Acoustic paramagnetic resonance (APR) is a phenomenon of resonant absorption of sound by a system of magnetic particles placed in an external magnetic field

Magnetic field

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

. It occurs when the energy of the sound wave quantum

Quantum

In physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...

 becomes equal to the splitting of the energy levels of the particles, the splitting being induced by the magnetic field. APR is a variation of electron paramagnetic resonance

Electron paramagnetic resonance

Electron paramagnetic resonance or electron spin resonance spectroscopyis a technique for studying chemical species that have one or more unpaired electrons, such as organic and inorganic free radicals or inorganic complexes possessing a transition metal ion...

 (EPR) where the acoustic rather than electromagnetic waves are absorbed by the studied sample. APR was theoretically predicted in 1952, independently by Semen Altshuler

Semen Altshuler

Semen Alexandrovich Altshuler was a Soviet physicist known for his work in resonance spectroscopy and in particular for theoretical prediction of acoustic paramagnetic resonance in 1952.-Early years:Altshuler was born in 1911 in Vitebsk, now a city in Belarus, near the border with Russia...

 and Alfred Kastler

Alfred Kastler

Alfred Kastler was a French physicist, and Nobel Prize laureate.Kastler was born in Guebwiller and later attended the Lycée Bartholdi in Colmar, Alsace, and École Normale Supérieure in Paris in 1921...

, 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

Sodium chlorate is a chemical compound with the chemical formula . When pure, it is a white crystalline powder that is readily soluble in water. It is hygroscopic. It decomposes above 250 °C to release oxygen and leave sodium chloride...

. This nuclear-APR work was extended to electron-APR in 1959. Further applications of APR to nuclear polarization

Dynamic nuclear polarisation

Dynamic nuclear polarization results from transferring spin polarization from electrons to nuclei, thereby aligning the nuclear spins to the extent that electron spins are aligned. Note that the alignment of electron spins at a given magnetic field and temperature is described by the Boltzmann...

 and acoustic maser

Maser

A maser is a device that produces coherent electromagnetic waves through amplification by stimulated emission. Historically, “maser” derives from the original, upper-case acronym MASER, which stands for "Microwave Amplification by Stimulated Emission of Radiation"...

s were later proposed by Kastler and Charles Townes

Charles Hard Townes

Charles Hard Townes is an American Nobel Prize-winning physicist and educator. Townes is known for his work on the theory and application of the maser, on which he got the fundamental patent, and other work in quantum electronics connected with both maser and laser devices. He shared the Nobel...

.

Mechanism

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

Magnetic moment

The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...

 and an associated with it spin

Spin (physics)

In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...

. 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.