Destruction of long-range magnetic order in an external magnetic field and the associated spin dynamics in Cu2GaBO5 and Cu2AlBO5 ludwigites

The quantum spin systems ${\mathrm{Cu}}_{2}{M}^{\ensuremath{'}}{\mathrm{BO}}_{5}$ $({M}^{\ensuremath{'}}\phantom{\rule{4pt}{0ex}}=\phantom{\rule{4pt}{0ex}}\mathrm{Al},\phantom{\rule{4pt}{0ex}}\mathrm{Ga})$ with the ludwigite crystal structure consist of a structurally ordered ${\mathrm{Cu}}^{2+}$ sublattice in the form of three-leg ladders, interpenetrated by a structurally disordered sublattice with a statistically random site occupation by magnetic ${\mathrm{Cu}}^{2+}$ and nonmagnetic ${\mathrm{Ga}}^{3+}$ or ${\mathrm{Al}}^{3+}$ ions. A microscopic analysis based on density-functional-theory calculations for ${\mathrm{Cu}}_{2}{\mathrm{GaBO}}_{5}$ reveals a frustrated quasi-two-dimensional spin model featuring five inequivalent antiferromagnetic exchanges. A broad low-temperature ${}^{11}\mathrm{B}$ nuclear magnetic resonance points to a considerable spin disorder in the system. In zero magnetic field, antiferromagnetic order sets in below ${T}_{\text{N}}\ensuremath{\approx}4.1$ K and $\ensuremath{\sim}2.4$ K for the Ga and Al compounds, respectively. From neutron diffraction, we find that the magnetic propagation vector in ${\mathrm{Cu}}_{2}{\mathrm{GaBO}}_{5}$ is commensurate and lies on the Brillouin-zone boundary in the $(H0L)$ plane, ${\mathbf{q}}_{\text{m}}=(0.45,\phantom{\rule{0.16em}{0ex}}0,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}0.7)$, corresponding to a complex noncollinear long-range ordered structure with a large magnetic unit cell. Muon spin relaxation is monotonic, consisting of a fast static component typical for complex noncollinear spin systems and a slow dynamic component originating from the relaxation on low-energy spin fluctuations. Gapless spin dynamics in the form of a diffuse quasielastic peak is also evidenced by inelastic neutron scattering. Most remarkably, application of a magnetic field above 1 T destroys the static long-range order, which is manifested in the gradual broadening of the magnetic Bragg peaks. We argue that such a crossover from a magnetically long-range ordered state to a spin-glass regime may result from orphan spins on the structurally disordered magnetic sublattice, which are polarized in magnetic field and thus act as a tuning knob for field-controlled magnetic disorder.