Fractalization drives crystalline states in a frustrated spin system

Area of Science:

• Condensed Matter Physics
• Quantum Magnetism

Background:

• The Hofstadter butterfly spectrum, a hallmark of fractal energy levels in magnetically confined fermions, requires extremely high magnetic fields unattainable in laboratories.
• Previous experimental realizations of the Hofstadter problem have been limited by the need for unachievably high magnetic flux densities or large lattice periods.

Purpose of the Study:

• To experimentally demonstrate a system exhibiting the Hofstadter butterfly spectrum using bosons confined by magnetic and lattice potentials.
• To investigate the emergence of stripe-like spin density-modulated phases from a fractal spectrum.

Main Methods:

• Utilized the geometrically frustrated spin system SrCu2(BO3)2.
• Applied magnetic fields up to 85 Tesla and temperatures down to 29 milliKelvin.
• Employed theoretical treatment including short-range repulsion in the Hofstadter model.

Main Results:

• Observed a sequence of magnetization plateaus at m(z)/m(sat) = 1/q (q ≥ 2) and p/q = 2/9 in SrCu2(BO3)2.
• These plateaus mimic the fractal behavior predicted by the Hofstadter butterfly for fermionic systems.
• Identified stripe-like spin density-modulated phases as emergent from the fractal spectrum.

Conclusions:

• SrCu2(BO3)2 provides an experimental platform for realizing the Hofstadter problem with bosons, mimicking fermionic behavior.
• The study demonstrates the emergence of complex magnetic phases from fractal energy spectra.
• This work bridges theoretical predictions of the Hofstadter butterfly with experimental observations in real materials.