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We consider a gauge-singlet complex scalar field $\Phi$ with a global $U(1)$symmetry that is spontaneously broken at some high energy scale $f_a$. As aresult, the angular part of the $\Phi$-field becomes an axion-like particle(ALP). We show that if the $\Phi$-field has a non-zero coupling $\kappa$ to theStandard Model Higgs boson, there exists a certain region in the $\left(f_a,\kappa\right)$ parameter space where the global $U(1)$ symmetry-breakinginduces a strongly first order phase transition, thereby producing stochasticgravitational waves that are potentially observable in current and futuregravitational-wave detectors. In particular, we find that futuregravitational-wave experiments such as TianQin, BBO and Cosmic Explorer couldprobe a broad range of the energy scale $10^3 \, {\rm GeV} \lesssim f_a\lesssim 10^{8} \, {\rm GeV}$, independent of the ALP mass. Since all the ALPcouplings to the Standard Model particles are proportional to inverse powers ofthe energy scale $f_a$ (up to model-dependent ${\cal O}(1)$ coefficients), thegravitational-wave detection prospects are largely complementary to the currentlaboratory, astrophysical and cosmological probes of the ALP scenarios.

Gravitational Waves from First-Order Phase Transition in a Simple Axion-Like Particle Model