Giant orbital polarization of Ni²⁺ in square planar environment

INTRODUCTION

Ever since the discovery, understanding the mechanism of high temperature superconductivity in cuprates remains an open problem in condensed matter physics Bednorz:1986p189 . Over the years, the importance of several factors, such as the antiferromagnetic, insulating phase of the parent compound, large orbital polarization, strong hybridization between Cu $d$ and O $p$ states, and Zhang Rice (ZR) physics have been recognized to play a role in the hole doped superconducting phase  Lee:2006p17 ; Fradkin:2015p457 ; Keimer:2015p179 . After the prediction of achieving cuprate like Fermi surface in a three-dimensional compound LaNiO₃ through orbital engineering Anisimov:1999p7901 ; Chaloupka:2008p016404 ; Hansmann:2009p016401 , various types of artificial structures of $RE$NiO₃ family have been extensively investigated Middey:2016p305 ; Freeland:2011p57004 ; Benckiser:2011p189 ; Wu:2013p125124 . However, the observed orbital polarization in an octahedral crystal field is low (maximum 25%) and superconductivity remains elusive there, prompting to search for other Ni based compounds with lower dimensional structure Poltavets:2010p206403 ; Cheng:2012p236403 ; Zhang:2017p864 .

The recent finding of superconductivity in Sr doped NdNiO₂ having Ni in a square planar oxygen environment is a monumental development Li:2019p624 , and strongly implies that the local structure ($O_{h}$ vs. $D_{4h}$ in Fig. 1(a)) plays a crucial role. This discovery has also led to a large number of works within a short span of time to understand the origin and nature of the superconducting phase Hepting:2020p381 ; li2020superconducting ; zeng:2020phase ; Botana:2020p011024 ; Lechermann:2020p081110 ; Jiang:2019p201106 ; karp:2020 ; Hu:2019p032046 ; adhikary2020orbital ; Mi:2020p207004 ; Hu:2019p032046 ; Zhang2020p023112 ; Zhang:2020p013214 ; Lang:2020doped ; karp:2020many ; Krishna:2020arxiv . While the parent members of the superconducting nickelate and cuprate family are isoelectronic ($d^{9}$), several key differences have been noted: unlike the antiferromagnetic insulating phase of the cuprate, NdNiO₂ is weakly conducting and nonmagnetic Li:2019p624 . Ni $d_{x^{2}-y^{2}}$ states are found to be strongly hybridized with Nd 5$d$ states Hepting:2020p381 and the superconducting $T_{c}$ of infinite layer nickelates is much smaller compared to the analogous hole doped CaCuO₂ li2020superconducting ; zeng:2020phase ; Azuma:1992p775 . There is also an ongoing strong debate about the location of doped holes (O $p$ vs. Ni $d$) and the nature of Ni spins states (singlet vs. triplet), which would be intimately connected with the orbital configuration and Hund’s coupling Lang:2020doped ; karp:2020many ; Mi:2020p207004 ; Hu:2019p032046 ; Zhang2020p023112 ; Zhang:2020p013214 ; goodge2020doping . However, the actual scenario is unknown due to the very limited amount of experimental literature available. This prompts us to probe other compounds containing both Cu and Ni in four fold coordinated environment of oxygen.

Sr₂CuO₃ (SCO) contains square planar CuO₄ polyhedral units, which form linear chains along the $b$ axis, as shown in Fig. 1(b) Motoyama:1996p3212 . This quasi one dimensional system undergoes antiferromagnetic ordering around 5 K Kojima:1997p1787 , and exhibits several intriguing phenomena, including spin-charge separation Neudert:1998p657 , spin-orbital separation Schlappa:2012p82 , and spin Seebeck effect Hirobe:2017p30 . Hole doping in SCO by incorporating excess oxygen further results in superconductivity Hiroi:1993p315 . In addition, one can replace a small fraction of Cu of SCO with Ni without modifying structure Karmakar:2015p224401 , providing us a unique platform to compare the electronic structure of Cu and Ni with a square planar environment.

