Magnetism tailored by mechanical strain engineering in PrVO$_3$ thin films

TL;DR

This study demonstrates that mechanical strain engineering in PrVO$_3$ thin films can significantly enhance their magnetic transition temperature and induce novel orbital-ordering, revealing new pathways to control properties of transition-metal oxides.

Contribution

The paper provides experimental and theoretical evidence that epitaxial strain can tailor magnetism and orbital order in PrVO$_3$ thin films, a novel approach in oxide material engineering.

Findings

Néel temperature increased by 40 K in thin films

Epitaxial compressive strain induces tetragonality

Strain promotes unique orbital-ordering of V$^{3+}$ electrons

Abstract

Transition-metal oxides with an ABO$_3$ perovskite structure exhibit strongly entangled structural and electronic degrees of freedom and thus, one expects to unveil exotic phases and properties by acting on the lattice through various external stimuli. Using the Jahn-Teller active praseodymium vanadate Pr$^{3+}$V$^{3+}$O$_3$ compound as a model system, we show that PrVO$_3$ N\'eel temperature T$_N$ can be raised by 40 K with respect to the bulk when grown as thin films. Using advanced experimental techniques, this enhancement is unambiguously ascribed to a tetragonality resulting from the epitaxial compressive strain experienced by the films. First-principles simulations not only confirm experimental results, but they also reveal that the strain promotes an unprecedented orbital-ordering of the V$^{3+}$ d electrons, strongly favouring antiferromagnetic interactions. These results show that an accurate control of structural aspects is the key for unveiling unexpected phases in oxides.

Tables

Table 1. Table 1: Summary of observed lattice parameters, experimental lattice mismatch, pseudo-cubic cell volumes, distortion (ratio of the out-of-plane to in-plane PVO lattice parameter), residual strain calculated out-of-plane i.e ϵ 110 subscript italic-ϵ 110 \epsilon_{110} , Néel temperature ( T N ) and coercivity ( H c ) of PVO films.

Substrate	In-plane lattice parameter of substrate [Å]	Lattice mismatch (%)	In-plane lattice parameter of film [Å]	Out-of-plane lattice parameter of film [Å]	Pseudo-cubic unit cell volume [Å3]	Distortion	Residual strain (out-of-plane) (%)	TN (K)	Hc (T)
YAO	3.710	-5.15	3.860	3.943	58.75	1.022	1.077	134	2.40
LAO	3.790	-2.93	3.830	3.995	58.60	1.043	2.412	172	3.25
LSAT	3.868	-0.85	3.868	3.961	59.26	1.024	1.540	125	2.70
STO	3.905	0.10	3.905	3.923	59.82	1.005	0.566	100	1.58

Full text

I Introduction

Transition metal oxides with an ABO3 perovskite structure are multi-functional materials displaying a large collection of properties such as ferroelectricity, metal-to-insulator transition, high TC superconductivity and colossal magneto-resistance (CMR) for instance MIT ; LMO ; HSC ; CMR . This richness of physical behaviors emerges through strongly coupled structural, electronic and magnetic degrees of freedom, enabling possibilities to control the material’s properties with external stimuli Interface physics . Among all approaches, strain engineering allowed by minute deposition of oxides as thin films on a range of commercially available substrates is likely the most adopted strategy to unveil hidden phases in bulk. Most striking examples achieved with strain engineering are (i) the observation of ferroelectricity in SrTiO3 films under tensile epitaxial strain nature2004 , an otherwise quantum paralectric compound in bulk; (ii) the rich ferroelectric phase diagram of BiFeO3 as a function of the applied epitaxial strain ReviewSandoBibes or (iii) the control of magneto-resistive properties in R1-xAxMnO3 films (R=rare-earth, A=Ca, Sr) RAMnO3 ; fontcuberta .

