Magnetic Ordering in 

Ce1-xYbxRhIn5 Heavy Fermions 

as a Function of Doping

JOHN CALIFF COLLINI 1

MENTOR: DR. STEVE DISSELER2

NCNR SURF GROUP AT NIST

1ROCHESTER INSTITUTE OF TECHNOLOGY

2NCNR CONDENSED MATTER SCIENCE GROUP

NIST August 5, 2015
One Definition:
Types of Magnetic States (only 3 shown)

Paramagnetic

< MM > = 0

MM = χχmmHH

Ferromagnetic

HH = − JJ �

ii,jj

ss⃗

ii � ss

⃗

jj

JJ > 0

Antiferromagnetic

HH = − JJ �

ii,jj

ss⃗

ii � ss

⃗

jj

JJ < 0

< MM > ≠ 0 < MM > = 0

Ex: Iron and Cobalt Ex: Common Metal-Oxides

TT > TTcc: DISORDERED TT < TTcc: ORDERED
Types of Magnetic States (only 3 shown)

Paramagnetic

< MM > = 0

MM = χχmmHH

Ferromagnetic

HH = − JJ �

ii,jj

ss⃗

ii � ss

⃗

jj

JJ > 0

Antiferromagnetic

HH = − JJ �

ii,jj

ss⃗

ii � ss

⃗

jj

JJ < 0

< MM > ≠ 0 < MM > = 0

Ex: Iron and Cobalt Ex: Common Metal-Oxides

TT > TTcc: DISORDERED TT < TTcc: ORDERED
Types of Magnetic States (only 3 shown)

Paramagnetic

< MM > = 0

MM = χχmmHH

Ferromagnetic

HH = − JJ �

ii,jj

ss⃗

ii � ss

⃗

jj

JJ > 0

Antiferromagnetic

HH = − JJ �

ii,jj

ss⃗

ii � ss

⃗

jj

JJ < 0

< MM > ≠ 0 < MM > = 0

Ex: Iron and Cobalt Ex: Common Metal-Oxides

TT > TTcc: DISORDERED TT < TTcc: ORDERED
Types of Magnetic States (only 3 shown)

Paramagnetic

< MM > = 0

MM = χχmmHH

Ferromagnetic

HH = − JJ �

ii,jj

ss⃗

ii � ss

⃗

jj

JJ > 0

Antiferromagnetic

HH = − JJ �

ii,jj

ss⃗

ii � ss

⃗

jj

JJ < 0

< MM > ≠ 0 < MM > = 0

Ex: Iron and Cobalt Ex: Common Metal-Oxides

TT > TTcc: DISORDERED TT < TTcc: ORDERED
What are Heavy Fermions?

Kondo Interactions

-Conduction spin screening

-Suppresses magnetic 

ordering

RKKY Interactions

-Coupled moments 

dependent on distance

-Enhances magnetic 

ordering

Combining Both

-Huge increase in effective 

mass.

-Kondo and RRKY 

interactions co-exist

-Possible unconventional 

superconductivity near QCP 

*from UNLP*

Also, increasing HH, P, doping, ect. 
What are Heavy Fermions?

Kondo Effect

-Electron spin screening

-Suppresses magnetic 

ordering
What are Heavy Fermions?

Kondo Effect

-Conduction spin screening

-Suppresses magnetic 

ordering

RKKY Interactions

-Coupled moments 

dependent on distance

-Enhances magnetic 

ordering

Non-magnetic

FerroAnti

r
What are Heavy Fermions?

Kondo Effect

-Conduction spin screening

-Suppresses magnetic 

ordering

RKKY Interactions

-Coupled moments 

dependent on distance

-Enhances magnetic 

ordering

Non-magnetic

FerroAnti

r
What are Heavy Fermions?

Kondo Effect -Conduction spin screening -Suppresses magnetic 

ordering

RKKY Interactions -Coupled moments 

dependent on distance -Enhances magnetic 

ordering

Non-magnetic

Ferro-

Anti-

r
What are Heavy Fermions?

