Oxygen vacancies at the origin of pinned moments in oxide interfaces the example of tetragonal CuOSrTiO 3 Benjamin Bacq-Labreuil1Benjamin Lenz2yand Silke Biermann1 3 4 5z

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Oxygen vacancies at the origin of pinned moments in oxide interfaces: the example of

tetragonal CuO/SrTiO3

Benjamin Bacq-Labreuil,1, ∗Benjamin Lenz,2, †and Silke Biermann1, 3, 4, 5, ‡

1CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, F-91128 Palaiseau, France

2Institut de Min´eralogie, de Physique des Mat´eriaux et de Cosmochimie,

Sorbonne Universit´e, CNRS, MNHN, IRD, 4 Place Jussieu, 75252 Paris, France

3Coll`ege de France, 11 place Marcelin Berthelot, 75005 Paris, France

4Department of Physics, Division of Mathematical Physics,

Lund University, Professorsgatan 1, 22363 Lund, Sweden

5European Theoretical Spectroscopy Facility, Europe

(Dated: October 28, 2022)

Obtaining an accurate theoretical description of the emergent phenomena in oxide heterostruc-

tures is a major challenge. Recently, intriguing paramagnetic spin and pinned orbital moments have

been discovered by x-ray magnetic circular dichro¨ısm measurements at the Cu L2,3-edge of a tetrag-

onal CuO/SrTiO3heterostructure. Using ﬁrst principles calculations, we propose a scenario that

explains both types of moments, based on the formation of oxygen vacancies in the TiO2interface

layer. We show the emergence of a paramagnetic 2D electron gas hosted in the interface CuO layer.

It is invisible at the Ti L2,3-edge since the valence of the Ti atoms remains unchanged. Strong struc-

tural distortions breaking both the local and global fourfold rotation C4symmetries at the interface

lead to the in-plane pinning of the Cu orbital moment close to the vacancy. Our results, and in

particular the pinning of the orbital moment, may have implications for other systems, especially

monoxide/dioxide interfaces with similar metal-oxygen bond length and weak spin-orbit coupling.

I. INTRODUCTION

Oxide heterostructures are promising hosts for a large

range of applications [1,2], and oﬀer countless possi-

ble conﬁgurations allowed by epitaxial thin-ﬁlm depo-

sition techniques [3]. A particular example are copper

monoxide CuO thin ﬁlms, which grow in a tetragonal

crystal structure on a SrTiO3(STO) substrate [4,5],

whereas its bulk counterpart displays a low-symmetry

monoclinic structure [6]. Tetragonal CuO (t-CuO) is

made of a staggered stacking of 2D CuO planes along

the caxis. Its tetragonal distortion is characterized by

the apical Cu-O distance being 1.37 times larger than

the basal distance [4,7]. t-CuO is arguably the cuprate

with the simplest crystal structure, making it an ideal

candidate for connecting the low-energy eﬀective models

for cuprates [8–13] to the real materials.

A key step in this direction is the understanding of

the properties of undoped t-CuO. The experimentally

observed tetragonal distortions were reproduced using

density functional theory (DFT) with hybrid function-

als [14], and traced back to Jahn-Teller orbital order-

ing [15,16]. In agreement with resonant inelastic x-ray

scattering (RIXS) [17] and muon spin resonance mea-

surements [18], it was shown that the CuO layers dis-

play an antiferromagnetic stripe order [14–16]. A ﬁrst

application of strongly-correlated electron techniques to

t-CuO [19] gave an explanation to the sublattice decou-

pling observed in RIXS [17], angle-resolved photoemis-

∗benjamin.bacq-labreuil@polytechnique.edu

†benjamin.lenz@sorbonne-universite.fr

‡silke.biermann@polytechnique.edu

sion spectroscopy [20], as well as scanning tunnelling mi-

croscopy (STM) [5].

