Investigation of microwave absorption in paramagnetic substances

Paramagnetic resonance (p.r.) at low temperatures has been investigated in a number of substances in the solid state. Paramagnetic ions in the solid state are subjected to strong crystalline electric fields which profoundly modify the magnetic properties of the free ion. The orbital momentum of the free ion is completely or partially "quenched", leaving the spin momentum unaffected, except to a small extent due to spin-orbit coupling. The ground state consists of a number of levels, generally singlets or doublets. The separations of these levels may be varied by the application of an external magnetic field.
If two levels have energies W1 and W2 and an external r.f. magnetic field, of frequency v such that hv = W1 - W2, is applied, transitions can be excited between the levels, within the limitations of certain selection rules. As the population of the two levels depends upon the Boltzman distribution there is a nett absorption of energy from the r.f. field when transitions occur. If this energy is lost to the crystal lattice quickly enough it is not reradiated. In practice a fixed frequency is chosen and the separation of the energy levels is adjusted by applying an external magnetic field so that the above condition is satisfied. By studying the fields at which the absorption occurs the position of the energy levels in zero field can be inferred.
The energies of the levels may be expressed concisely in the form of a "spin hamiltonlan" which involves a number of parameters which have to be found experimentally. The general spin hamiltonian for an ion in a field of rhombic symmetry is:
H = β(gxHxSx + gyHySy + gzHzSz) + D[S2z - 1⁄3S(S + 1)] + E(S2x - S2y) + AxSxIx + AySyIy + AzSzIz
S is the effective spin chosen so that the multiplicity of the ground state is 2S + l, β is the Bohr magneton, the g's are spectroscopic splitting factors along the axes of the crystal field. D represents the effect of the axial component of the field along the z axis and E represents the rhombic component of the crystal field. The transitions between the levels defined by these parameters give rise to the so-called fine structure lines. I is the nuclear spin and the terms in A, S and I represent the interaction between the magnetic moments of the electron and of the nucleus. This interaction splits each fine structure line into 2I + l equally Intense, equally spaced hyperfine lines. Thus the number of hyperfine lines defines the nuclear spin unambiguously. Also the separatlon between the lines proportional to tbe nuclear magnetic moment so that in certain cases this can be estimated.
The specimens used have usually consisted of single crystals of a diamagnetic salt containing about 1% of an isomorphous paramagnetic salt. This dilution separates the paramagnetic ions and reduces tbe line width caused by their mutual interaction.
Tbe experimental arrangement is of the standard type used in Oxford. Some refinements of technique have been used for particular experiments which needed them. Experiments have been performed at wavelengths between 10 em and 0.8 mm. A klystron oscillator, run from a stabilised power pack, feeds power to a half wave resonant cavity which contains tbe sample placed in a position where the r.f. magnetic field is strong. This cavity can be placed in a dewar vessel of refrigerant and between tbe poles of an electromagnet. A wavemeter measures the wavelength and a crystal detector rectifies tbe power coupled out of the resonant cavity. The external field has a small 50 c/s modulation superimposed on it so that an absorption signal is swept through 100 times a second. The signal from the detector may then be amplified in a video-amplifier. If the amplified signal is fed to the Y-plates of an oscilloscope, which has a correctly phased 50 c/s time base, the trace displays a graph of absorption agalnst magnetic field within the region covered by the field modulation. This technique enables a spectrum to be analysed very rapidly.
Complex Cyanides
The p.r. spectra of two complex cyanides of divalent ions, K4V(CN)63H2O and K4Mn(CN)63H2O, have been studied.
The orbital momentum of the vanadous ion is completely quenched so that it is in an S = 3/2 state and its behaviour resembles that of the same ion in ionic crystals. The g-value, 1.992, is closer to the free spin value and the crystal field parameters, D = -0.0264 &pm; 0.0004 em-1 and E = -0.0072 &pm; 0.0004 cm-1, are smaller showing that the effect of higher levels is less than in the ionic salts. The hyperfine structure constant A = - 0.00555 &pm; 0.00003 cm-1 is only 36% smaller than in the ionic salts, showing that the configurational interaction which produces the hyperfine structure is not greatly modified by the covalent bonding.
In the manganous ion the cubic field does not completely lift the orbital degeneracy of the ground state. The lowest triplet is split into a singlet and a higher doublet by the rhombic component of the crystal field so that the g-values differ widely from the free spin value. The ion behaves with effective spin S = 1/2 and has g-valuee gx = 2.624 ± 0.008, gy = 2.182 &pm; 0.008 and gz = 0.72 &pm; 0.05. The hyperfine structure is also anisotropic and the hyperfine structure constants are Ax = 0.00845 ± 0.00005 cm-1, Ay = 0.00465 ± 0.00005 cm-1 and Az = 0.0083 &pm; 0.0013 cm-1 . The manganous ion in this type of compound resembles the titanic ion in ionic compounds and an attempt has been made to fit the parameters with the titanium theory of Abragam and Pryce (1951). This gives reasonable values for the configurational interaction constant and the mean value of the radius of the electron orbit.
