Antiferromagnetic MnF2 Research Articles

Two-spin light scattering in rutile structure Heisenberg paramagnets

Two-spin light scattering in the disordered phase of rutile antiferromagnets MnF2 and NiF2 is investigated by means of a previously developed long-time approximation for the continued-fraction representation of the shape function. The procedure requires the evaluation of the lower-order frequency moments: the first frequency moment of the overall spectrum is found to be in good agreement with the experimental data for both compounds in the whole paramagnetic phase. Also the theoretical shapes are in fair agreement with the experimental spectra of MnF2 at various temperatures.

Lineshape calculations for light scattering from spin-waves in absorptive magnetic materials

Calculations are presented for the lineshapes associated with light scattering by spin-waves in absorptive (semi-opaque) magnetic materials at low temperatures. Scattering at normal incidence to the surface is considered, and it is predicted that the lineshapes are asymmetric and that there is an 'opacity broadening' contribution to their width. Both ferromagnetic and antiferromagnetic materials are considered, although it is shown that the effects may be considerably larger in antiferromagnets with small anisotropy. The theory is applied to obtain numerical results for the antiferromagnets RbMnF3 and MnF2.

Magnetic field dependence of nuclear relaxation in antiferromagnets

Abstract : The contributions of higher order scattering processes, in particular three magnon processes, to the nuclear spin lattice relaxation rate of F19 and Mn55 nuclei in antiferromagnetic MnF2 are examined. It is shown that this three magnon rate, aided by an exchange enhanced process, has a significant magnetic field dependence, for fields along the magnetic easy axis, as the spin flop transition is approached. The three magnon relaxation rate becomes comparable in magnitude to the two magnon rate in this magnetic field region. Theoretical curves are presented for the predicted three magnon spin lattice relaxation rate contribution in NMR experiments on MnF2. Other higher order processes are shown to yield smaller corrections to the relaxation rate as compared to this three magnon rate. (Author)

Linear Magnetic Birefringence in the Antiferromagnetic Iron Group Difluorides

AbstractThe linear optical birefringence of the iron‐group difluorides (rutile‐type) has been determined between 5 and 700 K. A magnetic contribution to the birefringence occurs during the ordering of the antiferromagnetic compounds MnF2, FeF2, CoF2, and the weak ferromagnetic NiF2; the linear magnetic birefringence (LMB) can be well separated from the temperature dependent natural optical anisotropy. Both the magnetic short‐range as well as the long‐range order contribute to the LMB. The temperature derivative of the LMB follows the course of the magnetic specific heat to a very good degree. It is shown that this proportionality is to be expected if all spin pair correlation functions exhibit the same temperature behaviour. Whether this condition is valid for the lattice distortions is discussed using the existing structural data. Assuming the observed LMB is mainly due to spontaneous lattice distortions, the influence of the fluorine parameter seems to play an important role.

Magnetic Circular Dichroism in Antiferromagnetic MnF2

The magnetic circular dichroism (MCD) properties of antiferromagnetic MnF2 in the 4T1(4G) region have been studied. We show that MCD is a useful technique in furthering our understanding of the spectra of these materials, particularly when complex assisted transitions are involved. Out of the complex band absorption, only a weak electric dipole feature at 18 536 cm−1 and the one-magnon sideband region exhibit magnetic circular dichroism. We present conclusive evidence that the weak electric dipole transition is a two-magnon sideband of the pure electronic line E2 in this manifold. The position and temperature dependence are in good agreement with other two magnon experimental data. The MCD splitting also yields an effective g factor for the two-magnon sideband which is in good agreement with existing data. We conclude that this three-center excitation is caused by a zone-center exciton plus two X2 zone-edge magnons. Fitting the observed MCD signal from the one-magnon sideband region to a calculated line shape gives us an estimate of the effective g factor for zone-edge magnons in MnF2.

Inelastic Neutron Scattering Studies of Critical Fluctuations in MnF2 Above and Below TN

Detailed inelastic neutron scattering measurements have yielded the behavior of the scattering function S(q, ω) for both the transverse and the longitudinal fluctuations throughout the critical region of the uniaxial antiferromagnet MnF2. The results are discussed in the light of the theory of dynamic scaling. The results below TN are discussed with reference to quasihydrodynamic theories of the spin fluctuations in the ordered state.

