Discovery of New Low Temperature Phase Transitions in Barium Hexaferrite

Abstract

The study of phase transitions in frustrated magnetic systems has been a frontline area of research in solid-state and material sciences. The most commonly investigated source of frustration is frozen-in substitutional disorder leading to a competition between ferromagnetic (FM) and antiferromagnetic (AFM) interactions. Such a competition and randomness in certain situations can prevent the emergence of long-range ordered (LRO) phases and instead give rise to a unique spin-glass state in which the spins are randomly frozen below a frequency (ω) and field (H) dependent peak, usually called as spin-glass freezing temperature (Tf), in the temperature dependence of magnetic susceptibility as a result of ergodic symmetry breaking. Frustration may also arise due to nearest neighbour AFM interactions alone due to the geometry of the lattice for spins arranged on the edge shared triangular (e.g. YbZnGaO4), corner shared triangular or kagome (e.g. (H3O)Fe3(SO4)2(OH)6 and SrGa12-xCrxO19), pyrochlore (e.g. Tb2Mo2O7), and spinels (e.g. MAl2O4 with M = Co, Fe, & Mn) lattices. Such geometrically frustrated systems have evinced enormous attention in recent years as many of them exhibit exotic spin liquid, spin ice and spin-glass transitions even in the absence of any apparent site-disorder. Recent theoretical calculations seem to suggest that in the absence of any site-disorder, and hence randomness, the ground state of the geometrically frustrated systems has macroscopic degeneracy with no phase transition down to the absolute zero temperature. Such systems, however, have the possibility of the degeneracy getting lifted by quantum or thermal fluctuations through an intriguing mechanism known as “order by disorder” even in the absence of site disorder. More recent theoretical studies have shown that even an infinitesimal random disorder in the few body exchange interactions caused by anisotropic exchange interactions due to nearest neighbour bond length variations and/or magnetoelastic strains or dipole-dipole interactions between uncompensated spin or spin clusters with intra-cluster geometrical frustration, can lift the degeneracy of the ground state and induce exotic phase transitions to spin liquid, spin glass and other complex ordered phases. Frustration resulting from the geometry of the lattice considered so far in the literature is pre-existing in the paramagnetic high-temperature phase due to its crystal structure. In contrast to the pre-existing geometrical frustration, this thesis presents evidence for emergent geometrical frustration in the LRO phase of an M-type hexaferrite, namely BaFe12O19 of immense commercial value worth about 4 billion dollars, at temperatures several hundred Kelvin below the ferrimagnetic transition temperature Tc ≃ 714 K. Further, the genesis of the emergent geometrical frustration as well as its consequences on the low-temperature behaviour of LRO ferrimagnetic phase of BaFe12O19 have been investigated in this thesis. A wide-ranging experimental techniques, involving X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) studies, X-ray and neutron powder diffraction studies, single-crystal neutron scattering studies, bulk magnetic susceptibility studies using both dc and ac fields on single crystals and powder samples, dielectric studies as a function of frequency and chemical pressure and specific heat studies on polycrystalline samples, have been employed in these investigations using in-house facilities as well as advanced synchrotron facility at Petra-III, DESY, Hamburg, FRM-II, Garching Germany and ISIS at Rutherford Appleton Laboratory, Harwell Oxford Didcot, UK, all as a function of temperature for T < 300 K. These studies have unravelled the complexity of the low-temperature phase transition behaviour of BaFe12O19 and its ground state. The most significant finding of the present work includes the discovery of as many as five spin-glass transitions involving either the longitudinal or the transverse components of the spins or the precession dynamics of the longitudinal conical magnetic structure in an ordered compound without any substitutional (site-) disorder and a quantum electric dipole glass state induced by a non-thermal variable. Presently, there no single theory that predicts a succession of five spin-glass transitions in a long-range ordered system with or without any substitutional site disorder. The present findings are expected to stimulate further theoretical and experimental studies in search of emergent geometrical frustration and its consequences in other hexaferrites as well as geometrically frustrated magnetic materials. The present thesis comprises ten chapters, as outlined below briefly: Chapter 01 gives a brief introduction and a short review of the relevant literature on hexaferrites. Chapter 02 gives the details of BaFe12O19 powder synthesis, sintering of these powders and crystal growth along with their characterization for