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YFe2Al10
…unravelling the origin of quantum criticality
André Strydom
Physics Department, University of Johannesburg
Acknowledgements
Frank Steglich (MPI‐CPfS, Dresden)
Michael Baenitz and co‐workers (MPI‐CPfS, Dresden)
Meigan Aronson (BNL & Stony Brook Univ., USA)
Devashibhai Adroja and Adrian Hillier (ISIS, UK)
Pararajasingham Peratheepan (Eastern Univ., Sri Lanka)
Overview of properties of the 1:2:10 series
Data on YFe2Al10 : a candidate for criticality of T=0 ferromagnetism?
Ferromagnetic quantum criticality: an enigmatic rarity
Examples of itinerant ferromagnets tuned into quantum criticality …
by doping (UNi1xCoxSi2, Ca1xSrxRuO3, CeRu1xFexPO,… )
or pressure (ZrZn2, MnSi, UGe2)– role of superconductivity?– is the end‐point continuous or not?
quantum critical fluctuations above TC = 3K in UCoGe…
…but magnetic field always seems malevolent to ferromagnetic quantum criticality!
Ferromagnetic quantum criticality: an enigmatic rarity
Case of NbFe2:
…proximity to ferrimagnetism
…proposed mechanism of vanishing carrier velocity
…competing q=0 and q ≠ 0 instabili es producing non‐Fermi liquid critical exponents
…and the key role of chemical doping
Haynes et al., PRB 85 (2012) 115137 Neal et al., PRB 84 (2011) 085133Tompsett et al., PRB 82 (2010) 155137Alam and Johnson, PRL 107 (2011) 206401
Ferromagnetic quantum criticality: a rarity
Tuning of a ferromagnet turns out to be more complex…
FM‐QCP reached through a tricritical point…
Belitz, Kirkpatrick, Rollbühler
PRL 94 (2005) 247205
YFe2Al10 : a candidate for accidental criticality of T=0 ferromagnetism?
RT2Al10: (R=Y, La, Ce,…Yb, Lu; T=Fe, Ru, Os) [1]
CeRu2Al10: a collection of very unusual properties [2]
Orthorhombic Cmcm,Al unique sites for Ce, Ru
Ce – Ce: 5.2 ÅCe
Ru
1. Thiede, Ebel, Jeitschko, J Mater Chem 8 (1998) 2. Strydom, Physica B 404 (2009) 2981
Two different anisotropic Kondo insulators…
CeRu2Al10
TN = 27 K… ; ord = 0.34 B ; k=(1,0,0) [3]8 meV spin gap [4] with strong c–f hybridization; depletion of
magnetic moment and low electrical conductivity along b–axiseasy magnetization along a–axisyet ordered moment and high conductivity along c–axisfavours description in terms in terms of ac–plane dimensionality
CeFe2Al10
Strong and highly anisotropic c–f hybridization, pseudogap from NMR 11 meV [5] or from neutrons 12‐15meV [6]
3. Khalyavin et al, Phys Rev B 82 (2010) 100405 4. Robert et al, Phys Rev B 82 (2010) 100404 5. Chen & Lue, Phys Rev B 81 (2010) 0751136. Adroja et al., unpublished
CeRu2Al10
A phase transition with a commonthread in resistivity, specific heat, and susceptibility…
Strydom, Physica B 404 (2009) 2981
CeRu2Al10
Characteristic Kondo Insulator (or Heavy‐Fermion semiconducting)susceptibility…
Nishioka et al., J. Phys. Soc. Japan 78 (2009) 123705
YFe2Al10
Exploratory susceptibility [1] and Mössbauer [7] reported absence of magnetic ordering above 2K
Our studies exposed T– and B– dependencies in various properties below 5 K…
Sample quality : elemental purity > 99.99 wt.‐%
homogeneity and composition using WDX:Y : Fe : Al = 1.00(1) : 2.00(1) : 9.55(3)a=8.97 Å, b=10.15 Å, c=9.02 Å
powder‐XRD profile refinement
Mössbauer to check for single species of Fe
7. Waerenborgh et al, J. Alloys Comp. 323‐324 (2001) 78
