The copper metaborate $\mathrm{Cu}{\mathrm{B}}_2{\mathrm{O}}_4$ (CBO) has been studied within the parametric space of magnetic field ($B$) and temperature ($T$), showing a series of distinct phases, including commensurate and incommensurate magnetic orders, as well as magnetic soliton phases. However, no single study has simultaneously demonstrated all these phases. Moreover, the existence of additional phases below 2 K or above 2 T for $B\perp c$ has been scarcely explored. This work presents a comprehensive construction of the complex $B-T$ phase diagram for $T=0.1–25$ K and $B=0–9$ T ($B\perp c$), utilizing thermodynamic probes, magnetic measurements, and neutron scattering on a single batch of CBO crystals. Our findings elucidate additional magnetic phases and regimes. First-principles calculations help to gain a deeper understanding of this complex phase diagram. The emergence of various phases within such a narrow $B$ and $T$ regime is attributed to two primary mechanisms: the delicate competition between ferromagnetic and antiferromagnetic interactions, and the weak exchange and superexchange interactions within and between the Cu(A) and Cu(B) sublattices. This competition also leads to a magnetically frustrated ground state at absolute zero where the total magnetic entropy release from high to low temperatures is only 0.76 $R\ln 2$, lower than $R\ln 2$ expected for copper spin-½. Using CBO as a model system, the present work elucidates the intricate mechanisms underlying the formation of complex magnetic phases.

Close

PrevNext

View figure in article

• Magnetic phase transitions
• Magnetism
• Phase separation
• Neutron scattering