Session T13: Focus Session: Low-Dimensional and Molecular Magnetism - Molecular Ferromagnetism and 2D Magnetism

Magnetic phase diagram of quasi-2D quantum Heisenberg antiferromagnets with XY anisotropy

The magnetic phase diagram of a quasi-2D quantum Heisenberg antiferromagnetic compound Cu(pz)2(Cl$_{\mbox{O4}\mbox{)2}}$ [1] has been determined by experimental measurements; TN shows a strong field dependence. The data reveal the presence of a small (0.5\%) amount of XY anisotropy. QMC simulations have been performed to examine the role of the anisotropy and the interlayer exchange (') upon the phase diagram [2,3]. Comparison of the QMC results with the experimental phase diagram will be presented. \\[4pt] [1] F. Xiao, F. M. Woodward, C. P. Landee, M. M. Turnbull, C. Mielke, N. Harrison, T. Lancaster, S. J. Blundell, P. J. Baker, P. Babkevich, and F. L. Pratt. Phys. Rev. B, 79(13): 134412 (2009) \\[0pt] [2] A. Cuccoli, T. Roscilde, R. Vaia, and P. Verrucchi. Phys. Rev. B, 68(6):060402 (2003). \\[0pt] [3] A. Cuccoli, T. Roscilde, R. Vaia, and P. Verrucchi. Phys. Rev. Lett., 90(16): 167205 (2003).   

Magnetic excitations of the S=1/2 square lattice antiferromagnet CuF$_{2}$(H$_{2}$O)$_{2}$(pyz) (pyz=pyrazine)

We have studied the magnetic structure and excitations of the two dimensional S=1/2 square lattice antiferromagnet deuterated CuF$_{2}$(H$_{2}$O)$_{2}$(pyz). The neutron diffraction measurements show that the antiferromagnetic structure is collinearly arranged with the estimated magnetic moment of 0.60$\pm $0.07 $\mu _{B}$/Cu. This value is much smaller than the single ion magnetic moment, reflecting the presence of strong quantum fluctuations. The spin wave dispersion from magnetic zone center to the zone boundary point ($\pi $/2 $\pi $/2) can be roughly described by a 2d Heisenberg model with a magnetic exchange constant J$_{2d}$=1.099 $\pm $ 0.002 meV and a tiny contribution from an inter-plane interaction (J$_{perp}$ is about 1{\%} of J$_{2d})$. This is close to the first principles DFT calculations while about two times larger than the value extracted by fitting of the magnetic susceptibility. Compared to ($\pi $/2 $\pi $/2), preliminary measurements of the spin excitation at the zone boundary point ($\pi $ 0) shows an obvious suppression of the excitation energy. This suppression is expected on the basis of quantum Monte Carlo and series expansion calculations for the quantum corrections of linear spin wave theory.   

Edge state and its stability of 2D antiferromagnetic quantum spin systems

Topological insulators (TIs) [1] have been of great interest in condensed matter physics. One of the most important points is that TIs are characterized by non-local quantities such as topological quantities of the bulk or gapless surface states [2]. The TI phase and the surface states are quite stable for any time-reversal symmetric perturbations. On the other hand, the Haldane-gap state in quantum spin systems is another class of the topological state [3], because, similarly to TIs, this gapped state has no local order and is characterized by the non-local (string) order parameter or free spins at the edges. In this study, motivated by the recent development of theories for topological phases and surface states, we consider properties of edge states in 2D quantum spin systems by applying the quantum Monte Carlo method. Particularly, we focus on the three points; (1) which spin systems can have gapless edge states, (2) the stability of the gapless edge states, and (3) the difference between the edge modes of TIs and spin systems. \\[4pt] [1] See, for example, M. Z. Hasan and C. L. Kane, RMP82, 3045 (2010). \\[0pt] [2] A. P. Schnyder, et al., PRB 78, 195125 (2008), A. Kitaev, AIP Conf. Proc. 1134, 22 (2009). \\[0pt] [3] F.D.M. Haldane, Phys. Lett. 93A, 464 (1983); PRL50, 1153 (1983).   

