Eects of charge doping on Mott insulator with strong spin-orbit coupling

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Eﬀects of charge doping on Mott insulator with strong spin-orbit coupling,

Ba2Na1−xCaxOsO6

E. Garcia,1R. Cong,1P. C. Forino,2A. Tassetti,2G. Allodi,3A. P. Reyes,4P.

M. Tran,5P. M. Woodward,5C. Franchini,2S. Sanna,2and V. F. Mitrovi´c1

1Department of Physics, Brown University, Providence, Rhode Island 02912, USA

2Department of Physics and Astronomy ”A. Righi”, University of Bologna, I-40127 Bologna, Italy

3Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit´a di Parma I-43124 Parma, Italy

4National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA

5Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA

(Dated: November 28, 2022)

The eﬀects of doping on the electronic evolution of the Mott insulating state have

been extensively studied in eﬀorts to understand mechanisms of emergent quantum

phases of materials. The study of these eﬀects becomes ever more intriguing in the pres-

ence of entanglement between spin and orbital degrees of freedom. Here, we present

a comprehensive investigation of charge doping in the double perovskite Ba2NaOsO6,

a complex Mott insulator where such entanglement plays an important role. We es-

tablish that the insulating magnetic ground state evolves from canted antiferromagnet

(cAF) [1] to N´eel order for dopant levels exceeding ≈10%. Furthermore, we deter-

mine that a broken local point symmetry (BLPS) phase, precursor to the magnetically

ordered state [1], occupies an extended portion of the (H−T) phase diagram with in-

creased doping. This ﬁnding reveals that the breaking of the local cubic symmetry is

driven by a multipolar order, most-likely of the antiferro-quadrupolar type [2, 3].

Introduction

Intricate interplay between strong electron correlations,

and intertwined spin and orbital degrees of freedom leads

to many diverse complex quantum phases of matter [4–7].

Often, correlations of the spin and orbital degrees of free-

dom can be treated on distinct energy scales. However,

this is not the case in systems containing 5dtransition-

metal ions, where spin-orbit coupling (SOC) and electron

correlations are comparable in size [5, 8–14]. As a result,

5dcompounds exhibit a wide range of exotic magnetic

properties, structural distortions, and multipolar order-

ing [1, 3, 4, 15–21]. The underlying physical ground state,

is controlled by the multiplet structure of the constituent

ions, the nature of the chemical bonds in the crystal,

and its symmetry. This complexity often leads to intri-

cate quantum “hidden” orders, elusive to most standard

experimental probes. Nevertheless, the structural, mag-

netic, and electronic properties can be ﬁnely tuned by

altering the degeneracy of a multitude of ground states

varying external perturbations, such as pressure, strain

and doping [20, 22–24].

The expectation, under the simplest picture, is that

Mott insulators with integer number of electrons per site

favor an antiferromagnetic ground state (AFM), and that

charge doping leads to a metal-insulator transition (MIT)

into a conducting state [25]. The most notable example

of doping is the superconducting state in cuprates be-

lieved to emerge from a parent antiferromagnetic Mott

state [26–28]. Speciﬁcally, as doping increases, antiferro-

magnetism gives way to exotic orders such as “stripe”,

unidirectional charge density wave, spin density wave,

and unconventional d-wave superconductivity and with

high enough doping the system becomes a Fermi liq-

uid [26, 28, 29]. In addition to this well known class

of MITs induced in Mott insulators by Coulomb interac-

tions [26, 27, 30–32], insulators purely driven by spin cor-

relations have been recently observed [33]. Yet another

interesting case arises in Mott insulators when a strong

SOC locally entangles the spin and orbital degrees of free-

dom. In such systems unconventional quantum magnetic

and multipolar orders may stabilize [5, 6, 17, 18, 22].

Furthermore, the eﬀects of charge doping are expected

to be strikingly diﬀerent than in systems where SOC can

be treated as a perturbation to electronic correlations

[5, 34–40], because multipolar orbital order and/or com-

plex multi-orbital arrangements favor charge localization.

A representative material of such Mott insulators is the

5d1double perovskite Ba2NaOsO6[41, 42] that evolves

to the 5d2conﬁguration upon charge doping.

This 5d1Os7+ Mott insulator displays a seemingly

contradictory combination of a weak ferromagnetic mo-

ment (∼0.2 µB/ formula unit) below TC≈6.8 K and

a negative Weiss temperature [43]. Its weak mo-

ment at low temperature derives from an exotic canted-

antiferromagnetic (cAFM) phase that is preceded by a

broken local point symmetry (BLPS) state [1, 44, 45].

