Exotic ordering phenomena in metallic ferromagnets and spin-triplet nematics
by
Frank Kruger(Rutherford Appleton Lab.)
→
Europe/Stockholm
Nordita West (122:026)
Nordita West (122:026)
Description
Fluctuations around quantum critical points are known to be responsible for many unexpected phenomena, e.g. the discontinuous phase transitions seen in itinerant ferromagnets at low temperatures. Such fluctuation-induced first-order behaviour is a consequence of the interplay between magnetic order parameter and soft electronic particle-hole fluctuations.
Using a fermionic version of the quantum order-by-disorder mechanism, we demonstrate that the ferromagnetic quantum critical point is unstable towards the formation of incommensurate spiral order [1]. The key idea is that certain deformations of the Fermi surface associated with the onset of competing order enlarge the phase space available for low-energy particle-hole fluctuations and self-consistently lower the free energy. This reveals a new way to achieve complex, spatially modulated order, not requiring Fermi-surface nesting, breaking of inversion symmetry, or frustration. We apply this theory to PrPtAl where spiral order on the border of ferromagnetism is observed in neutron and x-ray scattering experiments. In this system, the coupling of the itinerant electrons to the local Pr(3+) moments leads to magnetic anisotropies which have characteristic experimental consequences [2].
As a second example, we show that fluctuations in metallic ferromagnets with spin-orbit induced anisotropy can drive a moment re-orientation at low temperatures, from a magnetic easy direction towards a hard axis [3]. This phenomenon is discussed in the context of recent experiments.
We will conclude with an even more exotic example of electrons that interact through a quadrupole density-density repulsion. At mean-field, this interaction leads to a d-wave Pomeranchuk instability in the spin-triplet channel. The resulting spin-triplet nematic simultaneously breaks spin SU(2) rotation and spatial rotation symmetries and is characterised by elliptical Fermi-surface deformations of opposite signs for spin-up and spin-down electrons. This entanglement of spatial (orbital) and spin degrees of freedom leads to an interesting response of the system to both strain and magnetic fields. Since the Goldstone modes carry spin, they are detectable in inelastic neutron scattering experiments. We show that the excitations are underdamped and have a linear dispersion relation. As in the ferromagnet, fluctuations render the transitions first-order at low temperatures. We show that the first-order transition is pre-empted by a spin-triplet nematic state with a helical modulation of the spin directions. This state can be viewed as a continuum version of certain types of d-wave bond-density wave order.
[1] U. Karahasanovic, F. Kruger, and A.G. Green, Phys. Rev. B 85, 165111 (2012);
C.J. Pedder, F. Kruger, and A.G Green, Phys. Rev. B 88, 165109 (2013)
[2] G. Abdul-Jabbar, D. Sokolov, D. Wermeille, C. Stock, F. Demmel, F. Kruger, A.G. Green,
and A. Huxley, Nature Physics 11, 321 (2015)
[3] F. Kruger, C.J. Pedder, and A.G Green, Phys. Rev. Lett. 113, 147001 (2014)