tuning of magnetism in 4f-based correlated … › ... › wsuphysics2019mar20.pdfmagnetic...
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![Page 1: Tuning of magnetism in 4f-based correlated … › ... › WSUphysics2019mar20.pdfMagnetic Properties of Rare Earth Metals. Ruderman-Kittel-Kasuya-Yosida (RKKY) Ce3+ P. Coleman, Heavy](https://reader034.vdocuments.mx/reader034/viewer/2022042308/5ed4a749dfca6a6afc25d71a/html5/thumbnails/1.jpg)
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
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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
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System under study
Think: Find a system
Tune: control
parameter
Think: Study
H, magnetic fieldP, pressurex, chemicals substitution
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System under study: Think
• Why
• What
• How
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• Why❑ New science, application
❑ “Old system” new science
❑ New compound, new science?
❑ Single crystalline form (anisotropic properties etc.)
System under study: Think
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Why
Behind every crystal lies fascinating science!
CeCu2Ge2
TbFe2Ge2 ZrNiSn
TiSe2
LuGa3
GdFe2
RNi2B2C
BismuthBi
CeZn11
Beautiful!
CeAuBi2
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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
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What
“The road map/Palette/Pantry”: you can imagine making a huge number of compounds by combining different elements in different ratios....
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What
Fe-based high temperature superconductors
1mmCaFe2As2
J. T. Sypek et al., Nat. Commun. 8, 1083 (2017)
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What Rare-earth based intermetallics
4f
RNi2B2CP. C. Canfield, Peter L. Gammel, and David J. Bishop, Physics Today 51, 10, 40 (1998)
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What Rare-earth based intermetallics
4f
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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
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centrifuge
High-temperature flux methodHow
1200 0C
Spin temperature
Room temperature
1 mm
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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)
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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
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Outline
❑ La dilution of Kondo lattice CeCu2Ge2
❑ Physical properties of Weyl semimetal CeAlGe and it’s response to magnetic field
❑ Conclusions
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Outline
❑ La dilution of Kondo lattice CeCu2Ge2
“Old system” new physics
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P. Coleman, Handbook of Magnetism and Advanced Magnetic Materials (Wiley, New York, 2007), pp. 95–148, Vol. 1.
Single-ion Kondo -> Kondo lattice
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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
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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)
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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
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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)
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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)
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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
H.Hodovanets et al. Phys. Rev. Lett. 114, 236601 (2015)
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Possible origin:
• CEF (197 and 212 K)
• Spin glass
• TK of single-ion Kondo impurity
Ce1-xLaxCu2Ge2 : Specific heat
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
H.Hodovanets et al. Phys. Rev. Lett. 114, 236601 (2015)
M. Loewenhaupt et al. J. Appl. Phys. 111, 07E124 (2012)
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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
Ce1-xLaxCu2Ge2 : Specific heat
H.Hodovanets et al. Phys. Rev. Lett. 114, 236601 (2015)
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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
Ce1-xLaxCu2Ge2 : Specific heat
H.Hodovanets et al. Phys. Rev. Lett. 114, 236601 (2015)
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
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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
H.Hodovanets et al. Phys. Rev. Lett. 114, 236601 (2015)
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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
H.Hodovanets et al. Phys. Rev. Lett. 114, 236601 (2015)
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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 et al. Phys. Rev. Lett. 114, 236601 (2015)
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H. Hodovanets, Phys. Rev. Lett. 114, 236601 (2015)
Characteristic energy scales of Ce1-xLaxCu2Ge2
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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
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Outline
❑ La dilution of Kondo lattice CeCu2Ge2
❑ Type II Weyl semimetal CeAlGe
“New system” new physics
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• 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
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• 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
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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
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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.
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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
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Spin-flop transition H||a, (~0.5 of 2.14 B for Ce+3, M(H) data do not follow Arrot plot).
Magnetization: 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
H. Hodovanets et al. Phys. Rev. B 98, 245132 (2018)
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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
Magnetization: CeAlGe
H. Hodovanets et al. Phys. Rev. B 98, 245132 (2018)
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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
H. Hodovanets et al. Phys. Rev. B 98, 245132 (2018)
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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
H. Hodovanets et al. Phys. Rev. B 98, 245132 (2018)
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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
H. Hodovanets et al. Phys. Rev. B 98, 245132 (2018)
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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)
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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)
H. Hodovanets et al. Phys. Rev. B 98, 245132 (2018)
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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
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Outline
❑ La dilution of Kondo lattice CeCu2Ge2
❑ Type II Weyl semimetal CeAlGe
❑ Conclusions
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Conclusions
• Why❑ New science, application
❑ “Old system” new science
❑ New compound, new science?
❑ Single crystalline form (anisotropic properties) etc.
❑ How about other rare-earths?
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Conclusions
• Why❑ New science, application
❑ “Old system” new science
❑ New compound, new science?
❑ Single crystalline form (anisotropic properties) etc.
❑ How about other rare-earths?
Thank you!!!