The electronic properties of transition metal (TM) oxides are described very often within the scheme of well-known Zaanen-Sawatzky-Allen (ZSA) phase diagram Zaanen:1985p418 ; Nimkar:1993p7355 , which considers on-site Coulomb repulsion at TM site ($U$), TM-to-O charge transfer energy ($\Delta$) and the electronic hopping interaction strength ($t$). Cu in SCO has an extremely small value of $\Delta$ Maiti:1998p1572 , implying that the ground state of Cu²⁺ in SCO consists of a linear combination of $d^{9}$ and dominant $d^{10}\underline{L}$ configurations ($\underline{L}$ denotes a hole in O 2$p$ state) - contrary to the pure $d^{9}$ state expected from an ionic picture walters:2009p867 .

In this work, we have investigated the electronic and magnetic structure of Sr₂CuO₃ (SCO) and Sr₂Cu_0.9Ni_0.1O₃ (SCNO) single crystals by magnetic measurement, synchrotron based X-ray linear dichroism (XLD) measurements, density functional theory (DFT) and cluster calculations. We observed extremely large orbital polarization of Ni in Sr₂Cu_0.9Ni_0.1O₃ single crystal, which arises due to the low spin $S$=0 configuration with completely unoccupied 3$d_{x^{2}-y^{2}}$ orbitals of Ni²⁺. Ni doping of SCO also enhances the contribution of the $d^{9}$ configuration in the ground state of Cu²⁺. Our comprehensive study has also affirmed Mott Hubbard insulating nature of the NiO₄ unit and larger charge transfer energy compared to high $T_{c}$ cuprate.

RESULTS

Single crystals of SCO and SCNO, grown by the traveling solvent floating zone technique karmakar:2015p4843 have been investigated in this study. We first discuss the results of polarization dependent XAS (X-ray absorption spectroscopy) experiment on Cu $L_{3,2}$ edges, which is known to be a very powerful technique to probe orbital symmetry of cuprates Nucker:1995p8529 ; Knupfer:1997pR7291 ; Neudert:2000p10752 ; Chakhalian:2007p1114 . In Fig. 1(c), we compare linear polarization dependent XAS of Cu $L_{3}$ and $L_{2}$ edges for SCO and SCNO. XAS (I_ab) of SCO recorded with in-plane (H) polarized light consists of sharp peaks around 930.5 eV and 950.5 eV, which are associated with the transition from the spin-orbit split Cu $2p_{3/2}$ and Cu $2p_{1/2}$ core levels, respectively, and the final state configuration is 2$\underline{p}$3$d^{10}$ (2$\underline{p}$ denotes a core hole in Cu 2$p$ states). The much lower intensity of these peaks in XAS (I_c) with the out-of-plane (V) polarization signifies that the upper Hubbard band (UHB) is predominately contributed by Cu $d_{x^{2}-y^{2}}$ orbitals, which is expected for a $d^{9}$ electronic configuration in $D_{4h}$ symmetry. The features around 934 eV and 954.5 eV, which are much stronger for the out-of-plane polarization, are related to the transitions into Cu 3$d_{3z^{2}-r^{2}}$ derived states, which become partially unoccupied due to the hybridization with Cu 4$s$ states Neudert:2000p10752 . Upon Ni doping, the intensity of the white line increases significantly for both polarizations though the line shape remains unchanged (Fig. 1(c)). The origin of the increase of the $d^{9}$ configuration upon Ni doping will be discussed later in this paper.

Next, we have performed similar polarization dependent XAS experiments at Ni L_3,2 edges of SCNO at 300 K. As shown in Fig. 2(a), the two intense peaks around 853 eV & 870 eV in the spectra (I_ab) recorded with the in-plane polarization, correspond to the transitions from Ni $2p_{3/2}$ and Ni $2p_{1/2}$ core levels respectively. The spectrum (I_c) recorded with the out-plane polarization shows significantly low intensity indicating that the holes predominantly occupy the $d_{x^{2}-y^{2}}$ bands. The peaks around 856 eV and 874 eV, show higher intensity in I_c than I_ab . Similar to the case of Cu, these features are related to the hybridization of Ni 3$d_{3z^{2}-r^{2}}$ and Ni 4$s$ states. Since the experimental realization of large orbital polarization (OP) in Ni based oxides, with important implications for superconductivity, has been a topic of paramount interest Disa:2015p026801 ; Wu:2013p125124 ; Zhang:2017p864 ; Liao_2019 , we have further evaluated OP of Ni in the present case. According to the sum rule of linear polarization, the ratio of holes in $d_{3z^{2}-r^{2}}$ and $d_{x^{2}-y^{2}}$ Wu:2013p125124 is defined as

