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5f magnetism and its specific features
Ladislav Havela
Charles University, PragueCzech Republic
k-Workshop on Magnetism in Complex Systems
Vienna 2009
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Outline
1. Actinides - 5f (de)localization – between 3d and 4f+ strong s-o interaction
2. Development of the localization throughout the series
3. Where magnetism appears (U) .. Specific features of the 5f magnetism – exchange, anisotropy
4. …and where it disappears (Pu)…5f occupancy
Character of the 5f states seen by different methods
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Smith-Kmetko periodic table of transition elements
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Light actinides
- Pauli paramagnets (exchange enhanced)
Heavy actinides
- ionic magnetism; “Hund’s rules”
- but strong s-o coupling leads to j-j coupling
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• Th Pa U Np Pu Am…..
(mJ/mol K2) 4 6.6 10 14 22 2•
0 (10-8 m3/mol) 0.12 0.34 0.48 0.68 0.64 0.85• •
Cm Bk Cf Es TN (K) 64 34 51 (TC) eff (B) 7.55 9.7 9.7 11.3 (?)
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Hill limit separating the magnetic and superconducting regimes
H.H. Hill, Plutonium and Other Actinides, Santa Fe 1970
THE EARLY “ACTINIDES”: THE PERIODIC SYSTEM’S f ELECTRON TRANSITION METAL SERIES
Minimum inter-atomic spacing for appearance of magnetism
Ce……...3.4 Å
U……….3.4-3.6 Å
Np……..3.25 Å
Pu……..3.4 Å
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U compounds –large variety of magnetic properties (Np parallel, Pu not..)
Weak paramagnets – low , approaching magnetic ordering (spin fluctuations) – enhancement --> 5f band intersected by the Fermi level
5f-5f overlap…..U-U spacing…..Hill criterion
Superconductiong Magnetic
-U
U6Mn, U6Fe, U6Co, U6Ni…Tc < 3.7 K
U3Ir
U3Si2
UPt, UIr – ferro
UFe2, UNi2 (Laves ph.) – Ferro
UGa2 - Ferro
UGa2, UIn3, UPt3 AF
UPd3
UCu5, U2Zn17, UBe13
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Exceptions – large dU-U …non-magnetic UAl3, UNi5
Other mechanism must be in the game – 5f hybridization with electronic states of ligands
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Other mechanisms of delocalization suppress magnetism (in U, Np):
hybridization of 5f states with ligand states.
0
40
80
1200
40
80
120
Energy (Ry)
-0.8 -0.6 -0.4 -0.2 0.0 0.20
20
40
60
0
200
400
600
800
(d)
(c)
(b)
"Free Electrons"
Fe
UFeGe
DO
S, P
DO
S (
stat
es R
y-1 /
un
it c
ell (
a, c
), a
tom
(b
,d))
f - 5/2
(a)
Total
EF
d - 5/2d - 3/2
f - 7/2
U
In compounds with transition metals, mutual position (given by different electronegativity) is decisive
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Features of 5f-band magnetism: 1. Large orbital moments in itinerant systems
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Features of 5f-band magnetism: 2. Anisotropic hybridization-induced exchange interaction:
-stronger than conventional RKKY in strong f-bonding directions (if those can be specified), ferromagnetic
-UGa2 – Tc = 126 K, GdGa2, TN = 12 K.
- perpendicular to it weaker, ferro- or antiferromagnetic
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Relation of actinide magnetism with the 5f band width – density of states at EF (concept of the d-magnetism, i.e. itinerant one)
1. Curie-Weiss law 1/(T – p)
2. Spin waves E Dq2, D T5/2….Bloch law
3. Near TC – critical behaviour 1/(T-TC)4/3 …Heisenberg system
4. Resistivity – spin disorder scattering…..disordered moments above TC
Where the itinerant nature is manifest?
Ordered moments are in no relation to Hund’s rules
eff and s apparently uncorrelated. Low magnetic entropy S < Rln2..
Fast decrease of Tc by pressure
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Features of 5f-band magnetism: 2. Giant anisotropy
(hybridization-induced two-ion anisotropy)
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Ising ferromagnets from easy-axis spin fluctuators
Local moments from band states - no localized 5f states
5f band at EF (specific heat, PES) - except UPd3
0H (T)
0 10 20 30 40
M (
B/f
.u.)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0H (T)
0 20 40 60
M (
B/f
.u.)
0.0
0.1
0.2
0.3
0.4
0.5
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Pressure effects
2 band model needed
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Doniach "Kondo necklace" model
J0.0 0.1 0.2 0.3 0.4 0.5 0.6
EK
ondo
, ER
KK
Y
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
))(
1exp(k
FB
F
K EJNET
2
Bk JT
RKKY
For low J: RKKY wins
For large J: Kondo wins
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Electrical resistivity• Matthiessen’s rule
tot = 0 + ph-e + e-e+spd
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• Antiferromagnet
)(10
Tgmspdeeeph
tot
)(Tm Sublattice magnetization
g Truncation factor – captures a possible gapping of the Fermi surface by additionalBZ boundaries in AF state
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Hexagonal structure - ZrNiAl type
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T (K)
0 50 100 150 200 2500
50
100
150
200
250
300
350
(
c
m)
14 T
2 T
0 T UNiGa
i c-axis
i // c-axis
Upturn due to the Fermi sufrace gapping
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0.0
0.5
1.0
1.5
0.0
0.5
1.0
0
500
1000
0H (T)
Co
un
tsH // i // c-axis
T = 4.2 K
(a
.u.)
