Tuning bulk topological magnon properties with light-induced magnons Dhiman Bhowmick Hao Sun Bo Yang and Pinaki Sengupta

2025-05-06 0 0 866.23KB 9 页 10玖币

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Tuning bulk topological magnon properties with light-induced magnons

Dhiman Bhowmick , Hao Sun, Bo Yang, and Pinaki Sengupta

School of Physical and Mathematical Sciences,

Nanyang Technological University, Singapore

(Dated: June 27, 2023)

Although theoretical modelling and inelastic neutron scattering measurements have indicated the

presence of topological magnon bands in multiple quantum magnets, experiments remain unable

to detect signal of magnon thermal Hall eﬀect in the quantum magnets, which is a consequence

of magnons condensation at the bottom of the bands following Bose Einstein statistics as well as

the concentration of Berry curvature at the higher energies. In a recent work, Malz, et al. [Nature

Communications 10, 3937 (2019)] have shown that topological magnons in edge states in a ﬁnite

sample can be ampliﬁed using tailored electromagnetic ﬁelds. We extend their approach by showing

that a uniform electromagnetic ﬁeld can selectively amplify magnons with ﬁnite Berry curvature

by breaking inversion symmetry of a lattice. Using this approach, we demonstrate the generation

of bulk topological magnons in a Heisenberg ferromagnet on the breathing kagome lattice and the

consequent ampliﬁcation of thermal Hall eﬀect.

I. INTRODUCTION

The successful isolation of atomically thin magnets [1–

7] has triggered intensive investigation of topological

magnetic excitations in low dimensional quantum mag-

nets. Interest in bosonic topological phases has been

rising over the past several years since the band struc-

ture properties that underlie (non-interacting) topologi-

cal states are independent of the quantum statistics of the

particles. Topological band structures have already been

reported in such diverse bosonic systems as photons [8–

10], phonons [11,12], cold atoms [13,14], and magnons [1,

2,15–20]. Magnons, quantized low energy excitations in

quantum magnets obeying Bose-Einstein statistics[21],

are ideally suited for realizing complex bosonic phases

in a controllable manner, e.g., Bose-Einstein conden-

sation [22]. Microscopic modelling reveals that the

time reversal symmetry-breaking Dzyaloshinskii-Moriya

interaction (DMI) – present in many quantum mag-

nets – imparts ﬁnite Berry curvature to non-interacting

magnon bands. When eﬀects of interactions are added,

bosonic systems hold the promise of realizing new inter-

action driven topological phases that are not observed in

fermionic systems, due to the diﬀerent quantum statistics

obeyed by the two.

Magnons are charge neutral quasiparticles and hence

do not exhibit one of the key signatures of fermionic topo-

logical bands, viz., the topological Hall eﬀect where a

transverse current is induced by a longitudinal potential

gradient even in the absence of an external magnetic ﬁeld.

Instead they are expected to exhibit thermal (or magnon)

Hall eﬀect, where a longitudinal temperature gradient,

∆xT, produces a current of thermally generated magnons

that experiences a transverse force due to the geometric

magnetic ﬁeld, B, produced by the Berry phase of the

magnon bands. The resulting transverse magnon cur-

rent, JQ, constitutes a thermal Hall eﬀect of magnons[15–

17], or magnon Hall eﬀect (MHE), and is analogous to

the Topological (or Anomalous) Hall eﬀect in electrons.

However, while the MHE has been theoretically predicted

for many quantum magnets [1,2,15,16,18–20,23–30],

it has been experimentally observed only in Lu2V2O7[17]

and Cu[1,3 – benzenedicarboxylate][2]. Notably, while

neutron scattering experiments have shown the exis-

tence of gapped magnon bands in CrI3and Sr2Cu(BO3)2

consistent with theoretical calculations predicting topo-

logical magnon bands, experimental eﬀorts to observe

magnon Hall eﬀect have failed in both materials [31,32].

The reasons are threefold: (i) density of thermally ex-

cited magnons is concentrated at the band minimum –

magnons do not obey Pauli exclusion principle and a

magnon band cannot be “ﬁlled to the Fermi level” to ob-

serve edge states, (ii) the Berry curvature in the magnetic

Brillouin zone (MBZ) is often concentrated at momenta

away from the band minimum where density of thermally

excited magnons is low, and, (iii) the strength of intrinsic

DMI in most quantum magnets is weak. These inherent

diﬃculties make observing MHE and edge states in real

materials a formidable challenge.

In a recent work, Malz, et.al. [33] have proposed that

a robust edge current of magnons can be generated in

a kagome ferromagnet by a spatially varying electromag-

netic (EM) ﬁeld. However, their approach, by itself, is

not suﬃcient to amplify MHE for reasons discussed in de-

tail later. In this work, we have extended their approach

to excite magnons selectively at any arbitrary energy us-

ing a uniform electromagnetic ﬁeld. In particular, using

our approach, bulk magnons can be controllably gener-

ated in an isolated band, which is essential for amplifying

MHE signals. Crucially, we show that breaking of inver-

sion symmetry is necessary for selective ampliﬁcation of

bulk magnons and illustrate this in the breathing kagome

ferromagnet. Our results demonstrate that magnon Hall

eﬀect can be ampliﬁed by two orders of magnitude by

selectively amplifying magnons at ﬁnite Berry-curvature

points in reciprocal space using the proposed ampliﬁca-

tion scheme.

arXiv:2210.12087v2 [cond-mat.str-el] 25 Jun 2023

II. RESULTS

A. Symmetry analysis

The ampliﬁcation scheme introduced by Malz, et

al. [33] relies on the use of tailored electromagnetic (EM)

radiation to excite magnons. The interaction between

the EM wave and the quantum magnet is described by

the Hc=−E(t)·ˆ

P, where E(t) is the electric ﬁeld and

Pis the polarization operator. The ampliﬁcation consti-

tutes the absorption of a photon from the incident radia-

tion to create a pair of magnons with equal and opposite

momenta, Hc→Pkgk(a†

ka†

−kb+h.c.) where akand b

represent the magnon and photon operators respectively.

