Ver. 11p1 In-plane electronic anisotropy revealed by interlayer resistivity measurements on the iron-based superconductor parent compound

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Ver. 11p1

In-plane electronic anisotropy revealed by interlayer resistivity

measurements on the iron-based superconductor parent compound

CaFeAsF

Taichi Terashima,1, ∗Hishiro T. Hirose,2Yoshitaka Matsushita,3Shinya

Uji,1Hiroaki Ikeda,4, †Yuki Fuseya,5Teng Wang,6, 7 and Gang Mu6, 7, ‡

1International Center for Materials Nanoarchitectonics,

National Institute for Materials Science, Tsukuba, Ibaraki 305-0003, Japan

2Research Center for Functional Materials,

National Institute for Materials Science, Tsukuba, Ibaraki 305-0003, Japan

3Research Network and Facility Services Division,

National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan

4Department of Physics, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan

5Department of Engineering Science,

University of Electro-Communications, Chofu, Tokyo 182-8585, Japan

6State Key Laboratory of Functional Materials for Informatics,

Shanghai Institute of Microsystem and Information Technology,

Chinese Academy of Sciences, Shanghai 200050, China

7CAS Center for Excellence in Superconducting Electronics (CENSE), Shanghai 200050, China

(Dated: November 9, 2022)

arXiv:2210.09533v2 [cond-mat.supr-con] 8 Nov 2022

Abstract

Both cuprates and iron-based superconductors demonstrate nematicity, deﬁned as the spontaneous break-

ing of rotational symmetry in electron systems. The nematic state can play a role in the high-transition-

temperature superconductivity of these compounds. However, the microscopic mechanism responsible for

the transport anisotropy in iron-based compounds remains debatable. Here, we investigate the electronic

anisotropy of CaFeAsF by measuring its interlayer resistivity under magnetic ﬁelds with varying ﬁeld direc-

tions. Counterintuitively, the interlayer resistivity was larger in the longitudinal conﬁguration (𝐵k𝐼k𝑐)

than in the transverse one (𝐵⊥𝐼k𝑐). The interlayer resistivity exhibited a so-called coherence peak under

in-plane ﬁelds and was highly anisotropic with respect to the in-plane ﬁeld direction. At 𝑇= 4 K and 𝐵=

14 T, the magnetoresistance Δ𝜌/𝜌0was seven times larger in the 𝐵k𝑏𝑜than in the 𝐵k𝑎𝑜conﬁguration.

Our theoretical calculations of the conductivity based on the ﬁrst-principles electronic band structure quali-

tatively reproduced the above observations but underestimated the magnitudes of the observed features. The

proposed methodology can be a powerful tool for probing the nematic electronic state in various materials.

∗TERASHIMA.Taichi@nims.go.jp

†hikeda.uji@gmail.com

‡mugang@mail.sim.ac.cn

I. INTRODUCTION

The parent compounds of iron-based superconductors typically exhibit a tetragonal-to-orthorhombic

structural transition at temperature 𝑇𝑠[Fig. 1(a)], which is equal to or slightly higher than the

antiferromagnetic transition temperature 𝑇𝑁. When the two transitions are suppressed by chemical

substitution or pressure application, these compounds exhibit superconductivity [1–4]. How the

two transitions are related to superconductivity is currently being debated.

This structural transition has been proposed as a nematic transition of electronic origin because

the in-plane resistivity is signiﬁcantly anisotropic below 𝑇𝑠despite a tiny orthorhombic distortion

[5]. To probe the nematic ﬂuctuations above the transition temperature, Chu et al.[6] determined the

elastoresistance of Ba(Fe1−𝑥Co𝑥)2As2, which deﬁnes the resistance change under strain. Evidence

of the nematic electronic state was corroborated by the relevant band-energy shift in angle-resolved

photoemission spectroscopy [7], a unidirectional structure around impurities (dubbed “nemato-

gens”) in scanning tunneling microscopy images [8], and nematic ﬂuctuations in Raman scattering

data [9].

