Tuning of magnetism in 4f-based correlated … › ... › WSUphysics2019mar20.pdfMagnetic...

Halyna HodovanetsCenter for Nanophysics and Advanced Materials

Physics Department University of Maryland

March 2019

Center for Nanophysics

and Advanced Materials

Tuning of magnetism in 4f-basedcorrelated electron systems

Thank you to:

❑ Paul CanfieldSegey Bud’koRebecca Flint

❑ Valentin Taufour

❑ Johnpierre PaglioneHyunsoo KimChris EckbergJoshua HigginsDaniel CampbellSean WintersDaniel KraftPeter Zavalij

Center for Nanophysics

and Advanced Materials

System under study

Think: Find a system

Tune: control

parameter

Think: Study

H, magnetic fieldP, pressurex, chemicals substitution

System under study: Think

• Why

• What

• How

• Why❑ New science, application

❑ “Old system” new science

❑ New compound, new science?

❑ Single crystalline form (anisotropic properties etc.)

System under study: Think

Why

Behind every crystal lies fascinating science!

CeCu2Ge2

TbFe2Ge2 ZrNiSn

TiSe2

LuGa3

GdFe2

RNi2B2C

BismuthBi

CeZn11

Beautiful!

CeAuBi2

Why

Has it been studied before, how extensively, can you contribute substantially, cost, time… etc.

CeCu2Ge2

TbFe2Ge2 ZrNiSn

TiSe2

LuGa3

GdFe2

RNi2B2C

BismuthBi

CeZn11

Beautiful!

CeAuBi2

What

“The road map/Palette/Pantry”: you can imagine making a huge number of compounds by combining different elements in different ratios....

What

Fe-based high temperature superconductors

1mmCaFe2As2

J. T. Sypek et al., Nat. Commun. 8, 1083 (2017)

What Rare-earth based intermetallics

4f

RNi2B2CP. C. Canfield, Peter L. Gammel, and David J. Bishop, Physics Today 51, 10, 40 (1998)

What Rare-earth based intermetallics

4f

High-temperature flux method

AluminumAl

https://www.ameslab.gov/dmse/rem/what-are-rare-earths

How

Tm = 6600 C

Flux: Sn, In, Bi, Pb, and Sb

centrifuge

High-temperature flux methodHow

1200 0C

Spin temperature

Room temperature

1 mm

System under studyThink: Find a system Tune: control parameter Think: Study

❖Single crystal growth via high temperature solution growth

❖Basic properties• Powder (single crystal) x-ray and Laue• Magnetization (magnetic order)• Specific heat • Resistivity• Hall effect • Thermoelectric power (TEP)

Tune: control parameter

Ground state

Ground state ‘

Ground state ‘

Ground state ‘

magnetic field, H

pressure, P

Chemical substitution, x

System under studyThink: Study

Phase diagram: T versus x, H, P

Think: Find a system

Outline

❑ La dilution of Kondo lattice CeCu2Ge2

❑ Physical properties of Weyl semimetal CeAlGe and it’s response to magnetic field

❑ Conclusions

Outline


“Old system” new physics

P. Coleman, Handbook of Magnetism and Advanced Magnetic Materials (Wiley, New York, 2007), pp. 95–148, Vol. 1.

Single-ion Kondo -> Kondo lattice

High temperature Low temperature

R. Flint thesis Symplectic-N in strongly correlated materials (2010)

HF materials consist of free spins immersed in a sea of non-interacting conduction electrons.

The spins hybridize with the conduction electrons to form mobile, heavy electrons with masses 100 (Kondo lattice) to 1000 times that of the bare electrons.

Heavy fermion

RKKY interaction

Indirect exchange couples moments over relatively large distances. Interaction between rare-earth magnetic moments in a metal is mediated by the conduction electrons.Interaction strength oscillates with distance from between the spins due to a specific (Fermi) wavelength of electrons

A.J. Freeman. Magnetic Properties of Rare Earth Metals.

