Neutron spin-echo study of the critical dynamics of spin-52 antiferromagnets in two and three dimensions

Tseng, K. F.; Keller, T.; Walters, A. C.; Birgeneau, R. J.; Keimer, B.

doi:10.1103/PhysRevB.94.014424

Title: Neutron spin-echo study of the critical dynamics of spin- $\frac{5}{2}$ antiferromagnets in two and three dimensions

Journal Article · Tue Jul 19 00:00:00 EDT 2016 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.94.014424· OSTI ID:1466698

Tseng, K. F. ^[1]; Keller, T. ^[1]; Walters, A. C. ^[2]; Birgeneau, R. J. ^[3]; Keimer, B. ^[4]

Max-Planck-Institut fur Festkorperforschung, Stuttgart (Germany); Max Planck Society Outstation at the Forschungsneutronenquelle Heinz Maier-Leibnitz (MLZ), Garching (Germany)
Max-Planck-Institut fur Festkorperforschung, Stuttgart (Germany); Diamond Light Source Ltd., Oxfordshire (United Kingdom)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Max-Planck-Institut fur Festkorperforschung, Stuttgart (Germany)

Here, we report a neutron spin-echo study of the critical dynamics in the S= $\frac{5}{2}$ antiferromagnets MnF₂ and Rb₂MnF₄ with three-dimensional (3D) and two-dimensional (2D) spin systems, respectively, in zero external field. Both compounds are Heisenberg antiferromagnets with a small uniaxial anisotropy resulting from dipolar spin-spin interactions, which leads to a crossover in the critical dynamics close to the Néel temperature, T_N. By taking advantage of the μeV energy resolution of the spin-echo spectrometer, we have determined the dynamical critical exponents z for both longitudinal and transverse fluctuations. In MnF₂, both the characteristic temperature for crossover from 3D Heisenberg to 3D Ising behavior and the exponents z in both regimes are consistent with predictions from the dynamical scaling theory. The amplitude ratio of longitudinal and transverse fluctuations also agrees with predictions. In Rb₂MnF₄, the critical dynamics crosses over from the expected 2D Heisenberg behavior for T » T_N to a scaling regime with exponent z = 1.387(4), which has not been predicted by theory and may indicate the influence of long-range dipolar interactions.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1466698

Alternate ID(s):: OSTI ID: 1264792

Journal Information:: Physical Review B, Vol. 94, Issue 1; Related Information: © 2016 American Physical Society.; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 6 works

Citation information provided by
Web of Science

References (51)