In the search of multi-functional materials with possibly unprecedented properties, one must consider materials with nearly degenerate ground states that could be tailored by epitaxial strain. Along with the widely studied rare-earth manganites RMOphase ; RMOfe ; structure et magnetic , rare-earth vanadate perovskites RVO3 (R=Lu-La, Y) are prototypical compounds showing strongly coupled structural-spin-orbital properties orbital-spin ; charge . At high temperature, RVO3 compounds are paramagnetic insulators adopting the usual orthorhombic $Pbnm$ symmetry displayed by perovskites and characterized by $a^{-}a^{-}c^{+}$ octahedral rotations. Due to the intrinsic instability displayed by the V3+ $t_{2g}^{2}$ electronic configuration VarignonZunger-originGapsABO3 , a Jahn-Teller distortion appears and induces a symmetry lowering to a monoclinic $P2_{1}/b$ structure at the temperature $T_{oo}$. It produces a G-type orbital-ordering with alternating occupancy of the $d_{xz}$ and $d_{yz}$ orbitals on neighboring V sites according to a rock-salt like pattern – the second electron is located in the low energy $d_{xy}$ orbital on all V sites. It is then followed by a magnetic transition at $T_{N}$<$T_{oo}$ – except for LaVO3 for which $T_{N}$ is 2 K above $T_{oo}$ bulkPVO – to a C-type AFM order explained by Kugel-Khomskii and Goodenough-Kanamori rules Kugel-Khomskii ; Goodenough . Finally, for vanadates involving rare-earth with a small ionic radius (R=Lu-Dy, Y), the compound goes back to an orthorhombic $Pbnm$ symmetry characterized by an alternative Jahn-Teller motion producing a C-type orbital arrangement of $t_{2g}$ orbitals – columnar arrangement along the $c$ axis of alternating $d_{xz}$ and $d_{yz}$ orbitals – that is associated with a G-type AFM order at $T_{N2}$.

It is obvious that the chemical pressure induced by A site cations dramatically influences the electronic and magnetic states of the vanadates. Likewise, external stimuli such as hydrostatic pressure or partial A site substitution can also tune the material properties superexchange ; pressure controlled OO . Regarding thin films, a precise control of oxygen vacancies concentration in PrVO3 grown on a SrTiO3 substrate was recently shown to produce a substantial chemical strain, offering a pathway to modify the Néel temperature on a range of 30 K using a unique substrate type chemical strain engineering . Nevertheless, basic questions remain largely unexplored in these compounds: can we tune the vanadate properties using various epitaxial strains, and eventually promote new electronic phases? Aiming at providing answers to these important questions, we have studied the effect of epitaxial strains on the praseodymium vanadate perovskite using advanced experimental techniques. We show that the Néel temperature can be continously raised by 40 K with respect to the bulk by increasing the compressive epitaxial strain. Our first-principles simulations confirm the experimentally observed trend for $T_{N}$, but amazingly, they also reveal that this strong enhancement is associated with an unprecedented orbital-order of $t_{2g}$ levels.

II Methods

Experiments: PrVO3 (PVO) thin films (t $\sim$ 50 nm) were grown on various substrates such as (110)-YAlO3 (YAO), (100)-LaAlO3 (LAO), (100)-(La,Sr)(Al,Ta)O3 (LSAT), and (100)-SrTiO3 (STO) using the pulsed laser deposition (PLD) method. A KrF excimer laser ($\lambda$ = 248 nm) with repetition rate of 2 Hz and laser fluence of $\sim$ 2 J/cm2 was focused on stoichiometric ceramic targets. All the films used in this study were deposited at an optimum growth temperature (TG) of 650 ∘C and under oxygen partial pressure ($\textit{P}_{O_{2}}$) of 10*-6*mbar. The thickness of PVO films was kept nearly constant at 50 nm. To identify the lattice mismatch, the pseudo-cubic lattice parameters of YAO, LAO, LSAT and STO were used as: 3.700 Å, 3.790 Å, 3.868 Å and 3.905 Å respectively. The crystallinity and the structure were characterized using conventional High resolution x-ray diffraction (XRD) technique (Bruker D8 Discover diffractometer, Cu Kα1 radiation, $\lambda$ = 1.54056 Å). The surface morphology was investigated using atomic force microscopy (AFM) PicoSPM. The Resistivity ($\rho$(T)) measurements were performed using the four point probe technique in a Quantum Design Physical Properties Measurement System (PPMS). The magnetic measurements were obtained using Superconducting Quantum Interface Device magnetometer (SQUID), as a function of temperature (T) and magnetic field (H). Transmission Electron Microscopy (TEM) - Scanning Transmission Electron Microscopy (STEM) study was carried out on a JEM-ARM200F, operating at 200 kV, equipped with a cold Field Emission Gun and double TEM-STEM Cs correctors, ensuring lattice TEM or STEM image resolution below 0.1 nm, and JEOL EDS system. Thin TEM lamellae were prepared in a Dual-Beam system (FEI-HELIOS 600) equipped with Easy-lift manipulator designed for In-situ Lift-Out thin lamella preparations.