Kondo Interactions

-Conduction spin screening

-Suppresses magnetic 

ordering

RKKY Interactions

-Coupled moments 

dependent on distance

-Enhances magnetic 

ordering

Combining Both

-Huge increase in effective 

mass.

-Kondo and RRKY 

interactions co-exist

-Possible unconventional 

superconductivity near QCP 

*from UNLP*

Also, increasing HH, P, doping, ect. 
Ce1-xYbxRhIn5

QCP

-Kondo and RKKY on equal 

footing.

-Material can go 

superconducting under 

pressure.

-USC is similar to High Temp 

SC in copperates.

Pressure

USC or Other

CeRhIn5 goes superconducting under applied pressure
Ce(1-x)YbxRhIn5 (Heavy Fermion Material)

Ce/Yb site

In1

Rh

In2

a (‘x’ dependent)

c (‘x’ dependent)

Tetragonal:

a=b≠c

α=β=γ=90°

Space group:

P 4/m m m
Goal: Ce1-xYbxRhIn5 Magnetic Transitions

CeRhIn5 YbRhIn5 Increasing x

Turns antiferromagnetic

k=(1⁄2,1⁄2,0.297) 3

T=3.8 K

(incommensurate structure)

Metallic Paramagnet 4

Finding 

the transition

(in terms of T and x)

For magnetic ordering

Finding the transition

(in terms of T and x)

For change to commensurate structure

3Wei Bao, P. G. Pagliuso, J. L. Sarrao, J. D. Thompson, Z. Fisk,

J.W. Lynn, and R.W Erwin. Incommensurate magnetic structure of CeRhIn5. Phys. B 62-22

4Z. Bukowski, , K. Gofryk, D. Kaczorowski. Magnetic and transport properties of YbRhIn5 and 

YbIrIn5 single crystals . Solid State Communications 134-7.
CeRhIn5 

3

3Wei Bao, P. G. Pagliuso, J. L. Sarrao, J. D. Thompson, Z. Fisk,

J.W. Lynn, and R.W Erwin. Incommensurate magnetic structure of CeRhIn5. Phys. B 62-22
Goal: Ce1-xYbxRhIn5 Magnetic Transitions

CeRhIn5 YbRhIn5 Increasing x

Turns antiferromagnetic

k=(1⁄2,1⁄2,0.297) 3

T=3.8 K

(incommensurate structure)

Metallic Paramagnet 4

Finding 

the transition

(in terms of T and x)

For magnetic ordering

Finding the transition

(in terms of T and x)

For change to commensurate structure

3Wei Bao, P. G. Pagliuso, J. L. Sarrao, J. D. Thompson, Z. Fisk,

J.W. Lynn, and R.W Erwin. Incommensurate magnetic structure of CeRhIn5. Phys. B 62-22

4Z. Bukowski, , K. Gofryk, D. Kaczorowski. Magnetic and transport properties of YbRhIn5 and 

YbIrIn5 single crystals . Solid State Communications 134-7.
Samples go here

Include talk on concentration

Prepared by Sooyoung Jang of the Brian Maple group from UC San Diego

Actual sample 

concentration were not 

matching with the 

concentrations used to 

make these samples.

Needed a way to measure 

concentrations.

Made powders and headed 

to UMD for SQUID 

measurements.
SQUID Magnetometry for measuring μeff

(superconducting quantum interference device) 

SENSITIVE LOW TEMP MAGNETOMETER SQUID AT U MARYLAND COLLEGE PARK

* Hyperphysics SQUID Magnetometer 

Our powder sample

x=‘.5’; 25 mg

x=‘.6’; 32.7 mg
Sample reported as x=‘.5’

C= 0.967 +/- 0.004 [(emu K)/or]

Curie Temp= -43.2 +/- 0.4 [K]

μeff = 2.7814 +/- 0.0009 μB

x= 0.090 +/- 0.001

χχ TT =

μμbbbbbbbb (TT)

HH∗mmmmmmmmmm

=

CC

TT−θθmm

− χχ0

T - Temperature [K]