The theory of superlattice critical scattering Bruce, A. D. Journal of Physics C: Solid State Physics, Vol. 14, Issue 3 https://doi.org/10.1088/0022-3719/14/3/004	journal	January 1981
Inelastic Neutron Scattering from Mn $F_{2}$ in the Critical Region Schulhof, Michael P.; Nathans, Robert; Heller, Peter Physical Review B, Vol. 4, Issue 7 https://doi.org/10.1103/PhysRevB.4.2254	journal	October 1971
Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models Mermin, N. D.; Wagner, H. Physical Review Letters, Vol. 17, Issue 22 https://doi.org/10.1103/PhysRevLett.17.1133	journal	November 1966
The resolution function in neutron diffractometry. I. The resolution function of a neutron diffractometer and its application to phonon measurements Cooper, M. J.; Nathans, R. Acta Crystallographica, Vol. 23, Issue 3 https://doi.org/10.1107/S0365110X67002816	journal	September 1967
Spin correlations in the two-dimensional spin-5/2 Heisenberg antiferromagnet Lee, Y. S.; Greven, M.; Wells, B. O. The European Physical Journal B, Vol. 5, Issue 1 https://doi.org/10.1007/s100510050413	journal	September 1998
Magnetic excitations in pure, lightly doped, and weakly metallic ${La}_{2}$ ${CuO}_{4}$ Keimer, B.; Belk, N.; Birgeneau, R. J. Physical Review B, Vol. 46, Issue 21 https://doi.org/10.1103/PhysRevB.46.14034	journal	December 1992
Dynamic critical exponent $z$ in some two-dimensional models Mazenko, Gene F.; Valls, Oriol T. Physical Review B, Vol. 24, Issue 3 https://doi.org/10.1103/PhysRevB.24.1419	journal	August 1981
Spin-Wave Analysis of the Quadratic-Layer Antiferromagnets $K_{2}$ Ni $F_{4}$ , $K_{2}$ Mn $F_{4}$ , and ${Rb}_{2}$ Mn $F_{4}$ de Wijn, H. W.; Walker, L. R.; Walstedt, R. E. Physical Review B, Vol. 8, Issue 1 https://doi.org/10.1103/PhysRevB.8.285	journal	July 1973
The resolution function in neutron spin-echo spectroscopy with three-axis spectrometers Habicht, Klaus; Keller, Thomas; Golub, Robert Journal of Applied Crystallography, Vol. 36, Issue 6 https://doi.org/10.1107/S0021889803015681	journal	November 2003
Spin-wave stiffness of the Heisenberg antiferromagnet at zero temperature Hamer, C. J.; Oitmaa, J. Physical Review B, Vol. 50, Issue 10 https://doi.org/10.1103/PhysRevB.50.6877	journal	September 1994
Critical dynamics of isotropic dipolar antiferromagnets Fischer, T. M.; Frey, E.; Schwabl, F. Physics Letters A, Vol. 146, Issue 7-8 https://doi.org/10.1016/0375-9601(90)90729-8	journal	June 1990
Critical Spin Dynamics of the 2D Quantum Heisenberg Antiferromagnets ${Sr}_{2} {CuO}_{2} {Cl}_{2}$ and ${Sr}_{2} {Cu}_{3} O_{4} {Cl}_{2}$ Kim, Y. J.; Birgeneau, R. J.; Chou, F. C. Physical Review Letters, Vol. 86, Issue 14 https://doi.org/10.1103/PhysRevLett.86.3144	journal	April 2001
A neutron resonance spin echo spectrometer for quasi-elastic and inelastic scattering Golub, R.; Gähler, R. Physics Letters A, Vol. 123, Issue 1 https://doi.org/10.1016/0375-9601(87)90760-2	journal	July 1987
Critical magnetic fluctuations in MnF2 Dietrich, O. W. Journal of Physics C: Solid State Physics, Vol. 2, Issue 11 https://doi.org/10.1088/0022-3719/2/11/317	journal	November 1969
Nuclear Magnetic Relaxation near the Curie Temperature Moriya, Tôru Progress of Theoretical Physics, Vol. 28, Issue 2 https://doi.org/10.1143/PTP.28.371	journal	August 1962
Critical dynamics of the simple-cubic Heisenberg antiferromagnet ${RbMnF}_{3} :$ Extrapolation to $q = 0$ Tsai, Shan-Ho; Landau, D. P. Physical Review B, Vol. 67, Issue 10 https://doi.org/10.1103/PhysRevB.67.104411	journal	March 2003
Temperature and Spin Dependent Correlation Length of the Quantum Heisenberg Antiferromagnet on the Square Lattice Cuccoli, Alessandro; Tognetti, Valerio; Vaia, Ruggero Physical Review Letters, Vol. 77, Issue 16 https://doi.org/10.1103/PhysRevLett.77.3439	journal	October 1996