Theoretical calculations: first principles calculations are performed using Density Functional Theory with the VASP package VASP1 ; VASP2 . We have employed the PBEsol functional in addition to a U potential on V $d$ levels of 3.5 eV, entering as a single effective parameter LDA-Dudarev , in order to better cancel the spurious self-interaction term. This parameter was fitted in References chemical strain engineering, ; coupling, and was providing correct electronic, magnetic and structural features for PrVO3 ground state. Pr $4f$ electrons are not considered in the study and are included in the Projected Augmented Wave (PAW PAW potential. Unit cells used in our simulations correspond to a (2a,2a,2a) cubic cell allowing for the oxygen cage rotations and Jahn-Teller motions to develop (i.e. 8 formula units). The energy cut-off is set to 500 eV and a $4\times 4\times 4$ kpoint mesh is employed. Four magnetic states are explored in our simulations, namely the C, G and A-type SO as well as a ferromagnetic solution. We have considered two growth orientations for the films with the in-phase rotation axis (i.e the (001) $Pbnm$ axis) lying either along the substrate or perpendiculary to it. We then block two PrVO3 lattice parameters to those of the substrate and relax the magnitude of the remaining lattice parameter, although restriting it to be orthogonal to the substrate due to the presence of 90*∘* oriented domains chemical strain engineering .

Nearest neighbor magnetic exchange integrals J1 and J2, corresponding to interactions along the (110) (or (1-10)) and (001) directions respectively, are extracted by mapping energies of FM, A, C and G-type spin orderings on an Heisenberg model of the form $\hat{H}=-J\sum_{i<j}S_{i}.S_{j}$ where the sum runs over all possible sites i and j in the cell. The cell is fixed to the ground state structure for each strain value. In order to avoid modifications of the electronic structure due strongly entangled spin-orbital degrees of freedom in PrVO3 Kugel-Khomskii , we have frozen the $d$ orbital occupancies to that of the lowest energy state using the modified DFT+U routine of VASP Watson and we simply switched spin channels to account for the magnetic order. The Néel temperature is then computed using a mean-field model with $T_{N}\propto(2J_{1}+J_{2})$.

III Results and discussion

We have grown a series of PrVO3 (PVO) thin films using Pulsed Laser Deposition on (001) oriented substrates a priori yielding either nearly no epitaxial strain (SrTiO3 (STO) substrate) or compressive strain ((La,Sr)(Al,Ta)O3 (LSAT), LaAlO3 (LAO) and YAlO3 (YAO) substrates) with respect to the bulk PVO (see Figure 1a).

Figure 1b displays $\theta$ - 2$\theta$ scan for the epitaxially grown PVO thin films. For most of the substrates, clear thickness fringes are observed around the main diffraction peaks, confirming a uniform thickness and smooth interfaces of the films. The film thickness estimated using these fringes in the diffraction pattern is actually around 50 nm for all films leading to a growth rate ($\sim$ 0.09 Å/pulse). In the case of LAO substrate, these oscillations are however small and subtle, probably due to presence of twin domains in the LAO substrate CIO . The films surfaces are quite smooth, presenting clear steps and terraces (see inset of Figure 1b). For example, the RMS surface roughness of the PVO/LAO film was found around 2.3 Å indicating a flat surface. The evolution of the out-of-plane lattice parameter (calculated from XRD data) is plotted as a function of substrate lattice parameter in Figure 1c. Surprisingly, it presents a maximum for LAO substrate and a relatively lower lattice parameter for PVO/YAO film. This indicates the ability of PVO/LAO film to adopt large strain and a lower or no strain in PVO/YAO film, which is anticipated for such a large lattice mismatch.