YFe2Al10
Sample quality (continued)
nearest‐neighbour FeFe : 4.48 Å
Fe in octahedral site symmetry
YFe2Al10
Sample quality (continued) : recent single‐crystal analysis [8]reported no significant deviation from ideal Fe and Al site compositions through refinement of site occupations
Y environment… Fe environment…
8. Kerkau et al., Z. Kristallogr. NCS 227 (2012) 289
YFe2Al10: physical properties: Thermal behaviour
Susceptibility
Curie‐Weiss at high T (> 120 K), eff ≈ 0.4 Bac shows no frequency dependence (1 – 1000 Hz)…
Strydom & Peratheepan, PSS‐RRL 4 (2010) 356
YFe2Al10: physical properties: Thermal behaviour
Susceptibility
Park et al., PRB 84 (2011) 094425 Strydom & Peratheepan, PSS‐RRL 4 (2010) 356
YFe2Al10: physical properties: Thermal behaviour
Susceptibility
Park et al., PRB 84 (2011) 094425
(T ) T 1.28(T ) T 1.28
YFe2Al10: physical properties: Thermal behaviour
Susceptibility
Key results of Park et al.: YFe2Al10 can be tuned into a Fermi liquidusing magnetic field,
(T ) T 1.28
Susceptibility scaling exponents are not reconcilable with either mean‐field nor with disorder or impurity models
Park et al., PRB 84 (2011) 094425
YFe2Al10: physical properties: Thermal behaviour
Magnetization
Continuous curvature towards T=0…
yet / | → is still finite at 0.5 K
Strydom & Peratheepan, PSS‐RRL 4 (2010) 356
YFe2Al10: physical properties: Thermal behaviour
Magnetization
Strydom et al., J. Phys. Soc. Japan 80 (2011) SA043
T=0.78 K
YFe2Al10: physical properties: Thermal behaviour
Magnetization
Strydom et al., J. Phys. Soc. Japan 80 (2011) SA043
26Al‐NMR : suppression of spin fluctuations commences from B 1T…
T=0.78 K
YFe2Al10 physical properties: Magnetism
Inelastic neutron scattering
T = 4 K T = 100K
Ei = 25 meV
Ei = 6 meV
Adroja & Strydom (25 – 30 Oct 2012, ISIS, UK)
0 1 2 3 4 5 6 70
2
4
6
8
10
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22
|Q| (Å-1)
Ene
rgy
(meV
)
mar17975.spe, symd(1,2,3), s=4, Ei=25 meV0<|Q|<7, 0<Energy<22
0
0.2
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|Q| (Å-1)
Ene
rgy
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mar17978.spe, symd(1,2,3), s=4, Ei=25 meV0<|Q|<7, 0<Energy<22
0
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0 0.5 1 1.5 2 2.5 3 3.50
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3.5
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4.5
5
|Q| (Å-1)
Ene
rgy
(meV
)
mar17976.spe, symd(1,2,3), s=4, Ei=6 meV0<|Q|<3.5, 0<Energy<5
0
0.1
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0 0.5 1 1.5 2 2.5 3 3.50
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|Q| (Å-1)E
nerg
y (m
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mar17977.spe, symd(1,2,3), s=4, Ei=6 meV0<|Q|<3.5, 0<Energy<5
0
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YFe2Al10 physical properties: Magnetism
Inelastic neutron scattering
T = 4 K T = 100K
Ei = 25 meV
Ei = 6 meV
Adroja & Strydom (25 – 30 Oct 2012, ISIS, UK)
0 1 2 3 4 5 6 70
2
4
6
8
10
12
14
16
18
20
22
|Q| (Å-1)
Ene
rgy
(meV
)
mar17975.spe, symd(1,2,3), s=4, Ei=25 meV0<|Q|<7, 0<Energy<22
0
0.2
0.4
0.6
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1.6
1.8
2
0 1 2 3 4 5 6 70
2
4
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20
22
|Q| (Å-1)
Ene
rgy
(meV
)
mar17978.spe, symd(1,2,3), s=4, Ei=25 meV0<|Q|<7, 0<Energy<22
