1 INTRODUCTION From magnetic order to valence-change crossover in EuPd2Si1xGex2using He-gas pressure

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1 INTRODUCTION

From magnetic order to valence-change crossover in

EuPd2(Si1−xGex)2using He-gas pressure

Bernd Wolf, Felix Spathelf, Jan Zimmermann, Theresa Lundbeck, Marius Peters, Kristin

Kliemt, Cornelius Krellner, Michael Lang

Physikalisches Institut, J.W. Goethe-Universität Frankfurt(M), Max-von-Laue-Str. 1, 60438

Frankfurt, Germany

* wolf@physik.uni-frankfurt.de

October 25, 2022

Abstract

We present results of magnetic susceptibility and thermal expansion measurements per-

formed on high-quality single crystals of EuPd2(Si1−xGex)2for 0 ≤x≤0.2 and temperatures

2 K ≤T≤300 K. Data were taken at ambient pressure and ﬁnite He-gas pressure p≤0.5 GPa.

For x =0 and ambient pressure we observe a pronounced valence-change crossover centred

around T0

V≈160 K with a non-magnetic ground state. This valence-change crossover is char-

acterized by an extraordinarily strong pressure dependence of dT0

V/dp=(80 ±10)K/GPa.

We observe a shift of T0

Vto lower temperatures with increasing Ge-concentration, reaching

V≈90 K for x =0.1, while still showing a non-magnetic ground state. Remarkably, on fur-

ther increasing x to 0.2 we ﬁnd a stable Eu(2+δ)+ valence with long-range antiferromagnetic

order below TN=(47.5 ±0.1) K, reﬂecting a close competition between two energy scales

in this system. In fact, by the application of hydrostatic pressure as small as 0.1 GPa, the

ground state of this system can be changed from long-range antiferromagnetic order for p

<0.1 GPa to an intermediate-valence state for p≥0.1 GPa.

1 Introduction

In the search for novel collective phenomena one route of research focusses on correlated elec-

tron materials tuned to second-order critical points. As an example we mention the phenomenon

of critical elasticity recently observed upon pressure tuning an organic Mott insulator across the

second-order critical endpoint of the ﬁrst-order Mott transition line [1]. On approaching the crit-

ical endpoint a pronounced softening of the lattice was revealed indicating a particular strong

coupling between the critical electronic system and the lattice degrees of freedom. The work

by Gati et al. suggests that similar strong-coupling effects can be expected also for other critical

endpoints amenable to pressure tuning. In this context, the valence transition critical endpoint

represents a particularly interesting scenario as this transition involves electronic-, magnetic-, and

lattice degrees of freedom. The valence transition in Eu-based intermetallics was studied inten-

sively in the past [2]. The generic temperature-pressure (T-p) phase diagram derived from these

studies includes Eu(2+δ)+ states with local magnetic moments at low pressure giving rise to long-

range magnetic order at low temperatures. The energy gain associated with the formation of

magnetic order among stable moments deﬁnes one relevant energy scale in the system. With in-

creasing pressure the system crosses a ﬁrst-order valence transition line TV(p), separating that

arXiv:2210.12227v1 [cond-mat.str-el] 21 Oct 2022

2 EXPERIMENTAL DETAILS

high-volume Eu(2+δ)+ state at low pressure (and high temperatures) from a non-magnetic low-

volume Eu(3−δ0)+ state at high pressure (and low temperature) [3,4]. The energy gain associated

with the valence change marks the second relevant energy scale in the system. This ﬁrst-order

line TV(p)terminates at a second-order critical endpoint (Tcr ,pcr ). For some materials, a valence

change can be induced just by varying the temperature. Among them is EuPd2Si2, crystallizing

in the tetragonal ThCr2Si2structure, which shows a pronounced, yet continuous valence change

from Eu2.8+to Eu2.3+upon cooling through T0

V≈160 K [5–7]. In the valence-change crossover

regime, the crossover temperature T0

V(p), deﬁned by the position where the change in the mag-

netic susceptibility is largest, provides a measure of the energy scale associated with the valence

change. According to magnetic- [8]and thermodynamic [4]measurements on powder material,

EuPd2Si2is located on the high-pressure side of the second-order critical endpoint, i.e., in the

valence-change crossover regime. This material has become of interest recently due to the avail-

ability of single crystals of pure EuPd2Si2[3,9]and Ge-substituted EuPd2(Si1−xGex)2[10]which

opens up exciting possibilities for detailed investigations by using a wide range of experimental

tools. The motivation of the present study has been to identify a suitable chemical modiﬁcation

in the series EuPd2(Si1−xGex)2, corresponding to EuPd2Si2at a negative chemical pressure, so

that the critical regime can be accessed via ﬁne pressure tuning by using He-gas techniques. To

this end we performed measurements of the magnetic susceptibility and the thermal expansion

on selected single crystals of the series EuPd2(Si1−xGex)2at ambient and ﬁnite He-gas pressure.

Our study demonstrates that for x =0.2 the two energy scales, determining the material’s ground

state, become almost degenerate. Due to their different pressure dependencies, the application

of a weak pressure as small as 0.1 GPa is sufﬁcient to alter the ground state of the material from

antiferromagnetic order with TNaround 47 K at low pressure to an intermediate-valence state for

p≥0.1 GPa.

2 Experimental details

Single crystals of EuPd2(Si1−xGex)2with nominal Ge-concentration x =0 (#1, #2), x =0.1 (#3),

and x =0.2 (#4, #5) were grown by using the Czochralski method. Table 1 summarizes the crys-

tals investigated and their nominal Ge-concentration. Details of the single crystals growth and

sample characterization are given in Refs. [9,10]. In what follows we refer to the crystals by their

nominal Ge-concentration and specify the crystal by giving the batch number. The susceptibil-

ity was measured by using a commercial superconducting quantum interference device (SQUID)

magnetometer (MPMS, Quantum Design) equipped with a CuBe pressure cell (Unipress Equip-

ment Division, Institute of High Pressure Physics, Polish Academy of Science). The pressure cell is

connected via a CuBe capillary to a room temperature He-gas compressor, serving as a gas reser-

voir, which enables temperature sweeps to be performed at p≈const. conditions, see Ref. [11]

for details. Thermal expansion measurements were performed by using two different methods.

This includes (1) a capacitive dilatometer [12,13], enabling length changes of ∆L≥5·10−3nm

to be resolved, combined with a He-gas pressure system, see Ref. [1,14]for details. This tech-

nique can be applied in those temperature and pressure ranges where the pressure-transmitting

medium helium is in its liquid phase, i.e., above the solidiﬁcation line Tsol(p), allowing the upper

capacitor plate of the dilatometer to move freely. In addition (2), a strain gauge technique in

combination with the He-gas pressure system was used for measuring length changes. The strain

gauge (CEFLA-1-11, Tokyo Measuring Instruments Lab.) was glued on top of the sample using

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1INTRODUCTIONFrommagneticordertovalence-changecrossoverinEuPd2(Si1xGex)2usingHe-gaspressureBerndWolf,FelixSpathelf,JanZimmermann,TheresaLundbeck,MariusPeters,KristinKliemt,CorneliusKrellner,MichaelLangPhysikalischesInstitut,J.W.Goethe-UniversitätFrankfurt(M),Max-von-Laue-Str.1,60438Frankfurt,Germany...

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1 INTRODUCTION From magnetic order to valence-change crossover in EuPd2Si1xGex2using He-gas pressure

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