Field-induced spin level crossings within a quasi- XYantiferromagnetic state in Ba 2FeSi 2O7 Minseong Lee1Rico Schoenemann1Hao Zhang2 3David Dahlbom3Tae-Hwan Jang4 Seung-Hwan Do5Andrew D. Christianson5Sang-Wook Cheong4 6Jae-Hoon Park4 7Eric

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Field-induced spin level crossings within a quasi-XY antiferromagnetic state in Ba2FeSi2O7

Minseong Lee,1, ∗Rico Schoenemann,1Hao Zhang,2, 3 David Dahlbom,3Tae-Hwan Jang,4

Seung-Hwan Do,5Andrew D. Christianson,5Sang-Wook Cheong,4, 6 Jae-Hoon Park,4, 7 Eric

Brosha,8Marcelo Jaime,1Kipton Barros,9Cristian D. Batista,3, †and Vivien S. Zapf1, ‡

1National High Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.

2Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA.

3Department of Physics and Astronomy, University of Tennessee, Knoxville, TN, USA.

4MPPHC-CPM, Max Planck POSTECH/Korea Research Initiative, Pohang, Republic of Korea.

5Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA.

6Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, Piscataway, NJ, USA.

7Department of Physics, Pohang University of Science and Technology, Pohang, Republic of Korea.

8Materials Synthesis and Integration, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.

9Theory Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.

(Dated: March 15, 2023)

We present a high-ﬁeld study of the strongly anisotropic easy-plane square lattice S= 2 quantum mag-

net Ba2FeSi2O7. This compound is a rare high-spin antiferromagnetic system with very strong easy-plane

anisotropy, such that the interplay between spin level crossings and antiferromagnetic order can be studied. We

observe a magnetic ﬁeld-induced spin level crossing occurring within an ordered state. This spin level crossing

appears to preserve the magnetic symmetry while producing a non-monotonic dependence the order parame-

ter magnitude. The resulting temperature-magnetic ﬁeld phase diagram exhibits two dome-shaped regions of

magnetic order overlapping around 30 T. The ground state of the lower-ﬁeld dome is predominantly a linear

combination of |Sz= 0iand |Sz= 1istates, while the ground state of the higher-ﬁeld dome can be ap-

proximated by a linear combination of |Sz= 1iand |Sz= 2istates. At 30 T, where the spin levels cross,

the magnetization exhibits a slanted plateau, the magnetocaloric effect shows a broad hump, and the electric

polarization shows a weak slope change. We determined the detailed magnetic phase boundaries and the spin

level crossings using measurements of magnetization, electric polarization, and the magnetocaloric effect in

pulsed magnetic ﬁelds to 60 T. We calculate these properties using a mean ﬁeld theory based on direct products

of SU(5) coherent states and ﬁnd good agreement. Finally, we measure and calculate the magnetically-induced

electric polarization that reﬂects magnetic ordering and spin level crossings. This multiferroic behavior provides

another avenue for detecting phase boundaries and symmetry changes.

I. INTRODUCTION

Antiferromagnets with strong easy-plane magnetic

anisotropy are a rich source of quantum magnetism and

quantum phase transitions1–3. In the limit of strong easy-

plane single-ion anisotropy, the Hamiltonian contains a

term HD=PiD(Sz

i)2with D > 0that is dominant

over the other interactions. This term splits the 2S+ 1

spin levels into an Sz= 0 ground state and excited states

with Sz=±1,±2,· · · ,±S, separated by energy gaps

of 12D,22D,· · · ,S2Dfor integer spin. The zdirection

coincides with the uniaixal anisotropy direction created

by HD. Since the Zeeman term generated by an external

magnetic ﬁeld parallel to the z-direction commutes with HD,

the eigenstates of the single-ion Hamiltonian are preserved

and the energy gaps evolve linearly with the ﬁeld. The energy

gaps between positive Szstates and the ground state are

suppressed by the ﬁeld, resulting in successive spin level

crossings. Small exchange interactions between neighboring

ions J < D disperse and broaden these levels, producing

a mean ﬁeld ground state that is direct product of linear

combinations of different |Szistates. The expectation value

of the in-plane component of the local magnetization is ﬁnite

in this wave function, leading to quasi-XY antiferromagnetic

long-range ordering occurring in dome-shaped regions of the

temperature-magnetic (T−H) phase diagram4–6. The order

parameter (planar staggered magnetization) can be described

as a complex number, whose amplitude is the magnitude of

the planar magnetization, while the phase determines the

direction of the spins. The pioneering work of Matsubara

and Matsuda showed that interacting spin-1/2systems can

be mapped into a interacting bosonic gas with hard-core

repulsion7. This mapping can be generalized for higher

spin systems8,9, implying that ﬁeld-induced quantum phase

transitions of magnets with uniaxial symmetry belong to

the Bose-Einstein condensation (BEC) universality class.