Fully doped, Ba2CaOsO6, on the other hand, is a

5d2Os6+ Mott insulator that possibly hosts a complex

ferro-octupolar order instead of a simple N´eel AF order

[17, 21, 46, 47]. Interestingly, recent theoretical work

reveals diﬀerent types of multipolar orders in 5d2Mott

insulators, such as ferri-octupolar [48], ferro-octupolar

[22, 49], and antiferro-quadrupolar ordering [2, 3]. Mi-

croscopic study of the magnetic and structural properties

arXiv:2210.05077v2 [cond-mat.str-el] 23 Nov 2022

-80 -60 -40 -20 0 20 40

H (kOe)

0.10

0.05

0.00

-0.05

-0.10

M (μB/f.u.)

1.6

1.2

0.8

0.4

0.0

μeff (μB)

ΘCW (K)

-50

-100

-150

-200

-250

PM state

T (K)

0 20 40 60 80

Vmag (%)

100

a b

0 0.2 0.8 1.00.4 0.6

x - Ca content

AFM

cAFM

7 T TN

11 T TN

0 T TN

1.4

1.2

1.0

0.8

0.6

0.4

Linewidth (MHz)

0.2

0.0

0 0.2 0.4 0.6 0.8 1.0

x - Ca content

1.4 K 11 T

4.2 K 11 T

5 K 7 T

0.006

0.004

0.002

0.000

|K|

1.4 K 11 T

4.2 K 11 T

5 K 7 T

T (K)

T = 2 K

60 80

x = 0

x = 0.125

x = 0.25

x = 0.375

x = 0.50

x = 0

x = 0.125

x = 0.25

x = 0.375

x = 0.5

x = 0.75

x = 0.9

x = 1.0

0.0 0.2 0.4 0.6 0.8 1.0

(μSR)

(NMR)

FIG. 1. Magnetic state evolution as a function of charge doping (x) in Ba2Na1−xCaxOsO6. (a) Magnetic

volume fraction extracted from µSR asymmetry for all doping levels. The magnetic transition temperature is deﬁned as

the 90% ﬁlling of the magnetic volume and increases monotonically with increasing Ca doping. (b) Magnetization as a

function of applied magnetic ﬁeld at 2 K. The results of high temperature (T&50 K) Curie Weiss ﬁttings for magnetic

susceptibility measurements in the PM state are shown in the inset. (c) 23Na NMR spectral linewidth (top) and absolute

value of Knight shift (bottom) as a function of doping concentration at various temperatures. (d) Magnetic phase diagram.

Markers denote magnetic transition to the canted AFM and collinear AFM state for zero-ﬁeld µSR and high ﬁeld NMR

measurements. Solid line serves as a guide to the eye. Typical error bars are on the order of a few percent and not shown

for clarity in panels a - c.

of the double-perovskite 5dcompounds with cubic sym-

metry, as presented here, provides essential guidance for

the development of the relevant theoretical framework for

the description of Mott insulators with strong SOC. Once

identiﬁed, such a theoretical framework can be extended

to more intricate lattices, such as the honeycomb and/or

triangular lattice, where novel types of exotic quantum

orders can be stabilized [2, 5, 14].

Here, we present a comprehensive study of the eﬀect

of charge doping on a Mott insulator with both strong

electron correlations and SOC, represented by the double

perovskite Ba2NaOsO6, from 5d1→5d2. Speciﬁcally,

we investigate the magnetic ﬁeld-temperature (H−T)

phase diagram evolution as a function of charge doping

(x) achieved by Na+/Ca++ heterovalent substitution in

Ba2Na1−xCaxOsO6, employing magnetic resonance tech-

niques. We ﬁnd that the system remains insulating at all

doping levels, implying that the dopants form an inho-

mogeneous electronic state. We compiled a magnetic and

structural phase diagram for dopant concentrations rang-

ing from x= 0 →1. The insulating magnetic ground

state evolves from canted antiferromagnetic (AF) [1] to

N´eel nearly-collinear AF state (hereafter referred to as

collinear AF state for brevity) for dopant levels exceed-

ing ≈10%. Analyzing the complex broadening of the

23Na NMR spectra, which onsets well above the mag-

netic transition, and temperature dependence of NMR

shift, we establish that a cubic to orthorhombic local dis-

tortion of the O-octahedra is present for all compositions

[50, 51]. The local distortion is the signature of a BLPS

phase, identiﬁed as a precursor to the magnetic state in

the single crystals of Ba2NaOsO6[1], and not a trivial

1.4

1.2

1.0

0.8

0.6

0.4

Linewidth (MHz)

0.2

0.0

0.006

0.004

0.002

0.000

|K|

Data

Simulated

Data

Simulated

0.25

0.20

0.15

0.10

Staggered moment (μB)

0.05

0.00

Canting angle (deg)

0.5

0.4

0.3

0.2

Gaussian blur (MHz)

0.1

0.0

0 0.2 0.4 0.6 0.8

0 0.2 0.4 0.6 0.8 1.0

00.2 0.4 0.6 0.8 1.0

0 0.2 0.4 0.6 0.8 1.0

[110]