Critical behavior of the three-dimensional Heisenberg antiferromagnet ${RbMnF}_{3}$ Coldea, R.; Cowley, R. A.; Perring, T. G. Physical Review B, Vol. 57, Issue 9 https://doi.org/10.1103/PhysRevB.57.5281	journal	March 1998
Antiferromagnetic Resonance in Mn $F_{2}$ Johnson, Fred M.; Nethercot, Arthur H. Physical Review, Vol. 114, Issue 3 https://doi.org/10.1103/PhysRev.114.705	journal	May 1959
Spin Correlations in an Isotropic Spin- $5 / 2$ Two-Dimensional Antiferromagnet Leheny, R. L.; Christianson, R. J.; Birgeneau, R. J. Physical Review Letters, Vol. 82, Issue 2 https://doi.org/10.1103/PhysRevLett.82.418	journal	January 1999
Spin fluctuations in random magnetic-nonmagnetic two-dimensional antiferromagnets. I. Dynamics Cowley, R. A.; Shirane, G.; Birgeneau, R. J. Physical Review B, Vol. 15, Issue 9 https://doi.org/10.1103/PhysRevB.15.4292	journal	May 1977
Polarization Analysis of Thermal-Neutron Scattering Moon, R. M.; Riste, T.; Koehler, W. C. Physical Review, Vol. 181, Issue 2 https://doi.org/10.1103/PhysRev.181.920	journal	May 1969
Role of Spin-Nonconserving Forces in the Critical Dynamics of Fe at the Curie Point Mezei, F. Physical Review Letters, Vol. 49, Issue 15 https://doi.org/10.1103/PhysRevLett.49.1096	journal	October 1982
Neutron Diffraction Studies of Antiferromagnetism in Manganous Fluoride and Some Isomorphous Compounds Erickson, R. A. Physical Review, Vol. 90, Issue 5 https://doi.org/10.1103/PhysRev.90.779	journal	June 1953
Critical Magnetic Neutron Scattering from Ferrous Fluoride Hutchings, M. T.; Schulhof, M. P.; Guggenheim, H. J. Physical Review B, Vol. 5, Issue 1 https://doi.org/10.1103/PhysRevB.5.154	journal	January 1972
Critical dynamics of a spin- $\frac{5}{2}$ two-dimensional isotropic antiferromagnet Christianson, R. J.; Leheny, R. L.; Birgeneau, R. J. Physical Review B, Vol. 63, Issue 14 https://doi.org/10.1103/PhysRevB.63.140401	journal	March 2001
Critical exponents and equation of state of the three-dimensional Heisenberg universality class Campostrini, Massimo; Hasenbusch, Martin; Pelissetto, Andrea Physical Review B, Vol. 65, Issue 14 https://doi.org/10.1103/PhysRevB.65.144520	journal	April 2002
Neutron scattering study of the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr2CuO2Cl2 Greven, M.; Birgeneau, R. J.; Endoh, Y. Zeitschrift f�r Physik B Condensed Matter, Vol. 96, Issue 4 https://doi.org/10.1007/BF01313844	journal	December 1995
Spin dynamics and spin correlations in the spinS=1 two-dimensional square-lattice Heisenberg antiferromagnet La2NiO4 Nakajima, K.; Yamada, K.; Hosoya, S. Zeitschrift f�r Physik B Condensed Matter, Vol. 96, Issue 4 https://doi.org/10.1007/BF01313845	journal	December 1995
Critical dynamics in isotropic ferromagnets Mezei, F. Journal of Magnetism and Magnetic Materials, Vol. 45, Issue 1 https://doi.org/10.1016/0304-8853(84)90374-3	journal	November 1984
Neutron Scattering Investigation of Phase Transitions and Magnetic Correlations in the Two-Dimensional Antiferromagnets $K_{2}$ Ni $F_{4}$ , ${Rb}_{2}$ Mn $F_{4}$ , ${Rb}_{2}$ Fe $F_{4}$ Birgeneau, R. J.; Guggenheim, H. J.; Shirane, G. Physical Review B, Vol. 1, Issue 5 https://doi.org/10.1103/PhysRevB.1.2211	journal	March 1970
Dynamic Scaling Theory for Anisotropic Magnetic Systems Riedel, E.; Wegner, F. Physical Review Letters, Vol. 24, Issue 13 https://doi.org/10.1103/PhysRevLett.24.730	journal	March 1970
Neutron resonance spin echo, bootstrap method for increasing the effective magnetic field Gähler, R.; Golub, R. Journal de Physique, Vol. 49, Issue 7 https://doi.org/10.1051/jphys:019880049070119500	journal	January 1988
