# Novel coexistence of superconductivity with two distinct magnetic orders.

**ABSTRACT** The heavy fermion system exhibits properties that range from an incommensurate antiferromagnet for small to an exotic superconductor on the Ir-rich end of the phase diagram. At intermediate where antiferromagnetism coexists with superconductivity, two types of magnetic order are observed: the incommensurate one of and a new, commensurate antiferromagnetism that orders separately. The coexistence of -electron superconductivity with two distinct -electron magnetic orders is unique among unconventional superconductors, adding a new variety to the usual coexistence found in magnetic superconductors.

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**ABSTRACT:**We performed the elastic neutron scattering experiments on the mixed compounds CeRh1-xCoxIn5, and found that doping Co into CeRhIn5 dramatically changes the antiferromagnetic (AF) structure. The incommensurate AF state with the propagation vector of observed in pure CeRhIn5 is suppressed with increasing x, and new AF states with an incommensurate and a commensurate modulations simultaneously develop near the AF quantum critical point: xc∼0.8. These results suggest that the AF correlations with the qc and q1 modulations enhanced in the intermediate Co concentrations may play a crucial role in the evolution of the superconductivity observed above x∼0.4.Physica B Condensed Matter 01/2009; 404(17):2539-2542. · 1.28 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We show using neutron diffraction that the magnetic structure of CeRhIn4.85Hg0.15 is characterized by a commensurate propagation vector (1/2,1/2,1/2). This is different from the magnetic structure in the parent compound CeRhIn5 , which orders with an incommensurate propagation vector (1/2,1/2,0.297). The special relation between the commensurate magnetic mode and unconventional superconductivity has been shown previously for this class of heavy fermion superconductors. This work provides further evidence for the ubiquity of this antiferromagnetic mode.Physical Review B 01/2009; 79(9). · 3.66 Impact Factor - SourceAvailable from: Giacomo Prando
##### Article: Nanoscopic coexistence of magnetic and superconducting states within the FeAs layers of CeFeAsO1-xFx

S. Sanna, R De Renzi, T Shiroka, G. Lamura, G. Prando, P. Carretta, M. Putti, A. Martinelli, M. R. Cimberle, M. Tropeano, A. Palenzona[Show abstract] [Hide abstract]

**ABSTRACT:**We report on the coexistence of magnetic and superconducting states in CeFeAsO1-xFx for x=0.06(2), characterized by transition temperatures T_m=30 K and T_c=18 K, respectively. Zero and transverse field muon-spin relaxation measurements show that below 10 K the two phases coexist within a nanoscopic scale over a large volume fraction. This result clarifies the nature of the magnetic-to-superconducting transition in the CeFeAsO1-xFx phase diagram, by ruling out the presence of a quantum critical point which was suggested by earlier studies. Comment: 4 pages, 3 figs, accepted for publication as PRB Rapid commPhysical Review B 08/2010; 82:060508. · 3.66 Impact Factor

Page 1

arXiv:cond-mat/0509780v1 [cond-mat.supr-con] 29 Sep 2005

Novel Coexistence of Superconductivity with Two Distinct Magnetic Orders

A.D. Christianson,1,2, ∗A. Llobet,1Wei Bao,1J.S. Gardner,3,4, †I.P. Swainson,3J.W. Lynn,4J.-M.

Mignot,5K. Prokes,6P.G. Pagliuso,1, ‡N.O. Moreno,1J.L. Sarrao,1J.D. Thompson,1and A.H. Lacerda1

1Los Alamos National Laboratory, Los Alamos NM 87545

2Colorado State University, Fort Collins CO 80523

3NRC Canada, NPMR, Chalk River Laboratories, Chalk River, Ontario KOJ IJO, Canada

4NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899

5Laboratoire L´ eon Brillouin, CEA-CNRS, CEA/Saclay, 91191 Gif-sur-Yvette, France

6BENSC, Hahn-Meitner-Institut, Glienickerstrass 100, D-14109, Berlin, Germany

(Dated: February 2, 2008)

The heavy fermion CeRh1−xIrxIn5system exhibits properties that range from an incommensurate

antiferromagnet for small x to an exotic superconductor on the Ir-rich end of the phase diagram.

At intermediate x where antiferromagnetism coexists with superconductivity, two types of magnetic

order are observed: the incommensurate one of CeRhIn5 and a new, commensurate antiferromag-

netism that orders separately. The coexistence of f-electron superconductivity with two distinct

f-electron magnetic orders is unique among unconventional superconductors, adding a new variety

to the usual coexistence found in magnetic superconductors.

