Unusual magnetic structure of high-pressure synthesized perovskites ACrO3(A=Sc, In, Tl)

TL;DR

This study reveals that metastable high-pressure synthesized perovskites ScCrO3, InCrO3, and TlCrO3 exhibit a C-type magnetic structure, differing from typical G-type, driven by specific exchange interactions and structural distortions.

Contribution

It uncovers the unique C-type magnetic ordering in these metastable perovskites and explains its origin through first-principles calculations and structural analysis.

Findings

ScCrO3 and InCrO3 have ferromagnetic nearest-neighbor interactions.

TlCrO3's magnetic order is stabilized by strong next-nearest-neighbor antiferromagnetic exchange.

The magnetic spins align along the orthorhombic b-axis due to single ion anisotropy.

Abstract

Magnetic structures of metastable perovskites ScCrO3, InCrO3 and TlCrO3, stabilized under high-pressure and high-temperature conditions, have been studied by neutron powder diffraction. Similar to the other orthochromites LnCrO3 (Ln=lanthanide or Y), these materials crystallize into the orthorhombic structure with Pnma10 symmetry. The spin configuration of the metastable perovskites has been found to be C-type, contrasting with the G-type structure usually observed in LnCrO3. First-principles calculations demonstrate that the Ctype structure found in ScCrO3 and InCrO3 is attributed to a ferromagnetic (FM) nearest-neighbor interaction, while in TlCrO3, this type of magnetic ordering is stabilized by a strong next-nearest-neighbor antiferromagnetic (AFM) exchange. The spins in the C-type magnetic structure line up along the orthorhombic b-axis, yielding the Pnma magnetic symmetry. The dominant mechanism controlling this spin direction has been concluded to be the single ion anisotropy imposed by a uniaxial distortion of CrO6 octahedra.

Tables

Table 1. Table 1: Structural parameters and Cr-magnetic moments for ACrO 3 perovskites refined from the neutron diffraction data collected at 1.5 K in the P ​ n ​ m ​ a ​ 1 ′ 𝑃 𝑛 𝑚 𝑎 superscript 1 ′ Pnma1^{\prime} space group (Wyckoff positions: A- 4 ​ c ​ ( x , 0.25 , z ) 4 𝑐 𝑥 0.25 𝑧 4c(x,0.25,z) , Cr- 4 ​ b ​ ( 0 , 0 , 0.5 ) 4 𝑏 0 0 0.5 4b(0,0,0.5) , O1- 4 ​ c ​ ( x , 0.25 , z ) 4 𝑐 𝑥 0.25 𝑧 4c(x,0.25,z) and O2- 8 ​ d ​ ( x , y , z ) 8 𝑑 𝑥 𝑦 𝑧 8d(x,y,z) ). Occupancies for all the atoms in the refinement procedure were fixed to the nominal chemical content, since attempts to refine them did not result in any significant deviation from the nominal values and did not improve the fitting quality.

	Parameter	ScCrO3	InCrO3	TlCrO3
	$a\left(\text{Å}\right)$	5.3613(1)	5.3539(2)	5.39539(7)
	$b\left(\text{Å}\right)$	7.3847(2)	7.5484(3)	7.6402(2)
	$c\left(\text{Å}\right)$	5.0296(1)	5.1603(1)	5.29163(7)
A	$x$	0.0709(3)	0.0615(4)	0.0466(3)
	$z$	0.9789(3)	0.9840(5)	0.9854(2)
	$B_{iso}\left({\text{Å}}^2\right)$	1.72(9)	1.2(1)	1.8(7)
Cr	$M\left({\mu }_B\right)$	2.70(2)	2.50(2)	2.46(2)
	$B_{iso}\left({\text{Å}}^2\right)$	0.31(7)	1.2(1)	1.3(1)
O1	$x$	0.4418(7)	0.4410(3)	0.4506(5)
	$z$	0.1294(5)	0.1239(4)	0.1094(4)
	$B_{iso}\left({\text{Å}}^2\right)$	1.03(9)	1.8(1)	1.4(9)
O2	$x$	0.3072(4)	0.3083(3)	0.2999(3)
	$y$	0.0694(2)	0.0667(2)	0.0577(2)
	$z$	0.6887(3)	0.6895(3)	0.6962(2)
	$B_{iso}\left({\text{Å}}^2\right)$	0.32(9)	1.6(1)	1.70(8)

