1. Quasiparticle anomalies near ferromagnetic instability A. A. Katanin A. P. Kampf V. Yu. Irkhin Stuttgart-Augsburg-Ekaterinburg 2004

2. Motivation Study of low-dimensional itinerant ferromagnetism : Layered systems Thin magnetic films Surface electronic states in 3D materials (ARPES) The properties of layered systems are expected to be completely different from cubic systems

3. The T- phase diagram: 2D vs 3D PM (Fermi liquid, well-defined QP) Ordered phase  T QPT 3D How do the physical properties evolve in the vicinity of a ferromagnetic instability ? PM (Fermi liquid, well-defined QP) ordered phase T *  0  C exp(T * /T)  T QPT RC 2D + small interlayer coupling T C  0 /ln(t/t')

4. Theoretical predictions for NMR MF theory: Q(  ) AFM: FM: PM state, 2D system: V. Yu. Irkhin and M. I. Katsnelson, Z. Phys. B 62, 201 (1986); Eur. Phys. J. B 19, 401 (2001) Q(  )

5. Theoretical predictions for ARPES A(k F,  )   similar to an AFM, where the suppression of the spectral weight is due to opening of a gap

6. Simple RPA-like calculation Im (k F,0) is divergent at T  0. This type of divergences was discussed earliar in the AFM context (A. M. Tremblay) and for gauge field theories (P. Lee et al.) 3D: Im  (k F,0) is only weakly (logarithmically) divergent at the magnetic phase transition temperature T = T c The source of potential divergencies [ ] Bare U: Renorm. U ef : 2D

7. Interpretation of the results  k   A( k,  )   k    Pre-formation of the two split Fermi surfaces already in the PM phase`at low T<<T* The spectral function depends on  -  k only

8. Qualitative physical picture What is the nature of the anomalies found in self-energy and spectral functions ?  Formation of dynamic “domains” of electrons with certain spin projection Formation of the two pre-split Fermi surfaces already in PM phase

9. Approximations  We have neglected: o momentum- and frequency dependence of the interaction; contributions of the channels of the electronic scattering other than the ph channel o self-energy and vertex corrections beyond the RPA-like diagrams

10. Functional renormalization-group approach . = =  V   G   S   S   G   V . VV

11. Self-energy in the fRG Results (Hubbard model, U = 4t, t'/t = 0.45, vH band filling n = 0.47, T = 0.1t)

12. Self-energy and vertex corrections Two types of corrections to the results of non-self- consistent approach:  Self-energy corrections in the internal Green functions  Vertex corrections  q,i  n )  k,i n )

13. Self-energy and vertex corrections Similar to QED: no equation for  ! Dyson equations Ward identity:  Similar approach was applied by Edwards and Hertz to the problem of strong FM

14. Approximations which are used Justification: is strongly enhanced at q=0 +1/N expansion where N is the number of spin components Self-consistent without vertex corrections (analogue of FLEX): The self-consistent solution with vertex and self-energy corrections:

15. Results of the solution

16. Other observable quantities The density of states The density of states is split already in PM phase Static magnetic susceptibility

17. Triplet pairing g(i , k )  kk  kk Enhancement of the triplet pairing amplitude at small ,  k  

18. Quantum critical regime What about QC regime ? T *  0  T QPT RC   There are no  solid theoretical results for the value of exponent    the quantum spin fluctuations are less important than classical, the “inverse qp lifetime” but there are no well-defined qps  the quantum spin fluctuations are more important than classical, the guess  “scattering rate” requires verification vs. vertex corrections; coincides with the result by W. Metzner et. al. near Pomeranchuk instability

19. Summary Ferromagnetic fluctuations invalidate quasiparticle picture at the paramagnetic FS at low T New quasiparticles emerge at the points of the Brillouin zone with  k    is the ground-state spin splitting  The density of states is pre-split at T « T* Triplet pairing amplitude is greatly enhanced at the ferromagnetic FSs already in the paramagnetic state

20. Future perspectives Non-perturbative semi-analytical tool of investigation of self-energy and vertex corrections in spin systems with strong forward scattering – Ward identity approach + 1/N expansion Possible extensions and applications: Inclusion of quantum fluctuations Long-range ferromagnetic order Extension to vH singularity problem More accurate description of QC regime Comparison with experimental ARPES data Description of criteria of ferromagnetism and spectral properties of 2D and 3D ferromagnetic systems between limits of weak (Moriya theory) and strong (saturated) (Edwards-Hertz approach) ferromagnetism

21. Possible experimental implication Layered manganite compound La 1+x Sr 2-x Mn 2 O 7 Phys. Rev. Lett. 81, 192 (1998) Phys. Rev. B 62, 1039 (2000). T C =126K

22. Spectral properties in mean-field theory  Direction of the magnetization along z-axis A(k F,  )    Direction of the magnetization perpendicular to the spin quantization axis: A(k,  )   