Novel ground states of frustrated spin systems under doping

In low-dimensional frustrated quantum spin systems quantum fluctuations often lead to unusual ground states that exhibit no magnetic ordering but a gapped, non-degenerate singlet ground state. Such state, also called a spin-liquid state, was recently recognized in a quasi-two-dimensional SrCu2(BO3)2 compound, whose outstanding magnetic properties have been attracting an enormous attention over the last seven years. The corresponding Shastry-Sutherland model therefore represents due to strong quantum fluctuations as well as due to exactly solvable ground state an exciting toy model in research of frustrated spin systems. While thermodynamic properties of the pure system are by now well known, there are open problems concerning the physical properties of a doped compound. One of the main targets of the proposed research project is to investigate theoretically the effects of doping on the spin-liquid ground state in a given highly-frustrated spin system. In this respect, I will introduce a variational approach, not limited to finite systems, to investigate static and dynamic properties of the spin polaron that forms around the nonmagnetic impurity introduced into the spin-liquid ground state of the Shastry-Sutherland model. The goal of these investigations is to explain the appearance of low-frequency peaks in recent inelastic neutron scattering experiments on SrCu2-xMgx(BO3)2 and to establish the nature of the spin polaron with the emphasis on its excited states and its effective mass. Within the proposed numerical framework, this will moreover allow me to examine the possibility of the occurrence of the superconducting state in the doped Shastry-Sutherland model at low temperatures. Such finding would certainly contribute to the understanding of, at present, one of the most fascinating open questions in the physics of condensed matter - what is the interplay between magnetism and superconductivity? Study of these systems is therefore interesting not only from the basic science point of view, leading to a possible discovery of novel magnetic phases and/or mechanisms towards superconductivity, but may also trigger a development in the field of novel superconducting materials based on the parent compound SrCu2(BO3)2.

I have developed a new numerical method for the calculation of eigenstates that builds its phase space by variationally adding new (basis) states. The method is not restricted to finite system sizes, and therefore to finite number of allowed wave vectors, however, it is limited by a finite number of basis states. For this reason, the method is particularly convinient for the calculation of thermodynamical quantities with variables that vary continously with the position in the real or reciprocal space. Especially, the method shows its strength when the true eigenstate is close to the initial (basis) state, which results in a rapid convergence. With a given method, I managed to investigate for the first time the ground state of the spin polaron and its few lowest excited states on the infinite Shastry-Sutherland lattice. I have confirmed the hypothesis that the spin polaron is anisotropic in space and extends only in to the vicinity of the nonmagnetic impurity. Given a polaron structure, I was able to correctly predict the position and the intensity of the in-gap excitation in the inelastic neutron scattering measurements on SrCu_(2-x)Mg_x(BO_3)_2.

During the development of the numerical method and its succesful application to the doped Shastry-Sutherland model, I have participated in various international conferences, published several original scientific publications, and established effective collaborations with the research groups in Europe and USA. In this way, I have contributed to the recognition of Slovenia as a modern European country with developed scientific-technological foundation.