C – Curie Number [(emu K)/or]

θθmm - Curie Temp. [K] (+ Ferro, - Anti)

CCmmmmmmmmmm =

NN μμ eeee

2 (xx)

3kkBB

μμ eeee

2 (xx) = xxxxYYbb+3

2 + 1 − xx CC +22

CC +3 = 2.54 μμBB

YYbb+3 = 4.54 μμBB
Sample reported as x=‘.6’

C= 0.799 +/- 0.002 [(emu K)/or]

Curie Temp= -29.8 +/- 0.4 [K]

μeff = 2.5280 +/- .0009 μB

x= -0.0043 +/- 0.0004

Effectively close to zero:

Only seems to be 

Ce+3 moment contributing.

Very small doping on the order

of <1%
Rietveld 

refinement

done with 

FullProf

Software

X-ray powder diffraction Ce1Yb0RhIn5 (x<1%)

In (101)
X-ray powder diffraction Ce.91Yb.09RhIn5 (x=.09)

Rietveld 

refinement

done with 

FullProf

Software 

In (101)
Why Neutrons? 

The power of neutron scattering

• Neutrons have spin and zero 

charge (nuclear and magnetic 

scattering).

• Large penetration depth (bulk 

probe).

• Cross-sections good for low Z 

elements (Nuclear 

interactions).

• (More easily) Controllable 

energies.

• Energy scale great for dynamic 

interactions (inelastic 

scattering).

N

e
BT4 Triple Axis Spectrometer 

Reactor 

source

Reactor Source

Entrance

slits

Sample

Stage

Analyzer and 

He3 Detector Monochrometer

(rotate to select 

incident energy)

Sample

(rotate to select 

area to study) 

Analyzer

(Rotate to select 

final energy) 
Measuring the Onset of Magnetic Ordering: x<1%

TN=3.48 +/- .06 K

(1⁄2 1⁄2 1.297) 

(Parent Compound TN=3.8 K)3

Same structure as parent 

compound. [(001)+k peak]
Measuring the Onset of Magnetic Ordering: x~50%

TN=2.94 +/- .03 K

(1⁄2 1⁄2 1⁄2) 

Changes from parent 

compound. New 

structure was formed!
Measuring the Magnetic Structure: x~50%

Each point represents the structure factor of a single diffraction peak
Ce1-xYbxRhIn5

k=(1⁄2 1⁄2 1⁄2) structure

μμeeeeee =

.345 ± .017

0

0

+

0

.119 ± .030

0

μμ eeee = .365 ± .034 μμBB

θθ ≅ 19 degrees
k=(1⁄2 1⁄2 1⁄2) structure [commensurate]

Intermediate Yb concentration

k=(1⁄2 1⁄2 .297) structure [spiral]

Low Yb concentration
Conclusion of Ce1-xYbxRhIn5

• We measured properties of Ce1-xYbxRhIn5 using a combination SQUID, XRD, and Neutron Scattering

• We found a limited solubility of Yb into CeRhIn5, which needs to be better understood to continue this study.

• Results:

1. At low Yb concentrations, these compounds have a lower ordering temperature. 

2. At intermediate Yb concentrations, the magnetic structure changes from incommensurate to commensurate.

3. A new magnetic structure was solved for these intermediate concentration.

• Future work :

1. Apply pressure and magnetic field at low temperatures to induce new interesting phase transitions.

2. Better measurements of the concentrations in these samples.

3. Study why the magnetic structure changes with Yb concentration.

4. Start to form a complete phase diagram from experiments to make better theories on how unconventional 

superconductivity works
A big thanks to: • NSF • Steve Disseler • William Ratcliff • Julie Borchers • Joseph Lesniewski • Arnold Rubinshtein (MML) • Shanta Ranjan Saha (UMD) • Brian Maple (UC San Diego) • Sooyoung Jang (UC San Diego)

References and Citations • Wei Bao, P. G. Pagliuso, J. L. Sarrao, J. D. Thompson, Z. 

