Interplay of magnetism and band topology in Eu 1xCaxMg 2Bi2x0 0.5 from rst principles study Amarjyoti Choudhury1N. Mohanta1and T. Maitra1

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Interplay of magnetism and band topology in Eu1−xCaxMg2Bi2(x=0, 0.5) from ﬁrst

principles study

Amarjyoti Choudhury,1N. Mohanta,1and T. Maitra1, ∗

1Department of Physics, Indian Institute of Technology Roorkee, Roorkee - 247667, Uttarakhand, India

(Dated: October 11, 2022)

Recent discovery of the time reversal symmetry breaking magnetic Weyl semimetals has created a

huge surge of activities in the ﬁeld of quantum topological materials. In this work, we have studied

systematically the ground state magnetic order, electronic structure and the interplay between the

magnetic order and band topology in one such materials, EuMg2Bi2(EMB) and its Ca doped

variant using ﬁrst principles method within the framework of density functional theory (DFT). The

detailed investigation unravels the existence of diﬀerent topological phases in this single material

which can be tuned by an external probe such as magnetic ﬁeld or chemical substitution. Our DFT

calculations including Coulomb correlation (U) and spin-orbit (SO) interaction within GGA+U+SO

approximation conﬁrms that the magnetic ground state of EMB is A-type Antiferromagnetic

(A-AFM) with Eu magnetic moments aligned along the crystallographic aor bdirection. Although

the ground state of EMB is A-AFM, the Ferromagnetic (FM) state lies very close in energy. We

observe a single pair of Weyl points connecting valence and conduction band very close to the

Fermi level (FL) along Γ-A direction in the FM state of EuMg2Bi2with Eu moments aligned along

crystallographic cdirection. On doping 50% Ca at Eu sites, we observe single pair of Weyl points

moving closer to the FL which is highly desirable for application purposes. Further we observe that

the separation between the Weyl points in the pair decreases in doped compound compared to that

in the parent compound which has direct consequence on anomalous Hall conductivity (AHC). Our

ﬁrst principles calculation of AHC shows high peak values exactly at these Weyl points and the peak

height decreases when we dope the system with Ca. Therefore, Ca doping can be a good external

handle to tune AHC in this system.

I. INTRODUCTION

Systems harbouring magnetic order driven topological

phases have recently drawn a great deal of attention

from the researchers in condensed matter physics and

materials science due to their versatility and tunability

in potential device applications such as spintronics1–4.

Since the discovery of topological insulators5, the ﬁeld of

topological phases of matter has exploded with activities

leading to the discovery of many exotic topological

states in materials such as Dirac semimetal6,7, Weyl

semimetal4, nodal line semimetal8,9etc. The robustness

of symmetry protected topological states in these systems

has immense implications for device applications. Very

recently magnetic materials hosting topological states

with strong correlation between magnetism and topology

have come to fore. In topological semimetals a fourfold

degenerate Dirac point can appear at the band crossing

of two bands each of which is doubly degenerate due to

Kramer’s degeneracy when both inversion symmetry (P)

and time reversal symmetry (T) are present. When either

inversion symmetry (P) or time reversal symmetry (T)

is broken, the bands become non-degenerate leading to

a two-fold degenerate point at the band crossing called

Weyl point. Thus a single Dirac point can break into two

Weyl points with opposite chirality. Many nonmagnetic

Weyl semimetal with broken inversion symmetry have

been found till date (e.g. in TaAs10–12 and WTe213 family

of compounds) whereas magnetic Weyl semimetals with

broken time reversal symmetry are still rare.

In non-magnetic materials, the Weyl points (WPs),

FIG. 1. The Hexagonal crystal structure of EuMg2Bi2with

space group P ¯m31 where Eu, Mg and Bi ions are shown in

brown, blue and pink colours respectively.

which appear due to breaking of inversion symmetry,

exist always as multiple of four in the full Brillouin

Zone (BZ) whereas in case of magnetic materials where

the inversion symmetry is preserved but time reversal

symmetry is broken due to intrinsic magnetism, the

possibility of ﬁnding a single pair of Weyl points exists14.

The presence of WPs in a material can give rise to

remarkable emergent phenomena such as the chiral

anomaly eﬀect, large magnetoresistance (MR), strong

intrinsic anomalous Hall and spin Hall eﬀects etc.15

The presence of a single pair of Weyl points in a

material is highly desirable for applications of such

arXiv:2210.04250v1 [cond-mat.mtrl-sci] 9 Oct 2022

eﬀects, for example, the anomalous Hall conductivity

(AHC) depends on the separation between the partners

in a single pair of Weyl points16. Further, a magnetic

material which hosts topological states where diﬀerent

long range magnetic orders have competing energies

can be extremely useful because of their tunability

by external magnetic ﬁeld. The change in magnetic

conﬁguration can substantially change the symmetry of

the material, which may lead to a diﬀerent topological

state.

