Segmented Band Mechanism for Itinerant Ferromagnetism

1
Segmented Band Mechanism for Itinerant
Ferromagnetism

• J. E. Gubernatis1 and C. D. Batista1
• J. Bonca2
• 1Los Alamos National Laboratory
• 2J. Stefan Institute and FMF, University of
  Ljubljana

PRB, 63, 184428 (2001) PRL, 88, 187203 (2002)
2
Outline

• New model of itinerant ferromagnetism.
• Realization in the periodic Anderson model.
• Numerical results.
• Relevance to experiment.
• Concluding remarks.

3
Features of the New Mechanism

• Explicit exchange forces are absent.
• Band features are important.
• Two bands are involved.
• Hybridzation is essential.
• Spin alignment occurs via the same physics as a
  Hunds coupling.
• Compensation of local moment is a property of a
  restricted set of band states and not a
  consequence of Kondo compensation.
• The mechanism disappears in infinite dimensions.

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Periodic Anderson Model

• The Hamiltonian
• Two bands (U0)

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Familiar Mechanism

• Local moment regime V ?? td ?? ?f ? EF,
  tf 0 (f orbital below the d band), fourth-order
  canonical transformation yields
• JRKKY V4 td2/U 5, very small

6
Some Observations U0, V?? W ?f

• Mixed valent regime
• Two subspaces in each band.
• Predominantly d or f character.
• Size of cross-over region ? V²/W.
• Very small.

7
New 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 ?.

8
New 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 ks are used.

9
New Mechanism

• Mechanism for partial saturation of effective
  moment,
• Moment is compensated within electrons in the d-
  band
• Absence of mechanism in infinite dimension,
• In infinite dimension the correlated band is
  reduced to an impurity level in an effective
  field.

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Typical Numerical Results
11
Finite size scaling
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Stability of FM vs. - finite size analysis
13
Stability of FM state vs. U
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Stability of FM state vs. V
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Numerical Consistency

• Observed ferromagnetic behavior in the mixed
  valent regime of the periodic Anderson model is
  consistent with this mechanism.
• In 1, 2 and 3 dimensions, ground-state is found
  by the Constrained-Path Monte Carlo method.
• In one dimension phase diagram agrees
  qualitatively with the one in calculated by DMRG.
• Key Quantity The electron density ?n(k)?
  projected onto the ? and ? states mirrors that of
  the mechanism.

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Numerical Consistency 1D
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Numerical Consistency 2D
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Experimental Relevance

• Ternary Ce Borides.
• CeRh3B2 highest TCurie (115oK) of any Ce
  compound with nonmagnetic elements.
• Small magnetic moment.
• Unusual magnetization and TCurie as a function of
  (chemical) pressure.
• Hexaborides ?
• Effective mass change, coexistence of localized
  and itinerant electrons,
• Uranium chalcogenides (UxXy , X S, Se, or Te).
• Some properties similar to Ce(Rh1-x Rux)3B2

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Phase Diagram of Ce(Rh1-xRux)3B2
St. Berger et al. PRB,64 134404 (2001).
20
Ce(Rh1-xRux)3B2

• Volume shrinks as a function of x.
• Increasing x lowers M and TCurie
• Peak in M mirrored by peak in Cp
• Raising T initially increase ordering and ordered
  state has more entropy.
• Similar effect seen in uranium chalcogenides.

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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 lt ?f , ? increases, and
  eventually ? ?.
• Different mechanism, eventually RKKY, dominates.
• Peak in Cp
• Thermal excitations will promote previously
  paired electrons into highly degenerate aligned
  states.

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LaxCe1-xRh3B2
S.A. Shaheen et al., Prb, 31 656 (1985)

• Volume expands as a function of x.
• Increasing increases M and lowers TCurie

23
Ce(M1-xXx)3 B2 CeRh3(N1-yYy)2
A.L. Cornelius, PRB 49, 3955 (1994)
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Concluding Remarks

• Proposed mechanism steps beyond past approaches.
• Coulomb interaction Fermi statistics band
  features.
• Band features set multiple energy scales and
  create a novel opportunity for itinerant
  ferromagnetism.
• Mechanism operates in a well known lattice model.
• Established by non-perturbative (not discussed)
  analytical and numerical studies.
• Mechanism appears qualitatively relevant for some
  f (and d) electron materials.
• Some important features
• Predicts Hi Tc, in a metallic state
• Unusual magnetization and TCurie as a funtion of
  (chemial) pressure
• Effective mass change at TCurie
• FM state consists of itinerant and localized
  electrons and also polarized and non-cpolarized
  electrons

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Concluding Remarks

• Stability of ferro-magnetic state
• Adding non-zero tf can stabilize (or destroy)
  the ferromagnetic state.
• Appearance of anti-ferromagnetic state
• Adding non-zero tf can generate an anti-
  ferromagnetic state.
• Antiferromagnetism otherwise occurs only when
  there is nesting.