Triangular Kondo lattice in YbV 6Sn6and its quantum critical behaviors in magnetic eld Kaizhen Guo1Junyao Ye1Shuyue Guan1and Shuang Jia1 2 3

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Triangular Kondo lattice in YbV6Sn6and its quantum critical behaviors in magnetic

ﬁeld

Kaizhen Guo,1Junyao Ye,1Shuyue Guan,1and Shuang Jia1, 2, 3, ∗

1International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China

2Interdisciplinary Institute of Light-Element Quantum Materials and Research Center

for Light-Element Advanced Materials, Peking University, Beijing 100871, China

3CAS Center for Excellence in Topological Quantum Computation,

University of Chinese Academy of Sciences, Beijing 100190, China

(Dated: October 24, 2022)

We report magnetization, heat capacity and electrical resistivity for a newly discovered heavy

fermion (HF) compound YbV6Sn6which is crystallized in a hexagonal HfFe6Ge6-type structure,

highlighted by the stacking of triangular ytterbium sublattice and kagome vanadium sublattice.

Above 2 K, YbV6Sn6shows typical HF properties due to the Kondo eﬀect on the Kramers doublet

of Yb3+ ions in crystal electric ﬁeld. A remarkable magnetic ordering occurs at TN= 0.40 K in

zero ﬁeld while a weak external ﬁeld suppresses the ordering and induces non-Fermi liquid (NFL)

behavior. In strong magnetic ﬁeld the compound shows a heavy Fermi liquid state. YbV6Sn6

presents as one of the few examples of Yb-based HF compounds hosting triangular Kondo lattice

on which a magnetic ﬁeld induces quantum criticality near zero temperature.

I. INTRODUCTION

The research on the heavy fermion (HF) compounds

has been an important part in strongly correlated physics

in the past few decades [1–3]. As the relevant energy

scales are small in the HF compounds, their ground states

can be readily tuned, which provides convenience for

the laboratory to induce quantum critical point (QCP)

through pressure, magnetic ﬁeld, and chemical substitu-

tion [4, 5]. Quantum ﬂuctuation dominates near QCPs,

which emerges highly collective excitation and exotic

quantum phases. The most striking is unconventional

superconductivity near antiferromagnetic (AFM) QCP,

which has been explored in many Ce- and U-based HF

compounds [6, 7]. Ferromagnetic (FM) QCP was re-

ported in the stoichiometric CeRh6Ge4[8] as well. Com-

pared with Ce- and U-based compounds, Yb-based HF

compounds are relatively rare. The scarcity is due to the

fact that Yb ions are more localized, or likely exist as non-

magnetic divalent ions. The large vapor pressure of Yb

element makes it diﬃcult to synthesize the compounds as

well. Unconventional superconductivity and non-Fermi

liquid (NFL) behaviors were observed in YbAlB4[9] and

YbRh2Si2[10]. Magnetic ﬁeld can induced various quan-

tum critical behaviors including NFL and multiple phase

transitions in YbPtBi [11] and YbAgGe [12] . The stud-

ies on the Yb-based HF compounds have advanced the

understanding of the NFL and Fermi surface reconstruc-

tion near the QCP [2, 13].

In a classical Doniach phase diagram, the competi-

tion between Kondo eﬀect and Ruderman-Kittel-Kasuya-

Yosida (RKKY) interaction determines the ground state

of the HF compounds [14]. While the Doniach scenario

predicts a single magnetic QCP between the AFM order-

∗gwljiashuang@pku.edu.cn

ing and heavy Fermi liquid (FL) state, recent experimen-

tal studies revealed it is insuﬃcient to cover the various

quantum critical behaviors in many HF compounds [15],

because frustration eﬀect plays an important role. The

studies on the HF compounds hosting geometric frus-

trated Kondo lattices, for example, Yb-based Shastry-

Sutherland lattice in Yb2Pt2Pb [16–18] and Ce-based

distorted kagome lattice in CePdAl [19–21] and CeRhSn

[22], have helped to understand a two-dimension global

diagram determined by the Kondo eﬀect and the strength

of magnetic frustration [23–25].

Ytterbium-based compounds containing geometric

frustrated triangular lattices are particularly interesting

because the eﬀective spin of the Kramers doublet of Yb3+

ion can be Jeﬀ = 1/2. These compounds provide a fer-

tile ground for exploring exotic quantum matters such

as valence bond solid (VBS) and quantum spin liquid

(QSL) caused by the frustration-enhanced zero-point mo-

tions of spins [24, 26]. The Yb-based triangular lattices

in insulating compounds YbMgGaO4[27] and NaYbO2

[28] were found to be platforms for exploring the QSL

physics. On the other hand, the inter-metallic com-

pounds containing Yb-based triangular lattices, in which

both the Kondo eﬀect and geometric frustration play the

role, have been less studied. Theoretical studies on the

triangular Kondo lattice have suggested multiple quan-

tum states from various chiral-type magnetic ordering

which may bring spontaneous Hall eﬀect [29, 30], to the

partial Kondo screening (PKS) state in which a subset

of moments forms Kondo singlet [31, 32]. Discovery of

Yb-based HF compounds with triangular Kondo lattice

will provide an ideal playground for exploring the exotic

states while the quantum control on the states will help

to better understand the global phase diagram [33, 34].