Table 2. Table 2: Results of the symmetry analysis for the 𝐤 = 𝟎 𝐤 0 \bf{k}=0 magnetic propagation vector and Cr 3+ cations at the 4 ​ b 4 𝑏 4b position of the parent P ​ n ​ m ​ a ​ 1 ′ 𝑃 𝑛 𝑚 𝑎 superscript 1 ′ Pnma1^{\prime} space group. The four Cr-sites are: Cr1=(0, 0, 0.5), Cr2=(0.5, 0, 1), Cr3=(0, 0.5, 0.5), Cr4=(0.5, 0.5, 1)). Irreducible representations (IRs) are given using the notation of Miller and Love Miller and Love ( 1967 ) ). Definition of the magnetic modes, using the four Cr-sites, are: F(+ + + +),G(+ - - +),C(+ - + -) and A(+ + - -) (Bertaut, 1968 ) .

IR		Cr(4b)		Space group
$mGM1+$		($G_x$,$C_y$,$A_z$)		$Pnma$
$mGM2+$		($C_x$,$G_y$,$F_z$)		$P{n}^{\prime }{m}^{\prime }a$
$mGM3+$		($F_x$,$A_y$,$C_z$)		$Pn{m}^{\prime }{a}^{\prime }$
$mGM4+$		($A_x$,$F_y$,$G_z$)		$P{n}^{\prime }m{a}^{\prime }$

Full text

I INTRODUCTION

Oxide materials with perovskite structure have drawn enormous amounts of interest for several decades due to their central role in fundamental research and technological applications. The remarkable properties of these materials such as colossal magnetoresistance Tokura and Nagaosa (2000), superconductivity Cava et al. (1988) and multiferroic behavior Tokura et al. (2014); Van Den Brink and Khomskii (2008) originate from the significant interplay between spin, charge and orbital degrees of freedom. A key ingredient of this success is the structural versatility of the perovskite lattice which can incorporate a wide range of elements. The diversity of the perovskite materials and their properties has been regarded as a playground to explore novel and unique phenomena. For example, a wide variety of interesting physics was found in the LnMnO3 family of manganites, including charge/orbital ordering and metal-insulator transition Tokura and Nagaosa (2000) as well as multiferroic properties Bousquet and Cano (2016); Kimura et al. (2003); Kenzelmann et al. (2005). Some of Fe3+-based perovskites, such as BiFeO3 Wang et al. (2003), GdFeO3 Tokunaga et al. (2009) and DyFeO3 Tokunaga et al. (2008), also exhibit coexistence of magnetism and ferroelectricity. The spin-state transition and electronic/ionic conductivity in LnCoO3 have been investigated Itoh et al. (2000) for decades. Metal-insulator transition associated with a charge disproportionation has been found in Ni-containing perovskites Alonso et al. (1999a, b).

Another interesting family of perovskite oxides is orthochromites LnCrO3, which crystallize into GdFeO3-type structure, with the $Pnma1^{\prime}$ space group. The magnetic properties of LnCrO3 compounds have been extensively investigated Bertaut et al. (1962); Shamir et al. (1981); Colin et al. (2012). It has been found that these materials undergo AFM transition with a simultaneous weak FM component. Neutron diffraction studies have revealed that they adopt a $G$-type magnetic structure, where all nearest neighbour spins are antiparallel to each other Bertaut et al. (1962); Shamir et al. (1981). The FM component observed in LnCrO3 was attributed to a spin canting, allowed by $Pn^{\prime}m^{\prime}a$ ($G_{y}$ -spin configuration) and $Pn^{\prime}ma^{\prime}$ ($G_{z}$ -spin configuration) magnetic symmetry. It was also noted that with a decrease of the radius of the Ln cation, the magnetic ordering temperature was monotonically reduced. Zhou et al. have discussed the relationship between structural distortions and AFM magnetic transition temperature Zhou et al. (2010). Their work highlights the important role of $t_{2g}-e_{g}$ hybridization, in addition to the reduction of the orbital overlap integrals. LnCrO3 perovskites also show some other interesting physical properties, such as spin-reorientation transition when Ln=Nd, Sm, Gd and Er Sardar et al. (2010). Recently, orthochromites have attracted revitalised interest due to the observation of a possible multiferroic behavior Bousquet and Cano (2016).