To identify the strain states, reciprocal space maps were recorded around (103)${}_{\textit{c}}$ (where the index c refers to the cubic perovskite sublattice) planes of LAO, LSAT and STO and (212) plane of YAO (Figure 1d). The X-ray reciprocal space mapping shows well-developed film peaks in the lower region and strong substrate peaks in the upper region for all the PVO films. Since the horizontal peak positions of the PVO film coincide with those of the substrate for both LSAT and STO, we deduce that the film is fully strained with the substrate, and has the same in-plane lattice constant. In the case of LAO, the small shift of the film peak to lower Qin value suggests an increase of the in-plane lattice parameter, and a partially relaxed film, which confirms a flexibility of the PVO structure for a large strain associated with large lattice mismatch of -2.9 %. Finally, we see that the PVO film is fully relaxed on YAO, indicating that the growth is not coherent for this peculiar substrate, which can be explained by large compressive lattice mismatch (-5.1%). Additionally, the film relaxes in order to minimize the accumulated strain energy CIO ; ferroelectricity ; strain .

The PVO unit-cell volume (pseudo-cubic) was extracted and reported in table 1. The lattice volume is slightly reduced compared to the bulk value (59.36 Å3) for PVO/YAO, PVO/LAO, PVO/LSAT and increased for PVO/STO. This means that for tensile and compressive strain, the conservation of volume is not perfect due to non ideal Poisson’s ratio CaMnO . Moreover, the out-of-plane lattice parameter is well above the bulk value (3.901 Å) for all PVO films irrespective of the strain (compressive/tensile). This is due to low oxygen partial pressures used during the growth which induces oxygen vacancies in the film, resulting in an enhancement of lattice parameter oxygen vacancies ; PVO on STO . Nevertheless, with increase of the in-plane compressive strain, the out-of plane lattice parameter is enhanced as expected when going from LSAT to LAO substrate. The out-of-plane lattice parameter of PVO/YAO film is however much smaller, which is in agreement with a relaxed film as shown in Figure 1d.

The residual strain was calculated using : ${\epsilon_{hkl}}$ = ${(d^{0}_{hkl}-d_{hkl})/d^{0}_{hkl}}$ ; where $d^{0}_{hkl}$ and $d_{hkl}$ are the pseudo-cubic PVO bulk and film out-of-plane lattice parameters respectively. Interestingly, across the series, the measured strain increases from $\sim$ 0.5 % for PVO/STO to $\sim$ 2.4 % for PVO/LAO (table 1). Furthermore, albeit the relaxing behavior of PVO film on YAO substrate, the calculated strain is larger than PVO/STO (see Figure 1d for RSM and table 1 for strain values). This inconsistency could be explained as below. As proposed by Herranz oxygen vacancies , the STO substrate acts as oxygen reservoir during deposition and consequently the film behaves like a source of the oxygen vacancies. Therefore, oxygen vacancies tend to diffuse from film into the STO substrate, making film deficient of oxygen vacancies. As a consequence, the strain in PVO/STO film is as a result of lattice mismatch which is significantly small (0.1%) and only partially due to oxygen vacancies. It is the other way round in PVO/YAO case i.e. the strain is induced by the oxygen vacancies in the film, and the impact of substrate in building the strain is minimum.

In order to obtain details of the microstructure, Transmission Electron Microscopy (TEM) studies were performed on cross-sectionnal thin lamellae prepared for each sample. The lamellae were oriented in order to observe both the out-of-plane axis, i.e. growth direction, and one in-plane axis, characteristic of the perovskite structure. The TEM study, through Electron Diffraction (ED), High Resolution TEM and Scanning-TEM imaging allowed a local characterization of the PVO films, in terms of orientation with respect to the substrate, evolution of the parameters (strain), nanostructure (domains) and quality of the film-substrate interface. A summary of the main observation is given in Table 1 of supporting information and more details can be found elsewhere preparation . The observed thickness of the PVO films is close to those calculated from XRD around 50 nm. The Selected Area Electron Diffraction (SAED) study is in complete agreement with X-ray Reciprocal Space Mapping. Almost no strain is observed on STO subtrate with a perfect adequation of in and out-of-plane lattice parameters (deduced from a perfect superposition of diffraction spots of substrate and film). In the case of YAO substrate, two electron diffraction patterns can be clearly distinguished, one exhibiting YAO parameters and the second related to PVO parameters, along both in and out-of-plane directions (figure 2 in supporting information). Thus, there is almost no interaction between YAO substrate and PVO film.

On LSAT and LAO substrates, both parameters are influenced : the strain being compressive, the PVO in-plane lattice parameter is decreased to fit the one of the substrate, leading to an increase of the out-of-plane lattice parameter. The PVO films always exhibit small domains (several tens of nanometers)(table 1 of supporting information). In most of the observations, the PVO [001]o lies in-plane, and the diffraction spots related to 2 x apc along growth direction are either weak (STO, YAO) or nonexistent (LAO).