Although nematicity has been well established in iron-based compounds, the microscopic

mechanism responsible for the transport anisotropy remains contentious. In particular, whether the

anisotropy arises from Fermi surface anisotropy or scattering phenomena is unclear. Optical studies

favor the former origin [10], whereas annealing and doping eﬀects suggest the latter [11, 12]. A

real-space picture based on nematogens has also been proposed [13, 14]. To gain further insight

into this fundamental issue, we apply here a new methodology to a compound whose nematicity

has not been previously studied.

Most published nematicity studies have been performed on 122-type iron arsenides such as

BaFe2As2because they form large, high-quality single crystals. In addition, angle-resolved pho-

toemission spectroscopy of 1111-type arsenides such as LaFeAsO suﬀers from contamination by

surface electronic structures [15]. The present study focuses on CaFeAsF, a variant of the 1111-

type arsenides with the same ZrCuSiAs-type structure as LaFeAsO but with a CaF layer replacing

the LaO layer of LaFeAsO [16]. High-quality single crystals exhibiting quantum oscillations can

be grown using the ﬂux method [17, 18]. CaFeAsF exhibits a nonmetallic temperature dependence

of electrical conduction, i.e., d𝜌/d𝑇 < 0, from room temperature down to 𝑇𝑠. In contrast, the

122 compounds show metallic conduction as the temperature decreases from room temperature.

The Fermi surface of CaFeAsF in the antiferromagnetic state below 𝑇𝑁is quasi-two dimensional

(Q2D), being composed of a tiny hole cylinder at the zone center surrounded by a pair of sym-

metrically arranged tiny Dirac electron cylinders [Fig. 1(a)]. This structure contrasts with the

three-dimensional Fermi surface of the 122 compounds in the antiferromagnetic state, which is

composed of closed pockets[19]. These diﬀerences between CaFeAsF and the 122 compounds

highlight the importance of studying nematicity in CaFeAsF.

Our main methodology is based on interlayer resistivity measurements under an applied mag-

netic ﬁeld. Since the discovery of angle-dependent magnetoresistance oscillations in organic

conductors [20, 21], interlayer resistivity measurements have become a powerful tool of fermiol-

ogy for Q2D electron systems, as exempliﬁed by their application to cuprates [22, 23]. Contrary

to usual expectations, we found that the magnetoresistance of the interlayer resistivity in CaFeAsF

is larger in the longitudinal conﬁguration (𝐵k𝐼k𝑐) where the Lorentz force acting on electrons

is expected to be minimal than in the transverse one (𝐵⊥𝐼k𝑐). We observed a coherence peak

under in-plane magnetic ﬁelds, which strongly depends on the in-plane ﬁeld direction. To calculate

the conductivity, we applied Chambers’ expression to the electronic band structure determined

using ﬁrst-principles calculations. The calculated results qualitatively reproduce the above exper-

imental observations. However, the magnitudes of the calculated features were weaker than the

experimentally observed magnitudes. We discuss possible origins of this quantitative discrepancy.

The paper is organized as follows: We begin with measurements of in-plane resistivity and

elastoresistance in Sec. II A to demonstrate the nematicity in CaFeAsF. In Sec. II B, we present

results of interlayer resistivity. We perform theoretical conductivity calculations in Sec. II C. We

discuss the results in Sec. III. Details of experimental procedures and theoretical calculations are

described in Appendices A and B, respectively.