High pressure synthesis is a well-known technique to expand stability of perovskite structure, which has very recently allowed new members of the Cr3+-based perovskites ScCrO3, InCrO3 and TlCrO3 to be investigated Belik et al. (2012); Yi et al. (2015); Belik and Yi (2014). Similar to LnCrO3, these materials crystallize into orthorhombic $Pnma1^{\prime}$ symmetry and undergo AFM transition at TN=73 K, 93 K and 89 K, respectively. The magnetic transition, however, is not accompanied by a weak FM behavior, reflecting that their magnetic structures might be different from the $G$-type one. In the present study, we explored the magnetic ordering in ACrO3 using neutron diffraction and studied the exchange interactions by means of density functional theory (DFT).

II Technical section

The polycrystalline samples of ACrO3 were prepared under high pressure and high temperature conditions as described in Refs. Belik et al. (2012); Yi et al. (2015). The neutron powder diffraction data were collected at the ISIS pulsed neutron and muon facility of the Rutherford Appleton Laboratory (UK), on the WISH diffractometer located at the second target station Chapon et al. (2011). The samples ($\sim 0.6$ g) were loaded into a cylindrical 3 mm diameter vanadium cans and measured in the temperature range of 1.5 - 110 K using an Oxford Instrument Cryostat. The data at the lowest and the highest temperatures were collected for 1.5 hours, and typical scans between these extremal temperatures were carried out with an exposition time of 20 mins. The temperature step was 10 K and 5 K, in the case of ScCrO3 and InCrO3 perovskites, respectively. For TlCrO3, the data between 1.5 - 80 K were collected with 5 K/step and then the temperature range of 80-95 K was measured with 2-1 K/step and exposition time of 40 mins, to explore the presence of a possible second magnetic transition at TN2 = 87 K (Yi et al., 2015); however, no evidence for the second transition was detected. Rietveld refinements of the crystal and magnetic structures were performed using the Fullprof program Rodríguez-Carvajal (1993) against the data measured in detector banks at average $2\theta$ values of 58*∘, 90∘, 122∘, and 154∘, each covering 32∘* of the scattering plane. Group-theoretical calculations were done using ISOTROPY Stokes et al. , ISODISTORT Campbell et al. (2006) and Bilbao Crystallographic Server (AMPLIMODES: Symmetry mode analysis Orobengoa et al. (2009) and Magnetic Symmetry and Applications Perez-Mato et al. (2015)) software.

A series of spin-polarized first-principles calculations was performed for ScCrO3, InCrO3, LuCrO3 and TlCrO3 using the projector augmented-wave (PAW) method Blochl (1994) as implemented in VASP Kresse and Hafner (1993). PAW datasets with radial cutoffs of 1.59, 1.64, 1.48, 1.32, 1.32, and 0.80 Å for Sc, In, Lu, Tl, Cr, and O, respectively, were employed. Sc-$3d$ and -$4s$, In-$5s$ and -$5p$, Lu-$5s$, -$6s$, -$5p$, -$5d$, and -$4f$, Tl-$6s$, -$6p$, and -$5d$, Cr-$4s$ and -$3d$ and O-$2s$ and -$2p$ were described as valence electrons. We adopted the Perdew-Burke-Ernzerhof generalized gradient approximation (GGA) Perdew et al. (1996) to the density functional theory. For correcting on-site Coulomb interactions in the Cr-$3d$ orbitals, we used the $+U$ scheme proposed by Dudarev et al. Dudarev et al. (1998), in which only $U_{eff}=U-J$ value has a meaning. Since early transition metals have moderate on-site Coulomb potential, we selected $U_{eff}=0$ and 2 eV, the former one is equal to the GGA without the $U$ correction. In all the calculations, lattice constants and internal atomic positions were fully optimized until the residual stresses and forces converged to less than 0.03 GPa and 0.005 eV/Å, respectively. Wave functions were expanded with a plane-wave basis set, and the cutoff energies were set to 550 eV.