The SAED pattern shown in Figure 2a,b illustrates these observations for PVO film grown on LAO substrate: several patterns are superimposed, one LAO and two PVO ones. The latter correspond to several diffracting domains (labelled I and II in Figure 2b) having the [110] reciprocal axis out-of plane. Moreover, the enlargment of SAED pattern shows a more complex splitting of PVO dots, that could be due to deformation of PVO framework from one domain to the other. The domain size was evaluated from several TEM images, covering about 0.5 ${\mu}$m of the PVO film. It appeared that despite an apparent columnar growth, several domains may be observed from the bottom to the surface of the film (Figure 2c). In addition, measurements suggest that domains are smaller in size when the PVO film is not strained (on STO and YAO substrates). Stacking faults were observed in the upper part of the PVO film, on about 1/4 of the thickness and usually extend parallely to the growth direction. They involve either the oxygen framework or both oxygen and cation ones.

To investigate the effect of biaxial strain on the physical properties, the transport properties ($\rho$(T)) of PVO films were investigated (see section 4 of supporting information). The insulator-like $\rho$(T) behavior was observed for PVO films on LAO, LSAT and YAO. On the contrary, the PVO/STO film displayed a conducting-like behavior, which is likely resulting from the presence of the oxygen vacancies in STO substrate PVO on STO ; oxygen vacancies ; Hall mobility ; two components .

To examine the effect of the biaxial strain on the magnetic properties of PVO films, the magnetization (M) of PVO films was measured as a function of the in-plane applied magnetic field (H) and temperature (T) (Figure 3, 4).

At low T, all PVO films show a small magnetization with a hysteresis loop indicating two magnetic phases, a soft and a hard one (figure 3a–d). For instance, for PVO/STO, the soft contribution shows a coercive field Hc at $\sim$ 0.2 T and the hard one at $\sim$ 1.8 T. While, O. Copie et. al. already observed a soft ferromagnetic behavior for the bulk PVO (our case) with Hc $\sim$ 0.019 T chemical strain engineering , a hard ferromagnetic behavior was also reported for bulk PVO in Ref. Tung ; bulk . This discrepancy of coercivity between bulk and PVO films could be explained by the microstructure. The presence of different variants of the PVO orthorhombic cell (see TEM section) induces different pinning centers, and thus increases the energy to return the magnetization, similar to what is observed in the orthoferrite YFeO3 YFO . Furthermore, it is interesting to note that the weightage of soft and hard magnetic phases can be modified by interplaying the epitaxial strain. For instance, hard and soft components were evaluated as: $\Delta$Mhard = 85 % and $\Delta$Msoft = 15 % for PVO/STO, $\Delta$Mhard = 70 % and $\Delta$Msoft = 30 % for PVO/LAO, $\Delta$Mhard = 60 % and $\Delta$Msoft = 40 % for PVO/LSAT, $\Delta$Mhard = 45 % and $\Delta$Msoft = 55 % for PVO/YAO (figure 3a-d), as in Ref. YFO (Section 5 in supporting information). In addition, the fact that PVO/YAO film has a large percentage of soft component is interpreted as a behavior similar to the bulk PVO, since the film is fully relaxed (as shown by XRD and TEM measurements) and a small hard component might come from pinning centers due to the microstructure. Figure 3e shows variation of the coercivity (Hc) of hard magnetic phase as a function of the residual strain, whereas Hc of soft phase remains constant at $\sim$ 0.2 T for all substrates. The coercivity of hard phase changes from 1.8 T for less strained PVO/STO film, to 3.6 T for PVO/LAO (figure 3e). This is presumably due to an increase of domain walls pinning strength in more strained films.

To understand the presence of soft and hard magnetic phases versus strain, the M-H measurements were performed at different temperatures i.e from 10 K to 100 K. Interestingly, it was observed that the soft component is present only at temperatures T< 20 K for PVO/STO and PVO/LSAT but persists up to $\sim$ 80-90 K for PVO/LAO (see section 5 of supporting information). This indicates the sensitivity of the soft phase for epitaxial strain and temperature and suggests a possible magnetic ordering in PVO films around these temperatures which triggers the rise of soft component, and will be discussed below.

