Orbital and magnetic ordering in the weak ferromagnet vanadium trifluoride <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>VF</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math>

We report on an investigation of the low-temperature structural, thermal, and magnetic properties of the binary trifluoride <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>VF</a:mi> <a:mn>3</a:mn> </a:msub> </a:math> by temperature-dependent magnetization, heat capacity, electron paramagnetic resonance, and synchrotron powder and neutron powder diffraction measurements. At room temperature the crystal structure of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>VF</b:mi> <b:mn>3</b:mn> </b:msub> </b:math> features <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msup> <c:mrow> <c:mi mathvariant="normal">V</c:mi> </c:mrow> <c:mrow> <c:mn>3</c:mn> <c:mo>+</c:mo> </c:mrow> </c:msup> </c:math> spin <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>S</e:mi> </e:math> = 1 regular triangular layers. At <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mo>∼</f:mo> <f:mn>120</f:mn> <f:mspace width="0.16em"/> <f:mi mathvariant="normal">K</f:mi> </f:mrow> <f:mo> </f:mo> <f:msub> <f:mi>VF</f:mi> <f:mn>3</f:mn> </f:msub> </f:math> undergoes a structural phase transition, and at <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mo>∼</i:mo> <i:mn>18</i:mn> <i:mspace width="0.16em"/> <i:mi mathvariant="normal">K</i:mi> </i:mrow> </i:math> it undergoes an antiferromagnetic phase transition. The structural phase transition involves a minute orthorhombic distortion of the regular octahedral fluorine coordination shell of the trivalent V cations, effecting a distortion to the monoclinic crystal system. The magnetic phase transition generates a weak ferromagnet with V magnetic moments essentially confined to the trigonal planes of the room temperature structure described in the space group <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mrow> <l:mi>R</l:mi> <l:mo>−</l:mo> <l:mn>3</l:mn> <l:mi>c</l:mi> </l:mrow> </l:math> . The ordered magnetic moments of the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi mathvariant="normal">V</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> <m:mo>+</m:mo> </m:mrow> </m:msup> </m:math> cations amount to <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:mrow> <o:mo>≈</o:mo> <o:mn>1</o:mn> <o:msub> <o:mi>μ</o:mi> <o:mi mathvariant="normal">B</o:mi> </o:msub> </o:mrow> </o:math> and is thus distinctly reduced from the spin-only magnetic moment of <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:mrow> <q:mn>2</q:mn> <q:msub> <q:mi>μ</q:mi> <q:mi mathvariant="normal">B</q:mi> </q:msub> </q:mrow> </q:math> . This finding and the weak ferromagnetic moment are discussed in view of the low-symmetry structure and spin-orbit effects on the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"> <s:mrow> <s:msup> <s:mrow/> <s:mn>3</s:mn> </s:msup> <s:msub> <s:mi>T</s:mi> <s:mn>1</s:mn> </s:msub> </s:mrow> </s:math> cubic ground term of the <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"> <t:msup> <t:mrow> <t:mi mathvariant="normal">V</t:mi> </t:mrow> <t:mrow> <t:mn>3</t:mn> <t:mo>+</t:mo> </t:mrow> </t:msup> <t:mo> </t:mo> <t:msup> <t:mi>d</t:mi> <t:mn>2</t:mn> </t:msup> </t:math> system.