with $\mathrm{I^{\prime}_{ab,c}}$=$\int\mathrm{I_{ab,c}}(E)dE$. By this definition, $X$=1 corresponds to equal hole population in $d_{3z^{2}-r^{2}}$ and $d_{x^{2}-y^{2}}$ orbitals and $X$= 0 signifies 100% $d_{x^{2}-y^{2}}$ character of holes. We have obtained $X\approx$ 0.23 (also see Supplementary Materials) in the present case. This implies 81% of the holes occupy Ni 3$d_{x^{2}-y^{2}}$ orbital, which is the highest among the existing literature of Ni based complex oxides (see Table  1).

The orbital polarization ($P$) is defined in the literature in terms of the electronic occupation as  Wu:2013p125124

where $n_{x^{2}-y^{2}}$= 2 - $h_{x^{2}-y^{2}}$ and $n_{3z^{2}-r^{2}}$=2 - $h_{3z^{2}-r^{2}}$ are the number of electrons in $d_{x^{2}-y^{2}}$ and $d_{3z^{2}-r^{2}}$ orbitals, respectively. It is important to note that the value of $n^{\prime}$ (=$n_{x^{2}-y^{2}}$ + $n_{3z^{2}-r^{2}}$) can not be determined unambiguously for many compounds due to the presence of charge transfer from O 2$p$ to Ni 3$d$ orbitals Wu:2013p125124 ; Peil:2014p045128 . In the present case, $n^{\prime}$ =2 as the ground state wavefunction is almost entirely contributed by the $d^{8}$ configuration (discussed in the later part of the paper). We have obtained $P\approx$ 63% for the SCNO, which is also larger compared to all existing literatures on Ni based complex oxides Middey:2016p305 ; Disa:2015p026801 ; Wu:2013p125124 ; Middey:2016p056801 ; Zhang:2017p864 ; Liao_2019 .

In order to understand the origin of this unprecedentedly large orbital polarization, we have calculated XAS [(I_ab + I_c)/2] and XLD [I_ab-I_c] of Ni $L_{3,2}$ edges considering a NiO₄ cluster with $D_{4h}$ symmetry and Ni²⁺ ionic configuration using CTM4XAS Stavitski:2010p687 and Quanty  retegan_crispy programs that incorporate ligand field multiplet theory. First, we have simulated the XAS and XLD spectra (Fig. 2(b)) for the high spin $S$ = 1 configuration  Utz_2017 ; van_der_Laan_1988 with $U$= 7 eV and $\Delta$ = 9 eV (all other parameters, used for the simulations have been listed in Ref. calc, ). Clearly, neither the simulated XAS nor the XLD matches with the corresponding experimental spectra. In particular, the experimentally observed $L_{2}$-edge XAS shows only one peak around 870 eV whereas the simulated spectra shows two peaks. The shape of the simulated XLD is completely different and the amount of anisotropy is significantly lower compared to the experimental data. We have also simulated XAS and XLD with the same values of $U$ and $\Delta$ but with low spin configuration ($S$ = 0) by adjusting crystal field parameters calc , which ensures the following expected crystal field splitting $d_{3z^{2}-r^{2}}<d_{xz/yz}<d_{xy}<d_{x^{2}-y^{2}}$ for a square planar environment Moretti_Sala_2011 . The excellent matching (Fig.  2(c)) between the experimentally observed and simulated spectra with low spin configuration establishes Ni²⁺ is in $S$=0 state in the square planar environment. The ground state of Ni²⁺ is strongly dominated by the $|d^{8}\rangle$ configuration ($\approx$ 0.97 $|d^{8}\rangle$ + 0.03 $|d^{9}\underline{\textit{L}}\rangle$). Simulated spectra with $U>\Delta$ also do not match with experimental observation (see Supplementary Materials), implying electronically NiO₄ belongs to the Mott Hubbard insulating region of ZSA phase diagram Zaanen:1985p418 - strikingly similar to the recent experimental reports of the hole doped NdNiO₂ Hepting:2020p381 ; goodge2020doping . Due to the large $\Delta$, Ni $d$ is less hybridized with O $p$, compared to the Cu $d$-O $p$ hybridization. Thus, the replacement of a fraction of Cu by Ni pushes holes from O $p$ towards Cu $d$ around the dopant Ni. This enhances the relative contribution of $d^{9}$ configuration (also confirmed by magnetic measurement, discussed later in the paper), resulting in the observed strong increase in the white line intensity in Cu XAS upon Ni doping (Fig. 1(c)).