M ( B
/U-a
tom
)UNiGa
0.0 0.5 1.0 1.5
R0H
(
cm
)
-0.20.00.20.40.6 H // c-axis
Large superzone boundary gapping results of of strong coupling of direction of U moments and conduction
electron sub-system…
…also other features as large Kerr rotation due to large
orbital moments
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eff (B) s (B) eff (B) s (B) LS coupling intermediate coupling
f3 3.62 3.27 3.68 3.33f4 2.68 2.40 2.75 2.46f5 0.85 0.71 1.01 0.86 f6 0 0
Np - quite analogous to U, suggesting the same mechanisms at work
Pu???
Free Pu ion - 5f6
Pu ion in solid - 5f5 (Johansson and Rosengren 1975)
Pu solid in conventional band theory - 5fn, n 5.0 (magnetic)
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-Pu has low and very weakly temperature dependent susceptibility
Fradin and Brodsky 1970 27Al NMR
Piskunov et al., PRB 71 (2005) 174410 69Ga NMR
Lashley et al. PRB 72 (2005) 054416 specific heat, neutron diffraction, scattering
Heffner et al. +SR Physica B 374 (2006) 163
NO MAGNETISM!
Olsen 1992
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T (K)
0 50 100 150 200 250 300
(1
0-9 m
3 /mo
l)
0
20
40
60
24% Am
5% Am
pure Am
Pu-6% Ga
dopant (at.%)
0 5 10 15 20 25 30
a (p
m)
450
455
460
465
470
475
URuAl
Am
Ga
Neither expansion makes any significant difference in 0.
There cannot be any narrow band at EF - expansion would lead to a further narrowing
But there is a high coefficient of specific heat in -Pu
(53±10) mJ/mol K2
Stewart and Elliott 1981
(64±3) mJ/mol K2 Lashley et al. 2003
(41±1) mJ/mol K2 Havela et al. 2009
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5f 5 5f 5 - 5f 6
(suggested e.g. by volume)
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U Np Pu U Np Pu
PuPt2 - TC = 6 K, = 0.2 B
Also
PuPt - TN = 44 K
PuPt3 - TN = 40 K, eff = 1.3 B/f.u.
PuPd3 - TN = 24 K, eff = 1.0 B/f.u.
PuGa3 - TN = 24 K, eff = 0.78 B/f.u. TC = 20 K, = 0.2 B/f.u.
Suggestion
A transfer from 5f states necessary to reach magnetic state in Pu. Does it mean that pure Pu
has more 5f electrons?
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Localization in the sequence of actinides observed by photoelectron
spectroscopy
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5f
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binding energy (eV)
0246
Am
PuSb
PuSe
1 ML Pu on Mg
-Pu
PuN
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One trick to bridge the area between localized and itinerant behaviour is the Mixed level Model (MLM). It assumes integral 5f occupancy of localized states plus some itinerant 5f states.
O. Eriksson, J.D. Becker, A.V. Balatsky, J.M. Wills, J.Alloys Comp. 287 (1999) 1
Conclude the 5f 4 localized manifold plus 1 5f electron in itinerant states
But Pu is quite stable against any attempt to make it magnetic!
MLM and LDA, GGA…all lead to magnetic ground state
L(S)DA+U “around mean field” calculations
A.B. Shick, V. Drchal, L. Havela, Europhys. Lett. 69 (2005) 588
A.O. Shorikov, A.V. Lukoyanov, M.A. Korotin, and V.I. Anisimov, Phys.Rev.B 72 (2005) 024458
Conclude that n5f > 5.0 for -Pu.
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Am a reduced to 94.7%
Pu volume expands by 7 % for 30% Am
Am at 6.5 GPa a = 4.613 Å
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Pu3Am
LSDA+U+Hubbard I - open 5f shell embedded in the sea of conduction electrons spectral density
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Can LDA+U calculations pick up the onset of magnetism when going from PuSe or PuTe to PuSb?
PuSb - ferro state, 5f 5 with ordered moment 0.75 B/Pu
G.H. Lander, A. Delapalme, P.J. Brown, J.C. Spirlet, L. Rebizant, O. Vogt, Phys.Rev.Lett. 53 (1984) 2262
Pu moments fast collapse in the Pu(Sb,Te) system
K. Mattenberger et al., J.Less Common. Met 121 (1986) 285
Calculations: n5f = 5.2 - total magnetic moment 0.76 B/Pu !!!
In PuTe n5f = 5.68, = 0
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n5f
4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2
PuC
PuSb
-Pu
Pu2C3
PuS,PuSe,PuTe
AmPuCoGa5
PuCPuSb
FLL
AMF
The 3 peaks reflect the 5f6 admixture into the 5f5 states.
Beyond n5f non-magnetic on LDA+U level
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Conclusions
1. U magnetism with large orbital moments and huge anisotropy has too low
Tc to offer any room temperature applications. Hope in thin-films and other
artificial structures combined with 3d metals.
2. To have U compounds magnetic:
- 5f band must be narrow and populated as much as possible
Large dU-U, compound with late transition metals with the d-states far below
EF (d-band filled close to top) or with large p-metals
3. To have Pu compounds magnetic:
- 5f states must be little depopulated to move away from non-magnetic 5f6.
(too high admixture of 5f6 suppresses magnetism even if dU-U is large)