III Results and discussion

The room temperature crystal structures of ACrO3 have been previously investigated using X-ray diffraction Belik et al. (2012); Yi et al. (2015). It has been shown that in all cases, A = Sc, In and Tl, the structure combines both in-phase and out-of-phase octahedral tilting with the $a^{+}b^{-}b^{-}$ tilting pattern in the Glazer’s notation Glazer (1972). This tilted pattern possesses the orthorhombic $Pnma1^{\prime}$ symmetry and is common for LnCrO3 and many other perovskite systems Howard and Stokes (1998); Woodward (1997). Our neutron diffraction data revealed that the $Pnma1^{\prime}$ symmetry of the nuclear structure of ACrO3 does not change down to 1.5 K and a polyhedral representation of the structure is shown in Fig. 1. The structural parameters refined at 1.5 K are summarized in Table  1. An important observation coming from the analysis of the structural parameters is the presence of uniaxial distortion of the octahedra, which is most pronounced in the case of InCrO3. The distortion implies that two Cr-O bond distances are notably longer than the other four (Fig. 1). This is in contrast with LaCrO3 and other orthochromites with relatively large Ln, in which the octahedra are nearly regular Zhou et al. (2010). The electronic configuration of the Cr3+ ions is not degenerate and the uniaxial elongation of the octahedra in the ACrO3 perovskites studied here is thus a secondary structural effect due to the large octahedral tilting rather than due to Jahn-Teller instability. This structural aspect seems to play a crucial role in the magnetic anisotropy of ACrO3 as discussed below.

Our neutron diffraction data are consistent with the previous magnetic susceptibility and heat capacity measurements, indicating the onset of long-range magnetic ordering below the relevant critical temperatures TN (Fig. 2). In all three cases, Sc-, In- and Tl-based compositions, the magnetic scattering looks very similar (Fig. 2), suggesting the same type of the spin ordering. In previous reports Belik et al. (2012); Yi et al. (2015), a possible second transition at lower temperature has been suggested from ac susceptibility measurement. However, our neutron diffraction data demonstrate that no variation of the relative intensities of the magnetic reflections occurs across the second transition, failing to reveal the nature of the low temperature anomalous behavior of the ac susceptibility. All the magnetic reflections can be indexed by k=0 propagation vector similar to the perovskites of the LnCrO3 family. A quantitative magnetic structure refinement (Fig. 3), however, revealed that it is different from the $G$-type spin configuration (usually found in LnCrO3).

The refinement procedure governed by the symmetry arguments Bertaut (1968) summarized in Table  2 yields the $C_{y}$-type of magnetic structure, with the $Pnma$ magnetic symmetry. This type of magnetic order implies the spins are ferromagnetically coupled along the $b$-axis and aligned antiferromagnetically in the $(ac)$ plane, as shown in Fig. 1. The spin structure is transformed by the $mGM1+$ irreducible representation which also transforms the $G_{x}$ and $A_{z}$ magnetic modes. This implies that the latter two are bi-linearly coupled as secondary order parameters to the primary $C_{y}$ magnetic orderings through the antisymmetric Dzyaloshinskii-Moriya exchange or single ion anisotropy effects. The $G_{x}$ and $A_{z}$ spin components, however, are too small to be detected in the powder diffraction experiment. The spin components in the primary $C_{y}$ magnetic modes were refined to be 2.70(2) $\mu_{B}$, 2.50(2) $\mu_{B}$ and 2.46(2) $\mu_{B}$ at 1.5 K in the case of ScCrO3, InCrO3 and TlCrO3 perovskites, respectively and their temperature dependences are shown in Fig. 3. The ordered moments in the latter two are notably smaller than the value expected for $S=3/2$ of Cr3+, which might be due to a significant hybridisation of the $d$-orbitals with oxygen or be a result of magnetic fluctuations. The values, however, are in fact very close to the ordered moments found in other orthochromites with non-magnetic $A$-site cations such as LaCrO3 Martinelli et al. (2011), LuCrO3 Shamir et al. (1981) and Bi1-xYxCrO3 solid solutions Colin et al. (2012). The full results of the magnetic structure refinement can be found in mcif files provided in the Supplemental Material SM .

The magnetic point group, $mmm$, deduced from the present neutron diffraction data is non-polar and does not allow any spontaneous magnetic moment in agreement with the previous magnetization measurements Belik et al. (2012); Yi et al. (2015). In addition, a linear magnetoelectric effect is forbidden as well, casting doubt upon the magnetoelectric nature of the dielectric anomaly at TN, suggested in Refs. Belik et al. (2012); Yi et al. (2015).