The increase of the $d^{9}$ component of Cu due to the presence of nonmagnetic Ni²⁺ is also evident in bulk magnetic measurements. The low-temperature magnetic susceptibility ($\chi$) plots of pristine, 1%, and 10% Ni doped SCO samples are shown in Fig.  3. As expected, $\chi$ for the pristine sample is very small due to the antiferromagnetic coupling between the neighboring Cu spins. Upon doping with Ni at the Cu-site, the -O-Cu-O-Cu-O- chain breaks into finite length segments due to an effective spin 0 on the Ni ion. The number of segments thus produced being $p$ + 1 $\sim p$ for large $p$, where $p$ is the concentration of Ni in the sample. Assuming a statistically random distribution of Ni ions over the chain length, it is reasonable to consider that one-half of the chain segments will have an odd number of Cu spins, and even for the remaining. Since Cu-spins are antiferromagnetically paired, the net moment on the even-length segments tends to 0 at sufficiently low-temperatures Ami:1995p5994 . In contrast, the odd-length segments remain with an uncompensated Cu spin, which results in an enhancement in the magnetic response of Ni doped samples, as seen in our measurement (Fig.  3). A very weak Curie-tail in the pristine sample can be attributed to the presence of intrinsic defects. We fitted the low-temperature susceptibility of our samples using the Curie-Weiss (CW) law: $\chi$=$\chi_{0}$+ $C/(T-\theta_{CW})$ where $\chi_{0}$ is the temperature independent contribution arising due to Van Vleck paramagnetism and core diamagnetism, $C$ is the Curie-constant, and $\theta_{CW}$ is the Weiss temperature. The best fit parameters for the three samples are tabulated in Table 2.

It is reassuring to note that the value of $C$ increases by a factor of 10 on increasing the Ni concentration from $p$ = 0.01 to 0.1. $\chi_{0}$ for SCNOis positive and about an order of magnitude higher than for SCO. Such an enhancement is likely due to the Van Vleck paramagnetism associated with unoccupied $d_{x^{2}-y^{2}}$ orbital of Ni²⁺ ion in the low-spin state van1932book . From $C$, the $\mu_{\mathrm{eff}}$ (=$\sqrt{8C}$) for the two Ni doped samples ($p$ = 0.01 and 0.1) turned out to be $\sim$ 0.12 $\mu_{B}$ and $\sim$ 0.38 $\mu_{B}$ per formula unit respectively. The average effective moment on the odd-length segments (=$\sqrt{8C/(0.5p)}$) turns out to be 1.74 $\mu_{B}$ and 1.70 $\mu_{B}$, respectively for the two samples. These values are close to an effective moment of $\sim$ 1.73 $\mu_{B}$ expected for a $S$ = 1/2 ($d^{9}$) system, confirming our conclusion of Cu XAS measurement.

