the O 2p-Fe 3d hybridized states can be resolved into two distinct twofold and threefold features. Normal and inverse MnFe 2 O 4 was investigated with HF level of theory in 1996. 98 From Mulliken population analysis and net spin density distributions, it was concluded that the charge states of Mn and Fe in the ground state show no evidence of charge transfer leading to Fe 2þ at A sites and Mn 3þ at B sites in the inverse spinel structure AB 2 O 4 . An early computational study of the band structure and magnetic moments of ferrites MFe 2 O 4 (M: Co, Fe, Mn, Ni, Zn) on LSDA level 99 only covered the metallic, hightemperature phase in the case of M ¼ Co, Fe, Mn, Zn. In contrast, NiFe 2 O 4 was described as an insulator. Table 3 compares experimental bandgaps of selected ferrites with calculated values gained by different theoretical protocols. It is obvious that plain DFT without any further corrections systematically underestimates the bandgap of the considered systems. The theory states that using a self-interaction corrected or a hybrid DFT approach reduces the error. Using a DFT+U framework provides results that show good agreement with the experimental data. This is easily explained by the added potential U, which is an empirical parameter that can be explicitly chosen to fit the experimental bandgap. There is no universal choice for the U parameter.

Magnetic Properties
Since the magnetic structure of ferrites (strongly) affects the calculated bandgap, 92 the magnetic properties also have to be taken into account when discussing electronic properties. The magnetic properties of MFe 2 O 4 (M: Co, Fe, Mn, Ni, Zn) were studied with DFT methods. 118 The theoretically obtained magnetizations were consistent with experimental results in the absence of an external field. GGA+U was applied to investigate the electronic structure and magnetic shows that LSDA+U and GGA+U allow for a good quantitative description of these materials. 110 The effect of epitaxial strain on the magnetocrystalline anisotropy was investigated and the results are in good agreement with experimental observations. The structure of partially inverse spinel CoFe 2 O 4 as well as its electronic and magnetic properties has been investigated by the GGA+U approach. 120 It was found that the Co and Fe ions prefer their high-spin configurations with higher spin moments at octahedral sites. Certain investigated inversion degrees show half-metallic behavior.

Structural and Thermodynamic Properties
A computational study of the inversion thermodynamics and electronic structure of (thio) spinels FeM 2 X 4 (M: Co, Cr, Mn, Ni; X: O, S) was published in 2015. 121 The analysis of the configurational free energies shows that Reactions leading to an excess of A or B, respectively, were found to be slightly exothermic in a number of spinel compounds. A set of effective chemical potentials (ECPs) that connect energies of MFe 2 O 4 (M: Co, Fe, Ni, Zn) spinels and oxides calculated at 0 K from DFT to free energies at high temperature and pressure in the presence of water was derived and tested. 109 The ECPs were used to calculate free energies of low index stoichiometric surfaces of nickel ferrite in water, predicting surface denuding at high temperatures. A computational study compares the performance of GGA-DFT and hybrid-DFT (B3LYP) for the equilibrium structure of Fe 3 O 4 . 104 The ground state calculated by GGA-DFT is metallic with Fd-3m symmetry while the hybrid level of theory yields a charge ordered semiconducting state with P2/c symmetry. Phonon frequency calculations showed that charge ordering causes symmetry breaking of force constants on symmetry lowering from the cubic unit cell to the monoclinic unit cell.

