Volume 42, Issue 4, 15 March 1971
 PROCEEDINGS OF THE SIXTEENTH ANNUAL CONFERENCE ON MAGNETISM AND MAGNETIC MATERIALS

 BUBBLE DOMAINS—DETECTION AND EPITAXIAL MATERIALS

Mobile Cylindrical Magnetic Domains in Epitaxial Garnet Films
View Description Hide DescriptionThe properties of cylindrical domains in wafers of bulk single crystals of various magnetic oxides have been extensively studied and described in recent months. Mobile cylindrical domains have been produced in single‐crystal thin films of gallium‐substituted yttriumirongarnet. The deposits are formed by chemical vapor deposition onto nonmagnetic garnet substrates greater than 1 cm^{2} in area. A model of magnetic anisotropy in epitaxialfilms is proposed and shown to be in good agreement with experimental domain observations. In a typical sample, a domain diameter of 8 μ is observed in a 6‐μ‐thick film at a bias field of 25 Oe. From the domain translational velocity of 5600 cm/sec, a cylindrical domain mobility of 1500 cm/sec Oe has been calculated. A fractional change in cylindrical domain diameter of −0.07%/°K has been measured at 300°K. Annealing at 1570°K for several hours did not alter the Néel temperature or the optical transmission spectrum.

Detection of Cylindrical Magnetic Domains
View Description Hide DescriptionCylindrical magnetic domains in thin platelets of anisotropic single‐crystal materials have been detected using the Hall effect in silicon, the pseudo‐Hall effect in Permalloy, flux change, and Faraday rotation. The silicon detector, active area ≈400 μ^{2}, active thickness ≈1 μ, input and output resistance ≈1.5 kΩ, and 8‐mA rated current, delivered 0.5‐mV signals from orthoferrite domains. For 20‐mA input current the Permalloy detector, input and output resistance ≈15 Ω, diameter ≈50 μ, and thickness ≈0.03 μ, yielded 0.9‐mV signals from 60‐μ‐diam domains in Sm_{0.55}Tb_{0.45}FeO_{3} orthoferrite. Domains in Y_{2.25}Tb_{0.75}Ga_{0.9}Fe_{4.1}O_{12}, diameter ≈7 μ, were read with a Permalloy detector approximately 7 μ in diameter. The output was 0.2 mV at 2‐mA input current. An output of 1 mV μsec was obtained by detecting the flux change on collapse of a TmFeO_{3} domain previously expanded 40 times in surface area. A Faraday‐rotation detection system consisting of a 5‐μW He–Ne laser, sheet polarizers, and an avalanche photodiode has operated at 10^{6} bits/sec with a 20‐dB signal‐to‐noise ratio. Among these detection methods, the Permalloy device appears most promising at this time. It offers the simultaneous advantages of relatively simple fabrication, small active area, small initial cost, and low power consumption. Additional experimental results relating to these detection methods are presented. Their relative merits and limitations are discussed and compared to those of the magnetoresistor and the magnetodiode. The problems associated with the detection of small domains at high speed are also considered.
 CRITICAL PHENOMENA IN MNF2 AND IN ONE DIMENSION

Inelastic Neutron Scattering Studies of Critical Fluctuations in MnF_{2} Above and Below T_{N}
View Description Hide DescriptionDetailed 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.
 BUBBLES AND DOUGHNUTS

Single‐Conductor Magnetic‐Bubble Propagation Circuits
View Description Hide DescriptionPropagation circuits for circular magnetic domains using only a single electric current conductor are described. A circuit which in addition uses Permalloy dots for domain stability and for determining the direction of propagation has been operated at 475 kHz with a 100‐mA amplitude current.

Magnetoresistive Detector for Bubble Domains
View Description Hide DescriptionThis paper describes a simple Permalloy magnetoresistive readout transducer for detecting magnetic bubble domains. The advantages over inductive detection are a large increase in signal and an independence of bubble velocity. The advantages over Hall effect detection are simpler fabrication and higher efficiency. The detector is a strip of thin Permalloy film with two contacts, both of which can be deposited onto the same overlay used for bubble propagation. As an example, a 250 Å×38 μ× 138‐μ device (52 Ω) was used with a measuring current of 7 mA to give a 2.3‐mV signal when detecting 138‐μ diameter bubbles in TmFeO_{3}. The response was constant up to the maximum data rate allowed by the bubble domain, in this case, 10^{6} bits/sec in DyFeO_{3}. The detector itself can switch in less than 10^{−8} sec. It can be used when conducting strip lines are used for bubble propagation, and also when a rotating field and Permalloy overlay are used. Optimum device placement and shape, as well as ultimate limitations, are discussed in terms of the stray field contours of the bubbles.