In order to further investigate the effect of strain on the magnetization of PVO films, the Field Cooled (FC) and Zero Field Cooled (ZFC) measurements were performed at an in-plane applied magnetic field of H${}_{\textit{in-plane}}$ = 50 Oe. For clarity, only FC measurements are shown in this report with a magnified view near TN (or TSO1) (Figure 4a). The derivative was calculated to visualize the magnetic transitions (see supporting information) and results are reported in Table 1.

Clearly, a magnetic transition (TSO1) is observed for all the films with transition temperature ranging from 100 K for PVO/STO, to 172 K for PVO/LAO (inset of Figure 4a). This corresponds to the magnetic transition from paramagnetic (PM) state to an antiferromagnetic (AFM) phase transition. While for bulk PrVO3, the transition at TSO1 was previously ascribed to the onset of a C-type spin ordering (C-SO) of the canted vanadium moments bulkPVO ; bulk , for epitaxial PrVO3 thin films, the substrate-induced strain results in a G-type SO chemical strain engineering . The AFM Néel temperature (named TSO1 here) for PVO/STO is however different from our previous report, where TN $\sim$ 80 K was reported PVO on STO . This discrepancy could be explained by different growth conditions (especially $\textit{P}_{O_{2}}$ = 10*-5* mbar, out-of-plane lattice parameter = 3.97 Å) which were adopted during deposition. More interesting is the remarkable difference of $\sim$ 70 K for the TN of PVO/LAO compared to PVO/STO. Notably, the MT curve also shows two other magnetic features at TSO2 and TSO3 for LAO, YAO and LSAT, while the former transition is strongly reduced for STO (TSO2 $\sim$ 30 K). These magnetic orderings were absent in bulk PrVO3 spin-orbital , but reported in other orthovanadates of smaller R ionic radii, with decreasing temperature TmVO3 ; LnVO3 ; DyVO3 . In addition, Reehuis et. al. clearly distinguished these transitions for a doped Pr1-xCaxVO3 compound PrCaVO3 . Upon decreasing the temperature to TSO3, a slight decrease in magnetization takes place and there is a change in the slope of the magnetizations as well as an anomaly in the inverse susceptibility (section 5 of supporting information). This is ascribed to the FM ordering of praseodymium sublattice and/or an AFM coupling between Pr3+ 4f and V3+ 3d moments, which results in decrease in the net magnetization below TSO3. Therefore, by comparing the MH measurements performed at different tempeatures (10 - 100 K) where a soft component in MH was observed at temperature T $\leq$ 20 K for PVO/STO and PVO/LSAT and up to 80 K for PVO/LAO (see supporting information) and the magnetic transition TSO3 in MT, we propose that the soft component in MH results from the AFM coupling between Pr and V3+ sublattice. It is worth noting that another Pr3+ magnetic state may exist at the surface of the PVO film. Indeed, as it has been shown in DyTiO3 thin films that over-oxidation at the surface could favor a higher valence state of the transition metal oxide dead layer . As a consequence, it would favor V4+ and then alter the exchange interactions with Pr ions, resulting in isolated paramagnetic Pr3+. Since the measured saturation magnetization remains low compared to 3.57 $\mu$B expected for isolated Pr3+, it seems that over-oxidized surface contribution is rather small. However, the fact that the soft component contribution is modified by changing the substrate indicates rather a modification through the entire film and not only at the surface.

Also, similar to earlier reported for bulk PrVO3 PrCaVO3 , the praseodymium sublattice begins to get polarized due to presence of exchange field produced by the vanadium sublattice, resulting in a ferrimagnetic structure upon cooling. Here, a small hump at T $\sim$ 90 K is also seen, which could be the emergence of another type of spin configuration and/or a phase coexistence between C-SO and G-SO. This seems consistent with the modification of hysteresis loop as the temperature is lowered through TSO2, due to switching of spins or change in the spin configuration (see section 5 of supporting information). However, the feature may be also just related to the overlap of transition regime TSO1 and TSO3. Further magnetic analysis will be published elsewhere.

