  Pulsar Timing Arrays (PTAs) are exceptionally sensitive detectors in the
frequency band $\text{nHz} \lesssim f \lesssim \mu\text{Hz}$. Ultralight dark
matter (ULDM), with mass in the range $10^{-23}\,\text{eV} \lesssim m_\phi
\lesssim 10^{-20}\,\text{eV}$, is one class of DM models known to generate
signals in this frequency window. While purely gravitational signatures of ULDM
have been studied previously, in this work we consider two signals in PTAs
which arise in presence of direct couplings between ULDM and ordinary matter.
These couplings induce variations in fundamental constants, i.e., particle
masses and couplings. These variations can alter the moment of inertia of
pulsars, inducing pulsar spin fluctuations via conservation of angular
momentum, or induce apparent timing residuals due to reference clock shifts. By
using mock data mimicking current PTA datasets, we show that PTA experiments
outperform torsion balance and atomic clock constraints for ULDM coupled to
electrons, muons, or gluons. In the case of coupling to quarks or photons, we
find that PTAs and atomic clocks set similar constraints. Additionally, we
discuss how future PTAs can further improve these constraints, and detail the
unique properties of these signals relative to the previously studied effects
of ULDM on PTAs.