In order to reveal the factors which underpin the unusual $C$-type magnetic structure in ACrO3, especially in TlCrO3 with the size of Tl3+ being larger than that of Lu3+ Yi et al. (2015); Shannon (1976), we performed a series of spin-polarized first-principles calculations. LuCrO3, which has the $G$-type magnetic structure experimentally, was chosen as a reference. Four magnetic configurations, i.e., FM and $A$-, $G$-, and $C$-type AFM, were taken into account. Fig. 4 shows the total energies of FM, $G$- and $A$-type AFM structures relative to that of $C$-type AFM. One can see that the calculated magnetic ground state of ScCrO3, InCrO3, and TlCrO3 is $C$-type AFM structure, in good agreement with the neutron diffraction experiment. On the other hand, the ground state of LuCrO3 is $G$-type AFM structure when $U$ is small, which also agrees with the documented experimental data Shamir et al. (1981), but the energy becomes closer to that of $C$-type AFM configuration as increases $U$. To understand the origin of the difference in these magnetic ground states, the exchange constants were estimated by mapping the total energy differences between the four magnetic configurations onto the Heisenberg Hamiltonian $H=-2\Sigma_{i>j}J_{ij}\bf{S_{i}\cdot S_{j}}$ Akamatsu et al. (2011, 2013), where $J_{ij}$ is the exchange constant of magnetic interactions between Cr $3d$ spins at the $i$ and $j$ sites (see Fig. 1) and $\bf{S_{i}},\bf{S_{j}}$ are the spin vectors at these sites. As the Cr ions are trivalent in ACrO3 and LuCrO3, they have a $d^{3}$ electronic configuration with $|\bf{S}|$=3/2. In the present analysis, we have considered up to second nearest neighbors for Cr pair interactions. The calculated magnetic interaction energies using $U_{eff}=0$ and 2 eV are shown in Fig. 5. $J_{12}$ shows significant AFM interactions in all four compounds. $J_{14}$ is also AFM but it displays remarkable system dependence and is particularly strong in TlCrO3. On the other hand, $J_{13}$ shows notably strong FM interactions in ScCrO3 and InCrO3, whereas it is AFM or very weak FM in LuCrO3 and TlCrO3. These results indicate that the $C$-type AFM structure in ScCrO3 and InCrO3 originates from the FM interactions of $J_{13}$. On the other hand, $C$-type AFM ordering in TlCrO3 is attributed to the strong AFM interactions of $J_{12}$ and $J_{14}$, which results in the FM alignment of Cr1 and Cr3 although $J_{13}$ can have a small AFM interaction. It should be also pointed out that $C$-type magnetic structure has been previously observed in some other perovskite systems such as (Sr/Ca)CrO3 Komarek et al. (2011); Streltsov et al. (2008); Lee and Pickett (2009), LnVO3 Ren et al. (1998); Ulrich et al. (2003) and Sr1-xLnxMnO3 Kurbakov et al. (2009); Martin et al. (1999). In all these cases, however, the degenerate electronic configurations of the transition metals lead to spontaneous Jahn-Teller distortions. The $C$-type magnetic structure in these compounds, therefore, can be attributed to anisotropic exchange interactions imposed by the orbital orderings.

Let us briefly discuss the electronic structures of ACrO3 series. Figure 6 shows the calculated density of states (DOS) of ACrO3 with the experimentally identified magnetic configurations using GGA+$U$ ($U_{eff}$ = 2 eV). Because Cr3+ ions are in a $d^{3}$ configuration, $t_{2g}$ orbitals in the spin-up channel are fully occupied, comprising the valence band maxima in ACrO3. At the same time, the unoccupied $e_{g}$ orbitals in the same spin channel are located at the bottom of the conduction band, resulting in the (indirect) band gaps in the four orthochromites. Among these, TlCrO3 has a very small gap, which is attributed to the unoccupied Tl-${6s}$ and O-${2p}$ bands. This tendency is the same as those of TlScO3 Belik et al. (2016) and TlMnO3 Yi et al. (2014).