Surfaces and Adsorption
The structure, electronic properties, and energetics of the NiFe 2 O 4 ð001Þ surface and its interaction with water both in the absence and in the presence of surface oxygen vacancies have been studied using DFT+U. 122 It was shown that water adsorbs dissociatively on the surface oxygen vacancies leading to the formation of surface hydroxyls. Furthermore, it was found that at high temperature, water desorbs leaving a surface containing oxygen vacancies. The reactivity of the NiFe 2 O 4 ð111Þ surface has been studied using DFT+U. 123 The surface reactivity is significantly higher in comparison with the Fe 3 O 4 ð111Þ surfaces. Dissociation of water was found to be highly favorable on the NiFe 2 O 4 ð111Þ surfaces. The activation barrier for the dissociation of a single water molecule was dependent on the termination of the surface. The electronic properties of CuFe 2 O 4 and the adsorption behavior of an NO molecule on the CuFe 2 O 4 (100) surface were studied using DFT +U. 124 The authors suggest that the ground state of CuFe 2 O 4 bulk has an inverse spinel structure and is a magnetic semiconductor. The NO molecule prefers to adsorb on the top site of the Fe atom on the (100) surface, forming an N-Fe bond. DFT+U calculations of the adsorption behavior of Ni and Ti on the Fe 3 O 4 ð001Þ surface have been carried out by Bliem et al. 125 For both atoms, an incorporation in an octahedral Fe site of the force-relaxed Fe 3 O 4 ð001Þ surface is energetically favorable. Boron adsorption on an Fe 3 O 4 ð100Þ surface was studied by GGA calculations in 2015. 126 It was shown that B adsorption induces half-metallicity at the Fe 3 O 4 ð100Þ surface.
The adsorption of group IV atoms (C, Si, Ge, Sn) on the Fe 3 O 4 ð100Þ surface has been investigated using GGA. 127 The results show that all these atoms prefer to bind on the surface oxygen atom, which has no tetrahedral Fe neighbor. The adsorption structures and energies of a single Au atom on six different terminations of the Fe 3 O 4 ð111Þ surface were computed using GGA+U. 128 It was found that the Au-atom adsorption energy decreases with increasing stability of the surface. Furthermore, the results indicate that the Au atom is reduced and has a negative charge on the iron-terminated surfaces, whereas it is oxidized and has a positive charge on the oxygen-terminated surfaces. Van Natter et al. 129 investigated with cluster models possible active sites on the (100), (110), and (111) surfaces of Fe 3 O 4 . Adsorption energies of oxygen adatoms located on exposed cation sites were calculated on hybrid-DFT (B3LYP) level of theory. The computed energies vary proportionally to the number of oxygen atoms missing from the normal octahedral coordination of the cation adsorption sites. A theoretical investigation of bare and water terminated NiFe 2 O 4 surfaces was carried out in 2014 using GGA+U. 130 It was found that surfaces that have more metal cations exposed are more stable. The most stable surfaces are shown to be along the (111) planes. Water adsorption on the NiFe 2 O 4 surfaces was found to be an exothermic process. In 2014, a DFT investigation of the NiFe 2 O 4 ð001Þ surface reported an overpotential of 0.42 V for the OER. 131 It was concluded that Fe-doped β-NiOOH and NiFe 2 O 4 could be the phases responsible for the enhanced OER activity of NiO x when it is doped with Fe.

Conclusion
As many ferrites are composed of metals with known electrocatalytic properties for the OER, 41 the development of cheap and varied electrode materials for PECs is a reachable target without the use of precious OER catalysts like IrO 2 or RuO 2 . However, the existing photoelectrochemical performances need to be enhanced for economically viable PEC applications. Though the fundamental semiconductor properties are satisfactorily understood, the mechanism of charge transport and the water oxidation at the surface is not well known yet. The improvement of new synthesis strategies enabling the formation of high crystalline materials at relatively low temperature (e.g., hydrothermal and microwave synthesis) is crucial to obtain high surface area materials. In addition, thin under layers or over layers of TiO 2 and Al 2 O 3 (but also other metal oxides) are expected to enhance the photocurrent either through adjusting band alignments or passivating surface recombination centers as was revealed for other iron-based photoelectrodes. 132 The formation of nanostructures with well-defined morphology, shape, and orientation will enhance the photoactivity by providing a high density of surface reaction sites and by reducing charge recombination as the size of nanostructures approaches the width of the space charge layer. Another strategy which can be exploited further is the use of heterojunctions to effectively separate the photogenerated charge carries with properly matched valence and conduction band edges. Furthermore, existing computational methods adequately predict the electronic and magnetic properties of spinel ferrites. The calculated bandgaps for some of them reasonably agree with experimental values, but for others, more refinements are needed. Most importantly, the relative band positions are key properties to determine the oxidation or reduction power, thus developing computational tools to predict the band positions is essential to understand the very scattered experimentally reported band positions of spinel ferrites.