Fisk,J.W. Lynn, and R.W Erwin. Incommensurate magnetic 

structure of CeRhIn5. Phys. B 62-22

• Z. Bukowski, , K. Gofryk, D. Kaczorowski. Magnetic and 

transport properties of YbRhIn5 and YbIrIn5 single crystals . 

Solid State Communications 134-7

• Tuson Park, F. Ronning, H. Q. Yuan, M. B. Salamon, R. 

Movshovich, J. L. Sarrao & J. D. Thompson. Hidden 

magnetism and quantum criticality in the heavy fermion 

superconductor CeRhIn5. Nature 440

• P. Coleman. Heavy Fermions: electrons at the edge of 

magnetism. Rugters.

• Gen Shirane, Stephen M. Shapiro, John M. Tranquada. 

Neutron Scattering with a Triple-Axis Spectrometer. 

Cambridge.

• Neil W. Ashcroft, N. David Mermin. Solid State Physics. 

Brooks/Cole.
Bragg’s Law for Crystal Diffraction

...

...

d

d

d

θθ

nnnn = 2222 ssssss θθ

θθ

d
Nuclear vs. Magnetic Unit Cell in Neutron Scattering

k=(1⁄2, 1⁄2, 1⁄2) 

(repeats every 2a,2b, and 2c)
Original Goal: Sm1-xCexCoIn5

SmCoIn5 CeCoIn5 Increasing x

Turns antiferromagnetic Turns superconducting Finding 

the transition

(in terms of T and x)
Sm(1-x)CexCoIn5 (Heavy Fermion Material)

Sm/Ce site

In1

Co

In2

a (‘x’ dependent)

c (‘x’ dependent)

Tetragonal:

a=b≠c

α=β=γ=90°

Space group:

P 4/m m m

Measured Parameters (x-ray)

(x=0 powder)

a = 4.5798 ± .0001 Å

c = 7.4708 ± .0002 Å
(00l) face

(h00) (0k0)

Laue x-ray diffraction

Sample
No Magnetic Peaks found for SmCoIn5

Why?

Cross Sections (1x10-24 cm2)

Element Formula Unit Atomic Wight (g/m) Coherent Incoherent Absorption

Sm 1 105.360 0.422 39.000 5072.236

Co 1 58.933 0.779 4.800 31.845

In 5 114.820 2.080 0.540 165.991

Data from NCNR Scattering and Activation Database

E=35 meV
Determining μeff and x using the SQUID

χχ TT =

μμbbbbbbbb (TT)

HH∗mmmmmmmmmm

=

CC

TT−θθmm

− χχ0

T - Temperature [K]

C – Curie Number [(emu K)/or]

θθmm - Curie Temp. [K] (+ Ferro, - Anti)

Curie-Weiss Law for Paramagnetism

Fit using:

μμbbbb bb(TT)

HH

=

aa

TT − θθmm

− bb

aa = mmmmmmmm (xx) ∗ CC(xx)

bb = mmmmmmmm xx ∗ χχ0

CCmmmmmmmmmm =

NN μμ eeee

2 (xx)

3kkBB

μμ eeee

2 (xx) = xxxxYYbb+3

2 + 1 − xx CC +22

CC +3 = 2.54 μμBB

YYbb+3 = 4.54 μμBB

*numbers and equations from Ashcroft Solid State Physics
Crash course in crystallography 

Lattice + Atomic Basis = Crystal

+ a 1 2
Crash course in crystallography 

Lattice + Atomic Basis = Crystal

Unit cell

a

c

a

c b

a

...

...

...

...
Crash course in crystallography 

Lattice + Atomic Basis = Crystal

Unit cell

Reciprocal space and the Miller 

indices

A measure of frequency. (001)
Crash course in crystallography 

Lattice + Atomic Basis = Crystal

Unit cell

Reciprocal space and the Miller 

indices

A measure of frequency. 

(100)
Crash course in crystallography 

Lattice + Atomic Basis = Crystal

Unit cell

Reciprocal space and the Miller 

indices

A measure of frequency. 

(110)