Magnetism and superconductivity are two major co-

operative phenomena in condensed matter, and the re-

lationship between them has been studied extensively.

Conventional superconductivity in phonon mediated s-

wave materials is susceptible to the Cooper-pair break-

ing by magnetic scattering[1, 2]. In cases where super-

conductivity and magnetic order coexist, such as rare-

earth based molybdenum chalcogenides, rhodium borides

and borocarbides, the superconducting d electrons and

localized f electrons are weakly coupled, and the com-

petition between superconductivity and magnetic order

is understood[2, 3] in terms of the theory of Abrikosov

and Gorkov[1].In contrast, strong magnetic fluctua-

tions have been observed in heavy fermion, cuprate and

ruthenate superconductors[4, 5, 6, 7], and magnetic ex-

citations have been proposed to mediate the Cooper

pairing in these unconventional superconductors[8, 9,

10, 11, 12, 13].Some of the U-based heavy fermion

compounds form an interesting subset of these super-

conductors where superconductivity develops out of a

magnetically ordered state.

magnetic state is a commensurate antiferromagnet; for

UNi2Al3[16, 17] an incommensurate antiferromagnet; for

UGe2[18] and URhGe[19] a ferromagnet. For UPt3[20],

three distinct superconducting phases[21, 22, 23] coex-

ist with a commensurate short-range antiferromagnetic

order. In analog to superfluid3He, intriguing coupling

between the magnetic and superconducting order param-

eters has been proposed[8].

For UPd2Al3[14, 15] the

Recently a new family of Ce-based heavy fermion ma-

terials has been discovered, which sets a record supercon-

ducting transition temperature of TC=2.3 K for heavy

fermion materials[24, 25, 26]. Coexistence of magnetic

order and superconductivity is observed in a wide com-

position range in CeRh1−xIrxIn5[27] [see Fig. 1(a)]; previ-

ously superconductivity was found only in heavy fermion

materials of the highest purity[18]. At one end of the

CeRh1−xIrxIn5series, CeIrIn5is a superconductor below

TC=0.4 K[25]. At the other end, CeRhIn5 orders mag-

netically below TNi=3.8 K in an antiferromagnetic spi-

ral structure with an ordering wave vector qi=(1

δ=0.297[28], that is incommensurate with the tetragonal

crystal lattice[29]. In the overlapping region of supercon-

ducting and antiferromagnetic phases, 0.25<

find unexpectedly an additional commensurate antiferro-

magnetic order that develops separately below TNc=2.7

K. This makes Ce(Rh,Ir)In5 unique among unconven-

tional superconductors in that the ground state exhibits

the coexistence of the superconducting order parameter

with two distinct magnetic order parameters.

2,1

2,±δ),

∼x<

∼0.6, we

Single crystals of CeRh1−xIrxIn5were grown from an

In flux with appropriate ratio of Rh and Ir starting

materials[27].Lattice parameters follow Vegard’s law

and the sample composition x is estimated to be within

±0.05 of the nominal composition[27]. Samples used in

this work were cut to a thickness ∼1.3 mm to minimize

problems due to the high neutron absorption of Rh, Ir

and In. The search for and collection of magnetic Bragg

neutron diffraction peaks in CeRh1−xIrxIn5(x =0.1, 0.2,

0.25, 0.3, 0.35, 0.4, and 0.5) were performed at the ther-

mal triple-axis spectrometers C5 and N5 of Chalk River

Laboratories, and BT2 and BT7 of NIST. Neutrons with

incident energy Ei=35 meV were selected using the (113)

reflection of a Ge crystal, the (002) of a Be crystal, or the

(002) of a pyrolytic graphite monochromator. At this en-

ergy, the neutron penetration length is longer than the

sample thickness. Polarized neutron diffraction exper-

iments were performed at BT2 of NIST with Ei=14.7

meV on a x=0.3 sample to verify magnetic signals and

to determine magnetic moment orientation. Pyrolytic

graphite filters were employed when appropriate to re-

move higher order neutrons. The sample temperature

was controlled by a top-loading pumped4He cryostat at

both Chalk River and NIST. Additional measurements of

Page 2

2

FIG. 1:

CeRh1−xIrxIn5. There are three distinct long-range orders:

superconducting (SC), incommensurate antiferromagnetic (I),

and commensurate antiferromagnetic (C). The diamonds rep-

resent the N´ eel temperature for the I phase, squares for the C

phase, and circles for TC of the SC phase. The open symbols

are from previous work[27], and the closed symbols from this

work. (b) Diamonds and squares represent squared magnetic

moments at 1.9 K for the I and C phases, respectively. The

circles represent the square of the total magnetic moment per

Ce in Eq. (4). The solid lines are guides to the eye. The

dashed lines delimit the I, I+C+SC and SC phases. Mag-

netic structures of the I and C phases are shown as insets to

(a) and (b), respectively.