Dynamic Scaling Theory for Anisotropic Magnetic Systems

A theory of dynamic critical phenomena in anisotropic magnetic systems by Wegner and the author is reviewed and compared with recent neutron scattering experiments, especially on the uniaxial antiferromagnets MnF2 and FeF2. Particular emphasis is placed on the spin-relaxation rates as functions of the anisotropy in ferromagnets and antiferromagnets in the paramagnetic critical state. Within a generalized dynamic scaling and mode-mode approach the anisotropy parameters are treated as additional ``critical'' variables. The theory applies to the entire critical state of weakly anisotropic systems and is not restricted to a small region around the critical point. Anisotropy is interpreted as introducing a second length into the critical behavior of the system. In this case the spin-relaxation rates cannot be characterized by a single set of critical exponents for all ranges of variables even in the critical state. Instead, simple corresponding-state relations are found, in which the analytical structure of the scaling functions is related to the basic symmetry and conservation-law properties of the system. It is shown that the anisotropy parameter, and in mode-mode approximation also the isotropic material parameters, enters only the amplitudes and reduced temperature and momentum variables in those relations. Quantitative results for the spin-relaxation rates are given for the uniaxial antiferromagnets MnF2 and FeF2 and, in the isotropic limit of the theory, for the ferromagnets Fe and Ni, and the antiferromagnet RbMnF3. Recent neutron scattering results on MnF2 and FeF2 by Schulhof et al. are in good agreement with the predictions of the theory.

Spontaneous magnetization from NMR measurements and critical exponents in nickel

Nuclear magnetic resonance of Ni61 has been studied in pure nickel metal (of natural isotope composition) in the vicinity of the Curie point. The temperature dependence of NMR frequency has been measured up to 0·96Tc. Determination ofTc was aided by initial susceptibility measurements. The analysis of these results yields β=0·336±0·002 for the critical exponent describing the decrease of spontaneous magnetization to zero atTc. This value ofβ is in excellent agreement with the corresponding values obtained from NMR experiments in ferromagnetic EuS and antiferromagnetic MnF2, it differs, however, from the values obtained for nickel by other methods. In a general discussion of this problem which uses the theoretical relations between various critical exponents the earlier data, in particular those of Weiss and Forrer, are reexamined.

Two-Magnon Spectra of Antiferromagnetic MnF2 and FeF2

Two-Magnon Spectra of Antiferromagnetic MnF₂ and FeF₂

Inelastic Scattering from MnF2 in the Critical Region

The scattering law S(q, ω) in the anisotropic antiferromagnet MnF2 has been measured over an extended range of ω, q, and temperature in the neighborhood of the transition. The data have yielded values for the relaxation rate of transverse (Γ⊥) and longitudinal (Γ∥) fluctuations, the range of the spin-spin correlations (ξ) and the static staggered susceptibilities.1 From our results we find the relaxation rate at TN linear in q3/2 for both longitudinal and transverse. Above TN for q = 0 the longitudinal Γ∥ ∝ [(T - TN) / TN]0.95±0.05. The relaxation rates, when plotted on a reduced scale Γ∥ (q, ξ) ξ3/2 vs qξ, fall on a single curve indicating the existence of a homogeneous scaling function. This substantiates the prediction of general dynamical scaling.2 The scaling function has a different behavior above and below TN, joining continuously as ξ becomes large. A detailed comparison of the experimental S(q, ω) with theory awaits a more explicit calculation of the behavior of the critical fluctuations in the anisotropic system.

The spin-wave contribution to the specific heat of MnF2, FeF2, CoF2 and NiF2

By making use of the recently measured spin-wave dispersion relations we have calculated the spin-wave contributions to the low-temperature specific heats of antiferromagnetic MnF2, FeF2, CoF2 and NiF2 from 0 to 50 °K (0 to 35 °K for CoF2) using two different numerical methods. The results are compared with the experimental measurements of Stout and Catalano for temperatures of 15 °K and above; it is suggested that further experimental measurements below 15 °K would be worth while.

Precision Measurements of the F19 NMR in FeF2 from 4.2°K to the Critical Region

A precise determination of the temperature dependence of the zero external field F19 NMR frequency in the antiferromagnet FeF2 has been made over the temperature range from 4.2°K to 0.99966TN. Ferrous fluoride, unlike the previously studied antiferromagnet MnF2, has a large single ion magnetic anisotropy. The present data, which were taken on a high-quality single crystal with one millidegree temperature control and measurement techniques, were carefully least-squares fitted to the equation ν19(T)/ν19(0)=D(1−T/TN)βover ranges θ <T/TN<0.99966. For θ=0.995, it is found that β=0.333±0.009, D=1.428±0.067, TN=78.373±0.005, while for θ=0.971, β=0.320±0.001, D=1.341±0.005, TN=78.367±0.001. The present data, which demonstrate the need for precise measurements and analysis over small ranges near TN, are at variance with the wider-range power law fits reported recently by Wertheim et al. A Kouvel-Fisher plot of the present data shows that the apparent value of β drops rather rapidly for θ<0.95. This behavior is distinctly different from MnF2, where the apparent value of β varies more slowly. Although no analysis of the data below the critical region has yet been made, its accuracy should prove helpful for comparison with spin-wave interaction theories.

