itinerant ferromagnetism: mechanisms and models
DESCRIPTION
Itinerant Ferromagnetism: mechanisms and models. J. E. Gubernatis, 1 C. D. Batista, 1 and J. Bonča 2 1 Los Alamos National Laboratory 2 University of Ljubljana. Magnetism. Outline. Basic models Traditional mechanism Interference (Nagaoka) mechanisms - PowerPoint PPT PresentationTRANSCRIPT
Itinerant Ferromagnetism:
mechanisms and models
J. E. Gubernatis,1 C. D. Batista,1
and J. Bonča2
1Los Alamos National Laboratory2University of Ljubljana
Magnetism
Outline
Basic models Traditional mechanism Interference (Nagaoka) mechanisms Mixed valent mechanism: strong ferromagnetism Relevance to experiment Summary
Approach
Analytic theory Generate effective Hamiltonians
Usually, 2nd order degenerate perturbation theory Identify physics by
Inspection Exact solutions Numerical simulations
Guide and interprets simulations of the original Hamiltonian
Numerical Simulation Compute ground-state properties
Constrained-Path Monte Carlo method Extend analytic theory
Standard Models f electrons
Kondo Lattice Model
Periodic Anderson Model
† †
, ,
†' ' '
', ,
( )
0 2
1; : Pauli matrices; J >0
2
iKLM i j j i ii j i
c
i is s s is s ss s
H t c c c c J S
n
c c
† †,
,
† †
2
0 2, 0 2, 0 4
f fPAM d i j j i i i
i j i
fi i i i f i
i i
d f d f
UH t d d d d n n
V d f f d n
n n n n n
Periodic Anderson Model
† †,
,
† †
2f f
d r r r r r rr r r
fr r r r f r
r r
UH t d d d d n n
V d f f d n
V
d
f
Standard Models
Anderson
Kondo
HubbardInfinite U
J/t >>10< nc <2
U/t >>1|EF-f|<<V0 <nd <2<nf >=1
J/t<<10< nc <1
U/t >>1|EF-f| >> V0< nd <1nf=1
Heisenberg RKKY
HubbardSegmented Band
U/t >> 1|EF-f| ~ 01< n <2
Mixed valent
weak
strong
Standard Models
Small J/t KLM and large U/t PAM connected by a canonical transformation, when |EF-f| >>V, nf=1 Emergent symmetry: [HPAM,ni
f]=0.
Result: JV2/ |EF-f|
Mixed valence regime: |EF-f| 0.
Traditional Mechanism
Competing energy scales TRKKY J² N(EF)
TKondo EF exp(-1/JN(EF)) Approximate methods
support this. Kondo compensation explains
moment reduction heavy masses.
T=0 critical point at J EF. Mixed valent materials are
paramagnetic.
O(1)
Traditional Mechanism
“The fact that Kondo-like quenching of local moments appears to occur for fractional valence systems is consistent with the above ideas on the empirical ground that only when the f-level is degenerate with the d-band is the effective Schrieffer-Wolff exchange interaction likely to be strong enough to satisfy the above criterion for a non-magnetic ground state of JN(0)=O(1).”
Doniach, Physica 91B, 231 (1977).
Ce(M1-xXx)3 B2 CeRh3(N1-yYy)2
Cornelius and Schilling, PRB 49, 3955 (1994)
Quantum Monte CarloBonca et al
Single Impurity Compensation
……
Compensation cloud
Exhaustion in strong mixed valent limit
Nagaoka-like mechanism for Ferromagnetism
Nagaoka Mechanism
Relevant for holes away from half-filing in a strongly correlated band (U/t >> 1).
Holes can lower their kinetic energy by moving through an aligned background. Hole can cycle back to original configuration.
Ground state wavefunction results from the constructive interference of many hole-configurations.
Nagaoka-like Mechanism in Weak Mixed Valent Regime
Adding tf << td embeds a Hubbard model in the PAM. When U/tf>>1, the
physics of the Nagaoka mechanism applies.
In polarized regime, conduction band is a charge reservoir for localized band Increasing pressure,
converts f’s to d’s, Decreasing pressure,
converts d’s to f’s.
U= Hubbard ModelBecca and Sorella, PRL 86, 3396 (2001)
Holes
Periodic Anderson Model
Mixed valent regime U/t>>1, |EF-f|~0
Observations at U=0 Two subspaces in each
band. Predominantly d or f
character. Size of cross-over region
V²/W. Very small.
Localized moment regime
mixedvalentregime
Mixed Valent Mechanism Take U = 0,
EF f and in lower band. Electrons pair.
Set U 0. Electrons in mixed valent
state spread to unoccupied f states and align.
Anti-symmetric spatial part of wavefunction prevents double occupancy.
Kinetic energy cost is proportional to .
Mixed Valent Mechanism A nonmagnetic state has an
energy cost to occupy upper band states needed to localize and avoid the cost of U.
Ferromagnetic state is stable if . TCurie
By the uncertainty principle, a state built from these lower band f states has a restricted extension. Not all k’s are used.
Numerical Consistency: 2D
Some Other Numerical Results
Local Moment Compensation In the single impurity model, a singlet ground state
implies
In the lattice model, it implies
In the lattice, the second term is more significant than the first. Mainly the f electrons, not the d’s, compensate the f
electrons.
2z z zf d f
i
S j S i S j
2z z z z zf d f f f
i i j
S j S i S j S i S j
Experimental Relevance
Ternary Ce Borides (4f). CeRh3B2: highest TCurie (115oK) of any Ce compound with
nonmagnetic elements. Small magnetic moment. Unusual magnetization and TCurie as a function of
(chemical) pressure. Uranium chalcogenides (5f)
UxXy , X= S, Se, or Te. Some properties similar to Ce(Rh1-x Rux)3B2
Challenges
Expansion case Doping removes
magnetic moments Increases overlap Tc decrease while M
increases
Compression case M does not increases
monotonically Specific heat peaks
where M peaks
(LaxCe1-x)Rh3B2
Increase of M. If CeRh3B2 is in a 4f-4d mixed valent state and EF
f, TCurie . With La doping,
f electron subspace increases so M increases. Localized f moment regime reached via occupation of
f states in upper band.
Ce(Rh1-xRux)3B2
Reduction of M. If CeRh3B2 is in a 4f-4d mixed valent state and EF
f, TCurie . With Ru doping, EF < f , increases, and
eventually ~ . Peak in Cp
Thermal excitations will promote previously paired electrons into highly degenerate aligned states.
Summary We established by analytic and numerical studies
several mechanisms for itinerant ferromagnetism. A novel mechanism operates in the PAM in the mixed
valence regime. It depends of a segmentation of non-degenerate bands and is
not the RKKY interaction. The segmentation of the bands is also relevant to the
non-magnetic behavior. Non-magnetic state is not a coherent state of Kondo
compensated singlets.
Summary
In polarized regime, we learned Increasing pressure, converts f’s to d’s, Decreasing pressure, converts d’s to f’s.
The implied figure of merit is |EF - f|. If large, local moments and RKKY. If small, less localized moments and mixed valent
behavior.
Summary In the unpolarized regime, the d-electrons are
mainly compensating themselves; f-electrons, themselves.
In the polarized regime, more than one mechanism produces ferromagnetism. The weakest is the RKKY, when the moments are spatially
localized. The strongest is the segmented band, when the moments
are partially localized.