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
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0 0.5 1 1.5 2 2.5 3 3.50
0.5
1
1.5
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2.5
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3.5
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4.5
5
|Q| (Å-1)
Ene
rgy
(meV
)
mar17976.spe, symd(1,2,3), s=4, Ei=6 meV0<|Q|<3.5, 0<Energy<5
0
0.1
0.2
0.3
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0 0.5 1 1.5 2 2.5 3 3.50
0.5
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1.5
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2.5
3
3.5
4
4.5
5
|Q| (Å-1)E
nerg
y (m
eV)
mar17977.spe, symd(1,2,3), s=4, Ei=6 meV0<|Q|<3.5, 0<Energy<5
0
0.1
0.2
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Further experiments: lower T, E, Q…
YFe2Al10 physical properties: Magnetism
26Al NMR:
Baenitz et al., 2012
0.1 10
YFe2Al10 physical properties: Magnetism
Muon spin resonance
Adroja, Hillier, Strydom, (27 – 28 Oct 2012, ISIS, UK)
T = 0.05 K
BL = 2500 G2000G1500G1000 G500 G50 G0 G
YFe2Al10 physical properties: Magnetism
Muon spin resonance
absence of cooperative magnetic effects confirmed down to 0.05 K
Complete absence of small‐field induced effects
Are spin fluctuations at 50 mK still too short‐lived for the ISIS SR time window…?
Adroja, Hillier, Strydom, (27 – 28 Oct 2012, ISIS, UK)
YFe2Al10: physical properties: ThermalSpecific heat : low T
Below 2K, Cp(T )/T = 0.0382(2) ∙ T 0.31(1)
YFe2Al10: physical properties: ThermalSpecific heat : the role of Fe stoichiometry
YFe2Al10: physical properties: ThermalSpecific heat : the role of Fe stoichiometry
Far from stoichiometric Fe… Fermi liquid
YFe2Al10: physical properties: ThermalSpecific heat : the role of Fe stoichiometry
Far from stoichiometric Fe… Fermi liquid
At stoichiometric Fe… non‐Fermi liquid
YFe2Al10: physical properties: ThermalSpecific heat : the role of Fe stoichiometry
CP(T )/T = + bT 2 + [dT 2 . ln(T/Tsf)] , Tsf = 15(2) K
Far from stoichiometric Fe… Fermi liquid
At stoichiometric Fe… non‐Fermi liquid
Near stoichiometric Fe… spin fluctuating
YFe2Al10: physical properties: ThermalSpecific heat : the role of Fe stoichiometry
non‐Fermi liquid behaviour does not scale with Fe concentration…
Far from stoichiometric Fe… Fermi liquid
At stoichiometric Fe… non‐Fermi liquid
Near stoichiometric Fe… spin fluctuating
YFe2Al10: physical properties: ThermalElectrical resistivity
0 ≈ 100 .cm, RRR ≈ 3 (polycrystal) 0 ≈ 75 .cm, RRR ≈ 2 (single crystal) [Aronson et al.]
TK ≈ 20 K
Conclusions
YFe2Al10 is a good metal, paramagnetic at room temperature
No magnetic ordering found down to 0.05K
Correlated phenomena develop below 2K in electronic specific heat, or below 20K in electrical resistivity
Notions of itinerant FM quantum criticality:Specific heat : Cp(T )/T T 0.33 (2D clean FM1)Susceptibility : (T ) T 4/3 (3D clean FM2)
1. Moriya & Takimoto, JPSJ 64 (1995) 960, Lonzarich, The Electron (1997) Cambridge2. Hertz PRB 14 (1976) 1165, Millis PRB 48 (1991) 7183
Questions
How to reconcile the dimensionality issue?
Is there magnetic ordering below T = 50 mK?
…or is the observed nFL scaling merely a spectator segment en route to a very lowT Fermi liquid?
Current work
(T) and (T) under pressure
(T) at low temperatures
THANK YOU !!