Scattering matrices for the Raman effect in magnetic crystals

The symmetry of a magnetic crystal can be described by one of the black and white Shubnikov point groups containing both unitary and anti-unitary elements. The theory is reviewed that enables a tensor to be symmetry adapted to any one of the irreducible corepresentations of a non-unitary group and it is applied to the determination of scattering matrices for the Raman effect in magnetically ordered crystals. An example is given in detail for the magnetic point group of antiferromagnetic MnF2 and complete tables are presented for all the fifty-eight black and white magnetic point groups.

Precision Thermometer for the Region 10–40 K

A low temperature thermometer based on the temperature dependence of the vF(T) of the 19F NMR frequency in antiferromagnetic MnF2 has been successfully operated in the 10–40 K temperature region. Novel features include the use of a MnF2 crystal with a sharp 19F NMR line as the temperature sensitive element in a solid state frequency-locking autodyne circuit that operates while completely submerged in liquid H2 or He. In the present design the circuit-sample combination takes the form of a compact probe. With this device temperature readings which are reproducible to ±10−4 K at 20 K have been obtained. Various applications for precision thermometry in the 10–40 K range using the device are proposed.

Light Scattering by Spin Waves

Light scattering by spin waves in the rutile-structure antiferromagnets MnF2 and FeF2 is reviewed. Emphasis is placed upon details of the experimental results and technique. The relations of first- and second-order spin-wave scatterings to the magnon dispersion relation are discussed. We show that for FeF2 the entire magnon dispersion curve can be inferred from results of a single light-scattering experiment.

Far-Infrared Absorption by Two-Magnon Excitations in Antiferromagnets

Far-infrared spectroscopy has been used extensively for the study of antiferromagnetic resonance, that is, single-magnon excitations at the Brillouin zone center. The recent discovery of two-magnon excitations in antiferromagnets by Halley and Silvera now permits precise measurements of magnon energies at selected points on the Brillouin-zone boundary. The discovery and theoretical interpretation of the two-magnon effect is described in this review paper. Experimental results for the antiferromagnets MnF2, FeF2, and CoF2 and for the canted-spin weak ferromagnets NiF2 and MnCO3 are also presented. The experimental data are discussed in relation to the current theoretical understanding of the two-magnon effect.

Exchange Splitting of the Ground State ofNi2+Ions in Antiferromagnetic MnF2, KMnF3, and RbMnF3

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Observation and Theory of New Line in Far-Infrared Absorption in Antiferromagnetic FeF2

A many-ion spin-orbit interaction in magnetic materials is pointed out which explains the existence of a previously anomalous infrared absorption line at a frequency of 154 cm−1 in antiferromagnetic FeF2. The interaction also provides a possible explanation for the existence of a magnon sideband recently observed in the antiferromagnet MnF2. The experiments on FeF2 are described and compared with the theory.

19F NMR Spin Echo in Antiferromagnetic MnF2

Spin echoes of 19F NMR have been observed, in zero external field, in various samples of antiferromagnetic MnF2. The decay of the echo envelope was always found to be exponential. This corresponds to a Lorentzian line profile, indicating that the Gaussian line shape previously observed with a cw spectrometer and found to be an order of magnitude broader, arises from inhomogeneous broadening. A previous calculation of the indirect nuclear spin-spin interaction via virtual magnon excitations predicts a 3-μsec T2 with a Gaussian envelope. However, (1) destructive interference between the 19F dipolar and indirect coupling mechanisms and (2) the appreciable contribution via the 19F−55Mn dipolar interaction of the much larger indirect coupling between 55Mn nuclei to the fourth moment of the line will reduce the 19F relaxation rate, the first, by only 20% but the second by approximately a factor of eight, and will change the line shape from Gaussian to Lorentzian. The derived value T2≅30 μsec is in agreement with the relaxation time T2=29±1 measured for a high-purity MnF2 sample. T2 is observed to monotonically decrease to a value of 22 μsec at 20.2°K. The temperature dependence of the nuclear spin lattice relaxation T1 in the same region is more dramatic, varying from 130 sec at 4.2°K to 3 msec at 20.2°K.

Study of energy transfer from 3d to 4f electrons in antiferromagnetic MnF2: Eu3+ crystals

AbstractThe spectrum and luminescence intensity of the antiferromagnetic crystals MnF2:Eu3+ are investigated experimentally for temperatures between 20 and 90 °K. This range includes the magnetic ordering temperature TN (≈ 68 °K). At the temperature TH (≈ 0,5 TN), corresponding to the spin ordering of the excited Mn2+ ions, the luminescence intensity due to these ions shows a sudden increase while the luminescence intensity due to the Eu3+ ions suffers a sudden decrease. This indicates that an anomalous change occurs in the transfer of energy between the Mn2+ and Eu2+ ions due to the condensation of the local magnetic vibrations of the optically excited Mn2+ ions.