Fraction of Bose-Einstein condensed triplons in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>TlCuCl</mml:mtext></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>from magnetization data

${\text{TlCuCl}}_{3}$ is a quantum-spin-$\frac{1}{2}$ system which shows a gap between the singlet ground state of the ${\text{Cu}}^{2+}$ dimers and the first excited triplet ${S}^{z}=+1$ state for magnetic fields ${\ensuremath{\mu}}_{0}H\ensuremath{\lesssim}{\ensuremath{\mu}}_{0}{H}_{c}\ensuremath{\approx}5.5\text{ }\text{T}$. At larger magnetic fields the gap is suppressed, and a Bose-Einstein condensation of triplets is supposed to occur, leading to a magnetic phase with antiferromagnetic long-range order of the transverse spin components. In this study we calculate the fraction of condensed magnetic quasiparticles of ${\text{TlCuCl}}_{3}$ from magnetization $M(T,H)$ data. At $T=0\text{ }\text{K}$ and right above the critical field ${H}_{c}$, this fraction is $\ensuremath{\approx}98%$ of the total number of triplons, and is independent of the direction of the magnetic field if we assume the presence of a small intrinsic magnetic background with $S=1$ magnetic moments.

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