Kedar Damle; Fractional spin textures and their interactions in a classical spin liquid

Kedar started by introducing the physics of frustrated magnets.
He introduced antiferromagnetic interactions between magnetic ions
and mentioned that the determination of exchange coupling J is not
always easy, but sometime may be measured by going into an order
phase (for example, by applying a magnetic field) as in Yb2Ti2O7.
Antiferromagnetic Ising interactions between magnetic ions in
triangular lattice is, for example, frustrated. This leads to macroscopic
degeneracy of classical ground states, leading to paramagnetic
liquid-like correlations with no magnetic order down to very
low temperature.

Then he turned to the question of impurities in real materials
and emphasized that these can be used to probe intrinsic properties
of the bulk system. For example, the local probe like NMR can measure
spin polarization histogram of local susceptibility at various distances
from impurity. This polarization histogram knows about the response of
the system to the impurity.

Kedar mentioned an example of the Haldane chain.
At the end of the open chain, we generate S=1/2 spins and this is
the characterics of topological order in the Haldane phase.
This was demonstrated in Y-NMR studies of the effect of
non-magnetic Mg^{2+} impurities in S=1 (Ni^{2+) chain) in
Y2BaNiO5. The data can be favorably compared to QMC simulation.
So the correlations encoded in intricate charge/spon textures
can be seed by impurities and picked up by the NMR local probe.

Now his main subject: SCGO

He is interested in non-magnetic Ga impurities in pyrochlore
slab magnet SCGO. This is an insulating magnet of
Cr^{3+}, S=3/2 system
The structure consists of Kagome bilayers with up and down pointing
tetrahedra - separated by Cr-Cr isolated spin pairs.
The idealized SrCr9Ga3O19 is not realizable and there is always
some disorder or impurities, so one may get about 5% Ga impurities
in isolated spin pairs and in Kagome bilayer

In experiments, the macroscopic susceptibility suggests
the Curie-Weiss temperature of \theta_CW = 500-600 K and there is
no sign of magnetic order down to T_f = 3-5K. There is some kind of freezing
or spin glassy behavior at T < T_f and the nature of phase for T < T_g not clear.

NMR measurements suggest that there is a broad, apparently symmetric,
Ga NMR line with broadening \Delat H = x/T for not-too-small x.
This may suggest short range oscillating spin density near defects
orphan spins.

Now turn to theoretical considerations.

The classical energy at T=0 can be minimized by making the spin sum
in each simplex or cluster to be zero.
Keadar demonstrated that, in the case of single Ga on any simplex,
there is no problem with simplex satisfaction, namely zero or minimum
spin sum in each simplex. On the other hand, for two Ga in one triangle,
one generates, <S_z_tot> = S/2 ! (at T=0, h/J->0). That is, one generates
half-orphan spins.

There is a way to formulate this using the so-called artificial electro-dynamics
using the mapping of
E_{\alpha}_i = S_i ^{\alpha} e_i, where E is an artificial electric field.
Then the simplex satisfaction condition becomes div E = 0 at T=0.
In this language, one defective simplex would correspond to
\div E^{\alpha}_triangle = S_{alpha}.
This leads to the T=0 Gauss law and 1/r decay of the spin-spin
correlation at T=0 for induced spin textures.

According to Moessner-Berlinsky's old work, defective tetrahedra/triangles
give Curie tail and no other simplex would give the Curie tail.
But what about correlation (long range) between simplifies ?
Also what about  the entropic effect at non-zero temperatures ?

Kedar looked at the large-N vector model which can describe classical
magnet with N-componet vector with the fixed length. Then he considers
the free energy, where he introduces phenomenological stiffness
parameters to write the entropy associated with the spins in Kagome
and apical simplices. Then he looked at the effective lone spin model
at the defective triangle and compute the spin polarization as a function
of magnetic field and temperature; it predicts the form of S B(hS/2T).
He tested the predictions of the effective theory of this lone spin
by doing Monte Carlo simulation.
He found the impurity susceptibility to be
\chi_omp = (S/2)^2 / 3T. That is it indeed shows the behavior of
fractional S/2 !
He also found that single defect does not lead to the Curie term, but
pairs of vacancies should lead to the Curie term. He also showed
the absence of three-body and higher order contributions.

Discussion on theory vs experiment followed.
Kedar found that \Delta H = A(x)/T = x /T captured correctly.
What is not captured in theory was discrepancy between the concentration
of impurities used to fit the susceptibility.
One interesting question:
are randomly positioned orphan spins interacting with each other ?

There were also some questions from the audience.

Q: Is there a possibility of charge density wave due to impurities explaining
the experiments ?
A: how to imagine it shows 1/r spin texture and Curie response etc

Q: does power decay necessarily mean the existence of fractional spin ?
A: while the theory presented here for pyrochlore lattice is pretty general,
there might be other situations that were not explored here.

Q: Why is the impurity concentration "x" in theory larger than experiment ?
A: There may be clustering or pair correlations between impurities in experiment.