Staircases of magnetic structure along the axial direction in the layered magnet Rb ₂ MnF ₄ Ikeda, H.; Tamura, T.; Nakashima, S. Journal of Physics C: Solid State Physics, Vol. 20, Issue 21 https://doi.org/10.1088/0022-3719/20/21/004	journal	July 1987
Two-dimensional quantum Heisenberg antiferromagnet: Effective-Hamiltonian approach to the thermodynamics Cuccoli, Alessandro; Tognetti, Valerio; Vaia, Ruggero Physical Review B, Vol. 56, Issue 22 https://doi.org/10.1103/PhysRevB.56.14456	journal	December 1997
Theory of dynamic critical phenomena Hohenberg, P. C.; Halperin, B. I. Reviews of Modern Physics, Vol. 49, Issue 3 https://doi.org/10.1103/RevModPhys.49.435	journal	July 1977
The NRSE-TAS spectrometer at the FRM-2 Keller, T.; Habicht, K.; Klann, H. Applied Physics A: Materials Science & Processing, Vol. 74, Issue 0 https://doi.org/10.1007/s003390201612	journal	December 2002
Crossover scaling functions for exchange anisotropy Pfeuty, P.; Jasnow, David; Fisher, Michael E. Physical Review B, Vol. 10, Issue 5 https://doi.org/10.1103/PhysRevB.10.2088	journal	September 1974
Nuclear-Magnetic-Resonance Studies of Critical Phenomena in Mn $F_{2}$ . I. Time-Average Properties Heller, Peter Physical Review, Vol. 146, Issue 2 https://doi.org/10.1103/PhysRev.146.403	journal	June 1966
Critical Magnetic Scattering in $K_{2}$ Ni $F_{4}$ Birgeneau, R. J.; Skalyo, J.; Shirane, G. Physical Review B, Vol. 3, Issue 5 https://doi.org/10.1103/PhysRevB.3.1736	journal	March 1971
Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition Onsager, Lars Physical Review, Vol. 65, Issue 3-4 https://doi.org/10.1103/PhysRev.65.117	journal	February 1944
Crossover effects in dynamic critical phenomena in MnF2 and FeF2 Riedel, E.; Wegner, F. Physics Letters A, Vol. 32, Issue 4 https://doi.org/10.1016/0375-9601(70)90320-8	journal	July 1970
Scaling Laws for Dynamic Critical Phenomena Halperin, B. I.; Hohenberg, P. C. Physical Review, Vol. 177, Issue 2 https://doi.org/10.1103/PhysRev.177.952	journal	January 1969
Critical dynamics of magnets Frey, E.; Schwabl, F. Advances in Physics, Vol. 43, Issue 5 https://doi.org/10.1080/00018739400101535	journal	October 1994
Dynamic correlations in a classical two-dimensional Heisenberg antiferromagnet Wysin, G. M.; Bishop, A. R. Physical Review B, Vol. 42, Issue 1 https://doi.org/10.1103/PhysRevB.42.810	journal	July 1990
Critical phenomena and renormalization-group theory Pelissetto, Andrea; Vicari, Ettore Physics Reports, Vol. 368, Issue 6 https://doi.org/10.1016/S0370-1573(02)00219-3	journal	October 2002
Neutron spin echo: A new concept in polarized thermal neutron techniques Mezei, F. Zeitschrift für Physik A Hadrons and nuclei, Vol. 255, Issue 2 https://doi.org/10.1007/BF01394523	journal	April 1972
Critical Behavior of Magnets with Dipolar Interactions. I. Renormalization Group near Four Dimensions Aharony, Amnon; Fisher, Michael E. Physical Review B, Vol. 8, Issue 7 https://doi.org/10.1103/PhysRevB.8.3323	journal	October 1973
Lifetimes of Antiferromagnetic Magnons in Two and Three Dimensions: Experiment, Theory, and Numerics Bayrakci, S. P.; Tennant, D. A.; Leininger, Ph. Physical Review Letters, Vol. 111, Issue 1 https://doi.org/10.1103/PhysRevLett.111.017204	journal	July 2013
Spin correlations in the two-dimensional S=1 Heisenberg antiferromagnet Birgeneau, R. J. Physical Review B, Vol. 41, Issue 4 https://doi.org/10.1103/PhysRevB.41.2514	journal	February 1990
Spin correlations in the 2D Heisenberg antiferromagnet ${Sr}_{2}$ ${CuO}_{2}$ ${Cl}_{2}$ : Neutron scattering, Monte Carlo simulation, and theory Greven, M.; Birgeneau, R. J.; Endoh, Y. Physical Review Letters, Vol. 72, Issue 7 https://doi.org/10.1103/PhysRevLett.72.1096	journal	February 1994