The mechanism dominating the magnetic anisotropy of Cr3+ in the ACrO3 and related LnCrO3 perovskites is not obvious. Basically, the preferred orientation of the spins in the Cr-sublattice clearly correlates with the size of the $A$-site cation in the perovskite lattice $AB$O3 Bousquet and Cano (2016). In compounds with relatively large Ln=La-Tb, the Cr spins tend to align along the $c$-axis ($a$-axis in the $Pbnm$ setting), like for instance in LaCrO3 and YCrO3, with non-magnetic $A$-site cations. In some cases, with a magnetic rare earth $A$-site sublattice, the direction of the Cr spins changes to be along the $b$-axis (along the $c$-axis in the $Pbnm$ setting) at lower temperatures. These spin reorientation transitions are well-known to be driven by anisotropy of the rare earth cations and the $f-d$ exchange between the $A$- and $B$-site sublattices Belov et al. (1979). In the perovskites with a smaller Ln=Dy-Lu, the Cr3+ spins prefer to order along the $b$-axis. The ScCrO3, InCrO3 and TlCrO3 perovskites follow this empirical correlation, exhibiting the spin configuration with the moments being along the $b$-axis. This change of the magnetic anisotropy seems to correlate with the development of the uniaxial distortion of the CrO6 octahedra in the perovskites with the small $A$-site cations. In LaCrO3, the octahedra are practically isotropic, suppressing the single ion anisotropy. The direction of the spins in this perovskite is believed to be governed by anisotropic antisymmetric exchange Belov et al. (1979). The $c$-axis is indeed the spin direction which activates the antisymmetric exchange imposed by the largest structural distortions, namely anti-phase and in-phase octahedral tiltings Khalyavin et al. (2014, 2015). However, in the perovskites with smaller $A$-site cations and distorted octahedra, the single ion anisotropy prevails, forcing the spins to be along the $b$-axis. The uniaxial elongation of octahedron lifts the degeneracy between the half-occupied $xy$, $xz$ and $yz$ orbitals of Cr3+, increasing the energy of the former and decreasing the energy of the latter two. In this case, the single ion anisotropy is assumed to be dominated by the spin-orbit interaction between the occupied $xy\uparrow$ and empty $x^{2}-y^{2}\uparrow$ electronic states, resulting in the easy axis type of anisotropy as suggested in the recent perturbation theory by Whangbo et al. Whangbo et al. (2015). This is the case of a non-degenerate perturbation with a weak magnetic anisotropy. Thus, locally, the easy axis of the Cr3+ spin is along the direction of the uniaxial elongation of octahedron. The local easy axes are tilted away from the $b$-direction, following the octahedral rotations (Fig. 1). When this type of anisotropy is combined with the strong symmetric superexchange interactions, requiring a collinear spin alignment, it yields the $b$-axis as the global easy axis of the nearly collinear magnetic structure. Finally, let us note that the swapping from the $G_{z}$ spin configuration in YCrO3 to the $G_{y}$ one in LuCrO3 due to a single ion anisotropy effect has been also proposed in the early work by Kadomtseva et al. Kadomtseva et al. (1981) based on the study of spin reorientation induced by external magnetic fields.

IV Conclusion

The high-pressure stabilized metastable perovskites ScCrO3, InCrO3 and TlCrO3 exhibit a long-range AFM order below T${}_{N}\sim$ 73 K, 93 K and 89 K, respectively. The primary spin configuration in all cases is $C_{y}$-type, where the spins are ferromagnetically coupled along the $b$-axis and antiferromagnetically along both $a$- and $c$-directions. In ScCrO3 and InCrO3, this magnetic structure is stabilized by the FM nearest-neighbour exchange interaction along the $b$-axis and AFM in the $(ac)$ plane, while in TlCrO3, it is due to a strong AFM next-nearest-neighbour exchange. The direction of the spins in the primary magnetic mode is governed by a single ion anisotropy imposed by uniaxial elongation of the CrO6 octahedra. It seems that antisymmetric exchange and single ion effects are in general the dominant mechanisms of the magnetic anisotropy of the Cr-sublattice in orthochromite perovskites with relatively large and small $A$-site cations, respectively.

V Acknowledgments

L. D. thanks support from the Rutherford International Fellowship Programme (RIFP). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreements No.665593 awarded to the Science and Technology Facilities Council. P. M. and D. D. K. acknowledge a support from the project TUMOCS. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreements No.645660. The work done at NIMS was supported by World Premier International Research Center Initiative (WPI Initiative, MEXT, Japan). The work done at Tokyo Institute of Technology was supported by the Grants-in-Aid for Young Scientists A (Grant No.15H05541).