NMR investigation of field-induced magnetic order in barium manganese oxide

As early as 1956, Matsubara and Matsuda found an exact correspondence between a lattice gas model and a quantum antiferromagnet model[1]. They paved the way for the language of integer spin boson particles to be used interchangeably with quantum magnetic insulator systems in a general manner. For example, an analogy of density of bosons is found in magnetization, and analogy of chemical potential is found in external field. Just as there exist corresponding parameters between these two seemingly unrelated systems, quantum magnets can also exhibit consequences of Boson particle systems. In particular, spin-ordering transition in quantum magnets can be interpreted as Bose-Einstein condensate (BEC) transition in Boson particle framework. Direct observation of BEC in Boson particles has been realized in 4He's superfluid transition and in dilute atomic gas clouds cooled to very low temperatures[2]. In this thesis, we try to realize and analyze BEC transition through field-induced spin-ordering transition in the S = 1 antiferromagnetic dimer system, Ba3Mn2O8.;We perform NMR measurements with 135,137Ba nucleus as a local probe. Although S = 1 spin properties of Ba 3Mn2O8 come from electronic spins on Mn atoms, hyperfine coupling between Mn electronic spins and Ba nuclear spins allow us to infer Mn electrons' spin information. Since there are 2 inequivalent Ba sites, Ba(1) and Ba(2), in Ba3Mn2O8, we essentially have two probes that provide a detailed picture of structure and nature of magnetism in this material. There are many antiferromagnetic BEC candidates, but there is a significant advantage of studying Ba3Mn 2O8. Unlike the other popular antiferromagnetic BEC candidates such as TlCuCl3[3] or BaCuSi2O6[4], we find no evidence of lattice deformation in Ba3Mn2O8 . This allows us an unprecedented clean look at magnetic properties.;Aside from the aforementioned simple technical advantage, there are new physics that we can learn from Ba3Mn2O 8. The geometric frustration of the triangular Mn5+ magnetic lattice of Ba3Mn2O8 coupled with interdimer interaction is predicted to result in incommensurate spin structure when the symmetry axis of Ba3Mn2O8 is aligned parallel to the field. Because of single ion anisotropy of the system, Ba3Mn 2O8 has phase diagram that depends on its alignment with respect to the external field[5]. This means that the microscopic spin structure is different depending on whether the material's symmetry axis is aligned parallel or perpendicular to the field. Also, since we are dealing with S = 1, we have potential to investigate spin-gap closure due to singlet and triplet states as well as triplet and quintet states if we are able to access high enough fields (15T to 30T). Measurements at National High Magnetic Field Laboratory (NHMFL), gives us a superficial taste of what it is like to be in the phase created by triplet and quintet gap closure.;The temperature range allowed by the Oxford dilution refrigerator system at Brown Lab, UCLA is from 1K down to 30mK. The magnetic field range allowed by the superconducting magnet at Brown Lab, UCLA is from 0T up to 12T. This combination of temperature and field range allows us to investigate the first quantum critical point (Hc1) in detail with various NMR measurements. Normal state frequency shift as a function of temperature near Hc1 reveals behavior consistent with dilute hardcore bose gas. Analysis of the lineshapes of NMR spectra going into spin order BEC phase as a function of field, we directly observe incommensurate nature of spin order and deduce development of order parameter consistent with mean-field theory. Finally, we verify that the language of dilute 3D Bosons also applies to Ba3Mn2O8 through T1 measurements. From critical behavior inferred in T1 measurements, we complete phase boundary diagram at low temperatures and apply general concept of softening in Goldstone mode near Hc1 to describe our T 1 dependence as a function of temperature.