Observations and Properties of a New Domain: Hollow Bubble
View Description Hide DescriptionA new type of domain structure, a hollow bubble or ring domain, has been studied. Calculations with zero Bloch‐wall pinning force show that these ring domains can exist in platelets of uniaxial materials within a narrow region of the magnetic field normal to the platelet. Within this region the dimensions of the ring change enormously; they can be changed by a factor 2 by a field variation, which is about 100 times less than the variation needed to change the bubble radius by the same amount. We observed that the presence of a pinning force strongly influences the field region for stable ring domains and their behavior under a varying magnetic field. For a high‐coercivity sample an experiment is reported, in which each cycle H _{1}‐H _{2}‐H _{1} of a varying magnetic field normal to the platelet diminishes the size of a ring. This experiment is in some sense the microscopic analogy to the ``bascule'' and ``reptation'' described by L. Néel.

Simple Method of Measuring Mobility in Cylindrical Domain Materials
View Description Hide DescriptionA simple method is described for measuring wall mobility in materials which support cylindrical domains. The mobility is determined from the initial velocity with which a domain wall responds to a field step. A sample, which is demagnetized into the stripe domain state, is subjected repetitively to a fast rise‐time pulsed field. The displacement of the stripe domain walls is observed optically as the domains adjust to the new equilibrium configuration. In the particular case of viscous damping and negligible wall mass, for a field step H _{0} which results in an equilibrium displacement x _{0}, the instantaneous displacement is x=x _{0}[1‐exp(‐ω_{ c } t)], where ω_{ c } is the ratio of the restoring force constant to the damping constant. The mobility μ=x _{0}ω_{ c }/H _{0}. The time‐dependent displacement can be displayed graphically in a few minutes by a sampling technique. Measurements on TmFeO_{3} yield results in good agreement with previous data. The mobility for DyFeO_{3} is found to be 330 cm (sec Oe)^{−1}.

Operational Method for Locating and Mapping Imperfections in Single‐Crystal Platelets of Rare‐Earth Orthoferrite
View Description Hide DescriptionAn instrumental technique has been devised for mapping crystalline imperfections which prevent the reliable operation of bubble‐domain devices. A special polarizing microscope permits the crystal to be automatically scanned through the field of view in a raster‐like manner. Photoelectrically detected distortions induced in a test domain by imperfections are plotted on an x‐y output of the scan. This sensitive method easily locates imperfections found with difficulty by other methods and has been used to locate crystals which have later been used successfully in devices.

Comparison and Discussion of Some Periodic Domain Structures
View Description Hide DescriptionThe energy density of seven periodic domain structures in sheets of uniaxial magnetic materials placed in a magnetic fieldH_{z} perpendicular to the sheet is calculated.^{1} The following periodic structures are considered: I. A hexagonal bubble lattice; within the cylinders the magnetization M_{s} is reversed with respect to H_{z} . II. The negative of I; within the cylinders, M_{s} and H_{z} have the same directions. III. A similar but square lattice of bubbles and its ``negative'' (IV). V. A honeycomb structure where the prisms are the reversed domains. VI. The negative of V. VII. A strip lattice. The energy density is minimized with respect to two variables. Comparing the structures I‐VII it is found that: (1) In a large field region a hexagonal bubble lattice (I) has the lowest energy. At low fields, VII has the lowest energy. (2) The structures where the reversed domains are connected with each other (II, IV, VI) have a higher energy than their negatives (I, III, V). (3) The radius of a bubble in a hexagonal lattice (I) differs at the same magnetic field considerably from the radius of an isolated bubble. (4) The energy of the honeycomb structure V is always higher than the energy of structure I. Comparing VI and II this is not the case: at higher field, structure VI has a lower energy than structure II. (5) Comparing the fields at which for I, III, V, and VII the lattice distance becomes infinite, we found the lowest field for VII and the highest for I and III. The occurrence of the different structures will of course not only be determined by the energy difference between them but also by the number of nucleation points and the possible energy barriers. The occurrence of I in zero field seems to be possible since the lattice distance for I is almost the same at zero field as at the lowest field for which I have the lowest energy. If I can occur at low fields the same holds for II, since it can be formed from I by reversing H_{z} . For higher fields, II will go over into VI. At a field where the lattice distance of VI becomes infinite, an isolated interconnected reversed domain will appear. This can be a hollow cylindrical domain. Changing the field in such a way that the well‐known transitions occur: ring→bubble→strip→strip lattice, a transition from I→VII via different structures has been described above. Such a transition was also found experimentally. Detailed calculations will be published elsewhere.^{1}