To obtain a microscopic understanding of our experimental observations, we have carried out first-principles density functional theory (DFT) calculations for Sr₂CuO₃ and Sr₂Cu_0.875Ni_0.125O₃ [see Methods for details of the calculations]. The calculated orbital projected density of states (DOS) are shown in Fig. 4. In contrast with the transition metal oxides with positive $\Delta$, the bonding states of SCO are primarily contributed by Cu $d$ orbitals due to negative $\Delta$ Ushakov:2011p445601 . The Cu $d_{xy}$, $d_{xz}$, $d_{yz}$ and $d_{3z^{2}-r^{2}}$ bonding states are spread around 6 eV below the Fermi level (Fig. 4(b)). The valence band and conduction band edge of undoped SCO comes predominantly from O $p$ states (inset of upper panel of Fig. 4(a)), as expected for the covalent insulating nature of SCO Maiti:1998p1572 . The $d_{x^{2}-y^{2}}$ antibonding states are partially unoccupied and show a pronounced contribution to the upper Hubbard band, in line with our XAS results. We find that the magnetic moment on Cu is close to 0.19 $\mu_{B}$. The slight overestimation of this moment, compared to the experimentally observed moment ($\sim$ 0.06$\mu_{B}$) Kojima:1997p1787 is likely to be related to the presence of the quantum fluctuation effects in SCO, which are not accounted for in a mean field approach like DFT.. The much smaller moment, compared to the expected moment of 1.73$\mu_{B}$ for a pure $d^{9}$ ($S$=1/2) configuration, again signifies that the ground state of Cu²⁺ in SCO is predominantly $d^{10}\underline{L}$ configuration with small admixture with $d^{9}$. In Ni doped SCO, there is a small increase in Cu magnetic moments, which range from 0.19 to 0.25 $\mu_{B}$ and a net moment of $\sim$ 0.13 $\mu_{B}$ per formulae unit. This also supports our observation about the increase of white line intensity of Cu XAS (Fig. 1(c)) and magnetic measurement i.e. the enhancement of $d^{9}$ configuration of Cu upon Ni doping. For Ni doped SCO, the contribution arising from different Ni $d$ orbitals is shown in Fig.  4(c) (also see lower panel of Fig.  4(a)). We find that the antibonding states of Ni $d_{x^{2}-y^{2}}$ orbital are completely unoccupied, while all other Ni 3$d$ states are completely filled. This low spin $S$=0 configuration of Ni with holes in the $d_{x^{2}-y^{2}}$ orbital is in excellent agreement with our experimental observations.

DISCUSSION

To summarize, our element sensitive X-ray absorption spectroscopy experiments with linear polarized light on Sr₂Cu_0.9Ni_0.1O₃ have found that 81% holes of Ni²⁺ sites occupy the $d_{x^{2}-y^{2}}$ orbital, which is the highest among all Ni containing oxides reported so far. Ni doping in Sr₂CuO₃ also results in hole transfer from O $p$ to Cu $d$ orbitals. Cluster calculations have not only confirmed the Mott Hubbard insulating nature of NiO₄ units but also revealed that the observed giant orbital polarization arises due to low spin ($S$=0) configuration of Ni²⁺. This nonmagnetic state of Ni²⁺ has been further corroborated by $ab$ $initio$ theory.

Finally, we also note that our investigated system has several parallels with the recently discovered superconducting nickelates. Our system comprises of NiO₄ units forming one dimensional chains, while the superconducting nickelates have a two dimensional NiO₂ plane. It is expected that the increase in the dimensionality of the system would further enhance $\Delta$ Maiti:1999p12457 , and therefore our conclusions about the Mott-Hubbard nature and the low spin configuration of Ni²⁺ should also hold for nickelate superconductors. The larger charge transfer energy might be responsible for the observed lower $T_{c}$ in hole doped nickelates Zhang:2020p013214 ; Lechermann:2020p081110 ; Jiang:2019p201106 .

MATERIALS AND METHODS

Single crystals of SCO and SCNO were grown under O₂ atmosphere using the traveling solvent floating zone technique as reported elsewhere karmakar:2015p4843 . All the experiments reported here are carried out on as grown crystals. The magnetic susceptibility was measured using a Physical Property Measurement System, Quantum Design, USA. X-ray absorption spectra (XAS) with vertically (V) and horizontally (H) polarized X-ray were recorded at room temperature in 4-ID-C beamline of Advanced Photon Source, Argonne National Laboratory, USA.

All theoretical calculations have been performed within the framework of density functional theory as implemented in the Quantum Espresso package Giannozzi:2009p395502 . The wave functions are expanded in a plane wave basis set with kinetic and charge density cut offs set to 45 Ry and 450 Ry respectively. The exchange-correlation interactions are taken into account by the Perdew-Burke-Ernzeroff form of generalized gradient approximation Perdew:1996p3865 . The ion-electron interactions are described by ultrasoft pseudopotentials Vanderbilt:1990p7892 . The on-site Coulomb interaction is modeled using LDA+$U$ approach in the linear-response method of Cococcioni and de Gironcoli Cococcioni:2005p3 , with $U$ = 5 eV and 9 eV on Ni and Cu, respectively.