II. RESULTS

A. In-plane resistivity and elastoresistance

First, we established nematicity in CaFeAsF from in-plane resistivity and elastoresistance

measurements. Figure 1(b) shows the in-plane resistivity (green curve) measured on a free-standing

sample and the elastoresistance (black curve) of the same sample. The sample was bar-shaped with

its longest dimension along the tetragonal [110] direction ([110]𝑡where the subscript 𝑡indicates

a tetragonal cell). We applied the electrical current and strain along this direction (see Appendix

A for details of the experiments). The strain was applied using a piezostack. From d2𝜌/𝑑𝑇 2

(light-blue curve), we obtained 𝑇𝑠=116.8K and 𝑇𝑁=106.3K for this sample. The resistivity

gradually increased as the temperature decreased from room temperature to 𝑇𝑠, but it decreased

sharply below 𝑇𝑠. The negative elastoresistance shows that the resistivity decreased with the

elongation of the sample, as also observed in BaFe2As2[6] and LaFeAsO [24]. The magnitude of

the elastoresistance increased as the temperature decreased to 𝑇𝑠. From the Curie–Weiss ﬁt to the

data between 200 K and 𝑇𝑠(red dotted curve), we determined the Weiss temperature to be 103.9

K, close to 𝑇𝑁. Although twinning prevents a straightforward interpretation of the elastoresistance

data below 𝑇𝑠, the elastoresistance exhibited a kink at 𝑇𝑁which was absent in the data reported for

Ba(Fe1−𝑥Co𝑥)As2and La(Fe1−𝑥Co𝑥)AsO [6, 24].

Figure 1(c) compares the in-plane resistivities of another sample before and after ﬁxing it to a

polyetheretherketone (PEEK) substrate. This sample was also bar-shaped, with its length oriented

along the [110]𝑡direction. As the free-standing sample is expected to be heavily twinned when

cooled below 𝑇𝑠, the resistivity measured before ﬁxing it to the PEEK substrate (green curve)

corresponds to the average of the resistivities along the 𝑎𝑜and 𝑏𝑜axes of the orthorhombic cell

(denoted by the subscript 𝑜). When both ends of the sample are ﬁxed to the PEEK substrate [see

Fig. 2(a)], the substrate shrinks more than the sample when cooled, so the [110]𝑡direction becomes

the shorter 𝑏𝑜direction of the orthorhombic cell below 𝑇𝑠through most of the sample volume.

Therefore, the resistivity measured after ﬁxing [pink curve, Fig. 1(c)] corresponds approximately

to the resistivity of the 𝑏𝑜axis. Figure 1(d) shows the in-plane resistivity of a third sample

before (green) and after (amber) it is ﬁxed to a quartz substrate. In this case, the cooled substrate

does not shrink; thus, the resistivity of the longer 𝑎𝑜axis is approximately measured below 𝑇𝑠.

Regardless of substrate, the resistivity peak at 𝑇𝑠is broadened considerably after ﬁxing because

the stress along the [110]𝑡axis enforces a ﬁnite nematic order parameter above 𝑇𝑠, analogously to a

magnetic ﬁeld applied to a ferromagnet. Figures 1(c) and (d) also show the normalized diﬀerences

Δ𝜌/𝜌=(𝜌ﬁxed −𝜌free)/𝜌free. The sign and rapid magnitude increase of the normalized diﬀerence

Δ𝜌/𝜌below ∼200 K are consistent with elastoresistance. The magnitude of the normalized

diﬀerence increased further below 𝑇𝑠, showing a kink at 𝑇𝑁. Assuming that both samples were

completely detwinned, we estimate 𝜌𝑏𝑜/𝜌𝑎𝑜to be 2.2 at 𝑇= 4.2 K, much larger than the value

reported for BaFe2As2[6].

There are some diﬀerences between the free-standing resistivity curves (green) in Figs. 1(b)–

(d). Although the exact origins are unclear, possible origins include the following: As the

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Ver.11p1In-planeelectronicanisotropyrevealedbyinterlayerresistivitymeasurementsontheiron-basedsuperconductorparentcompoundCaFeAsFTaichiTerashima,1,HishiroT.Hirose,2YoshitakaMatsushita,3ShinyaUji,1HiroakiIkeda,4,yYukiFuseya,5TengWang,6,7andGangMu6,7,z1InternationalCenterforMaterialsNanoarchitectonic...

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Ver. 11p1 In-plane electronic anisotropy revealed by interlayer resistivity measurements on the iron-based superconductor parent compound

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