Abstract
We explore the physics of highly frustrated magnets in confined geometries, focusing on the Coulomb phase of pyrochlore spin ices. As a specific example, we investigate thin films of nearest-neighbor spin ice, using a combination of analytic large-N techniques and Monte Carlo simulations. In the simplest film geometry, with surfaces perpendicular to the [001] crystallographic direction, we observe pinch points in the spin-spin correlations characteristic of a two-dimensional Coulomb phase. We then consider the consequences of crystal symmetry breaking on the surfaces of the film through the inclusion of orphan bonds. We find that when these bonds are ferromagnetic, the Coulomb phase is destroyed by the presence of fluctuating surface magnetic charges, leading to a classical Z_2 spin liquid. Building on this understanding, we discuss other film geometries with surfaces perpendicular to the [110] or the [111] direction. We generically predict the appearance of surface magnetic charges and discuss their implications for the physics of such films, including the possibility of an unusual Z_3 classical spin liquid. Finally, we comment on open questions and promising avenues for future research.
Highlights
The emergence of gauge structures in strongly correlated systems has proven to be an essential thread in the fabric of modern condensed matter physics [1,2,3,4]
We explore the physics of highly frustrated magnets in confined geometries, focusing on the Coulomb phase of pyrochlore spin ices
We find that (i) the characteristic pinch points found in the spin-spin correlations [14,15] of bulk spin ice remain intact for momenta parallel to the surfaces, a signature of a two-dimensional Coulomb phase [a classical Uð1Þ spin liquid]; (ii) the direct-space spin-spin correlations oscillate as a function of depth in the sample, with an amplitude that increases with decreasing temperature; (iii) by including orphan bonds to capture some of the crystal symmetry breaking of the film surfaces, we find that the Coulomb phase and its associated pinch points disappear when the exchange on the orphan bonds is ferromagnetic, yielding a classical Z2 spin liquid [32]
Summary
The emergence of gauge structures in strongly correlated systems has proven to be an essential thread in the fabric of modern condensed matter physics [1,2,3,4]. The strongly frustrated interactions between the magnetic moments give rise to a local “2-in/2-out” constraint on every tetrahedron in the ground state, a close analogue of the arrangement of protons in common water ice [11,12] This constraint can be rewritten in a form similar to Gauss’ law in electromagnetism [14], giving rise to an emergent Coulomb phase [15,16] in these materials. Some of the crystal symmetry breaking of the film surfaces, we find that the Coulomb phase and its associated pinch points disappear when the exchange on the orphan bonds is ferromagnetic, yielding a classical Z2 spin liquid [32]
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