phase purity and compositional stoichiometry. Chapter 03 presents evidence for the non-collinear magnetic structure of BaFe12O19 in its ground state using XAS and XMCD studies at 1.2 K and discovery of incommensurate longitudinal conical modulation of the magnetic structure in single-crystal neutron diffraction studies in the ground state of BaFe12O19. Chapter 04 presents evidence for large magnetic anisotropy using dc magnetization studies in the 2 to 950 K temperature range with a peak around 45 K, canting of 3dFe3+ spins with respect to the c-axis using temperature and incident angle dependent XAS and XMCD studies at the Fe L2,3-edges, splitting of the Fe-3d orbitals into eg and t2g bands due to crystal field effects and their further splitting due to exchange-correlations using XAS studies at the O K-edge and significant change in the exchange splitting around 15 K accompanied with change in the XMCD profile shapes and an upturn in dc magnetization perpendicular to the c-axis. Chapter 05 presents evidence for four successive spin-glass transitions in BaFe12O19 single crystals whose spin dynamics diverges at TSG ⁓ 46 K, ~ 25 K, ~ 15 K and ~ 4 K as per the Vogel-Fulcher and power-law fits for the spin relaxation time, anomalies in the temperature dependence of the specific heat in the CP/T3 versus T and CP/T versus T2 plots, diminution in the integrated intensities of the 006 and 101 reflections in single crystal neutron diffraction studies around the spin-glass freezing temperatures and confirmation of the co-existence of the spin-glass phases with the long-range ordered ferrimagnetic phase of BaFe12O19. Chapter 06 investigates in detail various characteristics of the first set of longitudinal and transverse spin-glass phase transitions occurring at higher temperatures, using ac susceptibility studies on polycrystalline samples as a function of temperature, frequency, time, aging and magnetic field. These studies confirm ergodicity breaking at the two critical spin-glass transition temperatures, presence of Gabay-Toulouse (G-T) and Almeida-Thouless (A-T) lines in the T-H plane, non-exponential relaxation of isothermal magnetization and memory and rejuvenation effects below TSG. These results are, surprisingly, in excellent agreement with the theoretically predicted T-H phase diagram for the disordered Heisenberg systems with negative single-ion anisotropy. Chapter 07 reports the discovery of another spin-glass transition in BaFe12O19 as revealed by the divergence of the spin relaxation time at TSG ~ 173 K, field (H) dependent shift of the spin-glass freezing temperature Tf(H) along the Gabay-Toulouse line, history dependent irreversibility of M(T), observation of non-exponential relaxation of the isothermal remanent magnetization as well as memory effects. Using high-resolution single-crystal neutron scattering studies, this chapter also presents evidence for longitudinal incommensurate conical modulation of the magnetic structure of BaFe12O19 at all temperatures upto 300 K, except a narrow temperature range ~ 15 K to ~ 35 K, where the modulation is commensurate. These studies reveal significant change in the integrated intensity of the satellite peaks and modulation wave vector across the spin glass transition suggesting that this transition may be linked with the precession dynamics of the 3dFe3+ spins in the longitudinal conical magnetic structure of BaFe12O19. Chapter 08 presents arguments for the deviation from the collinear Gorter model, as confirmed in chapters 3 to 7, due to canting of the spins at the 12k Wyckoff sites of BaFe12O19 unit cell, leaving the spins at the other sites aligned parallel or antiparallel to the c-axis as in the Gorter model. These arguments are used for the Rietveld analysis of the temperature-dependent neutron diffraction (NPD) patterns which reveal the emergence of fully frustrated kagome spin configuration as well as another kagome spin configuration with two-fold degeneracy as a function of temperature. Using temperature dependent powder XRD studies, evidence for the presence of significant anisotropic magnetoelastic strains below 175 K with magneto-volume effect in different temperature ranges is also presented in this chapter. These magnetoelastic strains may provide the desired randomness to the few body exchange interactions in BaFe12O19 required in the existing theories of spin-glass transition in geometrically frustrated ordered compounds. Chapter 09 presents the results of dielectric studies as a function of temperature and frequency from 1.66 K onwards to investigate the quantum critical behaviour of BaFe12O19 involving electric dipoles. This chapter provides confirmation of quantum electric dipole liquid (QEDL) like state using dielectric and specific heat studies and reports the discovery of a new quantum electric dipole glass transition induced by a non thermal variable which is chemical pressure in the present case. Chapter 10 summarizes the main finding of this thesis and list a few suggestions for future work.