Does a low-carrier density ferromagnet hold the key to understanding high temperature superconductors Gabrielle Beaudin Alexandre D esilets-Benoit and Andrea Daniele Bianchi

2025-05-03 0 0 626.45KB 6 页 10玖币

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Does a low-carrier density ferromagnet hold the key to understanding high

temperature superconductors?

Gabrielle Beaudin, Alexandre D´esilets-Benoit, and Andrea Daniele Bianchi∗

D´epartement de Physique, Universit´e de Montr´eal, Montr´eal, Canada†

Robert Arnold

School of Metallurgy and Materials, University of Birmingham,

Elm Rd, Birmingham, B15 2TT, United Kingdom

Stavros Samothrakitis, Nikola Anna Galvan Leos, Jorge L. Gavilano, and Michel Kenzelmann

Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut,

Forschungsstrasse 111, Villigen, CH-5232, Switzerland

Kilian D. Stenning

Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 2AZ, United Kingdom

Mark Laver

Department of Physics, University of Warwick, Coventry, CV4 7AL, United Kingdom

Simon Gerber

Laboratory for X-ray Nanoscience and Technologies, Paul Scherrer Institut,

Forschungsstrasse 111, Villigen, CH-5232, Switzerland

Michael Nicklas

Physics of Quantum Materials, Max Planck Institute for Chemical Physics of Solids,

N¨othnitzer Strasse 40, Dresden, 01187, Germany

Robert Cubitt and Charles Dewhurst

Large Scale Structures Group, Institut Laue Langevin,

71 avenue des Martyrs, Grenoble, 38042, France

(Dated: October 25, 2022)

We conducted a small-angle neutron scattering experiments (SANS) on the ferromagnetic semi-

metal EuB6, where we observed direct evidence for the presence of magnetic polarons. We carried

out SANS experiments over a large range of scattering vectors |~

q|from 0.006 to 0.140 ˚

A−1and 2

to 60 K. Just above TCour experiments show magnetic scattering intensity, which has a Lorentzian

dependence on the wave vector, which is characteristic for the presence of magnetic polarons. Below

TCthe polarons merge and most of the observed intensity is due to scattering from domain walls.

We were able to extract a correlation length ξwhich ranges from 100 to 300 ˚

A for the size of

the magnetic polarons. This size is much larger than one would expect for magnetic ﬂuctuations,

demonstrating the inﬂuence the magnetic polarons on the phase transition.

While we have a ﬁrm understanding of the physics of

a high density electron gas, we have only begun to un-

derstand the physics at low carrier densities [1, 2]. This

is particularly true for the case, where the charge car-

riers are added to a background of localized magnetic

moments. Contrary to intuition, the charge carriers will

interact strongly, with the localized moments and form

so-called magnetic polarons. Magnetic polarons can ex-

ist below TNin antiferromagnets and in the paramag-

netic phase of ferromagnets, as long as the carrier den-

sity is lower than the size of a magnetically correlated

volume [3–5]. However, until now, they have not been di-

∗andrea.bianchi@umontreal.ca

†Regroupement Qu´eb´ecois sur les Mat´eriaux de Pointe (RQMP)

rectly observed. Their presence is expected in high tem-

perature superconductors for example, where the par-

ent compound is a strongly correlated antiferromagnetic

Mott insulator, which then is typically doped with holes.

These holes are mobile impurities which are moving in

a background of strongly ﬂuctuating magnetic moments.

Due to strong interactions, they become dressed with a

magnetic cloud, the magnetic polaron [6–8]. Further-

more, the distribution of these holes does not remain uni-

form, but they attract each other, leading to an electronic

phase separation [6]. This competition lies at the heart of

a doping-dependent transition from an anomalous metal

to a conventional Fermi liquid, and was recently observed

in a quantum simulator of the Fermi-Hubbard model [9].

It is this strong interaction between the motion of the

holes and antiferromagnetism that is believed to be at

arXiv:2210.12210v1 [cond-mat.str-el] 21 Oct 2022

the heart of understanding the superconductivity in the

cuprates [8].

Magnetic polarons were ﬁrst proposed in the late six-

ties to describe the colossal magnetoresistive (CMR) ef-

fects in the Europium chalcogenides. Here, the mag-

netic polarons are thought to be formed by the spin

polarization of the mobile charge carriers by localized

4fmoments. This leads to the formation of magnetic

“bubbles” and the localization of charge carriers within

them [3, 4, 10–12]. It is this CMR eﬀect that could lead

to new spintronic transistors [13].

Here we present a small-angle neutrons scattering

(SANS) study in ferromagnetic EuB6, which we will ar-

gue is the ideal model system for studying magnetic po-

larons. Our results give for the ﬁrst time direct evidence

for magnetic polarons, and show their out-sized enhance-

ment of the ferromagnetic spin ﬂuctuations driving the

electronic phase transition.