(a) Temperature-composition phase diagram for

magnetic order parameters were performed at the triple-

axis spectrometer 4F2 of LLB-Saclay using a pumped

4He cryostat, and at the E4 diffractometer of BENSC

using a dilution refrigerator.

In a previous heat capacity study[27], a phase tran-

sition was observed in the range of 3.8 to 2.7 K for

0 ≤ x<

∼0.6, and was attributed to an antiferromagnetic

transition as in CeRhIn5[24] [open diamonds in Fig. 1(a)].

This is confirmed by the results of this neutron diffrac-

tion work which show that all samples (0.1 ≤ x ≤ 0.5)

have magnetic Bragg peaks characterized by the same in-

commensurate wave vector as in CeRhIn5[28]. The N´ eel

temperature, TNi, determined from the temperature vari-

ation of magnetic Bragg peaks is shown as filled diamonds

in Fig. 1(a).

Thermodynamic and transport measurements uncover

a superconducting state below 1 K in a wide composi-

tion range, 0.25<

∼x ≤ 1[27], [open circles in Fig. 1(a)].

In 0.25<

∼x<

∼0.6 where the superconducting and in-

commensurate antiferromagnetic phases coexist, we find

a second magnetic order below 2.7 K with a commensu-

rate antiferromagnetic ordering wave vector qc=(1

2,1

2,1

2)

TABLE I: Magnetic Bragg intensity, σobs, defined in Eq. (1),

observed at 1.9 K in units of 10−3barns per CeRh0.7Ir0.3In5.

The theoretical intensity, σcal, is calculated using Eq. (2) and

(3) for the incommensurate moment Mi = 0.73µB/Ce and

the commensurate moment Mc = 0.27µB/Ce, respectively.

q

σobs

σcal

q

σobs

σcal

(1

2

1

2δ )

21+δ )

1

22+δ )

1

23+δ )

1

24+δ )

1

25+δ )

(3

2

(3

2

(3

2

(3

2

(1

22

(1

22

(3

22

9.0(5)

9.6(3)

9.0(3)

5.7(3)

4.3(3)

2.9(3)

4.3(3)

5.4(15)

3.4(3)

2.5(4)

2.3(4)

0.8(2)

1.2(2)

9.3

12.1

10.8

7.7

4.9

2.7

4.2

4.2

3.9

3.1

3.2

1.1

1.1

(1

(1

(1

(1

(1

(1

(3

(3

(3

2

1

21-δ )

1

22-δ )

1

23-δ )

1

24-δ )

1

25-δ )

1

26-δ )

3

21-δ )

3

22-δ )

3

23-δ )

1

2

1

2

3

2

3

2

10.1(3)

9.9(3)

8.2(4)

5.7(3)

3.9(3)

2.7(5)

3.8(4)

5.0(4)

2.9(3)

2.3(2)

1.9(7)

1.3(2)

0.7(2)

10.8

12.0

9.6

6.5

3.9

2.1

4.2

4.1

3.6

2.6

2.7

1.1

1.0

(1

(1

(1

(1

(1

2

1

2

22

22

22

22

3

2δ )

21+δ )

3

22+δ )

3

23+δ )

1

2

3

2

2

(1

(1

(3

(3

2

1

2)

5

2)

1

2)

5

2)

3

2)

9

2)

3

2)

2

1

2

3

2

[filled squares in Fig. 1].

Table I lists integrated intensities of magnetic Bragg

peaks at 1.9 K for x = 0.3 of both commensurate and

incommensurate types, collected by rocking scans in the

two-axis mode and normalized to structural Bragg peaks

(002), (003), (004), (006), (111), (112), (113), (220),

(221) and (222) to yield magnetic neutron diffraction

cross-sections in absolute units, σ(q) = I(q)sin(2θ),

where 2θ is the scattering angle. In such units, the mag-

netic cross section is[30]

σ(q) =

?γr0

2

?2

M2

i,c|f(q)|2?

µ,ν

(δµν−? qµ? qν)F∗

µ(q)Fν(q),

(1)

where (γr0/2)2= 0.07265 barns/µ2

gered moment of the Ce ion in either the incommensu-

rate or commensurate antiferromagnetic structure, f(q)

the magnetic form factor which could be different for the

two type antiferromagnetic orders, ? q the unit vector of q,

and Fµ(q) the µth Cartesian component of the magnetic

structure factor per molecular formula.