Absence of magnetic order in low-dimensional (RKKY) systems

We extend the Mermin-Wagner theorem to a system of lattice spins which are spin-coupled to itinerant and interacting charge carriers. We use the Bogoliubov inequality to rigorously prove that neither (anti-) ferromagnetic nor helical long-range order is possible in one and two dimensions at any finite temperature. Our proof applies to a wide class of models including any form of electron-electron and single-electron interactions that are independent of spin. In the presence of Rashba or Dresselhaus spin-orbit interactions (SOI) magnetic order is not excluded and intimately connected to equilibrium spin currents. However, in the special case when Rashba and Dresselhaus SOIs are tuned to be equal, magnetic order is excluded again. This opens up a new possibility to control magnetism electrically. \\[4pt] References: D. Loss, F. L. Pedrocchi, and A. J. Leggett, Phys. Rev. Lett. \textbf{107}, 107201 (2011).   

Continuous and Discontinuous Quantum Phase Transitions in a Model Two-Dimensional Magnet

The Shasty-Sutherland model consists of a set of spin 1/2 dimers on a 2-dimensional square lattice which are predicted to change from isolated, gapped excitations to a collective, ordered ground state by tuning the ratio of the intra to inter-dimer coupling. We compress the model Shastry-Sutherland material, SrCu2(BO3)2, in a diamond anvil cell at cryogenic temperatures to continuously tune the coupling energies and induce changes in state. High-resolution x-ray measurements exploit a remarkably strong spin-lattice coupling to ascertain the physics of the magnetic transition. The singlet-triplet gap energy is suppressed continuously with increasing pressure, vanishing completely by 2 GPa. This continuous quantum phase transition is followed by a structural distortion at higher pressure corresponding to the onset of long-range order.   

Late-time Domain Growth in the Compressible Triangular Ising Net

We perform large scale Monte Carlo simulations of the long-tme domain growth behavior in a compressible, triangular Ising net. Unlike previous work,\footnote{Mitchell and DP Landau, PRL 97, 025701 (2006)} our model has no bond angle interactions or lattice mismatch. The system is quenched below the critical temperature from a homogenous disordered state to an ordered phase where multiple domains coexist. We include an elastic energy part in the Hamiltonian to adjust the rigidity of the model. Theory expects the domain size $R(t)$ grows as a power law $R(t)=A+Bt^n$, where $t$ is the time after the quench. For the rigid model we find the late-time domain size growth factor $n$ has Lifshitz-Slozov value of $\frac{1}{3}$. For weak flexible models, we get slight reduction from $\frac{1}{3}$. For the strongly flexible model, we get a bimodal distribution of bond lengths and a dramatically reduced value of $n$, which has similar behavior as the mismatch model.\footnote{Ibid.}   

Atomic-scale antiferromagnets with stable Neel states

A macroscopic antiferromagnet is characterized by long-range magnetic order, for example with the spin of neighboring atoms alternating their direction. Here we will discuss how far such concepts can be extended towards the atomic scale. We use low-temperature scanning tunneling microscopy with spin-polarized tips to investigate antiferromagnets consisting of a small number of Fe atoms on a thin Cu2N substrate. As few as 8 Fe atoms show two stable magnetic states in which the spin between neighboring atoms alternates. The STM can be used to switch between these two magnetic states. When heating the spins to about 10K, spontaneous switching occurs from which the switching dynamics is deduced. Small structures show a second switching mechanism that is not dependent on temperature but strongly dependent on the length of the antiferromagnetic chain, suggesting switching by quantum tunneling of magnetization (the Neel vector).   

