Page 70 - ILL Annual Report 2019

THEORY
Bruno Tomasello. Italian
The ILL (Oct. 2016–Sep. 2019)
‘I am interested in the physics of quantum many-body systems. As a junior theorist I specialise in rare-earth compounds and frustrated magnetism. I am also engaged in fostering co-operation amongst communities
and am committed to contributing to the unique know-how of large-scale scientific facilities.’
How monopoles determine dynamic correlations in spin ice
Spin ice materials are archetypical examples of frustrated magnets. This study highlights an intriguing and hitherto poorly understood correlation in the dynamics of spin ices, whereby a monopole locally alters the spin background and the
latter predetermines whether and how
fast the former can hop. We discover
a bimodal distribution of temperature- independent spin-tunnelling time scales dictated solely by the crystalline,
dipolar and exchange interactions.
The picture of spin ice that emerges is
one in which classical and quantum physics interact in a seductive way: the monopole is a classical quasi-particle,
but quantum tunnelling of individual spins is responsible for its stochastic diffusion.
AUTHORS
B. Tomasello (ILL)
C. Castelnovo (University of Cambridge, UK)
R. Moessner (Max Plank Institute for the Physics of Complex Systems, Germany) J. Quintanilla (University of Kent, UK)
ARTICLE FROM
Phys. Rev. Lett. (2019)—doi: 10.1103/PhysRevLett.123.067204
REFERENCES
[1] S.T. Bramwell and M.J.P. Gingras, Science 294 (2001) 1495
[2] C. Castelnovo, R. Moessner and S. L. Sondhi, Nature 451 (2008) 42
[3] L.D.C. Jaubert and P.C.W. Holdsworth, J. Phys. Condens. Matter 23
(2011) 164222
[4] K. Matsuhira, C. Paulsen, E. Lhotel, C. Sekine, Z. Hiroi and S. Takagi,
J. Phys. Soc. Jpn. 80 (2011) 123711
The magnetism of rare-earth crystals can vary substantially depending on the chemical elements and the geometry of
the lattice. A prominent characteristic of rare-earth ions is
their sizeable spin-orbit coupling; and in magnetic pyrochlore oxides, despite similarities in structure this leads to a wide variety of phenomena—spin glass, spin ice and spin liquid are just a few examples of so-called exotic phases. These arise because the natural tendency to develop long-range order is frustrated by the geometrical constraints of the crystal [1].
A system is said to be frustrated if competing interactions
lead to conflicting classical minima in energy. In spin ice,
the magnetic moments of the rare-earth ions, which sit at the vertices of a lattice of corner-sharing tetrahedra, are forced
by the crystal fields to point along the axis joining adjacent tetrahedral centres. At temperatures of a few kelvin, i.e. the order of spin-spin interactions, frustration and crystal field anisotropy favour correlated configurations with a degree of degeneracy that maps to the proton arrangement in water ice. Such spin configurations are summarised by the ‘ice rules’, which consist of two spins per tetrahedron pointing toward
its centre and another two pointing outward. These imply a ground state whose degeneracy scales with the size of the lattice. An illustrative example is presented in figure 1, which shows just 1 of the total 13 122 equivalent configurations
for the 2-in/2-out ground state of a unit cell of order 10 Å. Excitations above the ground state correspond to local violations of the ice rules: they consist of tetrahedra hosting
magnetic fields that are purely transverse to the h111i
axis of the RE3+ ion. The CF spectrum characterises
the timescales for the tunnelling rates ⌧ ⇠ h/∆E01,
with E01 being the single-ion GS splitting between the
quasi-bonding and quasi-antibonding combinations of the
crystal-field levels. (The behaviour of E01 as a function
of the transverse field is shown in Figs. (5-6) of Ref. [9].)
The strength and the direction of the field on the trans-
a) b)
Figure 1.
Comparison, for spin ice materials HTO and DTO,
ising the magnetic ion in a state | (0)i corresponding to the dipole polarised in one of the two |M = ±Ji states along the local easy axis. It is convenient to choose a system of coordinates x0, y0, z0 so that the quantisation
between the unit cell (left panel) and an eight-tetrahedra
cluster (right panel). On the left, the edges of the unit cell
ANNUAL REPORT 2019
(⇡ 10Å) are the black dashed lines, the RE-sites are repre- sented as green spheres, distances between nearest neighbours
Figure 1
verse plane produce different behaviour in the two ma-
a) Unit cell of a magnetic pyrochlore oxide. Green spheres represents rare-earth ions.
terials which are directly connected to the the different
b) Example of spin-ice anisotropies for the pyrochlore lattice contained powerlaws E /|B| foundforHTO(p=2)and
(2-in/2-out per tetrahedron).
01
p
in (a). Notice that (b) is an example of a ground-state configuration
DTO (p = 3). The time-evolution is studied by initial-
2
are shown by green bonds while the grey (thinner) lines con-
axis z coincides with the polarisation axis (this is also