The incommensurate magnetic structure for CeRhIn5

has been determined [inset in Fig. 1(a)] and the magnetic

cross section, Eq. (1), is reduced to[28]

B, Mi,c is the stag-

σi(q) =1

4

?γr0

2

?2

M2

i|f(q)|2?1 + |? q ·? c|2?,(2)

where ? c is the unit vector of the c-axis.

For the commensurate magnetic component, the sum-

mation in Eq. (1) is reduced to (1 − |? q ·?

where?

and |F(q)|2= 1. Polarized neutron diffraction measure-

ments at (1

2,δ), with a horizontal and

Mc|2)|F(q)|2,

Mc is the unit vector of the magnetic moment,

2,1

2,1

2) and (1

2,1

Page 3

3

FIG. 2:

surate (diamonds) magnetic Bragg peaks follow the magnetic

form factor of Ce3+(4f1) ion.

Both the commensurate (squares) and incommen-

vertical magnetic guide field respectively, indicate that

the magnetic moment in the commensurate antiferromag-

netic order, like in the incommensurate order[28], lies in

the tetragonal basal plane. The commensurate magnetic

structure is depicted in the inset in Fig. 1(b). There are

in general 8 symmetry-related?

and the easy axis within the basal plane cannot be de-

termined in a multidomain sample due to the tetragonal

symmetry. Assuming equal populations among these do-

mains during our unpolarized neutron diffraction exper-

iment, the magnetic polarization factor averages to[31]

?1 − |? q ·?

netic cross section for the commensurate antiferromag-

netic order is

?γr0

2

Mcdomains in the sample

Mc|2? =

?1 + |? q ·? c|2?/2. Therefore, the mag-

σc(q) =1

2

?2

M2

c|f(q)|2?1 + |? q · ? c|2?.(3)

Applying Eq. (2) and (3) to the data in Table I, a least-

square fit yields staggered magnetic moments Mi=0.73±

0.25µB and Mc=0.27 ± 0.10µB per CeRh0.7Ir0.3In5 at

1.9 K.

Measured magnetic intensities for CeRh0.7Ir0.3In5 in

Table I are plotted in Fig. 2 as a function of |q|

in scaled quantities 4σi(q)/?(γr0/2)2M2

and 2σc(q)/?(γr0/2)2M2

squared magnetic form factor, |f(q)|2, [Eq. (2) and (3)].

The solid line is |f(q)|2for Ce3+ion[32]. The fact that

the measured data for both commensurate (squares) and

incommensurate (diamonds) orders are well described by

the solid curve indicates not only the correctness of our

magnetic models in Eq. (2) and (3) for CeRh0.7Ir0.3In5,

but also that the Ce3+(4f1) ions are responsible for

both commensurate and incommensurate antiferromag-

netic orders. This is consistent with the thermodynamic

study[27] where entropy reaches the same value at ∼6

K for all samples from x=0 to x=1, suggesting that the

same f electrons are responsible for heavy fermion for-

mation, antiferromagnetic orders, and superconductivity

in CeRh1−xIrxIn5. Division of the f spectral weight was

i(1 + |? q · ? c|2)?

c(1 + |? q ·? c|2)?, which equal the

FIG. 3: Squared magnetic order parameters of the incom-

mensurate (diamonds) and commensurate (squares) antifer-

romagnetic transitions. The dotted line indicates the critical

temperature TC ≈ 0.5 K of the superconducting transition.

The solid lines are guides to the eye.

probed using neutron scattering in CeRhIn5[33] and was

further investigated in terms of a two-fluid model for this

family of heavy fermion materials[34, 35, 36].

Magnetic moments for other compositions were mea-

sured in a similar fashion, and are shown as squares and

diamonds for commensurate and incommensurate struc-

tures, respectively, in Fig. 1(b).

squared total magnetic moments per Ce,

The average of the

M2≡ ?(Mi+ Mc)2? = M2

i+ M2

c,(4)

is also shown in Fig. 1(b) as circles. A large staggered

magnetic moment of 0.85µB/U[15] coexisting with super-

conductivity in UPd2Al3has been considered a puzzling

anomaly[8], while UPt3[20] has a tiny moment of 0.02

µB/U, and the moment in UNi2Al3, 0.24 µB/U[17], is

also quite small. Here in the coexistence composition re-

gion of Ce(Rh,Ir)In5, M ranges from 0.27 to 0.78 µB/Ce,

bridging the gap between UNi2Al3and UPd2Al3.