To understand further the relationship between the magnetic properties and strain or distortion (ratio of out-of-plane to in-plane lattice parameters), the TN versus lattice strain is plotted for the PVO films, as shown in Figure 4b. The TN (TSO1) of the PVO films increases altogether with the residual strain, which is highest for LAO (TN $\sim$ 172 K) and lowest for STO (TN $\sim$ 100 K). While PVO film on YAO has TN close to the bulk PVO (TN $\sim$ 130 K). Furthermore, the PVO/YAO film is in-plane fully relaxed while out-of-plane lattice parameter is larger than the bulk. This produces a distorted structure with $c/a$ ratio $\sim$ 1.02. The enhancement of out-of-plane lattice parameter of PVO/YAO might be a result of defects in film such as oxygen vacancies etc. It is interesting to note that the influence of small compressive strain (LSAT) in PVO film is similar to bulk, where a small tensile strain (STO) decreases the TN by 30 K spin-orbital . On the other hand, it requires a large compressive strain of 2.4 % (LAO) to increase the same by 40 K cf. bulk.

To further explore the magnetic properties of PVO films and their dependence on strain, which lead to a tilting of BO6 octahedra or change in the B-O-B bond angle tilts ; LVO ; rotation ; quantifying octahedral rotation ; misfit strain accommodation , it is necessary to have a complete knowledge of distortion of the structure and the VO6-octahedral rotation. From previous studies of strained oxide perovskites, the degree of rotation of BO6 octahedra depends strongly on sign and the magnitude of the strain quantifying octahedral rotation ; misfit strain accommodation . Under tensile in-plane strain (c/a <1.01), the VO6 octahedra comprise of an enhanced in-plane V-O bond length and V-O-V bond angle close to 180*∘*. This decreases the in-plane AFM superexchange interaction between nearest neighbour sites, hence reduced TN. On the other hand, under compressive in-plane strain (c/a

1.01), it is the other way round i.e. a reduced in-plane V-O bond length and V-O-V bond angle <180*∘*. This, as a result, enhances the in-plane AFM interaction and therefore enhanced TN.

IV First-principles simulations

To get further insights on the role of the epitaxial strain on the magnetic properties of PrVO3 films, we have performed first-principles simulations using Density Functional Theory (DFT). Consistently with previous studies chemical strain engineering , DFT correctly predicts that bulk PrVO3 is a C-SO insulator in the ground state. Regarding the thin films, we find that the perovskite grows with the (001) and (1-10) $Pbnm$ axes aligned along the substrate for all the tested films (e.g. PrVO3 grown on STO, LSAT, LAO and YAO substrates, see insets of figure 5b for sketches of local axes and growth orientation). This yields films grown along the orthorhombic (110) direction, in sharp agreement with experiments. We emphasize here that due to the presence of small domains in the films inducing a mechanical constraint chemical strain engineering , we have considered growth conditions with the (110)o direction forced to be orthogonal to the substrate (i.e. the film is not allowed to tilt). With that additional constraint, the ground state is associated with a $P2_{1}/m$ symmetry with nearest neighbor V3+ spins antiferromagnetically coupled in all crystallographic directions. It yields a G-type spin ordering compatible with experiments. Finally, all films are insulating with band gaps ranging from 1.50 eV (YAO) to 1.78 eV (STO).

Although mean-field methods such as DFT can not provide accurate values of the Néel temperature, they nevertheless remain valuable technics for capturing trends as a function of external stimuli Green function . We report on Figure 5a the ratio of the Néel temperature with respect to that of PrVO3 grown on a STO substrate as a function of the pseudo tetragonality $c/a$ of the films extracted from our simulations (see method for details on evaluation of the Néel temperature). As one can see, DFT captures the trend observed experimentally with an enhancement of the Néel temperature going from STO to YAO substrates, although our computed $T_{N}/T_{N-STO}$ ratio is smaller than the experimental one for the LAO substrate. Amazingly, if the material could be stabilized on YAO without relaxation of the film, the Néel temperature is expected to be approximately multiplied by two with respect to that of PrVO3 films deposited on STO.