FIG. 2. Doping evolution of the staggered moment in the low temperature magnetic state. (a) Schematic of

the spin model used to ﬁt the NMR observables. Diﬀerent colors of the arrows denote diﬀerent spin environments at the

Os sites. The two planes with distinctly oriented moments from sub-lattice A and B are shown in diﬀerent shades. (b)

Schematic of the canted spin arrangement by angle φwith respect to the [110] direction in the XY plane. (c) Simulated

and measured NMR spectra linewidth and Knight shift at T= 1.4 K and H= 11 T as a function of Ca doping xin

Ba2Na1−xCaxOsO6.(d) Simulated evolution of the staggered moment, deﬁned as the projection of moments from two

sub-lattices, A and B, along the applied ﬁeld, as a function of doping in the magnetic state. The Gaussian blur, used

to properly account for magnetic broadening, of simulated spectra is shown in the inset. The blur increases abruptly for

x= 0.9. This might be related to the increased inhomogeneity of the local magnetic ﬁeld environment at the Na nuclei site.

Details of this simulation can be found in Supplementary Note 6. (e) Simulated evolution of the canted angle, deﬁned as

the angle between the sub-lattice FM spin orientation and the [110] easy axis, as a function of doping in the magnetically

ordered state. Typical error bars are on the order of a few per cent and not shown for clarity. Solid and dashed line serves

as guide to the eye.

consequence of a simple structural phase transition. The

observation of the breaking of the local cubic symmetry

and concurrent development of the NMR shift anisotropy

for the entire range of dopings investigated implies that

this symmetry breaking is driven by a multipolar order,

most-likely of the antiferro-quadrupolar type [2, 3]. Re-

markably, we ﬁnd that the cubic to orthorhombic local

distortion occurs independently of the exact nature of the

low temperature magnetic state, signaling that the pres-

ence of canted moments is not the sole consequence of

the BLPS [52]. In summary, our ﬁndings evidence that

local distortions persist in the doped samples and that

they favor the onset of an antiferro-quadrupolar order.

Results

We now describe details of our systematic study

of Ba2Na1−xCaxOsO6through the partial heterovalent

substitution of monovalent Na with divalent Ca for

0≤x < 1, performed to better understand the eﬀects of

doping and to elucidate the competing interactions that

drive distinct magnetic ground states utilizing muon-spin

relaxation (µSR), nuclear magnetic resonance (NMR),

and magnetization measurements. We found that the in-

sulting state persists at all doping concentrations despite

the injection of electrons and an evolution into the AFM

state. This ﬁnding is based on thorough examination of

the response of the NMR resonant circuit.

Magnetic state - µSR magnetic volume fraction.

First, we consider the evolution of the magnetic ground

state of Ba2Na1−xCaxOsO6as a function of the Na/Ca

substitution (0 6x61) as probed by zero ﬁeld muon

spin relaxation (ZF-µSR) measurements. In the absence

of an external ﬁeld (H= 0 T), the spin I= 1/2 muon

implanted in the sample precesses around the sponta-

neous local magnetic ﬁeld arising from the magnetically

ordered state at the muon site. The muon precessions are

reﬂected in damped oscillations of the muon asymmetry

decay, probing the fraction of precessing muons, which in

turn is proportional to the magnetic volume (see meth-

ods). Our ZF-muSR asymmetry measurements for the

end members x= 0 and 1 are in agreement with those

previously reported in Refs. [42, 48]. In Fig. 1a, we plot

the temperature evolution of the magnetic volume frac-

tion Vmag as a function of doping. We ﬁnd that samples

of all concentrations display a magnetic transition as the

volume fraction approaches 100% in the low temperature

limit. The transition temperature into a magnetically

ordered state, Tµ

N, deﬁned to be at Vmag = 90%, grows

monotonically from approximately T= 5 K to 40 K as

increasing doping induces a conﬁguration change from

the 5d1to the 5d2[23], as illustrated in Fig. 1d.

Magnetic state - magnetization. We have also per-

formed magnetization measurements to get a better in-

sight into the nature of the magnetic transitions ob-

served through ZF-µSR. In Fig. 1b, we plot magnetiza-

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EectsofchargedopingonMottinsulatorwithstrongspin-orbitcoupling,Ba2Na1xCaxOsO6E.Garcia,1R.Cong,1P.C.Forino,2A.Tassetti,2G.Allodi,3A.P.Reyes,4P.M.Tran,5P.M.Woodward,5C.Franchini,2S.Sanna,2andV.F.Mitrovic11DepartmentofPhysics,BrownUniversity,Providence,RhodeIsland02912,USA2DepartmentofPhysicsandAstro...

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Eects of charge doping on Mott insulator with strong spin-orbit coupling

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