acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...

, acoustic paramagnetic resonance (APR) is a phenomenon of resonant absorption of

sound In physics, sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the br ...

by a system of

magnet A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, ...

ic particles placed in an external

magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...

. It occurs when the energy of the sound wave

quantum In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This me ...

becomes equal to the splitting of the

energy level A quantum mechanics, quantum mechanical system or particle that is bound state, bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical mechanics, classical pa ...

s of the particles, the splitting being induced by the magnetic field. APR is a variation of

electron paramagnetic resonance Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy is a method for studying materials that have unpaired electrons. The basic concepts of EPR are analogous to those of nuclear magnetic resonance (NMR), but the spin ...

(EPR) where the acoustic rather than

electromagnetic wave In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength, ...

s are absorbed by the studied sample. APR was theoretically predicted in 1952, independently by

Semen Altshuler Semyon Alexandrovich Altshuler (also Altshuller, Al'tshuler or Al'shuller; ; ; September 24, 1911 – January 24, 1983) was a Soviet physicist known for his work in resonance spectroscopy and in particular for theoretical prediction of acoustic p ...

and Alfred Kastler, and was experimentally observed by W. G. Proctor and W. H. Tanttila in 1955.

History

After discovery of EPR in 1944, Evgeny Zavoisky predicted that the resonance phenomenon should not be restricted to radio or microwave absorption but could be extended to the sound waves. This idea was theoretically developed by his collaborator Semen Altshuler in 1952 and independently by Alfred Kastler; whereas Altshuler reported the effect on electron spins, Kastler calculated a nuclear spin system. The first experimental detection of the APR was reported in 1955 using ³⁵Cl nuclei in single crystals of

sodium chlorate Sodium chlorate is an inorganic compound with the chemical formula Na ClO3. It is a white crystalline powder that is readily soluble in water. It is hygroscopic. It decomposes above 300 °C to release oxygen and leaves sodium chloride. Sever ...

. This nuclear-APR work was extended to electron-APR in 1959. Further applications of APR to nuclear polarization and acoustic masers were later proposed by Kastler and

Charles Townes Charles Hard Townes (July 28, 1915 – January 27, 2015) was an American physicist. Townes worked on the theory and application of the maser, for which he obtained the fundamental patent, and other work in quantum electronics associated with b ...

Mechanism

The APR effect is very similar to EPR: every electron or nucleus, either free or in a solid, has a

magnetic moment In electromagnetism, the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field. The magnetic dipole moment of an object determines the magnitude ...

and an associated with it spin. The spin can take integer or half-integer values, e.g. 1/2, 1, 3/2, etc., and the corresponding magnetic components m_s = ±1/2, ±1, ±3/2, etc. Here, the levels for plus and minus spin values are degenerate, that is have equal energies. Upon application of external magnetic field, those spins align either along the field or opposite to it; in terms of energy diagram, the energy levels split as shown in the figure. If a sound wave with a certain quantum energy E irradiates this spin system, at certain value of magnetic field, when E is equal to the magnetic splitting ΔE, resonant absorption of sound takes place, that is the APR effect. Both in EPR and APR, the absorbed energy is transferred to the lattice via spin-phonon relaxation. However, whereas in EPR this process is of second order, and thus involves two phonons, the relaxation takes only one phonon in APR and is therefore much faster. This affects the lineshape of the resonance and its temperature dependence and allows probing the spin-lattice relaxation differently in EPR and APR.

Experimental setup

APR is commonly measured using the pulsed echo technique at high sound frequencies of the order 100 MHz – 100 GHz. Two opposite sides of a studied crystal are mirror polished and made parallel to each other, and a piezoelectric crystal is attached to one side. It generates an ultrasound wave which is detected after multiple bouncing between the flat sides, and the signal attenuation serves as the measure of the resonant absorption. The crystal is located inside the magnet capable of providing static field corresponding to the applied frequency. For an electron with spin 1/2 and the splitting factor of the energy levels (the so-called spectroscopic splitting factor g) g = 2, the required field is 33–33000 Gauss for frequencies 100 MHz – 100 GHz.Акустический парамагнитный резонанс
(in Russian)

References

{{BranchesofSpectroscopy Scientific techniques Electron paramagnetic resonance