Reduction of the Wall‐Motion Field of Polished Orthoferrite Platelets
View Description Hide DescriptionThe wall‐motion field H_{c} in an as‐polished orthoferrite platelet is generally too large (H_{c} >0.5 Oe) for use in domain propagation devices without further treatment. Very low values of H_{c} down to less than 0.02 Oe have previously been reported by Heinlein and Pierce^{1} using a 1500°C anneal in a highly purified atmosphere. We find that a simple anneal at 1200°C for one hour in ambient atmosphere produces samples having H_{c} of 0.25–0.50 Oe, but this is sufficiently low to demonstrate device operation. The annealing treatment was successful with samples mechanically polished by various methods including samples which were also etched in 250°C phosphoric acid.Temperatures lower than 1200°C do not lower H_{c} sufficiently, and somewhat higher annealingtemperatures lead to no further improvement. Annealing times longer than an hour do not lead to improvement in H_{c} and may cause surface damage. This simple technique has proven useful in obtaining samples for initial studies on domain propagation and device design.

Domain Nucleation and Boundary Effects in Thin Uniaxial Plates
View Description Hide DescriptionIn high‐mobility materials with large uniaxial anisotropy (K>2πM_{s} ^{2}) the magnetostatic wall‐energy model as applied to an infinite lamina apparently provides quantitative explanation of most observed domain structures. However, the presence of boundaries and nucleation energy barriers usually prevent the spontaneous development of the equilibrium (lowest energy)^{1}structures. To understand this, we argue that the confluence of any two domains (or a domain and an edge boundary), or the reverse process of separation, always involves an intermediate state of higher energy. Consequently, for example, the periodic stripe array should not be expected to spontaneously divide into a lattice of bubbles when the latter is a lower energy structure. Similarly, the repulsive interaction with the boundaries prevents the equilibrium field dependence of the lattice nearest‐neighbor distance. Our observations on an epitaxial Ga–YIG film^{2} are shown to be entirely consistent with these qualitative considerations, while the observed domain critical fields, sizes, and spacings are quantitatively predicted by the wall‐energy model. Calculations of the nucleation energy for radial growth were carried out for a semicircular (half bubble) domain at a crack and at a free edge. The latter process is even more costly energetically than volume nucleation while the former requires less than half the volume nucleation energy. At crack intersections the barrier is reduced still further. Our observations on the Ga–YIG film show that domain nucleation occurs readily at cracks and rarely at edges in agreement with the theoretical suggestions. A more complete discussion of this work will be published elsewhere.

Liquid Phase Epitaxial Growth of Uniaxial Garnet Films: Circuit Deposition and Bubble Propagation
View Description Hide DescriptionMagnetically uniaxial epitaxialfilms of Eu_{2}Er_{1}Ga_{0.7}Fe_{4.3}O_{12} and Er_{2}Eu_{1}Ga_{0.7}Fe_{4.3}O_{12} 5–20‐μ thick have been grown free of cracks from PbO·B_{2}O_{3}solutions on (110) and (111) Gd_{3}Ga_{5}O_{12} substrates, respectively. Bubble propagating T‐Bar and Y‐Bar circuits of nickel‐cobalt‐phosphorus were electrolessly deposited on these films. Operation in excess of one hundred steps has been achieved in T‐Bar and Y‐Bar bubble domain shift registers. Details of the growth procedure, magnetic properties, and circuit preparation are presented.
 CRITICAL PHENOMENA

Ising Model with Antiferromagnetic Next‐Nearest‐Neighbor Coupling. III. Disorder Points, Energy Points, and Scattering from a One‐Dimensional Model
View Description Hide DescriptionA general argument is presented that a change in the nature of the short‐range order will occur above a precisely located temperature T_{D} , the disorder point, for a class of magnetic models. The possibility of detecting a disorder point by neutron scattering is investigated by calculating the relative scattering intensity for a one‐dimensional model.

Phase Behavior of Models with Competing Interactions
View Description Hide DescriptionModels with competing nearest‐neighbor and very long‐range interactions are solved exactly for several one‐dimensional cases, including the usual Ising chain (ICCI), the XY model (XYCI), the transverse Ising model (TICCI), and the spherical model (SCCI). For certain ratios of the competing interaction strengths, ICCI and XYCI display triple points and two critical points in a field. In addition TICCI has an apparently enclosed phase in an H‐T phase diagram; however, this phase is really paramagnetic as can be seen when an extended phase diagram is used. The extended phase diagrams for ICCI, XYCI, and TICCI display tricritical points and the tricritical exponents have different values from the usual classical values. In contrast to the rich phase behavior of the preceding models, SCCI shows very simple phase behavior, which is directly related to the ground state. Finally, the introduction of a staggered field to ICCI and a simple transformation allows reinterpretation as a metamagnetic model. Using ICCI as a guide the observability of the tricritical exponents is discussed.