This set of experimental and theoretical works would

yield a coherent understanding of undoped t-CuO, if it

was not for the recent ﬁnding of an isotropic paramag-

netic spin and pinned orbital moment in t-CuO/STO

samples, by X-ray magnetic circular dichro¨ısm (XMCD)

measurements at the Cu L2,3-edge [18]. The existence of

these moments is puzzling since t-CuO is antiferromag-

netically ordered and does not contain any element with

strong spin-orbit coupling (SOC). Hernandez et al. has

advanced a scenario in Ref. 18, in which t-CuO would

be composed of ferromagnetically ordered CuO layers,

which are antiferromagnetically stacked along the caxis

(out-of-plane). The last CuO layer would be paramag-

netic hence would follow the magnetic ﬁeld, while an-

other layer would be uncompensated and therefore would

yield the pinned moments. Although this scenario would

qualitatively account for the experimental observations,

it encounters several diﬃculties: (i) the ferromagnetic or-

dering inside each layer is in contradiction with all previ-

ous experimental [17] and theoretical [14–16,19] ﬁndings,

(ii) the uncompensated layer is composed of spin mo-

ments and not orbital ones, whereas the observed pinned

moment is mainly of orbital character, (iii) there is no

reason why one layer should have a paramagnetic behav-

ior, especially if it is ferromagnetically ordered. An alter-

native explanation would reside in the existence of a 2D

electron gas (2DEG) at the t-CuO/STO interface, as was

found in other heterostructures such as BiMnO3/STO,

LaAlO3/STO and γ-Al2O3/STO [21–23]. However, in

these studies the spin moment is observed at the Ti L2,3-

edge, corresponding to the existence of a Ti3+ valence

conﬁguration, contrary to t-CuO/STO for which no Ti3+

arXiv:2210.15084v1 [cond-mat.mtrl-sci] 26 Oct 2022

a) b)

CuO-4 CuO-3 CuO-2 CuO-1 TiO2-2 SrO-2 TiO2-1 SrO-1

FIG. 1. (a) Layer-resolved DOS calculated for the t-CuO/STO junction without defect. The colored shaded area depicts the

occupied states, and the gray shaded patches highlight the gap in each layer. (b) Projected DOS on the px,y,z orbitals of the

O atoms in the two TiO2layers corresponding to the two framed panels in (a).

O Vacancy in TiO2

O Vacancy in CuO

O Vacancy in CuO above Ti

Double neighbour O Vacancy in TiO2

Double O Vacancy in TiO2

O Vacancy

FIG. 2. (a)-(c) Zoom on the two interface CuO-1 and TiO2-

2 layers presenting the 5 vacancy conﬁgurations considered

in this work. The black lines between O and Cu/Ti atom

show that half of the O in the CuO-1 layer do not have a Ti

neighbor.

signal was found [18]. The 2DEG scenario was therefore

ruled out in Ref. 18, leaving the question of the origin of

these moments open.

In this paper, using ﬁrst principles DFT+Ucalcula-

tions for the t-CuO/STO heterostructure, we show that

the 2DEG scenario is in fact not incompatible with the

recent XMCD measurements. Since oxygen vacancies

can generate a 2DEG, as was seen experimentally for

AlOx/ZnO [24], STO [25] and γ-Al2O3/STO [26], as well

as magnetic moments at the surface of STO [27,28], we

study the formation of oxygen vacancies at the interface.

By comparing diﬀerent vacancy conﬁgurations, we show

that a spin polarized 2DEG hosted in the CuO layer can

emerge when the defect is inserted in the TiO2interface

layer. Most importantly, in such a case the overall va-

lence of the Ti atoms remains unchanged with respect

to the bulk, such that the 2DEG would be invisible at

the Ti L2,3-edge. If in our calculations the 2DEG is spin

polarized due to the ﬁnite size of our unit cells and the

speciﬁc arrangement of stripes and vacancies, it would

be truly paramagnetic in the real material since the va-

cancies are randomly distributed. Moreover, large dis-

tortions are induced in the interface CuO layer, leading

to the breaking of both the local and global C4symme-

tries in the CuO layer above the vacancy. This translates

into a pinning of the in-plane component of the orbital

moment. Our scenario therefore provides a mechanism

for the paramagnetic spin moment, being a consequence

of the emergence of a 2DEG, as well as for the pinned

orbital moment, resulting from the breaking of the local

and global C4symmetries.

II. MODEL AND METHOD

To simulate the t-CuO/STO junction we use unit cells

of the type shown in Fig. 1(a): the CuO layers are

stacked onto a 2 unit cell-thick TiO2-terminated STO

substrate [7,29,30]. We apply DFT+U[31] using the

Perdew–Burke–Ernzerhof (PBE) functional [32], with a

local Hubbard interaction U= 6eV on the Cu dorbitals.

