Measurements are reported of the magnetic field dependence of excitations in the quantum critical state of the spin $S=1/2$ linear chain Heisenberg antiferromagnet copper pyrazine dinitrate (CuPzN). The complete spectrum was measured at $k_{B}T/J\le 0.025$ for $H=0$ and $H=8.7\mathrm{T}$, where the system is $\sim 30\%$ magnetized. At $H=0$, the results are in agreement with exact calculations of the dynamic spin correlation function for a two-spinon continuum. At $H=8.7\mathrm{T}$, there are multiple overlapping continua with incommensurate soft modes. The boundaries of these continua confirm long-standing predictions, and the intensities are consistent with exact diagonalization and Bethe ansatz calculations.

We present an introduction to the workings, units of measure, and general properties of magnetic materials. This is intended as a “primer to interpretation of magnetic data” for those who are entering the field, or those who are encountering magnetic measurements in the literature. We expect this work will serve as an initial guide to the reader to familiarize them with the basics in the hope that those working in the field of magnetochemistry will wish to explore additional, more detailed literature as their specific investigations demand. Topics covered include: magnetic fields and units (SI and cgs), paramagnetism (magnetization and magnetic susceptibility), Curie and Curie–Weiss behavior, magnetic exchange interactions, magnetic anisotropy, dimeric systems and exchange-coupled networks (including chains, ladders, and layers), and long-range order.

We study the magnetic-field-induced quantum phase transition from a gapped quantum phase that has no magnetic long-range order into a gapless phase in the spin-1/2 ladder compound bis(2,3-dimethylpyridinium) tetrabromocuprate (DIMPY). At temperatures below about 1 K, the specific heat in the gapless phase attains an asymptotic linear temperature dependence, characteristic of a Tomonaga-Luttinger liquid. Inelastic neutron scattering and the specific heat measurements in both phases are in good agreement with theoretical calculations, demonstrating that DIMPY is the first model material for an $S=1/2$ two-leg spin ladder in the strong-leg regime.

The magnetic susceptibility and magnetization of two layered $S=\frac{1}{2}$ Heisenberg antiferromagnets with moderate exchange are reported. The two isostructural compounds, $(2\mathrm{}-\mathrm{amino}-5-\mathrm{chloropyridinium}{)}_2{\mathrm{CuBr}}_4$ $\left[\right(5\mathrm{C}\mathrm{A}\mathrm{P}{)}_2{\mathrm{CuBr}}_4]$ and $(2\mathrm{}-\mathrm{amino}-5-\mathrm{methylpyridinium}{)}_2{\mathrm{CuBr}}_4$ $\left[\right(5\mathrm{M}\mathrm{A}\mathrm{P}{)}_2{\mathrm{CuBr}}_4],$ contain $S=\frac{1}{2},$ Cu(II) ions related by C centering, yielding four equivalent nearest neighbors. The crystal structure of the synthesized compound, $(5\mathrm{C}\mathrm{A}\mathrm{P}{)}_2{\mathrm{CuBr}}_4,$ shows the existence of layers of distorted copper(II)-bromide tetrahedra parallel to the $\mathrm{ab}$ plane, separated by the organic cations along the c axis. Magnetic pathways are available through the bromide-bromide contacts within the layers and provide for moderate antiferromagnetic exchange. Susceptibility measurements indicate interaction strengths to be 8.5(2) K and 6.5(2) K and ordering temperatures of 5.1(2) K and 3.8(2) K for $(5\mathrm{C}\mathrm{A}\mathrm{P}{)}_2{\mathrm{CuBr}}_4$ and $(5\mathrm{M}\mathrm{A}\mathrm{P}{)}_2{\mathrm{CuBr}}_4,$ respectively. High-field magnetization experiments on both compounds show upward curvature of $M(H,T).$ Magnetization measurements made at $T=1.3\mathrm{}\hspace{0.5em}\mathrm{K}$ show saturation occurs in $(5\mathrm{M}\mathrm{A}\mathrm{P}{)}_2{\mathrm{CuBr}}_4$ at 18.8 T and in $(5\mathrm{C}\mathrm{A}\mathrm{P}{)}_2{\mathrm{CuBr}}_4$ at 24.1 T. The magnetization curves are consistent with recent theoretical predictions. Single-crystal magnetization measured at 2.0 K indicates a spin-flop transition at 0.38 T and 0.63 T for $(5\mathrm{C}\mathrm{A}\mathrm{P}{)}_2{\mathrm{CuBr}}_4$ and $(5\mathrm{M}\mathrm{A}\mathrm{P}{)}_2{\mathrm{CuBr}}_4,$ respectively.

The material copper pyrazine dinitrate realizes an instructive paradigm of quantum criticality.