ESR investigations of the magnetic anisotropy in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>κ</mml:mi> <mml:mtext>−</mml:mtext> <mml:mrow> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mtext>BETS</mml:mtext> <mml:mo>)</mml:mo>

The two-dimensional molecular conductor <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>κ</a:mi> <a:mtext>−</a:mtext> <a:mrow> <a:msub> <a:mrow> <a:mo>(</a:mo> <a:mi>BETS</a:mi> <a:mo>)</a:mo> </a:mrow> <a:mn>2</a:mn> </a:msub> <a:mspace width="0.16em"/> <a:mi>Mn</a:mi> <a:msub> <a:mrow> <a:mo>[</a:mo> <a:msub> <a:mrow> <a:mi mathvariant="normal">N</a:mi> <a:mo>(</a:mo> <a:mi>CN</a:mi> <a:mo>)</a:mo> </a:mrow> <a:mn>2</a:mn> </a:msub> <a:mo>]</a:mo> </a:mrow> <a:mn>3</a:mn> </a:msub> </a:mrow> </a:math> has been studied because of the intriguing magnetic coupling of the molecular <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>π</d:mi> </d:math> electrons to the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msup> <e:mrow> <e:mi>Mn</e:mi> </e:mrow> <e:mrow> <e:mn>2</e:mn> <e:mo>+</e:mo> </e:mrow> </e:msup> </e:math> ions. Utilizing -band electron spin resonance spectroscopy we have performed comprehensive investigations of the magnetic properties, in particular on the temperature and angular dependences of the spin susceptibility, the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mi>g</f:mi> </f:math> factor, and the linewidth. Due to the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>π</g:mi> <g:mo>−</g:mo> <g:mi>d</g:mi> </g:mrow> </g:math> coupling, a rearrangement of the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mi>π</h:mi> </h:math> spins occurs: At low temperatures the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mi>g</i:mi> </i:math> factor shifts enormously with a pronounced in-plane anisotropy that flips as the temperature decreases, the lines broaden significantly, and the spin susceptibility increases upon cooling with a kink at the phase transition. By carefully analyzing the angular dependence of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:mi>g</j:mi> <j:mo>(</j:mo> <j:mi>θ</j:mi> <j:mo>)</j:mo> </j:mrow> </j:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mrow> <k:mi mathvariant="normal">Δ</k:mi> <k:mi>H</k:mi> <k:mo>(</k:mo> <k:mi>θ</k:mi> <k:mo>)</k:mo> </k:mrow> </k:math> we reveal the influence of anisotropic Zeeman interaction in addition to spin-phonon coupling. We conclude the presence of two magnetically distinct BETS chains and discuss the possibility of altermagnetic order.