To ﬁnd a material with minimum number of Weyl

points, i.e., a single pair of WPs in the entire BZ, is

a challenging task. The presence of a single pair of

WPs was predicted theoretically in the ferromagnetic

(FM) phase of the MnBi2Te417. However, experimental

veriﬁcation is not reported yet. Very recently, in

EuCd2As2, both experimental (ARPES) and theoretical

(DFT) work indicated the presence of a single pair of

Weyl points in its FM state with magnetic moments of

the Eu aligned along the caxis18,19. It has been also

found from density functional theory calculations20 that

in EuCd2As2the A-type AFM (ground state) and FM

(excited state) are very close by in energy which was later

supported by the experiment where it was shown that a

tiny external magnetic ﬁeld as small as 2T can turn this

system FM from A-type AFM19. Therefore, EuCd2As2

is the only known material so far to host a single pair of

Weyl points (an ideal Weyl semimetal)15. As discussed

by Wang et al.18, the materials which are either AFM

Dirac semimetal or AFM topological insulator with a tiny

band gap provide a fertile ground to search for a single

pair of WPs in their FM phase. Therefore, EuMg2Bi2

which is a topological insulator having a very tiny gap

as observed by Marshall et al.21 is an ideal compound to

explore for ﬁnding a single pair of Weyl points which is

the main objective of our study here.

In the family of Zintl phase there are many layered

122-type BX2Y2ternary intermetallic compounds which

crystallize mostly into ThCr2Si2-type (tetragonal)

structure, and rarely into CaAl2Si2-type (trigonal)

structure22,23. EuMg2Bi2(EMB) crystallizes in the

CaAl2Si2–type (trigonal) crystal structure with the space

group P¯

3m1(164). The structure consists of rare earth

magnetic Eu ions forming a triangular lattice in ab

plane with simple hexagonal stacking along caxis

separated by MgBi layers (see Fig. 1). Experiments

conﬁrm that the Eu+2 ions with spin 7/2 in EuMg2Bi2

undergo a magnetic transition from the paramagnetic to

antiferromagnetic state at a temperature close to 7K24.

The temperature dependent magnetic susceptibility

measurement by May et al.24 indicated an anisotropic

behaviour with susceptibility along cbeing lower than

that in the ab-plane from where the authors concluded

that the magnetic moments are aligned along caxis.

Later, Pakhira et al.25 by analyzing the anisotropic

magnetic susceptibility using the molecular ﬁeld theory

(MFT) proposed that the magnetic structure of the EMB

to be a c-axis helix AFM where the magnetic moments of

(d)(c)

(a) (b)

FIG. 2. Diﬀerent magnetic conﬁgurations considered in our

calculation (see text): (a) FMc, (b) A-AFMc, (c) A-AFMb

(d) A-AFMx.

Eu are ferromagnetically aligned in ab plane with a turn

angle of 120◦between adjacent Eu layers along the c

direction. Very recent neutron diﬀraction measurements

in single crystal EuMg2Bi2by two groups21,26 reveal

that the magnetic structure is A-type AFM (magnetic

moments are ferromagnetically aligned in the ab plane

whereas they are antiferromagnetically aligned along

cdirection) with Eu moments in the residing in the

ab-plane. DFT calculations performed by Marshall et

al. further shows that this compound is a topological

insulator21. Marshall et al.27 have also reported in

another very recent experimental work the Ca doping at

Eu sites in EMB and observed that upon increasing the

Ca doping the ground state magnetic structure changes

from A-AFM to FM in this system. To understand

the above all experimental observations which indicate a

strong interplay of magnetic and topological properties in

this compound similar to the compounds EuCd2As218,20

and EuCd2Sb228 where topological properties are seen to

vary with the magnetic conﬁguration we have carried out

a systematic study of magnetic order, electronic structure

and topological properties of EMB and its Ca doped

variant density functional theory calculations.

The paper is arranged in the following way. We provide

the details of the methods used in our calculations in

section II. In section III, we present our results in three

subsections: (A) Magnetic order and electronic structure,

(B) Magnetic order and Topological properties and (C)

Ca doped EuMg2Bi2: Topological properties). Section

IV contains conclusions and section V acknowledgements.

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InterplayofmagnetismandbandtopologyinEu1xCaxMg2Bi2(x=0,0.5)fromrstprinciplesstudyAmarjyotiChoudhury,1N.Mohanta,1andT.Maitra1,1DepartmentofPhysics,IndianInstituteofTechnologyRoorkee,Roorkee-247667,Uttarakhand,India(Dated:October11,2022)RecentdiscoveryofthetimereversalsymmetrybreakingmagneticWeylsem...

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Interplay of magnetism and band topology in Eu 1xCaxMg 2Bi2x0 0.5 from rst principles study Amarjyoti Choudhury1N. Mohanta1and T. Maitra1

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