Since we are interested in interpreting the XMCD mea-

surements of Ref. 18, we make sure that our unit cells en-

able the theoretically [14–16] and experimentally [17] ob-

served antiferromagnetic stripe ordering within the CuO

layers. The unit cell is doubled in the (x,y) plane (see

Fig. 2) when inserting an O vacancy. To keep the compu-

tations tractable we restrict our model to a 4 CuO layers

coverage. We refer to each layer following the nomencla-

ture of Fig. 1(a): CuO-{1,2,3,4}, SrO-{1,2}and TiO2-

{1,2}. It was shown that the experimental density of

states (DOS) is best reproduced using hybrid DFT with

a) b)

O Vacancy

2.314 Å

2.331 Å

1.908 Å

2.074 Å

1.930 Å

1.931 Å

2.076 Å

2.331 Å

2.074 Å

41.930 Å

1.908 Å

51.909 Å

1.909 Å

1.931 Å

2.076 Å

O vacancy

CuO-4

CuO-3

CuO-2

CuO-1

TiO2-2

SrO-2

TiO2-1

SrO-1

FIG. 3. (a) Layer-resolved DOS calculated for the case of an O vacancy in the CuO-1 layer. (b)-(c) Site and orbital projected

DOS for the Cu atoms at the CuO-1 interface layer corresponding to the framed panel in (a). (d) Spin density map of the

interface CuO-1 layer. (e) Band structure and projected DOS zoomed on the in-gap states along with the ﬁtted Wannier bands

(top) resulting in the Wannier orbitals showed in the bottom around the vacancy, which are centered on the four NN Cu sites

highlighted with the dotted frame in (d). The band color depicts the ratio λxy

λz22

between the contributions from dxy and dz2.

a 8 CuO layers coverage [29], so we chose to set the in-

terlayer distances (up to the 4th CuO layer) according

to the values obtained by Franchini et al. [29]. We use a

lateral lattice parameter a= 3.9

A for STO, as was ob-

tained with hybrid DFT [33,34] in excellent agreement

with the experiments [35].

We ﬁrst perform ionic relaxation calculations using the

Vienna ab initio simulation package (VASP) [36–38] with

a 6 ×6×1 Monkhorst-Pack grid, until the maximum

force is smaller than 10meV on each atom. The CuO

layers are relaxed while the STO atoms are kept ﬁxed ex-

cept when considering an oxygen vacancy in the TiO2-2

interface layer, in which case the whole structure is op-

timized. We use PAW-PBE pseudo-potentials [39] with

a cut-oﬀ energy of 400eV for the bare interface, which

is increased up to 600eV for the larger unit cells with

vacancies. Then, we extract all the results presented in

this paper from all-electron full-potential PBE+U calcu-

lations using the Wien2k package [40,41] with a 6×6×1

Monkhorst-Pack grid done on the relaxed structure as

obtained from VASP. Due to computational limitations

we controlled the size of the planewave basis set by reduc-

ing the RKmax value when necessary (the smallest value

being 5.14), and we checked that limiting the basis set

size did not have a signiﬁcant impact on the DOS. The

Wannier ﬁts were obtained using the wannier90 [20,42]

package.

III. RESULTS

A. Bare Interface

From previous studies on the t-CuO/STO junction we

know that the bare (i.e. defect-free) interface should not

yield a 2DEG [29,30]. This is consistent with our results,

see Fig. 1(a), in which we plot the layer-projected DOS.

The gap ∆DF T +U'1.5eV in t-CuO is layer independent

and in good agreement with previous DFT+U calcula-

tions [30], although smaller than the photoemission lower

bound ∆ARP ES = 2.4eV [20]. The situation is diﬀerent

in the STO substrate where a clear diﬀerence can be seen

between the interface and bulk TiO2layers: the gap is

reduced from 2eV in the bulk (TiO2-1) to 1.5eV at the in-

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Oxygenvacanciesattheoriginofpinnedmomentsinoxideinterfaces:theexampleoftetragonalCuO/SrTiO3BenjaminBacq-Labreuil,1,BenjaminLenz,2,yandSilkeBiermann1,3,4,5,z1CPHT,CNRS,EcolePolytechnique,InstitutPolytechniquedeParis,F-91128Palaiseau,France2InstitutdeMineralogie,dePhysiquedesMateriauxetdeCosmochimi...

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Oxygen vacancies at the origin of pinned moments in oxide interfaces the example of tetragonal CuOSrTiO 3 Benjamin Bacq-Labreuil1Benjamin Lenz2yand Silke Biermann1 3 4 5z

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