Magnetic ground state of NdB4 : Interplay between anisotropic exchange interactions and hidden order on a Shastry-Sutherland lattice

The neodymium tetraboride <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>NdB</a:mi><a:mn>4</a:mn></a:msub></a:math>, crystalizing into a tetragonal crystal structure, has the magnetic ions located on a Shastry-Sutherland lattice. The compound undergoes several magnetic phase transitions and exhibits a complex multi-<b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>k</b:mi></b:mrow></b:math> ground state that has so far been elusive. Here we report the solution and quantitative refinement of the magnetic ground state of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>NdB</c:mi><c:mn>4</c:mn></c:msub></c:math> based on neutron diffraction data. The magnetic structure consists of two separate components; one of them is confined within the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>a</d:mi><d:mi>b</d:mi></d:mrow></d:math> plane and makes an orthogonal all-in-all-out spin configuration maintaining translation symmetry of the crystal. Another is pointing along the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>c</e:mi></e:math> axis, and this component forms an anharmonic spin density wave consisting of three-up-two-down sequences with fivefold periodicity. The in-plane and out of plane spin structures represent distinct magnetic instabilities which normally would not coexist. Their simultaneous presence in the same phase is an interesting phenomenon associated with anisotropic exchange interactions and coupling to a symmetry breaking nonmagnetic order parameter undetectable by the available diffraction data.