Ruderman-Kittel-Kasuya-Yosida (RKKY)

Ce3+

P. Coleman, “Heavy fermions: Electrons at the edge of magnetism," in Handbook of Magnetism and Advanced magnetic Materials , Vol. 1 (John Wiley & Sons, Ltd, 2007)

QCP(quantum critical point)

TN ~ J

2N (E

F)

TK ~ Dexp[-1/JN(E

F)]

Fermi liquidAFM

T

JN(EF)

TK > T

RKKYTK < T

RKKY

Kondo effect:

RKKY:

Pressure P and chemical substitution x

Can tune with magnetic field H as well

Doniach phase diagram

magnetic orderlocal moments magnetic order

reduced moments

screened moment no magnetic orderheavy fermions

CeCu2Ge2

Kondo lattice compound, ThCr2Si2-type structure

• antiferromagnetic ordering TN ~ 4 K, TK ~ 4-10 K, = 0.1 J/mol-K2

• Pressure induced superconductivityTc = 0.64 K at p 10 GPa

• Field induced QCP Hc 300 kOe (H || a)

D. Jaccard et al. Phys. Lett. A 163, 475 (1992)

• “x” as we go from Kondo latticeto single-ion Kondo?

F. R. De Boer et al. J. Mag. Mag. Mat. 63, 91 (1987)

B. Zeng et al. Phys. Rev. B 90, 155101 (2014)

Ce1-xLaxCu2Ge2 single crystals

RE:Cu:Ge =0.05:0.475:0.475

2 h

250 C

11800 C 11800 C

8250 C

150 h5 h

Space group I4/mmm

One unique Ce site of 4/mmm symmetry

P. C. Canfield and Z. Fisk, Phil. Mag. B 65, 1117 (1992)

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

WDS

M(T)/H data fit

xL

a

xLa, nominal

0.0 0.2 0.4 0.6 0.8 1.0175

180

185

190

0.0 0.2 0.4 0.6 0.8 1.04.16

4.20

4.24

a (Å

)

a

c

x

10.1

10.2

10.3

c (Å

)

x

V (Å

3)

Ce1-x

LaxCu

2Ge

2

Tetragonal unit cell

H.Hodovanets et al. Phys. Rev. Lett. 114, 236601 (2015)

Ce1-xLaxCu2Ge2 : Specific heat

Cmag, max

0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

TN

d(T)/dT

C(T)

Ce1-x

LaxCu

2Ge

2

T (

K)

xLa

AFM

0 5 10 150

2

4

6

8

0 1 2 3 4 50.0

0.1

0.2

0.3

0.4

0.5

0.6(Ce

1-xLa

x)Cu

2Ge

2

Cp (

J/m

ol K

)

T (K)

x= 0

0.25

0.42

0.66

0.75

0.80

0.85

0.90

0.92

0.97

0.98

0.99

1

0.90

0.85

0.80

Cp (

J/m

ol K

)

T (K)

0.75


Possible origin:

• CEF (197 and 212 K)

• Spin glass

• TK of single-ion Kondo impurity


1 100

1

2

3

(Ce0.15

La0.85

)Cu2Ge

2

Cm

ag (

J/m

ol-

Ce

K)

T (K)

H=0 kOe

5 kOe

10 kOe

25 kOe

50 kOe


M. Loewenhaupt et al. J. Appl. Phys. 111, 07E124 (2012)

K. D. Schotte and U. Schotte,Phys. Lett. A , 55, 38 (1975)

1 100

1

2

3

4

5

6

TK=1.27 K

TK=1.04 K

Cm

ag/T

(J/K

2m

ol-C

e)

T (K)

+−=

T

T

T

TTRT

T

TC KKK

K

KI

22

1

21

22/

TK=0.83 K

offset by 1J/K2mol-Ce

0.97

0.98

0.99



K. Schotte and U. Schotte,Phys. Lett. A , 55, 38 (1975)

Peak in Cp atTmax =0.45TK

H. U. Desgranges and K. D. SchottePhys. Lett. A 91, 240 (1982)

Cmag, max

(Tmax

=0.45TK)

TK, single-ion Kondo fit

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

5

6

7

TN

d(T)/dT

C(T)

(Ce1-x

Lax)Cu

2Ge

2

T (

K)

xLa

AFM

TK

1 100

1

2

3

4

5

6

TK=1.27 K

TK=1.04 K

Cm

ag/T

(J/K

2m

ol-C

e)

T (K)

+−=

T

T

T

TTRT

T

TC KKK

K

KI

22

1

21

22/

TK=0.83 K

offset by 1J/K2mol-Ce

0.97

0.98

0.99



Cmag, max

0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

TN

d(T)/dT

C(T)

Ce1-x

LaxCu

2Ge

2

T (

K)

xLa

AFM

1 10 1000

20

40

(

cm

)

T (K)

Ce1-x

LaxCu

2Ge

2 H=0

0

0.25

0.66

0.80

0.90

1

TN

Ce1-xLaxCu2Ge2: Resistivity

0.2 0.4 0.6 0.8 1.0 1.215

20

25 CeyLa

1-yCu

2Ge

2

Tm

in (

K)