Along with validating the experimentally measured trend for TN as a function of the applied epitaxial strain, our first-principles simulations also provide microscopic insights on the origin of this physical behavior. We observe that both magnetic constants J1 and J2 between nearest V3+ neighbors along the (1-10) (or (110)) and (001) directions, respectively, increase with enlarging the compressive epitaxial strain. Firstly, this is ascribed to shorter V-O bond lengths along the (1-10) and (001) directions induced by strain. Secondly, we do not observe any significant modifications of oxygen cage rotations amplitude in the different films – the $a^{-}a^{-}c^{0}$ rotation amplitude is even slightly increasing with decreasing the substrate lattice parameter! – and thus the classical “$\widehat{V-O-V}$ angles going to 180*∘” argument cannot explain the strengthening of Js. Nevertheless, we find a crossover between two lattice distortions as a function of the epitaxial strain (see figure 5b): (i) for a moderate lattice mismatch (e.g STO and LSAT), we extract a large Jahn-Teller distortion, labelled M${}_{3}^{+}$, producing an asymmetry of V-O bonds on nearest V sites that is reminiscent of bulk RVO3 physics and (ii) for a large lattice mismatch (e.g LAO and YAO), the JT motion vanishes and is replaced by a M${}_{1}^{+}$ distortion unaffecting V-O bond lengths but distorting O-V-O angles in VO2 planes orthogonal to the (001) direction (see insets of figure 5b for sketches of the distortions). The amplitude of the latter distortion, absent in the bulk and roughly zero for films grown on STO and LSAT substrates, closely behaves like TN* as a function of the tetragonality of the material. In fact, the crossover between the amplitude associated with the M${}_{1}^{+}$ and M${}_{3}^{+}$ distortions highlights a clear modification of the electronic structure: the two V3+ $d$ electrons are located in the $d_{yz}$ orbital plus an alternating combination of the $d_{xz}\pm d_{xy}$ orbitals on neighboring sites for moderate strains while they lie in the $d_{xz}$ and $d_{yz}$ orbitals on all neighboring sites for large compressive epitaxial strain (see insets of Fig5.b for the definition of local axes). It follows that V-O bond length contractions combined with the modifications of V3+ $d$ orbital occupancies for LAO and YAO substrates favor superexchange in the three crystallographic directions and thus strongly promotes the enhancement of the Néel temperature.

This illustrates that not only cooperative octahedral-site rotation i.e rigid octahedra tilts and rotations may tune the physical properties but also octahedral-site disortion through electronic state modifications as reported for bulk orthorhombic perovskite Intrinsic ; RCrO3 . We show here that octahedral-site disortion can be driven by mechanical strain engineering and should be considered for other epitaxial orthorhombic perovskite thin films.

V Conclusion

In conclusion, we have successfully grown single-phased PrVO3 thin films on top of various single crystal substrates. The most distorted structure with c/a $\sim$ 1.04 is observed on LAO substrate where a large strain of 2.4 % is measured. Furthermore, a relationship between the magnetic properties and the structural distortion (c/a) in PrVO3 films was developed. We have also evidenced a clear ferromagnetic behavior of PrVO3 thin films at low temperature, and shown that the MH hysteresis loop comprises of two magnetic sublattices, which gives rise to a soft and a hard ferromagnetic-like component in MH. The magnetic phase diagram (TN vs. c/a) for PrVO3 films was mapped out for 1 <c/a <1.04. The most distorted film has TN $\sim$ 172 K, 40 K higher than the bulk. Whereas, the least distorted film has TN $\sim$ 100 K, 30 K lower than bulk, making PVO films an eligible candidate for application point of view for wide range tuning of its magnetic transition temperature. Finally, the first-principles simulations have confirmed that the compressive strain not only produces stronger magnetic interactions, but also promotes electronic states totally absent of the bulk.

VI acknowledgements

The authors thank F Veillon for his valuable experimental support. DK received his PhD from Region Normandie. This work is supported by Region Normandie,partly by french ANR POLYNASH and Labex EMC3. CUJ thanks université de Caen Normandie for his visiting fellowship. B. Domeng$\grave{e}$s acknowledges the financial support of the program EQUIPEX GENESIS, Agence Nationale de la Recherche (ANR-11-EQPX-0020) for TEM lamella preparation. Ph. Ghosez acknowledges the F.R.S/F.N.R.S PDR project HiT4FiT and ARC project AIMED. First–principles calculations were performed at Abel supercomputers through the PRACE project TheoMoMuLaM and at the Cartesius supercomputer through the PRACE Project TheDeNoMO. The authors also took advantage of the Céci–HPC facilities funded by F.R.S.–FNRS (Grant No 2.5020.1) and the Tier–1 supercomputer of the Fédération Wallonie–Bruxelles funded by the Walloon Region (Grant No 1117545).