In the studies on the RMn6Sn6family compounds

[35, 36], we noticed that HfFe6Ge6-type structure may

serve as an ideal framework for bearing the Yb-based

triangular Kondo lattice. The ‘166’ structure is high-

arXiv:2210.12117v1 [cond-mat.str-el] 21 Oct 2022

lighted by a kagome lattice of transition metal and a

triangular lattice of rare earth. Exploration of kagome

materials in ‘166’ family has motivated wide interest in

strongly correlated and topological physics while previ-

ous focus was the novel topological properties of the ﬂat

band and Dirac band in the kagome lattice [37–40]. Al-

though the rare earth elements play an important role in

magnetic structure and topological properties [36], the 4f

electronic strong correlation is less reported in the grand

‘166’ family. The studies on YbMn6Sn6and YbMn6Ge6

demonstrated the valence change and magnetic ordering

of Yb ions [41–43]. There are few reports for the physical

properties of other Yb-based ‘166’ compounds [44, 45].

We successfully grew the single crystals of two new Yb-

based ‘166’ compounds, YbV6Sn6and YbCr6Ge6in the

past two years. While the characterization for the later

will be presented somewhere else, we present the crys-

tal structure, magnetization, heat capacity and electri-

cal resistivity for YbV6Sn6in this study. The existence

of RV6Sn6(R = Y,Gd −Tm,Lu) family was ﬁrstly re-

ported by L.Romaka et.al. in 2011 [46], but the physi-

cal properties were not reported until very recently. In

general, RV6Sn6(R = Gd −Tm) demonstrate the phys-

ical properties of well-deﬁned 4f-local-moment bearing,

weakly interacted magnetic intermetallic compounds [47–

51]. Our measurements on YbV6Sn6above 2 K showed

typical manners of HF compounds, including large elec-

tronic speciﬁc heat and coherent peak in temperature-

dependent resistivity. Moreover, we found a remarkable

magnetic ordering at 0.40 K in zero ﬁeld while a weak

magnetic ﬁeld can suppress the ordering and induce NFL

behavior. In strong magnetic ﬁeld the compound enters

a heavy FL state with an electronic speciﬁc heat coeﬃ-

cient γ > 400 mJ/mol K2. We conclude that YbV6Sn6

presents as a rare example of HF compounds which hosts

Yb-based triangular Kondo lattice.

II. EXPERIMENT METHOD

Single crystals of YbV6Sn6and LuV6Sn6were syn-

thesized via self-ﬂux method. The starting elements

of Yb(pieces, 99.9%), Lu(pieces, 99.9%), V(grains,

99.9%) and Sn(shots, 99.97%) with the molar ratio of

R:V:Sn=1:6:20 were placed in an alumina Canﬁeld Cru-

cible Sets(CCS) [52] which is eﬀective to prevent sam-

ples from contacting the silica wool, and then sealed in

a vacuum silica ampoule. To avoid the slight reaction

between Yb and alumina crucible, the small pieces of

Yb and V were placed close together and surrounded by

Sn drops. The ﬂux mixtures were heated to 1125◦C,

dwell for 12 hours, then continuously cooled at 2◦C/h,

and ﬁnally centrifuged at 780◦C to remove excess ﬂux.

The yielded crystals were hexagonal plates with the di-

mension 1 ×1×0.2 mm3(Inset in Fig. 1 c). Other

RV6Sn6(R = Gd −Tm) single crystals can be grown by

this method as well. The samples were soken into dilute

hydrochloric acid for a short time to dissolve the excess

tin ﬂux on the surface. Crystal structure was conﬁrmed

by measuring the powder X-ray diﬀraction (PXRD) at

room temperature in a Rigaku Mini-ﬂux 600 instrument.

Resistance and heat capacity measurements were car-

ried out using a Quantum Design Physical Properties

Measurement System (PPMS). A standard four-probe

method was adapted in the resistance measurement with

the current ﬂowing perpendicular to the caxis. The heat

capacity was only measured when Hkcdue to the lim-

itation of crystals’ size in this study. A Dilution Refrig-

erator (DR) unit was used to measure low-temperature

resistance and heat capacity from 0.2 K to 4 K. To avoid

sample heating, we use the ac current I= 0.2 mA and

f= 33.6 Hz. Magnetization measurements was car-

ried out using a Quantum Design Magnetic Properties

Measurement Systems (MPMS-3) with a He-3 option.

The magnetization measurement revealed that the sam-

ple contains about 0.07 Vol. % of tin impurity which

contributes small diamagnetic signal below 4 K in a mag-

netic ﬁeld less than 400 Oe. To avoid misreading of the

low-temperature magnetic susceptibility in weak ﬁelds,

we subtracted the diamagnetic signal.

III. RESULTS

A. Crystal Structure

FIG. 1. (a) Crystal structure of YbV6Sn6; (b) Triangular

and kagome lattices formed by Yb and V atoms, respectively;

X-ray diﬀraction patterns. The vertical blue lines are calcu-

lated peak positions. Inset: a photograph of single crystals of

YbV6Sn6.

Most of the ‘166’ compounds consisting of R, transition

metal (T=V, Cr, Mn, Fe and Co) and germanium/tin

atoms crystallize in a P6/mmm HfFe6Ge6-type structure

[53] and so as YbV6Sn6. Highlighted by the pristine T-

based kagome and R-based trianglular lattices (Fig. 1 b),

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TriangularKondolatticeinYbV6Sn6anditsquantumcriticalbehaviorsinmagneticeldKaizhenGuo,1JunyaoYe,1ShuyueGuan,1andShuangJia1,2,3,1InternationalCenterforQuantumMaterials,SchoolofPhysics,PekingUniversity,Beijing100871,China2InterdisciplinaryInstituteofLight-ElementQuantumMaterialsandResearchCenterforLi...

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Triangular Kondo lattice in YbV 6Sn6and its quantum critical behaviors in magnetic eld Kaizhen Guo1Junyao Ye1Shuyue Guan1and Shuang Jia1 2 3

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