Contrasting low-dimensional magnetism in the 3D metal-organic frameworks [Cu(VF$_{6})$(pyz)$_{2}$]\textbullet 4H$_{2}$O and [Cu(HF$_{2})$(pyz)$_{2}$]SbF$_{6}$ (pyz = pyrazine)

[Cu(VF$_{6})$(pyz)$_{2}$]\textbullet 4H$_{2}$O (\textbf{1}) and [Cu(HF$_{2})$(pyz)$_{2}$]SbF$_{6}$ (\textbf{2}) form tetragonal frameworks that consist of 2D [Cu(pyz)$_{2}$]$^{2+}$ square lattices that are linked in 3D by bridging VF$_{6}^{2-}$ (\textbf{1}) or HF$_{2}^{-}$ (\textbf{2}) anions. Magnetic susceptibility data shows apparent paramagnetism, although not simple Curie-Weiss behavior, in \textbf{1}. For \textbf{2}, a broad maximum in $\chi (T)$ at 12.5 K and a sharp kink at 4.3 K indicate short- (SRO) and long-range (LRO) magnetic ordering, respectively. Additional experimental data for \textbf{1} (e.g., heat capacity and $\mu ^{+}$SR) however, indicate that a LRO state occurs below 3.6 K whereas pulsed-field magnetization data suggest a superposition of AFM Cu$^{2+}$ layers and fluctuating V$^{4+}$ moments. The structural and magnetic behavior of \textbf{1} and \textbf{2} will be described as well as possible new directions.   

Strong Exchange Anisotropy in Heavy Atom Radical Ferromagnets

The discovery twenty years ago of ferromagnetic ordering in ``light atom'' p-block (N, O based) radicals appeared to provide a major conceptual advance, suggesting the possibility of a new era in non-metal molecular magnetism. However, the weak through-space magnetic exchange interactions present in these early radical-based ferromagnets afforded very low Curie temperatures $T_C$ ($<$ 2 K), and the localization of spin density on light atoms ensured low coercive fields $H_c$ ($<$ 100 Oe). In this context, the observation of ferromagnetic ordering in ``heavy atom'' (Se) radicals, with $T_C$ as high as 17 K and coercive fields $H_c$ up to 1370 Oe (at 2 K), represents a significant improvement in properties. This presentation will provide a theoretical and experimental examination of the source of the large coercive fields reported for these ``heavy atom'' radical ferromagnets. High-field ferromagnetic resonance (FMR) measurements, interpreted in the context of the anisotropic exchange interactions between the radicals in the solid state, leads to the conclusion that spin-orbit effects are responsible for the large observed magnetic anisotropy. This conclusion is supported by detailed analysis of the symmetry and magnitude of the spin-orbit interactions. An interesting discussion is the extent to which these anisotropic exchange terms also contribute to the enhancement of $T_C$. That is, in the field of organic magnetism, where low dimensional magnetic structures are commonly found, long range ordering may depend crucially on such anisotropy. \\[4pt] See \emph{JACS} {\bf 130}, 8414-8425 (2008), \emph{JACS} {\bf 133}, 8126-8129 (2011).   

FMR Study of the Field Dependence of the Ferromagnetic Transition in an Organic Magnet

Organic heterocyclic thia/selenazyl radicals have unique magnetic properties. First and foremost, in their crystalline form, they experience a transition to a ferromagnetic state at temperatures that are the highest for any material containing only non-metallic elements. Second, their low temperature uniaxial anisotropy field is the highest among purely organic ferromagnets [Winter et al., JACS {\bf 133}, 8126 (2011)]. To investigate the effect of a magnetic field on the transition in the mixed Se-S compound ($T_c = 12.5$~K) at zero field, we employ ferromagnetic resonance (FMR) absorption as a measure of the anisotropy field for a single crystal. We also focus on the temperature and field dependence of the FMR linewidth. Our main finding is that the application of a field significantly broadens the ferromagnetic transition, with a noticeable FMR signal observed to as high as $2T_c$ in fields of a few tesla. Meanwhile, the FMR linewidth is relatively insensitive to frequency/field, though it becomes narrower upon decreasing the temperature and saturates below $T_c$. We will discuss the broadening of the ferromagnetic transition within the framework of scaling theory.