Problem of Using Kink‐Point Locus to Determine the Critical Exponent β
View Description Hide DescriptionIt is shown that depending on how one analyzesmeasurements of the temperature dependence of magnetization near the Curie temperature it is possible to conclude that the critical exponent changes near T_{c} . An apparent change in β can be obtained from analyzing data generated from an equation of state in which β does not change. The mathematical and experimental difficulties in the use of the kink‐point locus method are discussed.

Properties of the Ising Square Lattice with Next‐Nearest‐Neighbor Interactions
View Description Hide DescriptionThe thermodynamic properties of the N×N two‐dimensional Ising square lattice have been studied using a Monte Carlo technique. The critical temperature and types of long‐range order have been investigated over a wide range of ratios of nearest‐neighbor to next‐nearest‐neighbor interaction strengths.

Temperature Dependence of the Paramagnetic Resonance Linewidths in MnS and MnO
View Description Hide DescriptionThe temperature dependence of the EPRlinewidth in single crystal MnS and MnO have been measured at 35 GHz. The EPR in MnS abruptly stops at 152°±0.5°K as the temperature is decreased. The linewidth in MnS is proportional to (T‐T_{N} )^{−3/8} for 1° ≤ (T‐T_{N} ) ≤ 6°K. In both MnS and MnO the linewidth is proportional to T/(T‐T_{N} ) for T‐T_{N} > 10°K. In this high‐temperature region the constants of proportionality are 80 and 280 Oe, respectively. An applied field of 12 500 Oe does not shift the Néel temperature in MnS.

Parametric Equation of State Applied to the Magnetization of Nickel Near its Curie Temperature
View Description Hide DescriptionData for the surface of magnetization, temperature, and field for single crystalnickel are compared with the parametric equation of state of Schofield, Litster, and Ho [Phys. Rev. Lett. 23, 1098 (1969)]. An excellent fit to the magnetic isotherms is obtained by choosing a reduced temperature for each isotherm, and the variation of the reduced temperature with measuredtemperature is linear above and below the critical temperature. But whereas the five parameter equation would demand that the slope be the same above and below T_{c} , the experiments show a 15% change in slope. It is argued that a six parameter equation is needed for the experimental fit and a suitable equation is given.

Frequency Dependence of the EPR Linewidth in MnF_{2} Near the Critical Point
View Description Hide DescriptionEPRlinewidth measurements at 24.43 GHz have been made near the critical pointT_{N} of MnF_{2}. Comparison with similar measurements at 9 and 35 GHz shows that the EPRlinewidth near T_{N} depends on the Larmor frequency, its magnitude at a given temperature being smaller at higher frequencies. This is the first observation of this effect recently predicted by Kawasaki. It is suggested that the observed frequency dependence near T_{N} is due to breakdown of the usual exchange narrowing condition.

Specific Heat of CoCl_{2}·6H_{2}O Near Its Néel Point
View Description Hide DescriptionThe specific heat of a single crystal of CoCl_{2}·6H_{2}O has been measured with high resolution near T_{N} = 2.291 K using the continuous heating method. Our data have been fitted to the usual asymptotic form: C/R=Aε^{−α}+B, where α, A, and B may assume different values below and above T_{N} . By plotting log (∂C/∂T) vs log (ε) for different values of T_{N} we obtained values for α′, α from the slopes of linear fits. Limits on the ``unrounded critical region'' were defined by deviations from linearity on these plots. A least‐square fit of the unrounded critical regions was also made. Both techniques yield the same results: the specific heat is rounded over a region about 8 mK wide, T_{N} ‐T _{max} = 4 mK, α′ = −0.18±0.03 below T_{N} , and α = +0.32±0.07 above T_{N} . We have compared our results with the earlier measurements of Skalyo and Friedberg^{1} on a polycrystalline sample. Our specific heat peak is sharper near T_{N} and rises to a maximum about 7% higher, but for ε>4×10^{−2} the two sets of data agree quite well. Analysis of the rounding of the two peaks was made assuming the existence of subsystems having Gaussian distributions of ordering temperatures. Using this technique, we were able to fit our data in the rounded region quite well, and using the same form for the unrounded specific heat, but with a distribution half‐width twice as large, we obtained good agreement with the data of Skalyo and Friedberg.