In Fig. 3, the temperature dependences of the Bragg

peak intensities of (1

sented as the squared order parameters M2

of the incommensurate and commensurate antiferromag-

netic transitions, respectively. Data below 1.2 K were

taken at BENSC using a dilution refrigerator. There is no

thermal hysteresis for either magnetic phase transition.

When the commensurate phase transition occurs at 2.7

K, there is no abrupt change in the incommensurate order

parameter. Similarly, at the superconducting transition

TC ≈ 0.5 K (dotted line), no apparent anomaly occurs

in either magnetic order parameter. This is analogous

to the magnetic order parameter for the heavy fermion

superconductors UPd2Al3[37] and UPt3in the A and C

phases, but different from that for UPt3in the supercon-

ducting B phase[8, 20].

Note in Fig. 1(a) that the N´ eel temperatures TNiand

TNc both are nearly constant when they are non-zero.

2,1

2,1−δ) and (1

2,1

2,1

2) are pre-

i and M2

c

Page 4

4

This might suggest a phase separation scenario where

only a volume fraction of M2(x)/M2(0) is magnetically

ordered and the remaining is superconducting. However,

at x = 0.5, this would imply M2(x)/M2(0) = 0.08, which

is not consistent with a magnetic volume fraction of at

least 0.85 determined from a µSR study[38].

At the quantum critical point (QCP) of the supercon-

ducting phase near x = 0.25, the commensurate anti-

ferromagnetic order appears with Mcjumping from zero

[Fig. 1(b)]. This suggests a change in electronic struc-

ture at x ≈ 0.25 which produces a strong enough peak

at q = (1

2) in the RKKY interaction to induce the

new magnetic order. Several sheets of the Fermi sur-

face of differently enhanced masses have been observed

in the de Haas-van Alphen measurements of CeRhIn5

and CeIrIn5[39, 40] and the Fermi surface topology is

determined mostly by non-f electrons[41, 42]. The con-

currence of the superconductivity and commensurate an-

tiferromagnetic order observed here, therefore, suggests

that the responsible Fermi surface sheet for the supercon-

ductivity may be the one close to nesting at q = (1

Both Mi and Mc approach zero at a second QCP of

the antiferromagnetism near x ≈ 0.6, while the N´ eel

temperatures are insensitive to x (Fig. 1).

havior is similar to UPt3 under pressure[43], suggest-

ing that both belong to a distinct type of QCP. Recall

that TN ∝ JRKKYM2, where both the RKKY interac-

tion JRKKY and the saturated magnetic moment M are

controlled by the Kondo interaction. In both of these

systems the divergence of JRKKY and the reduction of

M appear to obey JRKKY ∝ M−2as this QCP is ap-

proached. Theoretical investigation of the physical pro-

cess maintaining the delicate proportional relation near

this type of QCP is warranted.

Insummary,theantiferromagnetic

Ce(Rh,Ir)In5 below ∼3.8 K is characterized by the

incommensurate antiferromagnetic spiral of wave vector

(1

2,±δ). In the coexistence composition region of su-

perconductivity and antiferromagnetism, an additional

phase transition to a commensurate antiferromagnet

characterized by (1

2) is discovered below 2.7 K.

The same f electron at each site, hybridizing with

other conduction electrons, is responsible for both the

superconductivity and the commensurate and incom-

mensurate antiferromagnetic orders.

the energy band(s) with Fermi surface nesting near the

(1

2) is responsible for the heavy fermion super-

conductivity.The novel coexistence of three different

types of cooperative ordered states adds a new variety

to the rich phenomena relating to the interplay between

magnetism and superconductivity.

We would like to thank G.D. Morris, R.H. Heffner,

C.M. Varma, Q. Si, S.A. Trugman, D. Pines, Ar. Abanov,

Y. Bang, P. Dai and S. Kern for useful discussions; A.

Cull for help at CRL, and P. Smeibidl and S. Gerischer

2,1

2,1

2,1

2,1

2).

This be-

phaseof

2,1

2,1

2,1

It is likely that

2,1

2,1

at HMI. Work at Los Alamos was performed under the

auspices of the US Department of Energy.

∗This work was part of ADC’s Ph.D. research project,

supervised by WB and AHL at LANL.

†Current address: Physics Department, Brookhaven Na-

tional Laboratory, Upton, New York 11973

‡Current address: Instituto de F´isica “Gleb Wathagin”,

UNICAMP, 13083-970, Campinas, Brasil

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