EuB6has a simple cubic crystal structure (P m¯

3m) but

displays a complex interplay between the electronic and

magnetic degrees of freedom due to its low carrier den-

sity [4, 5, 14]. The insulator-to-semi-metal transition in

EuB6is concomitant with a ferromagnetic phase tran-

sition [15]. A number of experiments have given indi-

rect evidence for the presence of magnetic polarons in

EuB6[16–20]. A scanning tunnelling microscopy (STM)

study showed that EuB6becomes electronically inho-

mogeneous for temperatures above TC. Here, at 20 K

the size of the inhomogeneities are of the order of 3 to

4 nm [21]. At the same time, measurements with a micro

Hall-bar pointed to magnetic inhomogeneities at these

temperatures [21], which are pinned to defects at the

surface [22]. This is the very electronic phase separation

expected for magnetic polarons.

Electronic inhomogeneity in EuB6was also observed

in an angle resolved magnetoresistance experiment [23].

This concurrence of magnetic polarons and electronic in-

homogeneity, as seen here in EuB6also manifests itself

in the high-Tc’s. Here, a quantum nematic was ﬁrst the-

oretically predicted for the doped two-dimensional Mott

insulator [24], and was later observed [25–29]. In the

high-TC’s the relation between nematic order and super-

conductivity, and its relation to a close-by structural in-

stability are hotly debated. Such a coupling of the quan-

tum nematic to the lattice is absent in EuB6[30], which

makes EuB6a clean experimental platform to study mag-

netic polarons.

EuB6is a magnetic semiconductor, which exhibits two

phase transitions [31]. Upon cooling from an insulating

state at high temperatures, it ﬁrst becomes a semi-metal,

indicated by a drop in resistivity at TMof 14.5 K (see

Fig. 3 of the Supplemental Material). At the Curie tem-

perature TCof 11.8 K, it orders ferromagnetically [15].

EuB6displays CMR behaviour near TC[17]. Also, EuB6

has a very low carrier density [32] of ≈1025 m−3at 20 K,

which coexists with localized pure spin 4fEu moments

(S= 7/2). This puts EuB6into the regime where mag-

netic polarons are expected to strongly aﬀect the electri-

cal conductivity [3–5]. This scenario, is supported by a

number of experiments [18–20, 33].

In our SANS experiment (see Fig. 1 of the Supple-

mental Material for a schematic), we probed the mag-

netic response of EuB6for three diﬀerent ranges of scat-

tering vectors q. We are able to distinguish three dif-

ferent sources of scattering in our SANS experiments.

Firstly, diﬀuse scattering which grows in size with de-

creasing temperature, which is originating from mag-

netic polarons. Secondly, we observe an incommensurate

magnetic peak which appears below the Curie tempera-

ture TC. Thirdly, below TCwe observe a second diﬀuse

scattering signal from ferromagnetic domain walls. An

overview is presented in Fig. 1.

0 5 10 15 20 25 30 35

100

Temperature (K)

Intensity (103counts/h)

Intensity (arb. units)

H = 0 T

H = 0.25 T

H = 0.5 T

10 20 30 40

q⊥H

q // H

ISDW H=0T

ISDW H=0.5T

FIG. 1. a) The solid black diamonds (empty red diamond)

shows I(|~

q|) of the incommensurate magnetic peak at 0 T

(0.1 T). The solid line is a ﬁt to a power law. The solid

blue circles are the data from the high q-regime (HQ) in ZF

averaged over the q-range from 0.050 to 0.140 ˚

A−1. The open

red circles are the average over the low qregime (LQ) in zero

ﬁeld from 0.006 to 0.025 ˚

A−1.b) The medium q-regime is

from 0.020 to 0.055 ˚

A−1(MQ). The full black circles show the

ZF data, the open blue circles are taken in 250 mT and the

full red squares in 500 mT. The inset shows the anisotropy

of the SANS signal when His applied perpendicular to the

neutron beam.

We start our discussion with the incommensurate mag-

netic peak which appears below TCas a spot on the de-

tector. At 1.5 K, its position corresponds to a |~

q|of

(18.4±0.2) ×10−3˚

A−1. This |~

q|-value is at wavelengths

above those required for double scattering and thus the

peak is due to an incommensurate spin density wave

(ISDW). An ISDW is expected for EuB6, as a group the-

oretical analysis using ISOTROPY [34] for the crystallo-

graphic space group P m3mof EuB6with a (100) prop-

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Doesalow-carrierdensityferromagnetholdthekeytounderstandinghightemperaturesuperconductors?GabrielleBeaudin,AlexandreDesilets-Benoit,andAndreaDanieleBianchiDepartementdePhysique,UniversitedeMontreal,Montreal,CanadayRobertArnoldSchoolofMetallurgyandMaterials,UniversityofBirmingham,ElmRd,Birmingh...

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Does a low-carrier density ferromagnet hold the key to understanding high temperature superconductors Gabrielle Beaudin Alexandre D esilets-Benoit and Andrea Daniele Bianchi

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