(yCe

)1/5

TcohTmin

0.1 1 10 100

2

4

6

8

10

(

cm

)

Ce1-x

LaxCu

2Ge

2

T (K)

~−log(T)

0.85

0.90

0.92

0.97

0.98

0.99

1


Ce1-xLaxCu2Ge2 : T-x phase diagram

Cmag, max

(Tmax

=0.45TK)

TK, single-ion Kondo fit

mag,max

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

5

6

7

Tcoh

TN

d(T)/dT

C(T)

R(T)

(Ce1-x

Lax)Cu

2Ge

2

T (

K)

xLa

AFM

Tmax

TK


T-x phase diagram of Ce1-xLaxCu2Ge2

•robust TN

•Robust Tcoh

9 % of Ce separates coherent state from single-ion Kondo impurity state

Simple cubic with NN+2NN+3NN pc= 0.0976

Ł . Kurzawski and K. Malarz Rep. Math. Phys., 70, 163 (2012) Ł . Kurzawski and K. Malarz Rep. Math. Phys., 70, 163 (2012)


H. Hodovanets, Phys. Rev. Lett. 114, 236601 (2015)

Characteristic energy scales of Ce1-xLaxCu2Ge2

Summary: Ce1-xLaxCu2Ge2

• we AFM order up to x 0.8

• Tcoh stays observable up to x 0.9

• percolation limit of 9 % of Ce separates coherent state fromsingle-ion Kondo impurity state

• (Tcoh)2 TN

• Neutron study, confirmed presence of AFM order up to x = 0.75B. G. Ueland et al., Phys. Rev. B 97, 165121 (2018)

Magnetic moment TN(Tcoh)2

It is still a question why AFM and coherence extend to such small Ce concentrations

Outline


❑ Type II Weyl semimetal CeAlGe

“New system” new physics

• CeAlGe (calculated ferromagnet, a-axis easy axis) has been recently suggested as a host of a new type of Weyl semimetal state that breaks both time-reversal symmetry and inversion symmetry (a new route for generating magnetic Weyl fermions)

G. Chang et al. PRB 97, 041104(R) (2018)

• CeAlGe: Polycrystalline work is inconsistent (AFM vs FM, two different crystal structures)

Motivation

• Can we unambiguously say what type of space group and magnetic order?

• Magnetic anisotropy?

• How well does it respond to magnetic field?

• Single crystals

Motivation

Grow as plates, naturally formed edges are a- and b- axes, c-axis is perpendicular to the plate

2 h

250 C

11500 C

7500 C

72 h12 h

Crystal structure: CeAlGeI41md I41/amd (50% Al doped CeGe2-x)

Non-centrosymmetric Centrosymmetric

AlCeGe ThSi2, tI12, 141 I41/amd O2 JSSCBI (1998) 137, 191-205AlCeGe LaPtSi, tI12, 109 I41md JMMMDC (1996) 152, 22-26

c

ba

Grow as plates, naturally formed edges are a- and b- axes, c-axis is perpendicular to the plate

Crystal structure: CeAlGe single crystal x-ray diffraction

CeAlGe – I41md non-centrosymmetric

I(hkl)=(1-x)|F(h,k,l)|2+x|F(-h,-k,-l)|2

where x is the Flack parameter, I is the square of the scaled observed structure factor and F is the calculated structure factor.

Magnetization: CeAlGe

eff = 2.56 B (Ce3+ )

p= -3.5 K

a > c, moment in the ab-plane

Curie –Weiss law fit

0 50 100 150 200 250 3000

1

M/H

(e

mu

/mol)

T (K)

a

c

ave.

CeAlGe

H = 1 kOe

2 4 60.0

0.5

1.0

M/H

(em

u/m

ol)

T (K)

TN = 4.6 K

H. Hodovanets et al. Phys. Rev. B 98, 245132 (2018)

Magnetic order

Spin-flop transition H||a, (~0.5 of 2.14 B for Ce+3, M(H) data do not follow Arrot plot).


0 20 40 60 80 100 120 1400.0

0.5

1.0

1.5

H||c

H||a

M (

B/F

.U.)

H (kOe)

T = 1.8 K

Frit

CeAlGe


Spin-flop transition H||a, (~0.5 of 2.14 B for Ce+3, M(H) data do not follow Arrot plot).

-5 0 5

-0.5

0.0

0.5

M (

B/F

.U.)

H (kOe)

1.8 K

H||a

CeAlGe

-4 -2 0 2 4-0.1

0.0

0.1

M (

B/F

.U.)

