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Zusammenfassung:
One-dimensional quantum systems are phenomenal because only collective excitations are
present and strong influences of quantum fluctuations occur. Fractionalisation of the mag-
netic excitations in one-dimensional anti-ferromagnetic spin chains is a paradigmatic ex-
ample in which low-energy excitations, known as spinons, carry fractional spin ∆S = 1/2.
Even though considerable progress has been made in the theoretical understanding of such
quantum magnets, experimental realisations of this low-dimensional physics are relatively
rare. In 2019, however, Wu et al. reported the realisation of a quantum S = 1/2 spin chain
system in the rare-earth perovskite YbAlO3, exhibiting both quantum critical Tomonaga-
Luttinger liquid behaviour and spinon confinement-deconfinement transitions in different
regions of the field-temperature phase diagram. At low-enough temperatures, Yb3+ Ising-
like moments experience anti-ferromagnetic exchange interaction along the c-axis, namely
the chain direction (J∥ = 2.3 K) and ferromagnetic coupling perpendicularly in the ab-plane
(J⊥ = 0.8 K). In zero field, a three-dimensional anti-ferromagnetic order is established below
0.88 K. For magnetic fields along the a-axis perpendicular to the spin chains, this order is
suppressed and replaced by an incommensurate anti-ferromagnetic ground state until a full
polarisation occurs above 1.5 T.
In former works, magnetisation and specific heat capacity were measured to demonstrate
various states of Tomonaga-Luttinger liquid, three-dimensional anti-ferromagnetic, incom-
mensurate anti-ferromagnetic and fully-polarised. Moreover, the theory predicts that the
incommensurate anti-ferromagnetic ground state comprises spin-density wave and transverse
anti-ferromagnetic sub-phases. Inelastic neutron scattering confirmed the fractionalisation
of the magnetic excitations in the Tomonaga-Luttinger liquid phase. Nonetheless, investig-
ating the transport properties and the scattering effects in the different phases and across
the transitions was missing. Hence, it was an open question whether magnetic excitations
in this compound carry heat and how they interact with phonons.
In this research, I experimentally study the low-temperature thermal conductivity of
YbAlO3, measured down to 30 mK in fields up to 6 T, with a focus on the contribution of the
magnetic excitations to thermal transport within different phases and their interactions with
lattice vibrations. A substantial enhancement of the thermal conductivity is observed in the
proposed Tomonaga-Luttinger-liquid region. In addition, the large variation of the thermal
conductivity throughout the phase diagram indicates strong magneto-elastic coupling. The
phase diagram is successfully reproduced with pronounced anomalies in both temperature
and field sweeps. Notably, my results agree with the previous reports, additionally providing
complementary information to thermodynamics probes and theoretical predictions. An
astonishing result is the high sensitivity of the thermal conductance to the phase transitions,
especially the Tomonaga-Luttinger liquid to three-dimensional anti-ferromagnetic, and the
commensurate to incommensurate ones. In addition, the diverse behaviour of the thermal
conductivity within different phases is notable. A clear V-shaped anomaly in the field
dependence at low temperatures is found at the crossover within the incommensurate phase,
which was suggested before based only on a tiny plateau appearing in the magnetisation
at 1/3 of the saturation value. I detected an additional plateau-type anomaly via the
delicate thermal-transport probe emerging in the field that the magnetisation is at 1/5 of
its saturation value. This feature is another outstanding result which was not observed
before.