In the presence of disorder or competing interactions, Bose

glass10–13 or even super-solidity14–17 can also occur. It is

important to note, however, that the Hamiltonians of real

spin systems always include terms that break the uniaxial

symmetry, but these terms are small for many compounds and

the BEC description becomes an excellent approximation,

particularly of the quantum phase transitions and their

excitations.2

Most work in this ﬁeld has been done on S= 1/2

dimers6,18 or monoatomic S= 1 systems2,19. Higher spin sys-

tems (S > 1) with strong easy-plane anisotropy DJare

rare. However, when they occur, the energy of more than one

high-spin states can be lowered by magnetic ﬁeld to become

the ground state in high ﬁelds, creating multiple domes of an-

tiferromagnetism in T−Hspace. For example, Ba3Mn2O8

forms exchange-coupled dimers of Mn5+(S= 1) spins5. In

applied magnetic ﬁelds, two dome-shaped regions of antifer-

arXiv:2210.14323v2 [cond-mat.str-el] 14 Mar 2023

(a)

yxab

(b)

J’

-κ

FIG. 1: Crystal structure and DC magnetic susceptibility of Ba2FeSi2O7. (a) Tetrahedra of FeO4interconnected by nonmagnetic SiO4

form a square lattice in ab-plane. The nearest super-exchange interaction is denoted as J. (b) Each ab-plane is separated by large Ba2+ ions

and the interlayer coupling is denoted as J0, which is much weaker than J. (c) The temperature dependence of the DC magnetic susceptibility.

The symbols are experimental data and the dashed line represents the Curie-Weiss ﬁt. Inset: temperature derivative of the DC magnetic

susceptibility, in which the peak signals the antiferromagnetic long-range ordering. The spin structure is presented in (a) with orange arrows.

(d) The spin energy levels as a function of magnetic ﬁeld, neglecting magnetic exchange broadening.

romagnetic order can be observed between 10 and 25 T and

between 35 and 41 T. However, to our knowledge there is no

example of monoatomic S= 2 systems with strong easy-

plane anisotropy that show this behavior. When the energy

scales for single-ion anisotropy and magnetic exchange are

not well separated, the low and high-ﬁeld domes overlap lead-

ing to a single double-peaked region of antiferromagnetism

with the unusual feature that the Szstate evolves within the

dome. Here we investigate this phenomenon in the S=2

easy-plane antiferromagnet Ba2FeSi2O7. The compound be-

longs to the Melilite family A2MB2O7(A= Ca, Sr, Ba, M

= divalent 3dtransition metals, B= Si, Ge) and forms in the

P¯

421m tetragonal structure.

The relatively strong spin-orbit coupling of Fe2+ (∼20

meV) ions combined with the crystal ﬁeld from the largely

compressed FeO4tetrahedra along c-axis is identiﬁed as the

source of an unusually large easy-plane anisotropy from a

THz spectroscopic study20. T.-H. Jang et al. recently reported

the growth of high-quality single crystals of Ba2FeSi2O7and

thermodynamic investigations show very strong easy-plane

single-ion magnetic anisotropy and the indication of well-

separated spin levels from the speciﬁc heat measurement21.

Neutron diffraction measurement at zero magnetic ﬁeld ﬁnds

antiferromagnetism with spins aligned along the diagonal di-

rection of the a- and b- axes as shown in Figure 1 (a). At

zero ﬁeld, S.-H. Do et al., observed the emergence, strong de-

cay, and renormalization of a longitudinal magnon mode in

Ba2FeSi2O7since the compound is close to a quantum criti-

cal point due to the large ratio of easy-plane anisotropy to the

Heisenberg exchange interaction (D/J)22. These experimen-

tal ﬁndings motivated us to investigate the interplay of mag-

netic order and spin level crossings at high magnetic ﬁelds.

Similar to the case of Ba3Mn2O8, Ba2FeSi2O7exhibits two

ﬁeld-induced domes associated with local mean ﬁeld states

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摘要：

Field-inducedspinlevelcrossingswithinaquasi-XYantiferromagneticstateinBa2FeSi2O7MinseongLee,1,RicoSchoenemann,1HaoZhang,2,3DavidDahlbom,3Tae-HwanJang,4Seung-HwanDo,5AndrewD.Christianson,5Sang-WookCheong,4,6Jae-HoonPark,4,7EricBrosha,8MarceloJaime,1KiptonBarros,9CristianD.Batista,3,yandVivienS.Zapf1...

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Field-induced spin level crossings within a quasi- XYantiferromagnetic state in Ba 2FeSi 2O7 Minseong Lee1Rico Schoenemann1Hao Zhang2 3David Dahlbom3Tae-Hwan Jang4 Seung-Hwan Do5Andrew D. Christianson5Sang-Wook Cheong4 6Jae-Hoon Park4 7Eric.pdf

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Field-induced spin level crossings within a quasi- XYantiferromagnetic state in Ba 2FeSi 2O7 Minseong Lee1Rico Schoenemann1Hao Zhang2 3David Dahlbom3Tae-Hwan Jang4 Seung-Hwan Do5Andrew D. Christianson5Sang-Wook Cheong4 6Jae-Hoon Park4 7Eric

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