H (kOe)

1.8 K

H||c

CeAlGe

0 20 40 60 80 100 120 1400.0

0.5

1.0

1.5

H||c

H||a

M (

B/F

.U.)

H (kOe)

T = 1.8 K

Frit

CeAlGe



Dynamic susceptibility: AFM or FM order

0.5

1.0

1.5

0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

', ''

(em

u/m

ol C

e)

T (K)

f = 7.57 Hz

CeAlGeH||a

(a)H

ac (Oe)

1

3

5

10

' (

em

u/m

ol C

e)

2 4 60.00

0.05

0.10

Hac

(Oe)

1

3

5

10

''

(em

u/m

ol C

e)

T (K)

0 10 20 300.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16(b)

H||c

', ''

(em

u/m

ol C

e)

T (K)

Ferrimagnet Antiferromagnet


Heat capacity: CeAlGe

Small gamma, low carrier density

LaAlGe: = 0.93 mJ/(mol K2 )

CeAlGe: = 50 mJ/(mol K2 ) above magnetic order

0 10 20 300

2

4

6

8

10

T (K)

Cp (

J/m

ol K

)

LaAlGe

CeAlGe


Transport: CeAlGe

0 20 40 60 80 100 120 1400

10

20

30

40

50

60

70

0 20 400

10

20

0 20 40 60 80 100 120 140

31

32

0 20 40 60 80 100 120 14028

30

32

34

36

0 50 100 150 200 250 300

30

40

50

60

70

80

90 (

-cm

)

T (K)

LaAlGe

CeAlGe

(a)

I||b

(b)

H||c, I||b

T (K)

300

250

200

150

100

75

50

30

25

20

15

10

7

5

4

3

2

H (

cm

)

H (kOe)

CeAlGe

H (

cm

)

H (kOe)

0 5 1035

36

(

-cm

)

T (K)

CeAlGe

(c)

LaAlGe

I||b

(

-cm

)

T (K)

1.8

3

4

5

H (kOe)

H||c

(d)

(

-cm

)

T (K)

H||a, I||b

20

12

10

9

7

5

4.5

4

3

1.8

H||c, I||b

2

H (kOe)

CeAlGe

RRR = 2


Transport: CeAlGe

n = 1.44 x 1020 cm-3

0 20 40 60 80 100 120 1400

10

20

30

40

50

60

70

0 20 400

10

20

0 20 40 60 80 100 120 140

31

32

0 20 40 60 80 100 120 14028

30

32

34

36

0 50 100 150 200 250 300

30

40

50

60

70

80

90

(

-cm

)

T (K)

LaAlGe

CeAlGe

(a)

I||b

(b)

H||c, I||b

T (K)

300

250

200

150

100

75

50

30

25

20

15

10

7

5

4

3

2

H (

cm

)

H (kOe)

CeAlGe

H (

cm

)

H (kOe)

0 5 1035

36

(

-cm

)

T (K)

CeAlGe

(c)

LaAlGe

I||b

(

-cm

)

T (K)

1.8

3

4

5

H (kOe)

H||c

(d)

(

-cm

)

T (K)

H||a, I||b

20

12

10

9

7

5

4.5

4

3

1.8

H||c, I||b

2

H (kOe)

CeAlGeH. Hodovanets et al. Phys. Rev. B 98, 245132 (2018)

T-H phase diagrams: CeAlGe

0 10 20 300

1

2

3

4

5

6

0 20 40 60 800

1

2

3

4

5

6

M(T)

M(H)

R(H)

II?

I

T (

K)

H (kOe)

H||a

CeAlGe

III

IV

(a)III

III

Cp

Cp

M(T)

M(H)

R(H)

T (

K)

H (kOe)

H||c

(b)


Summary for CeAlGe

• Crystal structure: I41md (non-centrossymetric) vs I41/amd (centrosymmetric)

• Magnetic order: AFM vs FM vs Ferrimagnetic

• Interesting magnetism further investigation is warranted (neutron scattering)

• Interesting transport properties in the ab-plane in the ordered state

Outline


❑ Type II Weyl semimetal CeAlGe

❑ Conclusions

Conclusions




❑ Single crystalline form (anisotropic properties) etc.

❑ How about other rare-earths?

Conclusions




❑ Single crystalline form (anisotropic properties) etc.

❑ How about other rare-earths?

Thank you!!!

Tuning of magnetism in 4f-based correlated … › ... › WSUphysics2019mar20.pdfMagnetic...

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