5f magnetism and its specific features

Ladislav Havela

Charles University, PragueCzech Republic

k-Workshop on Magnetism in Complex Systems

Vienna 2009

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

Smith-Kmetko periodic table of transition elements

Light actinides

- Pauli paramagnets (exchange enhanced)

Heavy actinides

- ionic magnetism; “Hund’s rules”

- but strong s-o coupling leads to j-j coupling

• 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 (?)

  

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

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

Exceptions – large dU-U …non-magnetic UAl3, UNi5

Other mechanism must be in the game – 5f hybridization with electronic states of ligands

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

Features of 5f-band magnetism: 1. Large orbital moments in itinerant systems

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

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

Features of 5f-band magnetism: 2. Giant anisotropy

(hybridization-induced two-ion anisotropy)

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

Pressure effects

2 band model needed

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

Electrical resistivity• Matthiessen’s rule

tot = 0 + ph-e + e-e+spd

• Antiferromagnet

)(10

Tgmspdeeeph

tot

)(Tm Sublattice magnetization

g Truncation factor – captures a possible gapping of the Fermi surface by additionalBZ boundaries in AF state

Hexagonal structure - ZrNiAl type

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

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

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)

-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

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

5f 5 5f 5 - 5f 6

(suggested e.g. by volume)

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?

Localization in the sequence of actinides observed by photoelectron

spectroscopy

5f

binding energy (eV)

0246

Am

PuSb

PuSe

1 ML Pu on Mg

-Pu

PuN

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.

Am a reduced to 94.7%

Pu volume expands by 7 % for 30% Am

Am at 6.5 GPa a = 4.613 Å

Pu3Am

LSDA+U+Hubbard I - open 5f shell embedded in the sea of conduction electrons spectral density

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

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

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)