Nuclear spins
The nuclear spin and magnetic moment of vanadium 50 has been measured in a crystal of K4Fe(CN)63H2O containing a few milligrams of vanadium enhanced to contain ~ 20% 50V. The spin was found to be six and the ratio of the nuclear gyromagnetic ratios of 50V/51V, 0.380, agrees well with the value measured by nuclear resonance of 0.3792. The spin and nuclear gyromagnetic ratio fit well with the values calculated by Hitchcock (1952) using a j-j spin-orbit coupling model of the nucleus and assuming &delta-function; potential.
The nuclear spin and magnetic moment of radioactive cobalt 57 have been measured in a crystal of K2Zn(SO4)26H2O containing >0.5 μgrams of 57Co. The crystal also contains some stable 59Co up to 2.4 μgrams total cobalt content. Only one set of hyperfine structure lines is resolved so tnat the spin and magnetic moment of 57Co are tht same as 59Co; i.e. the spin is 7/2 and the magnetic moment is 4.6 &pm; 0.2 nuclear magnetons.
Chromic methylamine alum
Paramagnetic resonance measurements on crystals of Cr(CH3NH3(SO4)12H22O show that the crystals undergo a change in strucure at 157 &pm; 3°K. Above this temperature the crystal symmetry is cubic and the Cr+++ ions are in a crystal field which has a small component. Below this temperature there is an additional rhombic componant in the crystal field and the crystal symmetry is lower, probably tetragonal. At both 90°k and 20°K the parameters in the spin hamiltonian are g = 1.975 &pm; 0.010, D = 0.0871 &pm; 0.0007 cm-1 and K = 0.0092 &pm; 0.0008 cm-1. These values give a stark splitting in zero field of 0.177 &pm; 0.002 cm-1 which disagrees with the value of 0.188 &pm; 0.007 cm-1 calculated by Kurti and Gardner (1954) from adiabatic demagnetisation measurements. Measurements at frequencies near the Stark splitting give results which lie between the two values so that it is not possible to say whether this descrepency is real. Measurements of nearest neighbour lines and of line widths indicate that there is extremely little exchange interaction between neighbouring Cr+++ ions.
The transition is possibly due to a freezing out of a random rotary motion of the methylamine radical as the substance is cooled through the transition temperature. This temperature is the same as that found by Griffiths and Powell (1952) at which there is a discontinuity in the value of the dielectric constant.
Interactions between neighbouring ions
The p.r. spectrum of two adjacent consists of a series of lines, corresponding to the various orientations of the spins with respect to one another, which occur as satellites to the iines by isolated ions, the number of acid separation these satellites depends upon the size and nature of the interaction between them. The magnetic interaction may be calculated if the distance between the ions is known, so that if allowance is made for this, the size and nature of exchange interaction may be inferred from the positions of the satellite lines. Investigations of this sort have been done in crystals containing about 10% paramagnetic salt in an isomorphous diamagnetic one, so that there is considerable chance of having two ions adjacent.
A study of lanthanum ethyl sulphate containing up to 30% neodymium shows that there is a small anisotropic exchange interaction with the two nearest neighbours and undetectable exchange interaction with the six next nearest. There is however no exchange with the next nearest neighbours in concentrated neodymium ethyl sulphate. This discrepancy is not explained.
A study of nearest neigbbour satellites was made in KCr(SeO4)212H2O. the problem is complicated by there being four ions in the unit cell all of which have different crystal field axes. It has not been possible to make an unambiguous interpretation of the results and the best interpretation does not agree with the results of adiabatic demagnetisation experiments of Kurti and Gardner (unpublished).
The results of this type of investigation are rather discouraging and seem to indicate that one can hope to obtain satisfactory results only in particular substances.
Rare earth ethyl sulphates
Paramagnetic resonance has been observed in terbium etbyl sulphate using the yttrium salt as a dilutant. The spectrum may be explained using the hamiltonian postulated for the praseodymium salt (Bleaney and Seovil, 1952): H = g// βHzSz + ASzIz + ASx where g// = 17.72 &pm; 0.02, S = 1/2, I = 3/2, A = 0.209 &pm; 0.002cm-1 and Δ = 0.387 &pm; 0.001cm-1. The lowest level is a doublet Jz = &pm; 6 which is admixed with Jx = 0 by the crystal field. This admixes the +6 and -6 levels and ΔM = 0 transitions are obtained if the r.f. magnetic field is placed parallel to tbe external field. The nuclear spin of terbium 159 is estimated to be 1.5 &pm; 0.4 nuclear magnetons.
The work of Bleaney and Seovil (1952) on praseodymium ethyl sulphate has been extended using yttrium ethyl sulphate as a dilutant. The assymmetrical line shape is explained as being tbe result of the splitting Δ in the above hatmiltonian not having a single value but a Gaussian distribution of values, the nuclear magnetic moment of praseodymium 141 is estimated to be 4.5 &pm; 1.1 nuclear magnetons.