In their work, Malz, et al. [33] uses spatially modulated

electromagnetic waves to excite edge state magnons. We

argue that symmetry constraints prevent ampliﬁcation of

magnons by this process selectively in an isolated band

in inversion symmetric lattices. Later, it will be shown

that such ampliﬁcation of isolated bands is crucial for

amplifying physical observables such as the MHE.

The Inversion symmetry operator ˆ

Itransforms the

magnon annihilation operator ˆ

˜ankat n-th band at mo-

mentum kand also transforms the electric ﬁeld ampli-

tude of light Eas,

Iˆ

˜an,k=ˆ

˜an,−k,ˆ

IE=−E.(1)

Consequently, the magnon ampliﬁcation term, which cre-

ates a pair of magnons in the same band, will transform

as,

IEˆ

˜a†

n,kˆ

˜a†

n,−k=−Eˆ

˜a†

n,−kˆ

˜a†

n,k= 0.(2)

Thus magnons in an isolated band can not be selectively

ampliﬁed in presence of inversion symmetry ˆ

I. The cen-

tral result of this work is the discovery that selective am-

pliﬁcation of magnons in isolated bands can be achieved

by breaking the inversion symmetry of the lattice. In

the following we show this for a Heisenberg ferromagnet

with additional Dzyaloshinkii-Moriya interaction (identi-

cal to the microscopic model considered in Ref.[33]) on

abreathing kagome lattice (that explicitly breaks the in-

version symmetry).

B. Selective magnon ampliﬁcation

Consider the following spin Hamiltonian on a breath-

ing kagome lattice,

H0=−J1X

⟨i,j⟩1

Si·ˆ

Sj−J2X

⟨i,j⟩2

Si·ˆ

+DX

⟨i,j⟩

νij ˆz·ˆ

Si×ˆ

Sj−BzX

i,(3)

where ⟨. . . ⟩denotes the nearest neighbour (NN) bonds.

The subscripts 1 and 2 denote the blue and black bonds in

Fig.1(a) respectively, and J1and J2are the correspond-

ing NN Heisenberg spin-exchange interactions. Dde-

notes the Dzyaloshinskii-Moriya interaction (DMI) which

is chosen to be equal on all NN bonds for simplicity (re-

sults are slightly modiﬁed by anisotropic DMI, see Ap-

pendix C). Bzis an external magnetic ﬁeld perpendicular

to the lattice. We set J1= 1.0, D= 0.1J1and Bz→0+

throughout this study; the parameter δJ =J2−J1de-

notes the breathing anisotropy.

The ground state of Hamiltonian (3) is ferromagnetic

for small values of Dthat are considered here. Low

energy magnon excitations above the ground state can

be described by the standard Holstein-Primakoﬀ (HP)

transformation. In its lowest order, the HP transfor-

mation reduces to the linear spin wave transformation

deﬁned by ˆ

S+

i=√2Sˆai,ˆ

S−

i=√2Sˆa†

i,ˆ

i=S−ˆa†

iˆai,

where ˆa†

iand ˆaiare the magnon creation and annihilation

operators respectively. Applying the HP transformation

to the Hamiltonian (3) results in the magnon Hmailto-

nian. Neglecting magnon-magnon interaction terms, and

applying Fourier transformation yields a tight-binding

magnon Hamiltonian,

H0=X

Ψ†

kH0(k)Ψk,(4)

where Ψk= (ˆa1,k,ˆa2,k,ˆa3,k)Tis the vector of magnon

operators in a unit cell and subscripts 1,2,3 denote the

three basis sites of kagome lattice (see Fig. 1(a)). H0(k)

is the non-interacting magnon Hamiltonian matrix ( Ap-

pendix B).

The (non-interacting) magnon bands are obtained by

diagonalizing H0(k). For the regular kagome lattice

without the breathing anisotropy (δJ = 0) and any

DMI (D= 0), the magnon spectrum consists of three

bands - dispersive lower and middle bands and a disper-

sionless (ﬂat) upper band. The lower and middle bands

touch at Dirac points at the corners of the Brillouin zone;

the middle and upper bands touch at a quadratic band

touching point at the zone center. For ﬁnite DMI (D̸= 0)

or breathing anisotropy (δJ ̸= 0), a band gap opens be-

tween the lower and middle bands at Kand K′points

(Figs. 1(d)-(f)). The Berry curvature distribution of the

lower and middle magnon bands as a function of breath-

ing anisotropy and DMI can be obtained using the lin-

earized eﬀective Hamiltonian near Kand K′points [34–

36]

Heﬀ =αv k′

xσz+k′

yσx+mασy,(5)

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Tuningbulktopologicalmagnonpropertieswithlight-inducedmagnonsDhimanBhowmick,HaoSun,BoYang,andPinakiSenguptaSchoolofPhysicalandMathematicalSciences,NanyangTechnologicalUniversity,Singapore(Dated:June27,2023)Althoughtheoreticalmodellingandinelasticneutronscatteringmeasurementshaveindicatedthepresenceo...

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Tuning bulk topological magnon properties with light-induced magnons Dhiman Bhowmick Hao Sun Bo Yang and Pinaki Sengupta

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